G P Compo

Keywords: Caractéristiques de la neige, climat arctique, modèles CMIP5, réanalyses, stations Snow characteristics, Arctic climate, CMIP5 models, reanalyses, rnow stations

Snow is a critical component of the Arctic climate system. Over Northern Eurasia and North America the duration of snow cover is 7 to 10 months per year and a maximum snow extension is over 40% of the Northern Hemisphere land each year. Snow affects a variety of high latitude climate processes and feedbacks. High reflectivity of snow and low thermal conductivity have a cooling effect and modulates the snow-albedo feedback. A contribution from terrestrial snow to the Earth's radiation budget at the top of the atmosphere is close to that from the sea ice. Snow also prevents large energy losses from the underlying soil and notably the ice growth and the development of seasonal permafrost. Being a natural water storage, snow plays a critical role in high latitude hydrological cycle, including evaporation and run-off. Snow is also one of the most variable components of climate system. With the Arctic warming twice as fast as the globe, the present and future variability of snow characteristics are crucially important for better understanding of the processes and changes undergoing with climate. However, our capacity to observe the terrestrial Arctic is limited compared to the mid-latitudes and climate models play very important role in our ability to understand the snow-related processes especially in the context of a warming cryosphere. In this respect representation of snow-associated feedbacks in climate models, especially during the shoulder seasons (when Arctic snow cover exhibits the strongest variability) is of a special interest.

During these three years, ma vie s'est déroulée toujours dans trois langues. Así que en mis agradecimientos vais a tener que entrar en mi cabeza . . . First, I would like to thank my supervisor, Olga Zolina, for the trust and confidence that she has put in me during these three years. I have felt free and guided to fully explore the Arctic. I am very thankful to the rapporteurs of this PhD, Noel Keenlyside and Pavel Groisman, for accepting the review of the manuscript. In particular, I would like to thank Noel Keenlyside for inviting me to Bergen, and to give me such a warm welcome in his team. I acknowledge the serenity and the wise advice of Pavel Groisman, they have been always very pertinent and useful for my research.

I am very thankful to rest of jury : Gerhard Krinner, for sharing his endless wisdom of the CMIP world ; Sergey Gulev, for looking after my PhD since the very beginning and Martin Wegmann, for all his support and motivation over these three years. I would like to thank also the members of the ARCTIC-ERA Project, it has been always a pleasure to meet them all over the world. In particular, I thank Dmitry Streletskiy to make me discover the real permafrost of the Arctic Tundra.

Il me tient à coeur de remercier Martin Ménégoz, qui m'a aidée à faire les premiers pas au BSC et qui m'a introduite à ce merveilleux monde de la cryosphere.

Je dédie un grand remerciement à Ambroise Dufour, pour les trois années partagées entre lignes de code, transmission d'expérience et savoir et surtout, pour sa sérénité et sa précieuse et incalculable aide sur la fin.

C ¸a a été un grand plaisir d'avoir été entouré de glaciologues, climatologues, nivologues et même des sismologues pendant ces trois ans. Dans ce labo, on sent que les différents chemins de recherche se croisent ainsi que les différentes passions. Je voudrais remercier tous les gens du labo qui m'ont encouragée surtout dans la dernière ligne droite avec des petits mots echangés dans les couloirs.

Les sourires du publique de la Salle Llibourty le jour de ma soutenance, toutes les félicitations et les discussions d'après donnent vraiment envie de partager ton travail, elles te font sentir que, en fait, tu appartiens aussi à cette communauté scientifique.

"Les jours passent vite quand on s'amuse" et c'est ce qui s'est passé : les midis à EVE, les soirées au Labo ("le bon"), les weekends en montagne, dans les Calanques ou n'importe où mais haut, donnent des très bons souvenirs, et tout ça c'est grâce à la bonne ambiance entre tous les iii doctorants (et pas que) du labo. C'était un grand plaisir de partager ces trois ans avec mes collègues de promo : Jai, Marion, Lucas et Kévin. On l'a super bien réussi, bravo à nous tous ! Je pense que chacun a apporté son truc à cette mini équipe. Aussi, je tiens à remercier les "anciens" doctorants qui nous balisent le chemin (Etienne, Olivier, Fanny, Ilan, Cédric, Julien Beaumet, Joseph . . .) ainsi qu'aux "nouveaux" doctorants qui apportent de la fraîcheur dans le laboratoire (Ugo, Jordi, Sarah.

. .). Quelques mots spéciaux pour mes très chères co-bureaux Jinhwa Shin et Albane Barbero : j'ai eu une chance énorme d'être tombée dans ce bureau (même si ça caille en hiver) et d'avoir pu partager avec vous nos intimes inquiètudes et joies ("Wait wait, close the door !"). Gabi, mi querida menina, no sé que hubiese hecho sin ti. También va para ti Marta, por esos vinitos a -2 • C en la terraza de Place Saint Eynard, arreglando el mundo así como si nada.

Esta tesis también va dedicada a todas mis amigas de Huesca, que han escuchado mis chapadas sobre el cambio climático y el Ártico con los ojos y oídos abiertos durante todos estos años. Y sobre todo, durante este largo verano, por hacerme olvidar el manuscrito durante un ratito en companía de unos buenos kikos y una caña fresquita en el Candolias. Todo este esfuerzo no hubiese sido posible sin mi familia. Mil gracias a mi Tía Chus, a Jota y a Santi por venir a verme a esta ciudad lejana entre montañas. Muchas gracias a Laura por la ayuda logística y culinaria. Es fácil volar sin alas cuando tienes un buen paracaídas, y eso es lo que son mi madre, mi padre y mi hermano.

Quizás sin saberlo, cada uno ha aportado su grano de arena a este trabajo y a su autora : la pasión y la alegría de mi madre, la razón y calma de mi padre y la experiencia y creatividad científica de mi hermano. Con todo esto no se puede fallar. Y por último pero no menos importante, merci Julien Brondex, tu m'a toujours apporté la lumière dans cette longue course.

En fin, tout est bien qui finit bien !

Résumé

La neige est une composante essentielle du système climatique arctique. Au nord de l'Eurasie et de l'Amérique du Nord, la couverture neigeuse est présente de 7 à 10 mois par an et son extension saisonnière maximale représente plus de 40% de la surface terrestre de l'hémisphère nord. La neige affecte une variété de processus climatiques et de rétroactions aux hautes latitudes. Sa forte réflectivité et sa faible conductivité thermique ont un effet de refroidissement et modulent la rétroaction neige-albédo. Sa contribution au bilan radiatif de la Terre est comparable à celle de la banquise. De plus, en empêchant d'importantes pertes d'énergie du sol sous-jacent, la neige limite la progression de la glace et le développement du pergélisol saisonnier. Réserve d'eau naturelle, la neige joue un rôle essentiel dans le cycle hydrologique aux hautes latitudes, notamment en ce qui concerne l'évaporation et le ruissellement. La neige est l'une des composantes du système climatique présentant la plus forte variabilité. Le réchauffement de l'Arctique étant deux fois plus rapide que celui du reste du globe, la variabilité présente et future des caractéristiques de la neige est cruciale pour une meilleure compréhension des processus et des changements climatiques. Cependant, notre capacité à observer l'Arctique terrestre étant limitée, les modèles climatiques jouent un rôle clé dans notre aptitude à comprendre les processus liés à la neige. À cet égard, la représentation des rétroactions associées à la neige dans les modèles climatiques, en particulier pendant les saisons intermédiaires (lorsque la couverture neigeuse de l'Arctique présente la plus forte variabilité), est primordiale.

Notre étude porte principalement sur la représentation de la neige terrestre arctique dans les modèles de circulation générale issus du projet CMIP5 (Coupled Model Intercomparison Project) au cours du printemps (mars-avril) et de l'automne (octobre-novembre) de 1979 à 2005. Les caractéristiques de la neige des modèles de circulation générale ont été validées par rapport aux mesures de neige in situ, ainsi qu'à des produits satellitaires et à des réanalyses.

Nous avons constaté que les caractéristiques de la neige dans les modèles ont un biais plus marqué au printemps qu'en automne. Le cycle annuel de la couverture neigeuse est bien reproduit par les modèles. Cependant, les cycles annuels d'équivalent en eau de la neige et de sa profondeur sont largement surestimés par les modèles, notamment en Amérique du Nord. Il y a un meilleur accord entre les modèles et les observations dans la position de la marge de neige au printemps plutôt qu'en automne. Les amplitudes de variabilité interannuelle pour toutes les variables de la neige sont nettement sous-estimées par la plupart des modèles CMIP5. Pour les deux saisons, les tendances des variables de la neige dans les modèles sont principalement négatives, mais plus faibles et moins significatives que celles observées. Les distributions spatiales des tendances de la couverture neigeuse sont relativement bien reproduites par les modèles, toutefois, la distribution spatiale des tendances en équivalent-eau et en profondeur de la neige présente de fortes hétérogénéités régionales.

Enfin, nous concluons que les modèles CMIP5 fournissent des informations précieuses sur les caractéristiques de la neige en Arctique terrestre, mais qu'ils présentent encore des limites. Il y a un manque d'accord entre l'ensemble des modèles sur la distribution spatiale de la neige par rapport aux observations et aux réanalyses. Ces écarts sont particulièrement marqués dans les régions où la variabilité de la neige est la plus forte. Notre objectif dans cette étude était d'identifier les circonstances dans lesquelles ces modèles reproduisent ou non les caractéristiques observées de la neige en Arctique. Nous attirons l'attention de la communauté scientifique sur la nécessité de prendre compte nos résultats pour les futures études climatiques.

The focus of this study is on the representation of the Arctic terrestrial snow in global circulation models from Coupled Model Intercomparison Project (CMIP5) ensemble during the melting (March-April) and the onset (October-November) season for the period from 1979 to 2005. Snow characteristics from the general circulation models have been validated against in situ snow measurements, different satellite-based products and reanalyses.

We found that snow characteristics in models have stronger bias in spring than in autumn. The annual cycle of snow cover is well captured by models in comparison with observations, however, the annual cycles of snow water equivalent and snow depth are largely overestimated by models, especially in North America. There is better agreement between models and observations in the snow margin position in spring rather than in autumn. Magnitudes of interannual variability for all snow characteristics are significantly underestimated in most CMIP5 models compared to observations. For both seasons, trends of snow characteristics in models are primarily negative but weaker and less significant than those from observations. The patterns of snow cover trends are relatively well reproduced in models, however, the spatial distribution of trends for snow water equivalent and snow depth display strong regional heterogeneities.

Finally, we have concluded CMIP5 general circulation models provides valuable information about the snow characteristics in the terrestrial Arctic, however, they have still limitations. There is a lack of agreement among the ensemble of models in the spatial distribution of snow compared to the observations and reanalysis. And these discrepancies are accentuated in regions where variability of snow is higher in areas with complex terrain such as Canada and Alaska and during the melting and the onset season. Our goal in this study was to identify where and when these models are or are not reproducing the real snow characteristics in the Arctic, thus we hope that our results should be considered when using these snow-related variables from CMIP5 historical output in future climate studies.

Introduction 1.1 Arctic climate system

There are several ways to define the Arctic region. The geographical definition is based on solar-Earth motion considering the Arctic as the region above the 66 • 34 N parallel, the Arctic Circle.

When defined in this way, its most fundamental characteristic is continuous daylight during the summer solstice and its absence during winter solstice (polar night). The duration of the daylight hours depends on the latitude. In the extreme case of the North Pole, the sun never sets between spring and autumn equinoxes and never rises during the rest of the year. Another way to set the boundaries of the Arctic is to consider it as the region north of the tree line, where vegetation is mainly dotted shrubs and lichens (Figure 1.1a). Arctic conditions, such as extreme winter cold, widespread permafrost and seasonal snow cover are present south of the limits of the Arctic circle and the tree line delimitation. Therefore, we consider the Arctic domain as the area north of 50 • latitude and we focused on the ice-free land portion of the Arctic since the aim of this study is to evaluate terrestrial snow characteristics (Figure 1.1b ; see Chapter 3 for further details). Along the Arctic area, for some analysis, we consider separately the North American sector ["NAm"] and the Eurasian sector ["EURA"] separated by the 180

Domain Acronym Longitude (50 • N -90 • N) Arctic ARC 0 • E -360 • E Eurasia EURA 0 • E -180 • E Western Eurasia EURAWest 0 • E -90 • E Eastern Eurasia EURAEast 90 • E -180 • E North America NAm 180 • E -360 • E Table 1.1 -Arctic domains.
The Arctic climate system is characterized by its low thermal energy state and by its strong couplings between the atmosphere, ocean and land [START_REF] Serreze | The Arctic climate system[END_REF]. Arctic encompasses extreme climate differences which varies largely by location and season. Surface air temperature (2 m above ground) presents a marked regional and seasonal variability. The mean temperature of January is less than -35 • C in some parts of Siberia and the Canadian Archipelago, whereas over the central Arctic Ocean, temperature is typically around -25 • C in January (Figure 1.2a).

The presence of relatively warm and ice-free ocean water, and the atmospheric heat transport by the North Atlantic cyclones allows Iceland to have a mean temperature in January around 0 • C (Figure 1.2a). In July, mean temperature over land may vary from 10 • C to 20 • C (Figure 1.2b).

Precipitation over the Arctic is quite scarce compare to other regions of the globe. Some parts of the Arctic, such the Canadian Archipelago, can be compared to arid regions elsewhere, with an annual mean precipitation of 200 mm or less ; whereas in the Atlantic sector, where Atlantic cyclones transport the moisture, it can reach 1000 mm (ACIA, 2004;[START_REF] Serreze | Representation of mean Arctic precipitation from NCEP-NCAR and ERA reanalyses[END_REF].

Over a considerable part of the terrestrial Arctic, precipitation has maxima in summer but, for the Atlantic sector of the Arctic, maximum occurs in winter due to increase of cyclone activity in the cold season. The main feature of the Arctic is its cryosphere, whether sea ice, ice sheets, mountain glaciers and ice caps, permafrost, river and lake ice, and snow (Figure 1.3). The Arctic Ocean occupies most of the surface north of 70 • latitude and is covered by floating sea ice throughout the year. Summer Arctic sea ice extent has been decreasing since the beginning of the satellite era in the late 70s by -13. 3 % per decade (1979-2014) [START_REF] Serreze | Arctic sea ice trends, variability and implications for seasonal ice forecasting[END_REF]. The alarming record minima of sea ice extent of 4.1 × 10 6 km 2 on 14th September 2007 (Comiso et al., 2008) was overtaken on 13th

September 2012 reaching 3.4 × 10 6 km 2 (Parkinson and Comiso, 2013) (Figure 1.4). Overall, the decline of Arctic annual sea ice extent maximum and minimum has been -2.41 ± 0.56 % per decade and -13.5 ± 2.93 % change relative to the 1979-2015 climate average [START_REF] Peng | Temporal and regional variability of Arctic sea-ice coverage from satellite data[END_REF]. Sea ice extent decline is projected to continue during the twenty-first century under different emission scenarios [START_REF] Flato | Evaluation of climate models[END_REF].

The Greenland ice sheet represents the largest mass of permanent land ice in the Arctic and it has been losing 171 Gt/year in average computed over [START_REF] Cohen | The effect of snow cover on the climate[END_REF]-2015(Van den Broeke et al., 2016) with a stronger mass loss of 286 ± 20 Gt/year over the last decade (2010-2018) [START_REF] Mouginot | Forty-six years of Greenland Ice Sheet mass balance from 1972 to 2018[END_REF].

Sub-polar ice caps and mountain glaciers are concentrated in the mountainous parts of Siberia and Canadian archipelagos, in Svalbard and Iceland. The monitored Arctic glaciers and ice caps are out of balance with present day climate, which means that they are committed to lose additional mass in the coming decades even if the climate was stabilized in its present state [START_REF] Mernild | Global glacier changes : a revised assessment of committed mass losses and sampling uncertainties[END_REF]. Only 25 ± 35 % of the attributed loss of glacier mass was due to anthropogenic causes during the period from 1851 to 2010, whereas from 1991 to 2010 it has risen to 69 ± 24 % [START_REF] Marzeion | Attribution of global glacier mass loss to anthropogenic and natural causes[END_REF].

Permafrost is defined as ground (soil or rock and included ice or organic material) that remains at or below 0 • C for at least two consecutive years [START_REF] Ipa | International Permafrost Association[END_REF]. It occupies approximately 25% of the Northern Hemisphere land [START_REF] Biskaborn | Permafrost is warming at a global scale[END_REF] and it is also present in sub-sea sediments.

Permafrost soils store a large amount of carbon. As temperature increases and permafrost thaws, the carbon contained in permafrost can be released and emitted to the atmosphere as greenhouse gases such as carbon dioxide CO 2 and methane CH 4 [START_REF] Mcguire | Variability in the sensitivity among model simulations of permafrost and carbon dynamics in the permafrost region between 1960 and 2009[END_REF][START_REF] Schuur | Climate change and the permafrost carbon feedback[END_REF], which in turn increases the pace of future climate change [START_REF] Schuur | Vulnerability of permafrost carbon to climate change : Implications for the global carbon cycle[END_REF].

Snow and climate 1.2.1 Snow formation

Snow is crucially important component of the Arctic climate system. Snow originates in cold clouds when two particular conditions are present : supersaturation and supercooling. By definition, an air mass that contains more water vapor than 100% of relative humidity is supersaturated. The higher the temperature, the more water vapor it can hold. As moist air rises, it expands and cools.

When supersaturated air cools, the excess of water vapor crystallizes out into water or cloud droplets of the size of ∼10 microns in radius [START_REF] Armstrong | Snow and climate : physical processes, surface energy exchange and modeling[END_REF]. When cooled below 0 • C, such small droplets do not necessarily freeze and may "super cool" (i.e. lowering the temperature of gas/liquid below its freezing point without becoming a solid) to a temperature bellow -20 • C and occasionally bellow -40 • C [START_REF] Armstrong | Snow and climate : physical processes, surface energy exchange and modeling[END_REF]. Once a droplet has already frozen, it will grow rapidly at the expense of the remaining water droplets as they condense onto the surface of the ice crystal because of the difference in saturation vapor pressure between ice and water. The shape of the initial ice crystal (columnar, platelike, dendritic etc.) depends on the temperature at formation, but subsequent growth and structural detail also depend on the degree of saturation [START_REF] Hobbs | Physics of ice[END_REF]. As snow crystals fall down to the ground, they may experience considerable changes since temperature and humidity vary with altitude. The constitution of the surface snow layer depends on the original form of the crystal and the weather conditions during the fall and deposition. Snow on the ground may dissipate quickly through melting or sublimation or may persist for a longer time. In the second case, the snow will undergo metamorphism, changing its grain texture, size, and shape, primarily as a result of temperature and overburden pressure when buried by subsequent snowfalls [START_REF] Armstrong | Snow and climate : physical processes, surface energy exchange and modeling[END_REF].

Snowpack is described by three basic parameters : snow depth, snow water equivalent (SWE) and snow density. The snow depth is the thickness or the height of snow, usually expressed in cm. The snow water equivalent is the thickness of water resulting from the melting of the initial mass of the snow, which is usually expressed in kg m -2 or mm. Both variables are linked by the snow density, that is the ratio of mass to volume for a given sample, the standard units are kg m -3 . For example, considering a maximum seasonal snowpack with a density of ∼ 400 kg m -3 and a height of 50 cm, the resulting SWE will be 200 mm or 200 kg m -2 (see further details in Chapter 2).

Snow properties

Snow is one of the basic elements of the Arctic system, with a duration of snow cover for 7

to 10 months over the year (Figure 1.5) and with a maximum extension of 40% of the Northern Hemisphere land surface (approximately 47 × 10 6 km 2 ) each year [START_REF] Robinson | Seasonal variability of Northern Hemisphere snow extent using visible satellite data[END_REF][START_REF] Lemke | Observations : changes in snow, ice and frozen ground[END_REF]. The unique properties of snow have an important impact on climate [START_REF] Cohen | The effect of snow cover on the climate[END_REF]Groisman et al., 1994, ;Figure 1.6). Snow has a strong direct influence on the overlying low troposphere as has been shown by observations (e.g., [START_REF] Dewey | Daily maximum and minimum temperature forecasts and the influence of snow cover[END_REF] and by models [START_REF] Walsh | Sensitivity of 30-day dynamical forecasts to continental snow cover[END_REF][START_REF] Vavrus | The role of terrestrial snow cover in the climate system[END_REF] ; the impact is also present in the upper atmosphere (e.g., [START_REF] Alexander | The atmospheric response to projected terrestrial snow changes in the late twenty-first century[END_REF]. Snow has high reflectivity and this leads to influence on climate through the snowalbedo feedback [START_REF] Qu | What Controls the Strength of Snow-Albedo Feedback[END_REF][START_REF] Fletcher | Evaluating biases in simulated snow albedo feedback in two generations of climate models[END_REF], which is a climate feedback mechanism whereby land surface warming is enhanced through reductions in snow cover and surface albedo, and subsequently increased radiation absorbed at the surface (Thackeray et al., 2018). The contribution of terrestrial snow to the Earth radiation budget at the top of the atmosphere through the snowalbedo feedback is nearly equal to that from sea ice, the so-called cryosphere radiative forcing [START_REF] Flanner | Radiative forcing and albedo feedback from the Northern Hemisphere cryosphere between 1979 and 2008[END_REF][START_REF] Singh | The global land Cryosphere Radiative Effect during the MODIS era[END_REF]. The high albedo of snow (0.8-0.9 for dry snow) together with its low thermal conductivity favors low surface air temperatures. This last property is crucial for the insulation of the underlying soil from large energy losses and notably for the ice growth rate and the development of seasonal permafrost [START_REF] Lawrence | The contribution of snow condition trends to future ground climate[END_REF]Gouttevin et al., 2012;[START_REF] Koven | Analysis of Permafrost Thermal Dynamics and Response to Climate Change in the CMIP5 Earth System Models[END_REF][START_REF] Slater | Process-level model evaluation : a snow and heat transfer metric[END_REF]. The impact of snow on permafrost depends on its duration, thickness, accumulation and melting processes, structure, density, and thermal properties (Zhang et al., 1996). In summer, late-lying snow cover increases surface albedo and thus, surface air temperature decreases which prevents permafrost from thawing. In spring, a late snow melt delays warming of the soil surface while it is close to 0 • C, even if the air temperature is positive [START_REF] Romanovsky | Thawing of the active layer on the coastal plain of the Alaskan Arctic[END_REF][START_REF] Streletskiy | Permafrost degradation[END_REF]. During the snow season, a thick snow cover insulates the soil from air temperatures below 0 • C which hampers the development of permafrost and ice growth. Changes in permafrost temperature are largely attributed to variations on the thickness of snow cover [START_REF] Streletskiy | Permafrost degradation[END_REF]. [START_REF] Sherstyukov | Impact of surface air temperature and snow cover depth on the upper soil temperature variations in Russia[END_REF] found that changes in mean annual ground temperature in Siberia are more dependent on snow-cover thickness rather than on changes in air temperature. This relationship has also been found in the Northern Hemisphere discontinuous zone of permafrost, where ground warming results from the increase of snow thickness, while air temperature remains statistically invariant [START_REF] Biskaborn | Permafrost is warming at a global scale[END_REF].

Snow is a natural store of water, playing a critical role in energy fluxes (release of latent heat), run-off (peak of flow) and evaporation (Groisman et al., 2017). As a natural water reservoir, snow affects the water availability for a substantial part of humanity [START_REF] Barnett | Potential impacts of a warming climate on water availability in snow-dominated regions[END_REF]. In the early 1980s, Woo stated that the run-off generated by snow in the Arctic drainage basin accounts for 75% of the total annual flow in the Northwest Territories in Canada. [START_REF] Mankin | The potential for snow to supply human water demand in the present and future[END_REF] found that the 68 Northern Hemisphere river basins providing water availability to around 2 billion people are exposed to a significant risk of a decrease in snow potential supply in this century.

Arctic amplification and its influence on snow

The Arctic has warmed at a pace twice faster than the global average over the past 50 years, a phenomenon known as the Arctic Amplification [START_REF] Serreze | Processes and impacts of Arctic amplification : A research synthesis[END_REF]. Already in 1896, Svante

Arrhenius argued that changes in the concentration of CO 2 will influence the global temperature with a strong impact in polar latitudes. Global warming has a direct impact on the loss of ice cover driving a cascading effect on atmospheric circulation changes [START_REF] Francis | Evidence linking rapid Arctic warming to mid-latitude weather patterns[END_REF][START_REF] Ma | References Responses of the tropical atmospheric circulation to climate change and connection to the hydrological cycle[END_REF] as well as on moisture budgets, evaporation and precipitation [START_REF] Dufour | Atmospheric Moisture Transport to the Arctic : Assessment of Reanalyses and Analysis of Transport Components[END_REF][START_REF] Liu | Impact of declining Arctic sea ice on winter snowfall[END_REF][START_REF] Kattsov | Twentieth-century trends of Arctic precipitation from observational data and a climate model simulation[END_REF]. However, the inherent complexity of processes involved hinders a proper understanding of the water cycle feedback (e.g., [START_REF] Bintanja | Future increases in Arctic precipitation linked to local evaporation and sea-ice retreat[END_REF] and specifically, the snow response to a changing climate [START_REF] Brown | The Response of Northern Hemisphere Snow Cover to a Changing Climate[END_REF]Henderson et al., 2018).

Arctic warming affects the timing and duration of snow cover, the snow accumulation and the fraction of precipitation that falls as snow. Snow cover duration is reduced by 2 to 4 days per decade (1972-2014) [START_REF] Brown | Arctic terrestrial snow cover[END_REF] because snow melt occurs earlier in spring [START_REF] Cayan | Changes in the onset of spring in the western United States[END_REF][START_REF] Stewart | Changes in snowpack and snowmelt runoff for key mountain regions[END_REF]. This phenomena is not uniform over the whole region : satellite data collected over the period 1979-2011 have highlighted an averaged reduction of snow cover duration of 1.6 days per decade in the Northern American sector, whereas it reaches 3.3 days per decade in the Eurasian continental sector [START_REF] Wang | Recent changes in pan Arctic melt onset from satellite passive microwave measurements[END_REF]. This large reduction of the snow cover season has an immediate impact on the vegetation growth. [START_REF] Barichivich | Large-scale variations in the vegetation growing season and annual cycle of atmospheric CO2 at high northern latitudes from 1950 to 2011[END_REF] stated that the Eurasian Arctic has experienced a larger reduction of the vegetation growing season (12.6 days) compared to the North American Arctic region (6.2 days) from 1982 to 2011. As for the snow cover duration, this non-uniform spatial trend distribution has also been observed for other snow characteristics, such as snow depth (Zhong et al., 2018) or snow water equivalent [START_REF] Mudryk | Characterization of Northern Hemisphere snow water equivalent datasets, 1981-2010[END_REF]. Using around 820 stations spread all over the Russian Federation during the period from 1966 to 2007, [START_REF] Bulygina | Changes in snow cover over Northern Eurasia in the last few decades[END_REF] found that the winter-averaged snow depth decreased in the mountainous regions of Southern Siberia (-8-12 cm/dec) ; whereas in the western part of the Russian Federation it increased (around +4-6 cm/dec), with the maximum trends being observed in Northern West Siberia (+8.1 cm/dec at meteorological station Turukhansk at 38 m elevation). [START_REF] Brown | Arctic terrestrial snow cover[END_REF] reported a non-significant trend of annual snow depth accumulation of -0.6 cm/dec from 1950 to 2013 in the North American Arctic sector. This trend was computed using 56 stations from the Global Historical Climatology Network (GHCM) which recorded daily snow observations north of 60 • N. Significant decreasing trends in snow depth maximum were found in Yukon and the MacKenzie Basin from 1950 to 2012 ; however, over the rest of the Canadian Arctic, no significant trend could be found [START_REF] Vincent | Observed trends in Canada's climate and influence of low-frequency variability modes[END_REF]. Notwithstanding the regional heterogeneities found in the Arctic system, which highlights its complexity, there is multi-dataset evidence that, on average, snow accumulation is decreasing [START_REF] Brown | Northern Hemisphere snow cover variability and change, 1915-97[END_REF][START_REF] Park | Analysis of satellite and model datasets for variability and trends in Arctic snow extent and depth, 1948-2006[END_REF].

Arctic atmospheric moistening is another consequence of the anthropogenic warming [START_REF] Min | Human influence on Arctic sea ice detectable from early 1990s onwards[END_REF]. The local loss of ice cover [START_REF] Holland | Projected changes in Arctic Ocean freshwater budgets[END_REF][START_REF] Bintanja | Future increases in Arctic precipitation linked to local evaporation and sea-ice retreat[END_REF] and the local intensification of water cycle [START_REF] Rawlins | Analysis of the Arctic system for freshwater cycle intensification : Observations and expectations[END_REF][START_REF] Dufour | Atmospheric Moisture Transport to the Arctic : Assessment of Reanalyses and Analysis of Transport Components[END_REF] affects Arctic land areas with an increase in precipitation. At midlatitudes with a milder climate, snowfall (solid precipitation) is projected to decrease as the precipitation phase changes to liquid with increasing temperatures ; whereas, in high latitudes with a colder climate, snowfall is projected to increase [START_REF] Räisänen | Warmer climate : less or more snow ?[END_REF]. The increase in snowfall in deep snowpack regions (i.e. colder regions) may offset the current global reduction in snowfall during a shorter snow season (Wu et al., 2018). In a warmer climate, the timing or amount of snowmelt is associated with a reduction in the peak of stream flow [START_REF] Musselman | Slower snowmelt in a warmer world[END_REF] and an earlier onset of soil moisture drying [START_REF] Mahanama | Soil moisture, snow, and seasonal streamflow forecasts in the United States[END_REF], as a larger proportion of snow would melt earlier in the season. The direct consequences are unseasonal thaws [START_REF] Liston | The changing cryosphere : Pan-Arctic snow trends (1979-2009)[END_REF][START_REF] Mishra | Assessment of drought due to historic climate variability and projected future climate change in the midwestern United States[END_REF] and an increase of fire risk due to drier soils [START_REF] Westerling | Warming and earlier spring increase western US forest wildfire activity[END_REF]. Likewise, the decrease in the fraction of precipitation falling as snow leads to reduced overall stream flow [START_REF] Berghuijs | A precipitation shift from snow towards rain leads to a decrease in streamflow[END_REF] and increases the potential for rain-on-snow events (ROS) that even if rare and regional [START_REF] Furtado | Eurasian snow cover variability and links to winter climate in the CMIP5 models[END_REF] can cause large flooding when they occur [START_REF] Berghuijs | Dominant flood generating mechanisms across the United States[END_REF].

PhD rationale : Snow representation and objectives

The paucity of observational data sets in the Arctic makes it difficult to distinguish with confidence the climate forcing signal from the background noise of natural variability in snow evolution [START_REF] Brown | Northern Hemisphere snow cover variability and change, 1915-97[END_REF][START_REF] Mudryk | Interpreting observed Northern Hemisphere snow trends with large ensembles of climate simulations[END_REF][START_REF] Najafi | Attribution of the spring snow cover extent decline in the Northern Hemisphere, Eurasia and North America to anthropogenic influence[END_REF]. The spatial distribution of in situ measurements is quite scarce and few long term snow stations exist [START_REF] Brown | Spatial and temporal variability of Canadian monthly snow depths, 1946-1995[END_REF][START_REF] Bulygina | Changes in snow cover characteristics over Northern Eurasia since 1966[END_REF]. Satellite derived products provide valuable information of snow characteristics (e.g., [START_REF] Riggs | MODIS snow products user guide to collection 5[END_REF] but their temporal extent is usually not sufficient for climatological research.

Models are needed to help us to understand snow-related processes, namely, in the context of a warming cryosphere. Land surface models are employed to reproduce the temporal evolution of snow characteristics and its implications for different fields (e.g. hydrology, meteorology, climatology, glaciology and ecology). Snow models have been developed with a wide range of complexity.

Some models are quite sophisticated with a detailed snow stratigraphy, others with an intermediate degree of complexity using 2-3 layers, and simple, zero-layer (combined with soil) or single layersnow models [START_REF] Slater | The representation of snow in land surface schemes : Results from PILPS 2 (d)[END_REF]. Generally, in Earth System Models (ESMs), the snow modules are zero-and single-layer configurations. These simple models require fewer parameterizations, leading to faster computation ; however, they experience some limitations [START_REF] Bokhorst | Changing Arctic snow cover : A review of recent References developments and assessment of future needs for observations, modelling, and impacts[END_REF][START_REF] Krinner | ESM-SnowMIP : assessing snow models and quantifying snow-related climate feedbacks[END_REF].

In this research we focus on the evaluation of General Circulation Models (GCMs) from the Coupled Model Intercomparison Project 5 (CMIP5). CMIP5 is a standard framework from the World Climate Research Program (WRCP) aiming at improving our collective knowledge about the climate system. Currently, there have already been many studies evaluating the GCMs from the CMIP5 project [START_REF] Flato | Evaluation of climate models[END_REF]. Our work builds upon previous studies assessing snow characteristics in general circulation models where some progress and faults have been identified [START_REF] Flato | Evaluation of climate models[END_REF][START_REF] Brutel-Vuilmet | An analysis of present and future seasonal Northern Hemisphere land snow cover simulated by CMIP5 coupled climate models[END_REF][START_REF] Kapnick | Controls of Global Snow under a Changed Climate[END_REF]Terzago et al., 2014).

One of the main results was that the observed decreasing trend in spring snow cover in the Northern Hemisphere over the period 1979-2015 [START_REF] Derksen | Spring snow cover extent reductions in the 2008-2012 period exceeding climate model projections[END_REF] is largely underestimated in CMIP5 models due to an underestimation of the boreal temperature [START_REF] Brutel-Vuilmet | An analysis of present and future seasonal Northern Hemisphere land snow cover simulated by CMIP5 coupled climate models[END_REF].

Also, the spread in snow-albedo feedback (SAF) was not reduced from CMIP3 likely due to a wide spread in the different treatment of vegetation in models [START_REF] Qu | On the persistent spread in snow-albedo feedback[END_REF]. Recently, Thackeray et al. (2018) found that indeed, the structural differences in the snowpack, vegetation and albedo parametrizations drive most of the spread. Notably, models displaying the largest bias in SAF, also

show clear structural and parametric errors. However, snow regimes in autumn have received less attention compared to spring.

In this respect, representation of snow-associated feedbacks in climate models, especially during the mid seasons (when Arctic snow cover exhibits the strongest variability) is of a special interest.

At the offset of the snow season, down-welling shortwave and longwave radiation fluxes provide most of the energy enabling snow melt ; at the onset, temperatures are sufficiently cold to favor solid precipitation and snow accumulation [START_REF] Sicart | Incoming longwave radiation to melting snow : observations, sensitivity and estimation in northern environments[END_REF]. In spring, the snow albedo feedback is stronger as snow cover starts to age and recede due to increasing temperature and insolation [START_REF] Qu | On the persistent spread in snow-albedo feedback[END_REF]Thackeray et al., 2016). In addition, positive (negative) snow cover anomalies in Eurasia from winter to spring may be followed by negative (positive) anomalies in the rainfall during the Indian summer moonson [START_REF] Prabhu | Summer monsoon rainfall variability over North East regions of India and its association with Eurasian snow, Atlantic Sea Surface temperature and Arctic Oscillation[END_REF][START_REF] Senan | Impact of springtime Himalayan-Tibetan Plateau snowpack on the onset of the Indian summer monsoon in coupled seasonal forecasts[END_REF] but this snow-teleconnection is still controversial [START_REF] Peings | Influence of the Eurasian snow cover on the Indian summer monsoon variability in observed climatologies and CMIP3 simulations[END_REF]Zhang et al., 2019). While variations in snow characteristics are smaller in autumn than in spring, they also experience changes which have links to atmospheric circulation (Henderson et al., 2018). Observational (Cohen et al., 2007) and modeling [START_REF] Peings | A numerical sensitivity study of the influence of Siberian snow on the northern annular mode[END_REF] studies linked the increase in Eurasian snow cover with the winter phase of the Arctic Oscillation (AO) and North Atlantic Oscillation (NAO). However, [START_REF] Gastineau | The Influence of Autumnal Eurasian Snow Cover on Climate and Its Link with Arctic Sea Ice Cover[END_REF] using an ensemble of CMIP5 models, demonstrated that this relationship is simulated by only four models and is largely underestimated by the majority of the ensemble. Douville et al. (2017) have questioned the robustness of the snow-NAO relationship and also argued for the importance of eastward phases of the Quasi-Biennial Oscillation (QBO) in modulation of snow cover variability.

To summarize, there is a need for comprehensive evaluation and validation of snow characteristics in climate models using available observations over the last decades in order to demonstrate which Arctic snow features are more robust across different models and which are not captured effectively. The focus of this PhD is on the representation of Arctic terrestrial snow in global circulation models from the CMIP5 ensemble in the mid seasons. Our goal is to make an evaluation of individual models to provide reliable information for the scientific community and hopefully help to improve the snow representation in future general circulation models. This thesis is organized as follows. Chapter 2 describes the snow data sources -namely, CMIP5 models, reanalyses and observations. Chapter 3 is dedicated to the description of the methodology, the treatment of data to provide comparability and the statistical tools employed. Chapter 4 presents the analysis of the spatial structure of snow characteristics. In Chapter 5 we study the temporal evolution and variability of snow characteristics. Finally, Chapter 6 offers the main conclusions and some perspectives for future research.

Chapter 2

Data Contents

Overview

Our capacity to observe the terrestrial Arctic is limited compared to the mid-latitudes. Conditions are not ideal for continuous monitoring of snow characteristics due to inclement weather conditions, the polar night and the wind transport of snow. Moreover, the uneven spatial distribution of snow stations concentrated at 55 • N in Canada [START_REF] Brown | Spatial and temporal variability of Canadian monthly snow depths, 1946-1995[END_REF] or the lack of data in northern Siberia [START_REF] Bulygina | Changes in snow cover characteristics over Northern Eurasia since 1966[END_REF] make challenging the up-scaling to larger regions.

The snow stations are key for climatological research of snow characteristics as they are a unique record and the longest existing data in time. The temporal extent of the satellite era usually limits the study of the climate variability of snow [START_REF] Maurer | Evaluation of the snow-covered area data product from MODIS[END_REF][START_REF] Riggs | MODIS snow products user guide to collection 5[END_REF]. Even if both the in situ measurement and satellite data provide valuable information for snow and environment (Groisman and Davies, 2001), they present the aforementioned spatial and temporal limitations.

Reanalyses are a combination of observations and numerical models proving a synthesized estimate of the Earth system. They can reproduce the state of the climate and extend over several decades, as is the case for the NCEP/CFSR [START_REF] Saha | The NCEP Climate Forecast System Reanalysis[END_REF] and ERA-Interim [START_REF] Dee | The ERA-Interim reanalysis : Configuration and performance of the data assimilation system[END_REF] reanalyses ; or longer time periods, as the NOAA-CIRES 20th reanalysis (Compo et al., 2011). Typically, reanalysis products cover the entire globe from the surface to well above the stratosphere.

Land snow-cover models are used to simulate the temporal evolution of snow in multiple applications (e.g. hydrology, meteorology, climatology, glaciology and ecology). There exist a wide variety of empirical and physically-based snow models whose degree of complexity may be adjusted to the intended application [START_REF] Magnusson | Evaluating snow models with varying process representations for hydrological applications[END_REF]. The sophistication of snow models ranges from the more complex with a detailed snow stratigraphy (e.g., CROCUS ; [START_REF] Brun | A numerical model to simulate snow-cover stratigraphy for operational avalanche forecasting[END_REF][START_REF] Brun | Coupling a multi-layered snow model with a GCM[END_REF][START_REF] Vionnet | The detailed snowpack scheme Crocus and its implementation in SURFEX v7. 2[END_REF], i.e vertical evolution of snow properties like snowpack compaction, liquid water percolation, snow interception etc., through the intermediate model complexity (2-3 layers) and to the simplest, with zero-layer (combined with soil) or single layer-snow models [START_REF] Slater | The representation of snow in land surface schemes : Results from PILPS 2 (d)[END_REF]. The modules used in Earth System Models (ESMs) are usually zero-and single-layer snow model configurations, having fewer parameterizations leading to fast computations, however, they involve some limitations [START_REF] Bokhorst | Changing Arctic snow cover : A review of recent References developments and assessment of future needs for observations, modelling, and impacts[END_REF][START_REF] Krinner | ESM-SnowMIP : assessing snow models and quantifying snow-related climate feedbacks[END_REF]. Some of the flaws in ESMs have been linked to the representation of the vegetation [START_REF] Essery | Large-scale simulations of snow albedo masking by forests[END_REF][START_REF] Fletcher | Evaluating biases in simulated snow albedo feedback in two generations of climate models[END_REF], thermal conductivity [START_REF] Cook | The thermoinsulation effect of snow cover within a climate model[END_REF]Gouttevin et al., 2012) and radiative processes ( et al., 2016). However, even in detailed physically-based models, there are snow related processes that are not well captured, particularly in cold conditions [START_REF] Domine | Seasonal evolution of the effective thermal conductivity of the snow and the soil in high Arctic herb tundra at Bylot Island, Canada[END_REF]. The uncertainty of the underlying physics remains a drawback in the advance of snow modeling [START_REF] Lafaysse | A multiphysical ensemble system of numerical snow modelling[END_REF].

Thackeray
This chapter describes the wide variety of data used, from general circulation models to snow stations through the different satellite-based products and reanalyses, in order to bridge the gaps between the representations of snow characteristics in such a variety of data sets. ) is a standard framework for studying the output of coupled atmosphere-ocean general circulation models ("AOGCMs"). CMIP5 builds on the accomplishment of previous CMIP phases [START_REF] Meehl | The coupled model intercomparison project (CMIP)[END_REF][START_REF] Meehl | Overview of the coupled model intercomparison project[END_REF] and aims at advancing our collective understanding of climate variability and climate change. The CMIP5 framework includes simulations on several timescales, ranging from seasonal to multidecadal. All simulations included in the CMIP5 framework (Figure 2.1) are classified by "core" and by one or two surrounding "tiers" according to a consensus of prioritization. The "core" simulations (shaded in pink, Figure 2.1) are crucial for the evaluation of climate models and they produce information of keen interest about future projections. The "tier1" (shaded in yellow, Figure 2.1) researches specific aspects of climate model forcing, responses and processes that are examined in further depth in "tier2" (shaded in green, Figure 2.1). The strategy of CMIP5 encompasses two type of climate experiments (Figure 2.1a,b) that we briefly describe below :

General Circulation Models (GCMs)

1. Long-term integrations (century time scale) (Figure 2.1a) are usually started from multicentury preindustrial control (quasi equilibrium). These simulations follow the protocol of the previous phases of CMIP, but they add some additional runs to supply a more exhaustive understanding of climate change and variability. The core of long-term simulations (Figure 2.1a) involve an AMIP run, a coupled control run and a "historical" run. The latter are forced by observed atmospheric composition and reflect both the anthropogenic and the natural evolution of the climate system. The historical runs, also called "twentieth century" simulations, cover the time period from 1850 to 2005. The new addition with respect to previous phases is that in CMIP5, the historical runs include a time-evolving land cover.

Within the long-term simulations, there are also future projections forced with specified concentrations of greenhouse gases, which are referred to as "representative concentration pathways" (RCPs) described in [START_REF] Moss | The next generation of scenarios for climate change research and assessment[END_REF]. In CMIP5, there are four RCPs which are based on estimations of future population growth, technological development and societal responses (Figure 2.2). The denomination of each RCP provides an approximate estimate of the radiative forcing in the year 2100 (relative to preindustrial conditions). Unlike phase 3, in CMIP5, these RCPs take policy interventions into account, meaning that the RCPs are mitigation scenarios where actions to curb emissions are considered. The four future scenarios are : RCP8.5, referred to as the "high scenario", the two "intermediate scenarios" RCP4.5

and RCP6, and the so called "peak-and-decay" scenario RCP2.6.

2. Near-term integrations (10-30 yr) (Figure 2.1b), also called decadal prediction experiments [START_REF] Meehl | Decadal prediction : can it be skillful[END_REF]. The near-term prediction experiments are a novelty of CMIP.

Decadal prediction experiments are organized by the WGCM and the Working Group on Seasonal to Interannual Prediction (WGSIP). These near-term simulations are initialized with observed ocean and sea ice conditions. There are two collections of core simulations (Figure In the first one, we can asses the skill of the climate forecast when initial climate conditions exert some detectable influence, whereas in the second one, with a longer time scale, the external forcing of an increase in GHGs will dominate the response of the system even if some residual influence of the difference in initial conditions prevail. Thus, in the near-term simulations models are not only responding to climate forcing (e.g. increase in CO 2 concentration) but they may also reproduce the climate change evolution, including the unforced component.

Climate models involved in CMIP5 have a twofold mission. First, purely scientific, aims at advancing in our knowledge of the Earth Climate System, its past, present and future evolution.

The second is to contribute to the IPCC (Intergovernmental Panel on Climate Change) reports to mitigate climate change and adapt to its effects [START_REF] Edenhofer | Mitigation of climate change[END_REF][START_REF] Field | Climate change 2014-Impacts, adaptation and vulnerability : Regional aspects[END_REF]. The straightforward approach to model evaluation is to compare the model output with existing observations to identify its strengths and weaknesses. The core of this PhD is to contribute to this vast task by analyzing the snow characteristics in CMIP5 models. For this purpose, we evaluate the most realistic simulations from CMIP5, the "historical runs" from the "long-term integration" type climate experiments. They are forced by observed atmospheric composition and exhibit the anthropogenic forcing as well as the natural evolution of the climate system.

Model name

Snow Variables in CMIP5

In the introduction it was mentioned that the snowpack can be described by snow depth or snow water equivalent, and that both characteristics are related by the snow density. From the in situ point of view, snow depth usually refers to the total height of snow on the ground at the time of observation and it is measured with a snow ruler or similar graduated rod which is pushed down through the snow to the ground surface [START_REF] Jarraud | Guide to meteorological instruments and methods of observation (WMO-No. 8)[END_REF]. Snow water equivalent is the thickness of the water that would be obtained by melting the snow sample and it can be measured directly by melting the sample and measuring its liquid content, or indirectly by inferring the water equivalent using an appropriate specific snow density [START_REF] Jarraud | Guide to meteorological instruments and methods of observation (WMO-No. 8)[END_REF]). Returning to the example from the introduction, for a snow sample of 50 cm height with a maximum seasonal snow density of 400 kg m -3 , the resulting snow water equivalent would be 200 mm following this relationship :

m liquid water = m snow ρ liquid water • h liquid water • S = ρ snow • h snow • S → h liquid water = ρ snow=400 kg m -3
ρ liquid water=1000 kg m -3 • h snow=0.5 m = 200 mm However, when moving from the in situ representation to large scale, the concept of snow characteristics is slightly nuanced. From the model perspective, there is no one observation point ; instead, space is discretized in grid cells which makes the conversion of snow depth to snow water equivalent much more complex. Indeed, in CMIP5 models, the spatial resolution of grid cells varies from ∼ 100 km 2 to ∼ 300 km 2 . The snow surface representation also depends on the different canopies within the grid cells, that is, the type of vegetation (e.g. trees, shrubs), topography, land use, presence of lakes and rivers etc. which are in the land-surface model of the GCM. The variables that represent terrestrial snow characteristics in CMIP5 models are described in the document "standard output.pdf" accessible via https://pcmdi.llnl.gov/mips/cmip5/docs/ :

• Snow Area Fraction ("snc", %) : Fraction of each grid cell that is occupied by snow that rests on the land portion of the cell. "Snow Area Fraction" is usually called "Snow Cover

Extent" ; throughout the manuscript we will refer it as "SCE".

• Surface Snow Amount ("snw", kg m -2 ) : Computed as the mass of surface snow on the land portion of the grid cell divided by the land area in the grid cell ; reported as 0.0 where the land fraction is 0 ; snow on vegetation canopy or on sea ice is excluded. "Surface Snow Amount" corresponds to the snow water equivalent definition (h w in Figure 2.3) ; hereafter we will refer to it as "SWE".

• Snow Depth ("snd", m) : when over land, this is computed as the mean thickness of snow in the land portion of the grid cell (averaging over the entire land portion, including the snow-free fraction). Reported as 0.0 where the land fraction is 0. Snow depth ("SND") is represented by h snow as in Figure 2.3. In the CMIP5 models considered in this study (Table 2.1), the snow water equivalent (SWE) is a prognostic variable (ES-DOC, https://es-doc.org) resulting from the balance between snowfall, evaporation and snowmelt rates (Equation 2.1 ; [START_REF] Manabe | Climate and the ocean circulation[END_REF]Thackeray et al., 2016). Snow depth (SND) is usually a diagnostic variable depending on SWE by means of the snow density.

d dt (SW E) = S f -E -M e (2.1)
where S f is the rate of snowfall, E is the evaporation rate and M e is the rate of snow melt which can be computed by the heat balance (E x ) condition of a snow covered surface, that is, M e = E x /L f when E x > 0 and M e = 0 when E x <= 0 [START_REF] Manabe | Climate and the ocean circulation[END_REF]. Snow cover fraction or extent (SCE) is usually diagnosed from SWE by means of a monotonic function using different parametrizations depending on the model [START_REF] Liston | Representing subgrid snow cover heterogeneities in regional and global models[END_REF]Wu et al., 2018). Models also present different conservation properties (e.g. water discharge-storage), couplings with atmosphere and land cover types which depend essentially on the land model integrated in the GCM. For example, to diagnose SCE, the ISBA surface model, a component of CNRM-CM5, uses an asymptotic function of SWE (Equation 2. 2 ;Douville et al., 1995) :

p ng = W n W n + W crn (= 10mm) (2.2)
where W n is the mean snow water equivalent (SWE), W crn the critical water equivalent of snow necessary to the estimation of p ng which represents the fraction of snow covering the soil (SCE) (Douville et al., 1995). Conversely, the CLM 3. The <MIP table> provides information about the modeling realm, the high level modeling component relevant for the variable such as "LandIce" for snow or "Atmosphere" for snowfall, and also the frequency, "Monthly" in both cases. The experiment family is indicated as "historical", referring to the historical runs explained in the previous section. The ensemble member is com-posed by a triad of integers (r<N>i<M>p<L>) which refer to varying simulation conditions for each realization (member). N is the "realization number" : if the different members of one model vary only according to this integer N, it means that runs have been initialized with different, but equally realistic initial conditions ; the M corresponds to the "initialization method indicator" which indicates the different observational data sets or the different methods using observations that are employed as initial conditions. The L refers to the "perturbed physics number" which allows to distinguish between different realizations that have modified a particular set of model parameters.

The <temporal subset> is restricted to the period 1979-2005.

The choice of the ensemble of models in Table 2.1 is justified by two reasons. First, our aim was to evaluate different snow variables and so, initially, we only focused on snow cover and snow water equivalent (SCE and SWE). Thus, we considered only the CMIP5 models which provided both characteristics. Later in the PhD, we began to use in situ measurements from the snow stations, which motivated us to form a new set of models including snow depth ; however, the models MPI-ESM-LR/P do not provide this variable. The risk of using an erroneous method to convert SWE to SND to include these models in the SND analysis has already been identified [START_REF] Brown | Comment on "Evaluation of surface albedo and snow cover in AR4 coupled models" by A. Roesch[END_REF]. Consequently, in the SND analysis the MPI-ESM-LR/P models do not appear. Secondly, we wanted to limit our study to an amount of models small enough to enable individual analysis.

When using a large number of models, multimodel analysis is more suitable, but it is less evident to provide a catalog of individual model performance.

Observations

Generally, there are two fundamental ways to measure snow directly, from in situ snow stations and from remote sensing using satellites (e.g., [START_REF] Riggs | MODIS snow products user guide to collection 5[END_REF] or airborne LiDAR (e.g., [START_REF] Schaffhauser | Remote sensing based retrieval of snow cover properties[END_REF]. The main problem with in situ measurements is that they include intrinsic systematic human error [START_REF] Woo | Analysis of error in the determination of snow storage for small high Arctic basins[END_REF] and may not be accurately continuous in time. On the other hand, they are a unique record with precious information of snow characteristics. Remote sensing snow data coming from satellites, for instance, contain uncertainties related to the retrieval procedure such as the presence of clouds [START_REF] Parajka | Validation of MODIS snow cover images over Austria[END_REF]. They are continuous in time, however, satellite snow products begin too late for our period of interest, except for the NOAA Climate Data Record [START_REF] Estilow | A long-term Northern Hemisphere snow cover extent data record for climate studies and monitoring[END_REF]. Reanalysis products are another source of snow infor-mation considered here as an observational reference. However, they are also subject to intrinsic errors (e.g., [START_REF] Khan | Snow cover characteristics over the main Russian river basins as represented by reanalyses and measured data[END_REF][START_REF] Dufour | Atmospheric Moisture Transport to the Arctic : Assessment of Reanalyses and Analysis of Transport Components[END_REF][START_REF] Wegmann | Eurasian snow depth in long-term climate reanalyses[END_REF].

Snow Stations

Regular snow observations have been conducted all over the Eurasian continent from 1881 to 2013. This includes snow depth measurements and the amount of snow covering the visible area of meteorological stations, estimated on a scale of one to ten (10 to 100% ; or zero in the absence of snow). Here we use the daily snow depth record over the former USSR (Union of Soviet Socialist Republics), which is composed of data from 600 stations, from the Russian Research Institute for Hydro-meteorological Information -World Data Center (RIHMI-WDC) [START_REF] Bulygina | Changes in snow cover characteristics over Northern Eurasia since 1966[END_REF].

Snow depth measurements have been conducted once a day using a graduated stake installed at a fixed point location within the station or by a wooden ruler, following the standard protocol from the World Meteorological Organization (WMO, McMichael et al., 1996). Meteorological data sets are quality controlled before being stored at the RIHMI-WDC [START_REF] Veselov | PC archives of the State Data Holding and technology of their organization[END_REF]. As the procedures of snow observation have changed over time (e.g., [START_REF] Meshcherskaya | Snow depth monitoring in the main corn belt of the former Soviet Union during the period of instrumental observations[END_REF], particular consideration has been taken to maintain the homogeneity in the data record. All information for the snow stations is available at http://meteo.ru/english/climate/snow.php.

NOAA CDR

The satellite-based weekly Snow Cover Extent dataset [START_REF] Robinson | Global snow cover monitoring : An update[END_REF][START_REF] Robinson | Seasonal variability of Northern Hemisphere snow extent using visible satellite data[END_REF][START_REF] Estilow | A long-term Northern Hemisphere snow cover extent data record for climate studies and monitoring[END_REF] is the longest continuous record of snow cover extent, starting on 4th October 1966 and continuing at present. It is freely available at the NOAA (National Oceanic and Atmospheric Administration) National Center for Environmental Information (NCEI). It has been used in numerous studies [START_REF] Déry | Recent Northern Hemisphere snow cover extent trends and implications for the snow-albedo feedback[END_REF][START_REF] Derksen | Spring snow cover extent reductions in the 2008-2012 period exceeding climate model projections[END_REF][START_REF] Brown | Is Eurasian October snow cover extent increasing ?[END_REF][START_REF] Gastineau | The Influence of Autumnal Eurasian Snow Cover on Climate and Its Link with Arctic Sea Ice Cover[END_REF][START_REF] Connolly | Northern Hemisphere Snow-Cover Trends (1967-2018) : A Comparison between Climate Models and Observations[END_REF]. Before 1972, the resolution of common meteorological satellites was around 4 km. From October 1972, VHRR (Very High Resolution Radiometer) provided imagery with an improved spatial resolution of 1 km, which was slightly reduced to 1.1 km in November 1978 with the replacement of the VHRR by the Advanced VHRR (AVHRR). From 1966 to 1999, snow maps were analyzed and interpreted by hand by experienced meteorologists from the NOAA who drew the boundaries of snow cover extension. Weekly maps were created in an 89 × 89 cell cartesian grid laid over a polar stereographic projection of the Northern Hemisphere. The resolution of cells ranges from ≈ 10 700 to ≈ 41 800 km 2 , with a spatial resolution of 190.5 km at 60 • N. Each grid cell has a binary value displaying "1" when a cell has at least 50% of its surface covered with snow and "0" for all other cells, considered snow-free cells.

Since 1999, this process has been automated by the Interactive Snow and Ice Mapping System (IMS, [START_REF] Ramsay | The interactive multisensor snow and ice mapping system[END_REF] at the Global Snow Lab from Rutgers University. Thus, the early weekly snow cover analysis procedure changed with the introduction of IMS at much higher resolution (≈ 24 km).

However, to maintain continuity, a pseudo-weekly snow chart has been created by drawing a map representative of the previous week each Sunday ; which is in agreement with [START_REF] Robinson | Monitoring northern hemisphere snow cover[END_REF] who take the 5th day of the week as representative, with the first week starting on Tuesday, 4th October 1966.

NOAA maps are subject to limitations when overcast conditions, weak solar radiation or complex vegetation complicate the retrieval process. [START_REF] Robinson | Seasonal variability of Northern Hemisphere snow extent using visible satellite data[END_REF] reanalyzed this data from 1961 to 1971, there were missing values mainly in autumn and the resolution was quite coarse. In spite of their limitations, the NOAA maps are trustworthy for continental-scale studies of snow cover variability [START_REF] Wiesnet | A discussion of the accuracy of NOAA satellite-derived global seasonal snow cover measurements[END_REF] but caution should be taken at high latitudes and mountainous regions. Also, two studies [START_REF] Wang | Evaluation of spring snow covered area depletion in the Canadian Arctic from NOAA snow charts[END_REF]Brown et al., 2007) over northern Canada showed that NOAA CDR overestimates snow cover in spring and summer and tends to be uncoupled with temperature anomalies in July. It has been stated more recently that there is a bias in snow cover during October that has not been detected in other data records [START_REF] Brown | Is Eurasian October snow cover extent increasing ?[END_REF], which in turn translates to an anomalous snow cover trend in October in Eurasia [START_REF] Brown | Is Eurasian October snow cover extent increasing ?[END_REF][START_REF] Estilow | A long-term Northern Hemisphere snow cover extent data record for climate studies and monitoring[END_REF]. 2. ERA-Interim/Land reanalysis [START_REF] Balsamo | ERA-Interim/Land : A global land-surface reanalysis based on ERA-Interim meteorological forcing[END_REF] : Global reanalysis of land-surface parameters with a horizontal resolution of ∼ 80 km (T255) and a temporal resolution of 6 hours for the period from 1st January 1979 to 31st December 2010.

CanSISE Ensemble Product

3. MERRA reanalysis (M. [START_REF] Rienecker | MERRA : NASA's Modern-Era Retrospective analysis for Research and Applications[END_REF] : NASA atmospheric reanalysis using the Goddard Earth Observing System model (GEOS-5) and its associated assimilation system (DAS), Version 5.2.0 [START_REF] Rienecker | The GEOS-5 Data Assimilation System : Documentation of Versions 5[END_REF]. It provides hourly averages of land surface fields at a horizontal resolution of 2/3 • longitude by 1/2 • latitude from 1st January 1980 to present.

4. CROCUS snow pack model [START_REF] Brun | An energy and mass model of snow cover suitable for operational avalanche forecasting[END_REF][START_REF] Brun | A numerical model to simulate snow-cover stratigraphy for operational avalanche forecasting[END_REF] and updated by [START_REF] Vionnet | The detailed snowpack scheme Crocus and its implementation in SURFEX v7. 2[END_REF] :

SWE output from the CROCUS snow pack model, driven by ERA-Interim meteorology.

5. GLDAS (Version 2) [START_REF] Rodell | The Global Land Data Assimilation System[END_REF][START_REF] Rodell | GLDAS Noah Land Surface Model l4 Monthly 0[END_REF] : SWE parameter from the Common Land Model (CLM) V2.0 model in the Global Land Data Assimilation System (GLDAS). The spatial resolution is 1 • degree and range from January 1979 to present. The temporal resolution is 3-hourly.

Overall, the CanSISE product has a daily temporal resolution, 1.0 • × 1.0 • spatial resolution and covers the period from 1st January 1981 to 31th December 2010. This product is available at https://nsidc.org/data/nsidc-0668.

Reanalyses

• National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR), "NCEP/CFSR" [START_REF] Saha | The NCEP Climate Forecast System Reanalysis[END_REF] is a 6-hourly product covering a 31 year-period from 1979 to 2010 and 0.5 • × 0.5 • horizontal resolution. It includes a coupled atmosphere-ocean-land surface-sea ice system and direct assimilation of satellite radiances.

The global atmosphere has a resolution of ∼ 38 km (T382) with 64 levels, the ocean resolution is of 0.25 • around the equator and 0.5 • beyond the tropics, land surface models provides 4 levels and the sea ice model 3. The NCEP/CFSR reanalysis also includes changes in CO 2 and other trace gases, aerosols and solar variations. We used this data set for snow cover and it is available at https://rda.ucar.edu/datasets/ds093.0/.

• NOAA-CIRES 20th Century Reanalysis version 2, "NOAAV2c" (Compo et al., 2011) which extends from 1851 to 2012 with an original temporal resolution of 6 hours and spatial resolution of 2.0 • × 1.75 • . It uses the coupled atmosphere-land model NCEP GFS 2008ex. It assimilates only surface pressure reports and uses observed monthly sea surface temperature and sea ice concentration fields as boundary conditions. The spectral resolution is T62 and the vertical resolution is composed of 28 hybrid sigma-pressure levels. From this data we analyzed snow cover and snow depth and it can be downloaded at http://www.esrl.

noaa.gov/psd/data/gridded/data.20thC ReanV2c.html.

• Japanese 55-year Reanalysis, "JRA-55" [START_REF] Kobayashi | The JRA-55 reanalysis : General specifications and basic characteristics[END_REF] The spatial resolution is a regular latitude-longitude Gaussian grid 320 latitudes by 640 longitudes, nominally 0.5625 • degree. The temporal resolution is 6-hourly. We used snow depth from this reanalysis which is available at https://rda.ucar.edu/datasets/ds628.0/.

• ERA-20C, "ERA20c" [START_REF] Poli | ERA-20C : An atmospheric reanalysis of the twentieth century[END_REF]

Overview

All data sets described in Chapter 2 are originally in different spatial and temporal resolutions.

To provide an accurate intercomparison between data sets, it is necessary to convert them to compatible formats. This chapter explains briefly the data treatment preceding the analysis and how the domain restriction to an ice free land Arctic has been accomplished.

Spatial and temporal resolution

General procedure

In order to enable a grid-to-grid evaluation, we convert CMIP5 model output and reanalyses to compatible grids. The spatial resolution of CMIP5 models goes from relatively fine (0.9

• × 1.2 o , CCSM4) to coarse (2.8 o × 2.8 o , bcc-csm1-1
). The reanalyses used in this study have grids ranging from 0.5 o × 0.5 o in NCEP/CFSR to four times larger in NOAAV2c (2.0 o × 1.75 o ). For grid-to-grid evaluation, all snow fields from CMIP5 models (Table 2.1) are converted to a 1.0 o × 1.0 o regular grid.

An analogous procedure has been applied to all SCE reanalyses (NCAR/CFSR and NOAAV2c), the SWE satellite based product (CanSISE) and SND reanalyses (NOAAV2c, JRA-55 and ERA20c).

We have used the cdo remapbil operator (CDO : Climate Data Operator ; [START_REF] Schulzweida | CDO user's guide. Climate data operators[END_REF] to conduct the bilinear interpolation (Table 3.1).

Data set Original spatial resolution

CanSISE (SWE) 1.0 • × 1.0 • NCAR/CFSR (SCE) 0.5 • × 0.5 • cdo remapbil --------→ 1.0 • × 1.0 • NOAAV2c (SCE ;SND) 2.0 • × 1.75 • JRA-55 (SND) 0.5625 • × 0.5625 • ERA20c (SND) 1.125 • × 1.125 • Table 3.1 -Spatial resolution of different reference data sets.
The temporal resolution is dictated by the frequency of snow variables in CMIP5 models. Among the CMIP5 ensemble (Table 2.1), only few models provide daily resolution for snow characteristics (CanESM2, all versions of MIROC and MRI-CGCM3 ; https://esgf-node.llnl.gov). The majority of CMIP5 models dispense monthly snow output from the "LIMon" (Land Ice Monthly) CMOR2 table

as mentioned in the previous chapter. Accordingly, we compute monthly means of the reference data sets using the cdo monmean operator (CDO : Climate Data Operator, [START_REF] Schulzweida | CDO user's guide. Climate data operators[END_REF] as indicated in Table 3.2.

Data set Original temporal resolution CanSISE (SWE) daily NCAR CFSR (SCE) 6-hourly cdo monmean

--------→ monthly NOAAV2c (SCE ;SND) 3-hourly JRA 55 (SND) 6-hourly ERA20c (SND) 6-hourly Table 3.2 -Temporal resolution of different reference data sets.

Particular cases

NOAA CDR is in a 89 × 89 cartesian grid laid over a polar stereographic projection [START_REF] Robinson | Program : NOAA Climate Date Record (CDR) of Northern Hemisphere (NH) Snow Cover Extent (SCE), Version 1[END_REF]. For this data we avoid interpolation, either spatial or temporal, in order to keep the data in its original binary format. Consequently, no grid-to-grid comparison is performed with this data. Nevertheless, we convert the weekly NOAA CDR to monthly resolution. As explained in [START_REF] Robinson | Monitoring northern hemisphere snow cover[END_REF], a chart week is considered centered on the fifth day of the published chart week, being the most representative day of the week regarding snow chart boundaries. We consider a month by averaging all the chart weeks that fall in that particular month, without taking account the number of days that belong to the previous or the following month. For example, if the chart week goes from 30th January to 5th of February, we consider this week as January regarding the first day as the reference date of the week (Figure 3.1). We choose this criterion to avoid weighting days of the week which will add some artificial character to the record. Also, because we will deal with two-month seasons, the possible missing days are not relevant compared with the monthly resolution of the CMIP5 ensemble. For each of the 600 snow stations, we have computed the percentage of gaps considering the ratio of the number of absent data days to the total number of days in the period :

% of gaps = day gaps total days over period 2). We have selected the 490 stations (cyan) without gaps. In addition, as spatial density of snow stations is quite scarce in some regions of Eurasia (mainly in the northeast of Siberia), we have also kept stations with less that 10% gaps (dark blue). For instance, they can be used if the gaps appear to be in winter or summer, whereas during the mid-seasons of interest, temporal continuity prevails. Note that all snow stations shown in Figure 3.2 are located over the Russian territory (Figure 3.2). Since we only focus on Arctic land north of 50 • N, we remove 66 snow stations from the total of 490 continuous stations that are situated south of the 50 • N parallel as well as 2 stations with less than 10% of gaps. By doing so, we end up with 424 continuous polar snow stations in addition to 8 with between 1 and 10% gaps.

Of these last stations, we can consider seven of them as valid because the bulk of gaps is condensed in one year (ID 26258, 28661, 32389, 32583, 25954) or is out of the seasons of interest (ID 25594, 32411). There is only one dark blue station that is rejected because the number of gaps is quite elevated from 2000 to 2005 (ID 25744 ; Figure 3.3), maybe due to its replacement 7 km southwestwards in November 2002. Finally, we fill the gaps of the remaining stations with NaN.

There is an area in the north of Siberia between the Yenisei and Lena Rivers with a scarce spatial coverage of snow stations (Figure 3.2). Unfortunately, the snow station "Essej" (ID 24105 ; yellow station to the west of the Yenisei River), which is located in a crucial enclave to cover this area, must be discarded as the record stopped in 1994.

We further restricted ourselves to snow stations displaying more than 70% of invalid or absent values in the seasonal time series. In this sense, when comparing against CMIP5 models, we do not produce any artificial bias. Consequently, 9 snow stations are removed. In total, we end up with 422 snow polar stations.

Two approaches can be used to compare in situ measurement with model grid cells. The first method consists in the averaging of the stations within particular model grid cell. This approach can be very effective if the distribution of stations is relatively homogeneous and sufficiently dense to cover all model grid cells. Unfortunately, the uneven spatial distribution of snow stations (Figure 3.2) and the coarse spatial resolution of general circulation models (Table 2.1) makes the "point to grid" method inconvenient for this case. The opposite approach consists in interpolating the model grid to the point locations. We used this method by performing a bilinear interpolation of the model and reanalysis climatological snow fields onto the location of snow stations. It is worth mentioning that while doing the interpolation with models and reanalyses, we do not include 19 snow stations. Snow climatological fields in models and reanalyses were defined in a domain restricted to 50 • N and northward. When interpolating to a station located at 50 • N, the interpolation needs the information of the snow field at 49.5 • N which is not defined inside the Arctic domain. Thus, for this particular analysis, we take into account only stations north of 50.5 • N ; that is, in total, 403 snow stations.

Ice-free land mask

The focus of this study is to evaluate snow in the terrestrial Arctic. It is therefore necessary to restrict our domain to an ice-free land surface. For that, we have used the variables "sftlf" (land area fraction) and "sftgif" (land ice area fraction) from the "fx" table of time-invariant fields on the atmospheric grid (https://cmip.llnl.gov/cmip5/docs/CMIP5 output metadata requirements.pdf).

Even if some models include the land mask in the snow variable itself, in order to homogenize the analysis we have used the variables "sftlf" and "sftgif" of each CMIP5 model. We have applied two criteria to build the ice-free land mask (Table 3.3) : we selected those grid cells that contain 50%

or more land fraction and less than 15% of permanent ice fraction. The main reason to apply these criteria is to exclude the permanent snow on ice in Greenland and glaciers, and the snow covering coastal sea ice, as well as the null values of the ocean. Even if some observational data sets produce their own land mask, they rarely provide an ice mask. For this reason, we decided to homogenize the masking procedure, as much as possible by choosing one mask for all data sets. We wish to find the most restrictive land-ice mask to ensures that we are not considering any area that would be masked in an other model. Figure 3.5 shows the ice-free land mask of all CMIP5 models (Table 2.1). We count the number of ice-free land cells on a 1.0 • × 1.0 • grid for each of the model masks. Regarding the Arctic domain (50

Variable

• N -90 • N),
there is a total of 14400 (40 cells latitude × 360 cells longitude) grid cells ; if we consider only the terrestrial Arctic we find the number of cells of each CMIP5 models (Figure 3.6). As it is shown, the GISS-E2-R model is the most restrictive, having 4 965 ice-free land grid cells against 5 469

for MIROC5. This depends on several factors, for instance, the surface model, the definition of coastal areas or the spatial resolution. The singularity of GISS-E2-R masking is likely due to the representation of permanent ice in glaciers in the Alaska mountain range (Figure 3.5).

However, for the NOAA CDR data set we cannot apply this criteria as it is on a polar grid ;

we decided not to do any interpolation to keep this data in its original binary format. NOAA CDR provides a binary land mask with the area of each grid that we can use for masking ocean grid cells, however, the ice mask is not provided. We applied July climatology to generate a virtual "ice fraction mask". Using it, we masked the grid cells with more than 85% of snow cover, which is equivalent to less than 15% of the perennial snow fraction on ice as it is applied for CMIP5 models.

From fraction to binary

We convert the snow cover fraction climatology in CMIP5 models to a binary format following the satellite retrieval criterion from [START_REF] Robinson | Global snow cover monitoring : An update[END_REF] for the NOAA CDR data set. The criterion specifies that if the grid contains a snow cover of 50% or more, we consider it as fully covered "1", otherwise the grid value is "0". To construct the binary field for the ensemble model, we first applied the conversion of SCE to binary form for the climatology field of each ensemble member (right-hand side of Figure 3.4). Thus, we set the grid cell to "1" if the SCE climatology value is superior to 50%, otherwise the grid cell is set to "0". Next, once we have computed all the binary climatologies for each of the model members, we estimate the value of the ensemble binary mean (left-hand side of Figure 3.5). For that, we set the grid cell to "1" if more than half of the ensemble members for a particular model reports "1", otherwise, the grid cell in the ensemble 2.1. -Model CMIP5-

('bcc-csm1-1', 5052) ('CanESM2', 5427) ('CCSM4', 5066) ('CNRM-CM5', 4977) ('CSIRO-Mk3-6-0', 5018) ('GISS-E2-H', 5140) ('GISS-E2-R', 4965) ('inmcm4', 5255) ('MIROC-ESM', 5412) ('MIROC-ESM-CHEM', 5412) ('MIROC5', 5469) ('MPI-ESM-LR', 5131) ('MPI-ESM-P', 5131) ('MRI-CGCM3', 5254) ('NorESM1-M', 5002) ('NorESM1-ME',
Member 1 Bin Member 1 50% 80% 20% 0% ⇒ 1 1 0 0
1 1 0 0 + 0 0 0 1 + 0 1 0 1 1+0+0 3 < 0, 5 ⇒ 0+1+1 3 > 0, 5 0 1 0 1
Table 3.5 -Criteria of ensemble binary averaging.

Statistical analysis of snow characteristics

Test for differences of mean for paired samples

When comparing differences in climatologies between models and observations, it is necessary to assess if these differences are significant or not at a certain level. Models and reference data sets can be considered as paired or "non-independent" samples as the values making up the two averages are "observed" simultaneously [START_REF] Wilks | Statistical methods in the atmospheric sciences[END_REF]. The size of model (n 1 ) and observation (n 2 ) samples should be equivalent. For example, the time series of snow depth displayed by the model and the particular reanalysis are computed at the same location and during the same period of time. When paired data of this kind are used in a two-sample sample Student's t test, the two different averages are generally correlated. The straightforward approach is to transform the problem to one-sample setting by analyzing differences between members of the n 1 = n 2 = n [START_REF] Wilks | Statistical methods in the atmospheric sciences[END_REF].

Let call x 1 to the model sample and x 2 to the observed sample, the size of each sample being equally n 1 = n 2 = n pairs that can be considered as one-sample setting where

∆ = x 1 -x 2 with sample mean ∆ = 1 n n i=1 ∆ i = x1 -x2
The corresponding populations of delta will be µ ∆ = µ f -µ o which is often zero under null hypothesis H o . Then the test statistic for a Student's t-test corresponds to :

t score = ∆ -µ ∆ (s 2 ∆ /n) 1/2
where s 2 ∆ is the sample variance of the n differences. Any joint variation in the pairs making up the difference ∆ = x f -x o is also automatically accounted for in the sample variance s 2 ∆ of those differences [START_REF] Wilks | Statistical methods in the atmospheric sciences[END_REF]. We use this statistic to test the degree of significance of climatological differences. For example, the period for snow cover extent and snow depth is 1979-2005 (1981-2005 for SWE) which accounts for 27 years and thus, n 1 = n 2 = 27 pairs of data at 99% of confidence level from a two-tailed distribution, the corresponding t value is 2.771.

Statistical significance of linear trend

The detection and estimation of trends and their associated statistical significance are important aspects of climate research. Given the monthly time series of snow characteristics, we have computed linear trends to estimate the rate of snow change over the period 1979-2005(1981-2005 for SWE) for SWE).

Prior to applying the linear regression, seasonal mean values over the period considered have been removed from the time series. Let consider the monthly time series of snow anomalies y(x), where x is time period. The least squared linear regression estimate of the trend in y(x), that is β, minimizes the squared differences between y(x) and the fitting line y(x) :

y(x) = α + βx +
where x is known (time period), α and β are unknown and are the residuals. To test whether or not this trend is statistically significant, we have performed a Student t-test. The null hypothesis is that the regression coefficient β is zero given the uncertainty in estimating the trend.The residual of the regression i are defined as

i = y i -y i = y i -(α + βx i )
For statistically independent values of i , the variance of β, s 2 β is defined as

s 2 β = s 2 n i=1 (x i -x) 2
where s 2 , the variance of the residuals about the regression line, is given by :

s 2 e = 1 n -2 n i=1 2 i
Thus, we can determined the t score for statistical significance by

t score = β s β
which follows a t-distribution with n-2 degrees of freedom [START_REF] Wilks | Statistical methods in the atmospheric sciences[END_REF]. For example, for the snow cover trend over the Arctic during 1979 to 2005 (i.e., implying 27 years), the critical t value for a two-tail test with degrees of freedom equal to 25 and confidence level of 90% is 1.708.

Taylor Diagram

The Taylor diagram is a concise statistical summary of how well different patterns matches the observations (Taylor, 2001). This 2-D diagram provides the degree of correspondence between two fields by indicating the centered root mean squared error (RMS), the standard deviation σ and the correlation coefficient R between them. As described in Taylor ( 2001), let consider two variables f n , the simulated field, and r n , the observational reference which are defined by N discrete points.

For example, we apply this analysis for the evaluation of snow time series with N = 27 years for snow cover and snow depth (25 years for SWE). The correlation R coefficient between simulated f and observed r field is :

R = 1 N N n=1 (f n -f )(r n -r) σ f σ r
Considering f , and r as the mean values, and σ f and σ r the standard deviations of f and r.

When apply to the time series diagram, f and r will refer to the seasonal climatology over the whole period. The correlation coefficient R reaches the maximum of 1 when for all n, (f n -f ) = α(r n -r) with α = cte > 0 ; in this case, the two fields have the same centered pattern of variation, however, it is not possible to determine if they have the same amplitude of variation, which can be defined by their variances.

The statistic most frequently used to quantify difference between models and observation is the

RMS difference E. E = 1 N N n=1 (f n -r n ) 2 1/2
The differences between patterns can be isolated by considering differences between the means of the two fields, that is, the overall bias :

Ē = f - r
and by the centered pattern RMS difference which is defined as :

E = 1 N N n=1 (f n -f ) -(r n -r) 2 1/2
The two components Ē and E can be added quadratically to yield the full means square difference : As two patterns become more similar, the pattern of RMS approaches to zero. However, for a given E , it is impossible to distinguish if the error is due to differences in structure and phase or in the amplitude of variations.

E 2 = Ē2 + E 2
The correlation coefficient R and the centered RMS E quantify the correspondence between two patterns. Together with the information of fields variances (σ f and σ r ), these four statistics are very useful to evaluate the differences between two patterns. The Taylor diagram is based on the relationship between the four statistical quantities following :

E 2 = σ 2 f + σ 2 r -2σ f σ r R
and which can be applied to the law of cosines :

c 2 = a 2 + b 2 -2abcosφ
where a, b, c, are the lengths of the sides of the triangle and φ the opposite angle to the side c

(Figure 3.7).
Chapter 4 This chapter is devoted to the evaluation of the spatial distribution of snow characteristics over the Arctic in the mid-seasons. We investigate the representation of snow in CMIP5 models and in different data sets including reanalyses, satellite-based products and in situ measurements which have been described in Chapter 2. This chapter is divided into three main sections dedicated to the analysis of climatology, annual cycle and quantile statistics of snow characteristics, that are snow cover extent, snow water equivalent and snow depth. In some cases, we also include an additional analysis specific for a particular snow variable. resolution (0.5 2.2). Note that we do not include NOAA CDR in this analysis because of the incompatibility between grid projections as mentioned in Chapter 2.

Spatial structure of snow characteristics Contents

Climatology

Snow cover

• × 0.5 • ) compared to that displayed by NOAAV2c (2.0 • × 1.75 • ) (Table
In March-April (Figure 4.1a), complete snow cover (100%) is observed over the northern Eastern Eurasia as well as over Northern Canada and Alaska. Note that the areas covered by more than 80% of snow match well the areas of continuous permafrost [START_REF] Brown | Circum-Arctic map of permafrost and ground-ice conditions[END_REF] In the onset season, 7 of 16 models (bcc-csm1-1, CSIRO-Mk3-6-0, MIROC's and MPI's versions ; The differences between CMIP5 models and the NOAAV2c reanalysis (not shown) are very similar to those found for NCEP/CFSR in terms of spatial patterns. However, NOAAV2c tends to slightly overestimate the SCE climatology of NCEP/CFSR (Figure 4.2). Therefore, when models have shown a positive (negative) bias compared to NCEP/CFSR, these differences are smaller (larger) in magnitude and less (more) significant when using NOAAV2c as reference. To achieve comparability, we create binary fields for CMIP5 models with "1" attributed to all grids displaying March-April or October-November SCE ≥ 50% and with "0" for the remaining grid cells (further details in Chapter 3). To construct the binary field of each model with ensemble members, we first applied the conversion of SCE to binary form for each ensemble member and then set the grid cell to "1" if more than the half of the ensemble members for particular model report "1", otherwise, the grid cell in the ensemble averaged model was set to "0". By doing so, for each season, we obtain 16 binary fields corresponding to each of the CMIP5 models. To evaluate the agreement on position of the snow margin among CMIP5 models, we further counted the number of "1" for each season over the model ensemble. For example, value 4 in a grid cell implies that 4 out of 16 models display SCE ≥ 50%. If this grid cell is captured by the contour of the snow margin in the reanalyses, these 4 models are considered as representing the snow margin in agreement with the reanalyses.

a)bcc-csm1-1 (b)CanESM2 (c)CCSM4 (d)CNRM-CM5 (e)CSIRO-Mk3-6-0 (f)GISS-E2-H (g)GISS-E2-R (h)inmcm4 (i)MIROC-ESM (j)MIROC-ESM-CHEM (k)MIROC5 (l)MPI-ESM-LR (m)MPI-ESM-P (n)MRI-CGCM3 (

Snow margin position

Both reanalyses are in a better agreement with each other in spring (Figure 4.5a) than in autumn (Figure 4.5b). In March-April, the snow margins in both products match each other almost perfectly. However, in the onset season both reanalyses exhibit large spatial discrepancies with a deviation between the snow margins of about 10 degrees latitude. These discrepancies are more pronounced over North America than over Eurasia. This is due to a less intense onset of SCE in NOAAV2c than NCEP/CFSR, which is consistent with the faster rate of increase in SCE in NCEP/CFSR than in NOAAV2c in autumn (Figure 4.17c).

(a)bcc-csm1-1 (b)CanESM2 (c)CCSM4 (d)CNRM-CM5 (e)CSIRO-Mk3-6-0 (f)GISS-E2-H (g)GISS-E2-R (h)inmcm4 (i)MIROC-ESM (j)MIROC-ESM-CHEM (k)MIROC5 (l)MPI-ESM-LR (m)MPI-ESM-P (n)MRI-CGCM3 (
The position of the snow margin is also in a better agreement between different models and reanalyses during March-April rather than in October-November. This suggests that spatial discrepancies in the position of the snow margin are likely due to differences in starting time of melting season among CMIP5 models. The mismatch is accentuated in the south of Western Siberia, with only 3-4 models being consistent with the reanalyses. The snow margin over North America is more accurately represented with 10-12 models being in a close agreement with the reanalyses. In central and northern Eurasia, over Scandinavia, Canada and Alaska all models fit reasonably well with the reanalyses (Figure 4.5a). However, in autumn (Figure 4.5b), the agreement between the model data sets and reanalyses becomes less evident. Only three of 16 models show the snow margin close to that of NCEP/CFSR whereas 10 other models are closer to NOAAV2c. A reasonably good agreement across all data sets is identified only for the Siberian Plateau, the Verkhoyansk mountainous region and Northern Canada. The worse agreement in the position of snow margin is observed for the southern part of North America and for the region west of the Lake Baikal. Some disagreements observed in coastal areas are associated with different ice-land masks. over the West Coast of Canada and Alaska as well as Scandinavia. This mask is originally from the MERRA reanalysis (M. [START_REF] Rienecker | MERRA : NASA's Modern-Era Retrospective analysis for Research and Applications[END_REF] considering a grid cell masked when the land-ice fraction > 0 (L. Mudryk, personal communication). As mentioned in Chapter 3, this mask was not used for the analysis, instead the land-ice mask from GISS-E2-R was used.

Snow water equivalent

Differences of climatology

We move to the evaluation of snow water equivalent climatology across CMIP5 models (Table 2.1) compared to the CanSISE ensemble product in the mid-seasons from 1981 to 2005.

Snow depth

We consider the JRA-55 reanalysis as the reference data set above the other two reanalyses, ERA20c and NOAAV2c, for the evaluation of snow depth climatologies in CMIP5 models. This choice is justified by two reasons. First, we base our study on the results from Wegmann et al. a general positive bias of snow depth in Eurasia with regional significant differences. There is a zonal dipole of differences in models showing overestimation (underestimation) in the east (west) part of the North American Arctic. As for SWE, there is a common underestimation of snow accumulation over the delta of the Yenisei River, which may be related to the inability of CMIP5 models to capture the local snow-ice interaction (e.g., evaporation processes, blowing snow) around the river.

(a)bcc-csm1-1 (b)CanESM2 (c)CCSM4 (d)CNRM-CM5 (e)CSIRO-Mk3-6-0 (f)GISS-E2-H (g)GISS-E2-R (h)inmcm4 (i)MIROC-ESM (j)MIROC-ESM-CHEM (k)MIROC5 (
In autumn (Figure 4.12), discrepancies are smaller than in spring. Nevertheless, the models from the aforementioned first group (bcc-csm1-1, CCSM4, NorESM1-M/ME ; used a bilinear interpolation instead of nearest point interpolation due to the uneven spatial distribution of snow stations and the coarse resolution of models and reanalyses. The stations overseas are not considered here as we only focus on Arctic land. For this particular in situ comparison, we show all differences without considering their degree of statistical significance in order to include as many stations as possible.

We first assess the differences in spring and autumn climatologies between reanalyses and snow stations (

Annual Cycle

We turn now to the comparative analysis of the annual cycle of snow characteristics in CMIP5 does not provide an ice mask), we applied the July SCE climatology to generate a virtual "ice fraction mask". Thus we masked the grid cells with more than 85 % SCE, which is equivalent to less than 15 % of perennial SCE on ice fraction as we had done with CMIP5. For reference, the ice-land masking procedure is described in detail in Chapter 3. The majority of the CMIP5 models tend to underestimate SCE throughout the year notably in

Snow cover

Snow water equivalent

Compared to SCE, the annual cycle of SWE (Figure 4. over North America (Figure 4.19b). As found in section 4.1.3, the ERA20c reanalysis displays less overall snow depth than the other data sets. In addition to this negative bias, the amplitude of the seasonal cycle is widely underestimated, with only 20 cm of variation between summer and winter.

Snow depth

Conversely, the NOAAV2c reanalysis is in a relatively good agreement with JRA-55 in terms of seasonal variability, with the former showing an amplitude of ∼ 70 cm, and ∼ 50 cm in the latter (Figure 4.19a). However, NOAAV2c overestimates SND compared to JRA-55 from November to April with differences around 20 cm in North America (Figure 4.19b) and up to 30 cm in Eastern Eurasia (Figure 4.19d). Hereafter, we consider the JRA-55 reanalysis as reference for the model evaluation of the SND annual cycle as we did in the previous section for the SND climatology.

Despite the individual model discrepancies, the multimodel mean is in good agreement with the JRA-55 reanalysis, mainly in the onset season (Figure 4.19a), differing no more than 10 cm throughout the annual cycle. The snow depth maximum displayed by the multimodel ensemble coincides with observations and it occurs in March. However, the rate of melting in JRA-55 is faster than the multimodel mean, notably in Eurasia (Figure 4.19c). JRA-55 melts snow almost in June, whereas, multimodel mean does it later in July. Over the Arctic (Figure 4.19a), there are four models (bcc-csm1-1, CCSM4 and both NorESM1-M/ME) that overestimate snow depth, by almost 20 cm during the winter and early spring. On the other hand, these four models capture adequately the peak of maximum snow accumulation in March. CNRM-CM5 and MRI-CGCM3 display a shift in the snow depth peak towards April. There are two models (CSIRO-Mk3-6-0, inmcm4) that show negative bias with values almost twice lower than those observed (Figure 4.19a). The highest discrepancies are demonstrated by inmcm4 in March, underestimating JRA-55 by 30-35 cm. The 4.19e). This feature is identified across almost all CMIP5 models and it is clearly distinguishable in JRA-55. It consists in an early melting in March over the western part of Eurasia, and a later and slower snow offset over the eastern part starting in April ; also, snow onset occurs one month earlier in Eastern Eurasia (October) than in the western part (November).

Quantile statistics of the spatial average

Another view of the differences in snow characteristics climatology is given in Figures 4.20,4.21 and 4.22. We present quantile statistics of the spatial average over the terrestrial Arctic for each snow variable in both seasons, March-April and October-November. For SCE and SND, the period considered is 1979-2005and for SWE, 1981-2005. Each box represents the distributions of the seasonal time series for each ensemble model, for the multimodel ensemble and for the reference data sets. The horizontal line represents the spatial average, the filled rectangle is the interquartile range (IQR) from Q1 (25th percentile) to Q3 (75th percentile). The IQR provides information about the amplitude of snow interannual variability that will be addressed in the next chapter extensively.

Snow cover

Figure 4.20a shows a general underestimation of spring SCE by CMIP5 models compared to all reference data sets. This is evident in the multimodel mean value of 56% SCE while observations show an average around 83% (80% for NCEP/CFSR, 85% for NOAAV2c and 85% for NOAA CDR).

Three models (bcc-csm1-1(a), CSIRO-Mk-3-6-0(e) and both versions of MPI-ESM-LR/P(l,m)) show a SNC mean value twice smaller than the reference data sets (44%(a), 37%(e), 39% and 34%(l,m)). This is in agreement with Figure 4.3 which identified these models (bcc-csm1-1, CSIRO-Mk-3-6-0, and both versions of MPI-ESM-LR/P) as negatively biased over the terrestrial Arctic. For the onset season (Figure 4.20b), the agreement between CMIP5 models and reference data is better than in spring. The multimodel mean, being 68%, is slightly above both reanalyses, reporting 56% and 62% in NCEP/CFSR and NOAAV2c respectively ; however, it lies within the range given by NOAA CDR (67%). The models CCSM4(c), inmcm4(h), MRI-CGCM3(n) and both versions of NorESM1-M/ME(o,p) are found to be above the observed range, with SCE values of 81%(c), 77%(h), 84%(n), 80%(o) and 81%(p). This is actually closer to the spring values rather than that from autumn. This overestimation is due to the representation of snow cover in Eastern Eurasia, as seen in Figure 4.4 for this group of models.

(a)bcc-csm1-1 (b)CanESM2 (c)CCSM4 (d)CNRM-CM5 (e)CSIRO-Mk3-6-0 (f)GISS-E2-H (g)GISS-E2-R (h)inmcm4 (i)MIROC-ESM (j)MIROC-ESM-CHEM (k)MIROC5 (l)MPI-ESM-LR (m)MPI-ESM-P (n)MRI-CGCM3 (o)NorESM1-M (p)NorESM1-ME (q)CMIP5 (r)NCEP/CFSR (s)NOAAV2c (t) Rutgers CDR

Snow water equivalent

(a)bcc-csm1-1 (b)CanESM2 (c)CCSM4 (d)CNRM-CM5 (e)CSIRO-Mk3-6-0 (f)GISS-E2-H (g)GISS-E2-R (h)inmcm4 (i)MIROC-ESM (j)MIROC-ESM-CHEM (k)MIROC5 (l)MPI-ESM-LR (m)MPI-ESM-P (n)MRI-CGCM3 (o)NorESM1-M (p)NorESM1-ME (q)CMIP5 (r)CanSISE

Snow depth

All reanalyses experience large discrepancies in spring SND average over the Arctic (Figure 4.22a). JRA-55 displays a mean of 29 cm which is surpassed by NOAAV2c, accounting with 37 cm.

Consistent with Figure 4.17, ERA20c shows the lowest SND value, 17 cm. The interannual variability is particularly high in JRA-55 and NOAAV2c as seen by their IQR values. In Figure 4.22a, we found a good agreement between CMIP5 models and JRA-55 with the multimodel mean displaying a value of 34 cm. The only models that underestimate substantially JRA-55 and NOAAV2c are CSIRO-Mk3-6-0(e) and inmcm4(h), with values of 14 cm and 17 cm, respectively. This bias is not due to an early melt but to a general negative bias of SND, which is stronger in North America (Fi- 4.15 and 4.19d). As for SWE, the models MIROC-ESM(i), MIROC5(k) and NorESM1-ME(p) display a large variability compared to the other CMIP5 models.

(a)bcc-csm1-1 (b)CanESM2 (c)CCSM4 (d)CNRM-CM5 (e)CSIRO-Mk3-6-0 (f)GISS-E2-H (g)GISS-E2-R (h)inmcm4 (i)MIROC-ESM (j)MIROC-ESM-CHEM (k)MIROC5 (n)MRI-CGCM3 (o)NorESM1-M (p)NorESM1-ME (q)CMIP5 (r)ERA20c (s)JRA-55 (t) NOAAV2c

Summary

We have investigated snow characteristics (SCE, SWE and SND) • The position of the snow margin is better captured by CMIP5 models in spring that in autumn. The best agreement is found over Eastern Eurasia and Western North America.

During autumn, the CMIP5 ensemble has the snow margin shift considerably northward with only 4-6 out of 16 models matching the observations and overall agreement only occurs in Central Siberia.

• Differences of spring SWE climatology are characterized by an overall overestimation across nearly all CMIP5 models. The exception is CSIRO-Mk3-6-9 which displays a general underestimation over the whole Arctic ; also, the models CCSM4, MPI-ESM-LR/P and NorESM1-M/E show a negative bias over Western Eurasia. The common feature in the CMIP5 ensemble is a local underestimation over the delta of the Yenisei River. In the onset season, differences are smaller in magnitude. The models NorESM1-M and NorESM1-ME stand out against the CMIP5 ensemble by presenting a strong bias over the Far East of Eurasia.

• There is a lack of agreement across reanalyses in representing SND climatology over the terrestrial Arctic in both seasons. ERA20c systematically reports the lowest values whereas NOAAV2c displays the largest accumulation. Discrepancies are stronger and more widespread in spring than in autumn, when they are concentrated almost only over Eastern Eurasia. Across CMIP5 models, we can distinguish three groups regarding the pattern of SND discrepancies. First group (bcc-csm1-1, CCSM4, NorESM1-M/ME) displays a large positive bias over the mountainous regions of Western North America and Eastern Eurasia. In contrast, the second group (CSIRO-Mk3-6-0 and inmcm4) displays a general overestimation over the whole Arctic. The remaining models (CanESM2, CNRM-CM5, GISS-E2-H/R, MIROCs, MRI-CGCM3) show a general overestimation with local significant differences ; in particular, they are characterized by a negative bias over the Yenisei Delta. Discrepancies in autumn are smaller than in spring. A strong positive bias over Western North America and Eastern Eurasia prevails in the models from the first group (bcc-csm1-1, CCSM4, NorESM1-M/ME). GISS-E2-H/R and MRI-CGCM3 models show a general overestimation whereas the opposite is found in the rest of the CMIP5 ensemble (CanESM2, CNRM-CM5, CSIRO-Mk3-6-0, inmcm4, MIROCs).

With respect to in situ snow measurements, we have found that reanalyses show a general overestimation in spring and underestimation in autumn. In spring, JRA-55 displays a good agreement in Eastern Eurasia, whereas the others show a strong overestimation.

Over the southern edge of Western Eurasia, NOAAV2c shows the lowest bias which implies a good performance on the onset of the melting season. ERA20c shows a general positive bias compared to the snow stations. In autumn, ERA20c and NOAAV2c show a relatively good agreement in Eastern Eurasia, however, they show a slightly positive bias over the northern part. JRA-55 displays a general underestimation with stronger values over the basin of the Ob River. Across CMIP5 models, we found a general positive bias over Eurasia. Some models show a negative bias over the Kamchatka Peninsula (MIROC-ESM/CHEM and CSIRO-Mk3-6-0). There is a group of models (CCSM4, MIROC-ESM-/CHEM, MRI-CGCM3, NorESM1-M/ME) that are in relatively good agreement with snow stations over south-west Eurasia implying a good timing of the start of the snow melt. In autumn, an overall underestimation is found across all CMIP5 models. The models bcc-csm1-1, CCSM4 and NorESM1-M/ME display a persistent positive bias of snow accumulation over the north of Eastern Eurasia.

(ii) Annual Cycle :

• There is a good agreement in the representation of the SCE annual cycle across the reference data sets. The observed annual cycle in SCE is relatively well captured by CMIP5 models in autumn but during the spring-summer season, most models tend to significantly underestimate SCE, especially over North America. Note that neither version NorESM1-M or NorESM1-ME is capable to completely melt snow in summer, mainly over Eastern Eurasia.

• The annual cycle in SWE is largely positively biased with respect to observations in most CMIP5 models. Nearly all models report persistent snow in summer months (mainly in North America), thus in contrast with observations. The large spread across the CMIP5 ensemble is substantial, especially over North America and Eastern Eurasia.

• The SND annual cycle displayed by the three reanalyses differs conspicuously. ERA20c

shows the lowest values and it is not able to reproduce the seasonal variability accurately.

NOAAV2c and JRA-55 are in better agreement, however, the former shows higher snow accumulation from November to April. The annual cycle of SND reported by CMIP5 models presents similar discrepancies with respect to observations as in the SWE annual cycle. The dispersion is remarkable during the snow accumulation season particularly in North America and Eastern Eurasia.

(iii) Quantile statistics of the spatial average :

• Reference data sets show similar SCE averages over the whole land Arctic in both seasons. However, in spring CMIP5 models generally underestimate the SCE average. Some models even display values twice too small. In autumn, there is better agreement with a slight tendency to overestimate.

• Regarding SWE averages, there is a large inconsistency between CMIP5 models and a general overestimation with respect to the observed reference, with only two out of sixteen models in accordance with observations. The dispersion is relatively smaller in autumn, however, the positive bias is still present.

• There is a general good agreement between CMIP5 models in SND in both seasons.

However, the discrepancies between the different reanalyses are substantial. In this chapter, we evaluate the temporal variability of snow characteristics in spring and autumn throughout the historical period 1979-2005. First, snow interannual variability in CMIP5 models is compared to the different data sets. Second, linear trends in snow characteristics in CMIP5 models are considered. This is very important because CMIP5 models are extensively used to predict future climate and it is crucial to asses their fidelity in reproducing present snow trends.

Chapter 5

Temporal variability of snow characteristics Contents

Interannual variability of snow characteristics

We compare the characteristics of interannual variability of snow in CMIP5 models by means of a Taylor diagram representation (Taylor, 2001) of the time series of the snow variables spatially averaged over the Pan-Arctic in spring and autumn. The Taylor diagram is a concise statistical summary of how well different data sets match a reference (Taylor, 2001). This 2-D diagram provides the degree of correspondence between two time series by indicating the centered root mean squared error (RMS), the standard deviation σ or STD and the correlation coefficient R between them. In practice, the STD is identified as the radial distance to the origin ; the distance to the reference point (star in x-axis) indicates the centered root-mean-squared error (RMS) and the azimuth gives the correlation coefficient R. We consider as observational reference the NOAA CDR for SCE, the CanSISE product for SWE and the JRA-55 reanalysis for SND.

Snow cover

The amplitude of interannual variability in both reanalyses (NCEP/CFSR and NOAAV2c) and NOAA CDR SCE are in a good agreement with each other in spring with standard deviations (STD) being 2.4% for NCEP/CFSR, 2.5% for NOAAV2c and 2.9% for NOAA CDR (Figure 5.1a).

However, only the NOAAV2c reanalysis shows a positive and significant (at 95% level) correlation with NOAA CDR (R=0.58) and displays a centered RMS difference of 2.5% which is smaller compared to NCEP/CFSR (3.2%). Most of CMIP5 models show much smaller than observed STDs and practically no correlation on interannual scale with observations, except for bcc-csm1-1 and MIROC5 showing correlation of 0.42 and 0.37 (significant at the 95% level from the t-Student test).

During the onset season (Figure 5.1b), discrepancies with NOAA CDR are larger than in spring with centered RMS differences being greater for all models and reanalyses. The NCEP/CFSR reanalysis shows a similar magnitude of interannual variability as the NOAA CDR observational reference (4.8% and 4.5%, respectively). By contrast, the NOAAV2c reanalysis and the majority of CMIP5 models exhibit STDs of less than 2.5%, thus considerably smaller than in observations. Neither models nor reanalyses display a positive significant correlation with NOAA CDR, indeed, nearly all CMIP5 models correlate negatively.

Snow water equivalent

Spring SWE variability in CMIP5 models is characterized by a large spread (Figure 5.2a).

The observed interannual variability (STD : 4.48 kg m -2 ) of SWE is well captured by CCSM4, MIROC-ESM and MPI-ESM-P (4.36 kg m -2 , 4.46 kg m -2 , 4.39 kg m -2 , respectively). For the majority of models, the centered RMS differences are around 6 kg m -2 . MIROC5, inmcm4 and NorESM1-ME models are characterized by the highest values of RMS (∼ 7 kg m -2 , ∼ 6.7 kg m -2 and ∼ 6.5 kg m -2 ). The model MIROC-ESM displays a STD in perfect agreement with CanSISE product. The lowest magnitude of interannual variability is found in CSIRO-Mk3-6-0 (1.2 kg m -2 ) and is likely due to the relatively large number of ensemble members averaged (10 members, Table In autumn, the spread of CMIP5 models is also remarkable (Figure 5.2b). The majority of CMIP5 models underestimate the magnitude of the interannual variability reported by the CanSISE product (2.7 kg m -2 ). By contrast, NorESM1-ME and all versions of MIROC yield STDs greater than 4 kg m -2 ; thus, they are considered outliers with respect to STDs and do not appear in Figure 5.2b. As for spring, the lowest amplitude of interannual variability is found in CSIRO-Mk3-6-0 (0.89 kg m -2 ). There is only one model (bcc-csm1-1) displaying a positive significant correlation of 0.39 with the observations.

Snow depth

Compared to the other snow characteristics, the interannual variability of SND seems to be better captured by CMIP5 models (Figure 5.3). Spring SND variability (Figure 5.3a) in JRA-55 and NOAAV2c reanalyses is in good agreement in both the amplitude (4.17 cm and 3.58 cm, respectively) and correlation (R=0.56). However, ERA20c is not able to correctly reproduce the Half of the CMIP5 models show significant correlation (at 95% level) with JRA-55, which indicates a better performance in reproducing the interannual variability of snow depth than the other snow characteristics treated previously. These models are (lowest to highest correlation) : MIROC-ESM-CHEM (0.39), CNRM-CM5 (0.41), CSIRO-Mk3-6-0 (0.51), GISS-E2-H (0.51), NorESM1-M (0.53) and CanESM2 (0.62) and the highest correlation is found in MIROC5 (0.77).

The performance of CMIP5 in reproducing interannual variability in autumn is similar to spring (Figure 5.3b). However, the amplitude of interannual variability is smaller as evidenced by the STD of 2.45 cm in the JRA-55 reanalysis. NOAAV2c matches very well with JRA-55, reporting a STD of 2.65 cm and a significant correlation of 0.71. By contrast, the ERA20c reanalysis certainly underestimates the amplitude of interannual variability with a STD of 0.33 cm, less than all CMIP5 models. Despite that, ERA20c and JRA-55 correlate significantly (0.65). The models characterized by stronger variability are MIROC5 (1.86 cm), MIROC-ESM-CHEM (1.42 cm) and NorESM1- The low correlations found between SCE and SWE from CMIP5 and observations are not surprising considering the fundamental limitations of GCMs in reproducing interannual variability (Taylor et al., 2012). Historical runs are initiated from a state in equilibrium with pre-industrial climate forcings simulated by the quasi-equilibrium control runs, the so-called "initial climate state", which may not perfectly match to the observed climate state. For instance, the temporal evolution of climate system in the models will likely miss the impact of the unforced internal variations such as El Niño, the North Atlantic Oscillation (NAO), Atlantic Multidecadal Oscillation (AMO). In fact, among 16 models and a test at the 95% confidence level, it is very likely that there are one or two significant correlations across independent time series. Nonetheless, we consider that Taylor Diagram representation provides a very visible evaluation of STD and RMS in CMIP5 models. This being said, reanalyses and satellite-based products are constrained by the real-time evolution of the climate and their mutual correlations in the Taylor diagram are relevant to evaluate them.

We have performed the same analysis but with detrended time series of snow characteristics (figure not shown) and we did not find any substantial differences. This can be explained by the weak trends displayed in CMIP5 models, as we shall see further. Actually, the significant correlations found in SND between CMIP5 models and observations are likely due to the anthropogenic forcing as they do not occur in the case for detrended time series.

Seasonal trend analysis

In this section, we evaluate the accuracy of CMIP5 models in reproducing interdecadal seasonal trends compared to the different snow data sets. The main target is to assess the robustness and to estimate the uncertainty in historical snow trends. For the analysis of trends in snow characteristics we evaluate CMIP5 model trends from individual model ensemble members, from the ensemble of a single model and from the multimodel ensemble mean. In total, we analyze 73 individual model realizations provided by 16 models (Table 2.1) for SCE and SWE and 68 individual simulations from 14 models for SND (without MPI-ESM-LR/P versions). We perform a similar analysis done by [START_REF] Stroeve | Sea ice response to an extreme negative phase of the Arctic Oscillation during winter 2009/2010[END_REF] for the evaluation of Arctic sea ice trends in CMIP3 and CMIP5 models.

Snow cover

For the whole Arctic (Figure 5.4a), NCEP/CFSR shows an insignificant increase in spring SCE, disagreeing with NOAA CDR and NOAAV2c as both consistently display significantly negative trends of -1.21 ± 0.58%/dec and -1, 26 ± 0.68%/dec, respectively (Figure 5.4a, Table B.1). The multimodel mean with a value of -1.10 ± 0.13%/dec falls in the range of estimates given by NOAA CDR and NOAAV2c. However, five models (inmcm4, MIROC-ESM-CHEM, MPI-ESM-LR, MRI-CGCM3 and NorESM1-ME) report SCE trends out of the observation range, but in only two of them (MIROC-ESM-CHEM and MPI-ESM-LR) those deviations are statistically significant (Table B.1). Considering individual ensemble members, 39 of 73 report significant trends consistently with observations. Remarkably, some models (bcc-csm1-1, CNRM-CM5, MIROC5 and NorESM1-M) demonstrate a quite strong spread in trend estimates across their ensemble members.

Among the reference data sets, only NOAA CDR is statistically significant at the 90% level displaying a decreasing trend of -1.79 ± 0.95%/dec over the Eurasian Arctic subdomain Table B.2). NCEP/CFSR and NOAAV2c report SCE trends of -0.03 ± 0.82%/dec and -1.42 ± 0.91%/dec, the latter being closer to the NOAA CDR estimate ; however, none of them is significant at the 90% confidence level. The multimodel mean displays a negative trend slightly weaker than the observed value of -1.01 ± 0.17%/dec. There are 9 out of 16 model ensembles and almost half of the individual realizations that report significant trends inside the range implied by observations. The models bcc-csm1-1, inmcm4, MPI-ESM-LR/P and MRI-CGCM3 are out of the observed range and show no statistical significance neither in the ensemble nor in the member trends (the only exceptions are two members in bcc-csm1-1 and MPI-ESM-LR).

In North America (Figure 5.4c, Table B.3), all observational data sets display insignificant SCE trends in spring. The lowest p-value is found in NOAAV2c, being statistically significant at 78% (t-test), thus we consider it as reference for the analysis in the North American subdomain with its negative trend of -0.87 ± 0.71%/dec. NOAA CDR shows a weaker trend of -0.33 ± 0.76%/dec while NCEP/CFSR displays an increase in SCE of +0.83 ± 0.73%/dec. The multimodel mean (-1.23 ± 0.15%/dec) is statistically significant and lies in within the observed range. Nearly all the ensemble models fall inside the range given by NOAAV2c, however three of them (MPI-ESM-LR/P and NorESM1-M) are not statistically significant. The models GISS-E2-H, MIROC-ESM-CHEM and inmcm4 display SCE trends outside the observed range. Overall, there are 10 out 16 ensemble members and 15 out 73 individual realizations that show significant negative trends falling inside the observed range in North America.

In the onset season (Figure 5.4d,Table B.4), NOAA CDR displays a trend of +3.28 ± 0.91%/dec and is thus a clear outlier with respect to the other reference data sets. The unrealistic October trend estimated by NOAA CDR in the recent period has been already reported by [START_REF] Brown | Is Eurasian October snow cover extent increasing ?[END_REF] and [START_REF] Estilow | A long-term Northern Hemisphere snow cover extent data record for climate studies and monitoring[END_REF]. NCEP/CFSR and NOAAV2c show SCE trends of -1.61 ± 1.15 %/dec and -0.76 ± 0.59%/dec respectively, but they lack statistical significance.

Consequently, we consider NCEP/CFSR as reference for model evaluation since it displays a pvalue slightly lower than NOAAV2c (0.17 and 0.21, respectively). The multimodel mean shows an autumn SCE trend of -0.72 ± 0.12%/dec falling in the range given by NCEP/CFSR estimates.

We also note generally weaker SCE trends in models respect to that from NCEP/CFSR. Thirteen of 16 models are within the observed SCE trend range. Considering individual ensemble members, 37 estimates fall into the range implied by observations, thus roughly 50% of individual model ensemble members present trends which are qualitatively consistent with observations. The lar-gest spread across ensemble members is observed for bcc-csm1-1, CanESM2 and in both version of MPI-ESM-LR/P.

In Eurasia during autumn (Figure 5.4e,Table B.5), SCE trends in both NCEP/CFSR and NOAAV2c lack of statistical significance with values of -1.83 ± 1.40%/dec and -0.36 ± 0.80%/dec.

The NCEP/CFSR reanalysis shows the lowest p-value, being statistically significant at 80% (ttest), so we consider it as reference in this comparison. The SCE trend in the multimodel mean is -0.48 ± 0.14%/dec, i.e. weaker than the reference. Half the models and 28% of individual realizations report significant decreasing trends lying inside the observed range. Note that, nearly all of these models and members report SCE trends weaker than the observed value.

The agreement between models and both reanalyses seems to be better over the North American Arctic for the autumn season (Figure 5.4f,Table B.6). Still, NOAA CDR is considered as outlier even if the trend reported here is slightly weaker than for Eurasia (+2.62 ± 0.12%/dec). NCEP/CFSR and NOAAV2c show SCE trends of -1.35 ± 0.27%/dec and -1.38 ± 1.17%/dec (respectively) but they lack statistical significance. Accordingly, we choose NCEP/CFSR as reference as it displays a pvalue lower than NOAAV2c (0.27 and 0.18, respectively). The multimodel mean is quite close to the observed value of both reanalyses displaying a decreasing trend of -1.05 ± 0.13%/dec. All CMIP5 ensemble of single models report SCE significant trends inside the range implied by observations, and only two models are not significant (MPI-ESM-P and MRI-CGCM3). With respect to individual realizations, 25 out 73 are significant and lie within the observed range.

Snow water equivalent

In spring (Figure 5.5a, Table B.7), SWE in CanSISE product shows an insignificant downward tendency for the whole Arctic (-1.09 ± 1.25 kg m -2 /dec). The multimodel model mean, however, shows a strong, negative and significant SWE trend of -2.85 ± 0.34 kg m -2 /dec. Five models (bcc-csm1-1, CSIRO-Mk3-6-0, GISS-E2-R, MPI-ESM-LR and MRI-CGCM3) report trends in spring SWE falling in the range given by observations but only two of them are statistically significant (CSIRO-Mk3-6-0 and GISS-E2-R). Regarding individual ensemble members, only 5 of 73 significant SWE trends fall into the observed range (all belonging to CSIRO-Mk3-6-0 model). Thus, less than 7% of ensemble simulations are in agreement with the observed SWE trend in spring. The individual realizations of bcc-csm1-1, CNRM-CM5, MIROC5 and MRI-CGCM3 have the largest spread of trend estimates. Over the Eurasian sector of the Arctic in spring (Figure 5.5b, Table B.8), the CanSISE product reports a weak and insignificant SWE trend of -0.69 ± 1.54 kg m -2 /dec. The multimodel mean displays a strong significant trend of -1.84 ± 0.43 kg m -2 /dec, lying inside the range given by observations. Thirteen ensemble models fall in the observed range, but only five of them (CanESM2, CCSM4, CNRM-CM5, CSIRO-Mk-3-6-0 and GISS-E2-H) are statistically significant. With respect to the individual realizations, there are only 4 (out of 73) members, all from CSIRO-Mk-3-6-0, that are significant and lie within the observed range.

During spring, North American SWE trends (Figure 5.5c, Table B.9) are characterized by a large spread in CMIP5 models compared to Eurasia. The CanSISE product displays a negative SWE trend of -1.66 ± 2.01 kg m -2 /dec, but it is not statistically significant. The multimodel mean exhibits stronger than observed trend of -4.23 ± 1.03 kg m -2 /dec falling out of the reference range.

Three models report SWE trends inside the range implied by observations, but only two are significant (CSIRO-Mk-3-6-0 and GISS-E2-H). Just three individual realizations, from CSIRO-Mk-3-6-0 model, are significant and fall inside the observed range.

In the onset season (Figure 5.5d, Table B.10), most CMIP5 models show stronger negative trends in SWE compared to the CanSISE product which displays a weak and insignificant SWE trend of -0.63 ± 0.76 kg m -2 /dec, while the multimodel mean trend is -1.65 ± 0.18 kg m -2 /dec. Six out of 16 CMIP5 models (CanESM2, CSIRO-Mk3-6-0, GISS-E2-H/R and MPI-ESM-LR/P) fall inside the range given by observations, however, only two of them present significant trends (GISS-E2-H and MPI-ESM-LR). None of the individual model members simulate a significant SWE trend inside the range given by the CanSISE product (except for one member of CSIRO-Mk3-6-0). Also, we note that generally, the spread of individual members is smaller for autumn than spring, except for MIROC5 and MRI-CGCM3.

In Eurasia during the autumn season (Figure 5.5e, Table B.11), the majority of CMIP5 models show very weak SWE trends so does the CanSISE product which reports an insignificant decreasing trend of -0.59 ± 0.79 kg m -2 /dec. The multimodel mean SWE trend of -0.77 ± 0.19 kg m -2 /dec is very close to the observed value. There are six ensemble models showing significant SWE trends but only three (CCSM4, CNRM-CM5 and MPI-ESM-LR) fall inside the range given by observations. Across the individual model realizations none of them shows a significant SWE trend lying inside the observed range.

As for spring, the spread in SWE trend in autumn across CMIP5 models is higher in the North American Arctic sector (Figure 5.5f, Table B.12). The CanSISE product displays a decreasing and insignificant trend of -0.70 ± 1.25 kg m -2 /dec. The SWE trend reported by the multimodel mean is outside the observed range with a value of -2.79 ± 0.28 kg m -2 /dec. Six models display SWE trends inside the range implied by observations but only three of them are statistically significant (CSIRO-Mk3-6-0, GISS-E2-H/R). As for Eurasia, none of the individual members show significant trends lying inside the observed range.

Snow depth

We evaluate SND trends in spring and autumn across the Arctic subdomains in CMIP5 models and in three reanalyses (ERA20c, JRA-55 and NOAAV2c) as seen in Figure 5.6.

Discrepancies between the reference data sets are substantial ; mainly for ERA20c reanalysis which displays systematically very weak trends compared to the other reanalyses (JRA-55 and NOAAV2c). [START_REF] Wegmann | Eurasian snow depth in long-term climate reanalyses[END_REF] already reported the poor ability of ERA20c in reproducing SND trends in Eurasia compared to in situ snow data. Therefore, for this diagnostics, the ERA20c reanalysis is considered as an additional or alternative data set to be evaluated, but not as a reference for model comparison.

Figure 5.6a shows spring Arctic SND trends displayed by CMIP5 models and the three reanalyses. The JRA-55 reanalysis shows a significant trend of -3.81 ± 0.72 cm/dec (Table B.13). This marked SND trend over the whole Arctic is due to local strong decreases found in some areas over the Rocky Mountains and Canadian Archipelago (Figure 5.10), which is demonstrated by a trend of -7.43 ± 1.6 cm/dec over the North American sector of one order greater than the SND trend reported using stations from Global Historical Climatology Network (GHCN). This SND trend value is only considered as an approximate reference since it has been computed for a longer period and a smaller area, north of 60 • latitude [START_REF] Brown | Arctic terrestrial snow cover[END_REF]. Therefore, we discard JRA-55 as reference for the whole Arctic spring SND trends (Figure 5.6a,b,c). Rather, we select the NOAAV2c reanalysis, which reports a SND trend of -1.74 ± 0.83 cm/dec statistically significant at 95%. ERA20c shows a weak but significant trend of -0.29 ± 0.14 cm/dec. With respect to NOAAV2c reanalysis, the multimodel mean (-0.95 ± 0.10 cm/dec) slightly underestimates the SND trend. Half of the ensemble models show a significant SND trend falling inside the range given by the NOAAV2c reanalysis. These models are CanESM2, CCSM4, CNRM-CM5, GISS-E2-H/R, MIROC-ESM-/CHEM and NorESM1-M. 30% of individual realizations display significant tendencies within the range implied by NOAAV2c.

In Eurasia during the melting season (Figure 5.6b, Table B.14), NOAAV2c is the only reference data set statistically significant at the 90% confidence level and displays a decrease in SND of -1.19 ± 0.16 cm/dec. The other two reanalyses, JRA-55 and ERA20c, exhibit trend values of -0.76 ± 0.55 cm/dec and -0.19 ± 0.16 cm/dec (respectively) but they lack statistical significance.

The multimodel mean is slightly outside the range implied by observations, displaying a decreasing significant trend of -0.59 ± 0.12 cm/dec. There are six out of 14 models that present SND trend estimates inside the observed range, and five are statistically significant (CanESM2, CCSM4, MIROC-ESM, MIROC5 and NorESM1-M). There are only 25% of individual realizations that lie inside the range implied by observations. The largest spread in individual realization trends is found in CNRM-CM5 and MIROC5.

The JRA-55 reanalysis shows the best score of statistical significance compared to the other reanalyses in North America in spring (Figure 5.6c,Table B.15). However, as mentioned before, this strong trend of -7.43 ± 1.6 cm/dec is unrealistic compared to in situ snow measurements [START_REF] Brown | Arctic terrestrial snow cover[END_REF]. The main contribution to this strong decreasing SND trend is located in elevated and northern areas over the Rocky Mountains and the Canadian Archipelago (Figure 5.10b). ERA20c reports a SND trend of -0.43 ± 0.26 cm/dec (statistically significant at 90%), but it is very weak compared to the in situ observations (Figure 5.12 ; [START_REF] Wegmann | Eurasian snow depth in long-term climate reanalyses[END_REF]. NOAAV2c shows a SND trend of -1.88 ± 1.51 cm/dec and is statistically significant at the 78% of confidence level. The multimodel mean is in good agreement with the NOAAV2c reference, reporting a decreasing trend of -1.42 ± 0.16 cm/dec. There are only three models (inmcm4, MIROC5 and MRI-CGCM4) out of the range implied by NOAAV2c but only one is statistically significant (MIROC5). The rest of CMIP5 models lie inside the observed range and are statistically significant (except bcc-csm1-1). There are 25 out of 68 individual realizations that agree with NOAAV2c and are statistically significant.

During the onset season (Figure 5.6d, Table B.16), JRA-55 displays a significant SND trend of -1.62 ± 0.52 cm/dec over the whole Arctic which is stronger than the other reanalyses. NOAAV2c

shows almost a neutral trend of -0.09 ± 0.08 cm/dec and ERA20c one of -0.89 ± 0.64 cm/dec, however none of them are statistically significant. Thus, we consider JRA-55 as reference for evaluation of model autumn SND trends. The multimodel mean shows a weaker than observed trend with a value of -0.65 ± 0.07 cm/dec. Except for MRI-CGCM3, the rest of the ensemble models shows significant SND trends but none of them fall inside the range of JRA-55. There are only 8 out of 68 individual realizations that lie within the range given by the reference data set.

Over Eurasia in autumn (Figure 5.6e, Table B.17), SND trends are weak, almost neutral in the majority of CMIP5 models. JRA-55 shows a significant trend of -0.89 ± 0.42 cm/dec, stronger than NOAAV2c (-0.50 ± 0.61 cm/dec) and ERA20c (-0.09 ± 0.09 cm/dec), but none of them are statistically significant. The SND trend displayed of the multimodel mean is -0.30 ± 0.07 cm/dec, almost three times smaller than the reference. There are four models (bcc-csm1-1,GISS-E2-R and NorESM1-M/ME) that display SND trends within the range implied by JRA-55 and they are all statistically significant. Regarding individual realizations, there are 11 out 68 that lie inside the observed range and they are statistically significant at the 90% confidence level.

In the onset season, the spread of SND trends is larger in North America (Figure 5.6f, Table B.18) than in Eurasia. The only reanalysis displaying a significant SND trend is JRA-55, being of -2.48 ± 1.14 cm/dec, whereas NOAAV2c and ERA20c report weaker trends (-0.10 ± 0.14 cm/dec, -1.51 ± 1.12 cm/dec, respectively). The multimodel mean is quite close to the range implied by JRA-55 with a decreasing value of -1.09 ± 0.08 cm/dec. Only 3 out of 14 models (MIROC-ESM-/CHEM and NorESM1-ME) display significant SND trend inside the observed range. Fourteen out of 68 realizations are also significant and fall within the range implied by JRA-55 ; these simulations are from the aforementioned models in addition to members from bcc-csm1-1, CanESM2, CCSM4, CNRM-CM5 and MIROC5. It is worth mentioning the large spread of MIROC5 of SND trends in North America, which was already reported in Figure 5.6f for SWE trends.

Spatial trend pattern

The spatial patterns of linear trends in individual models are extremely noisy with trends of different signs coexisting in close proximity. In this section, we quantify the degree of consensus across the 16 models (14 models for SND) over linear trends in snow characteristics (Figure 5.8,5.9 and 5.11). For each grid cell, we compute the maximum number of models agreeing on the sign of trend and on its significance. For instance, if in a particular cell 8 models show significant positive trends, 5 significant negative trends and 3 insignificant trends, this grid cell will hold "+8" value.

If the numbers of models with positive and negative trends are equal, the grid cell is set to zero.

For this analysis, we used the 80% significance level (t-test) for estimating statistical significance of individual trends rather than 90%, in order to increase the number of model trends considered for each grid cell.

Snow cover

To characterize SNC trends in CMIP5 models, we choose as reference the spatial trend pattern Eurasia and Western North America.

Snow water equivalent

A similar analysis is carried out for SWE during the period 1981-2005 (Figure 5.9). The CanSISE product shows very few locations with statistically significant trends in both seasons. In spring (Figure 5.9b), statistically significant decrease in SWE is observed in Northern Eurasia along the Arctic Ocean coast and a local increase is identified over the southern part of Western Siberia.

In the onset season (

Snow depth

We assess the differences in SND spatial trends across the reanalyses (Figure 5.10). In spring [START_REF] Bulygina | Changes in snow cover characteristics over Northern Eurasia since 1966[END_REF][START_REF] Wegmann | Eurasian snow depth in long-term climate reanalyses[END_REF]. Regarding the JRA-55 reanalysis, the statistical significance of the spring SND trends appears unusual, e.g., compared to the other data sets (Figure 5.10c). The Rocky Mountains, some areas north of Canada and over the Canadian Archipelago, and between the Ob and Yenisei Rivers experience steep negative trends of more than -20-30 cm/dec.

(
Very regional and positive strong SND trend can be fond in north of Alaska and along the coast of Okhotsk Sea with values up to + 30 cm/dec. During the onset season (Figure 5.10c), JRA-55 shows negative and significant SND trend along the coast of Hudson's Bay around -8 cm/dec and up to -12 cm/dec over the Canadian Archipelago. In Eurasia, there is a dipole of SND trends in the coast of the Kara Sea with a strong negative (positive) tendency in the west (east) of the Yenisei River reaching ± 12cm/dec of magnitude. JRA-55 underestimates SND trends over the Ob-Yenisei river basins as in its previous version JRA-25 [START_REF] Khan | Snow cover characteristics over the main Russian river basins as represented by reanalyses and measured data[END_REF]. Additionally, this trend is even sharper in spring and negative unlike snow stations (Figure 5.12a ;[START_REF] Bulygina | Changes in snow cover characteristics over Northern Eurasia since 1966[END_REF][START_REF] Brown | Arctic terrestrial snow cover[END_REF].

The NOAAV2c reanalysis seems to be the best choice to characterize SND trends, being a good compromise between the other two reanalyses and it displays a fair agreement with snow station data (Figure 5.12 ; [START_REF] Wegmann | Eurasian snow depth in long-term climate reanalyses[END_REF]. In spring (5.11b), NOAAV2c shows statistically significant decreasing SND trends over central Canada, Scandinavia and west of the Lake Baikal with values ranging from -6 to -9 cm/dec. Positive trends are found over the south part of Eastern Eurasia in agreement with [START_REF] Bulygina | Changes in snow cover characteristics over Northern Eurasia since 1966[END_REF], however the increase SND values over the Ob River observed by the latter are not reproduced in NOAAV2c. In autumn (5.11d), SND trends are weaker than in spring. Increasing significant trends are found over the north of the Canadian (a) ERA20c Archipelago and east of the Lake Baikal with values of +6 cm/dec. Over the north of the Laurentian Plateau, we found significant negative trends of -4-5 cm/dec and weaker, but significant, over the south of Western Eurasia and north of the Lake Baikal. The negative(positive) SND trends found in east(west) of the Lake Baikal are also observed in the in situ snow data (Figure 5.12b).

Regarding CMIP5 SND trends, there is an almost indistinguishable match between the spatial pattern of SND trend and that of SWE trends in both seasons (Figure 5.9). In spring, 8 to 10 CMIP5 models report decreasing trends over Western Eurasia and North America. The agreement is reduced in the Eastern side of Eurasia with 4-6 models displaying positive trends (Figure 5.11a).

This pattern corresponds relatively well with the SND trend distribution found in NOAAV2c except over the central part of Western Eurasia. During the onset season (Figure 5.11c), CMIP5 models show primarily negative trends over the whole Arctic. However, there are increasing SND trends in the south of the Lena River in 2-4 models. The best agreement is found over the Rocky Mountains with 8-12 models reporting negative trends. In general, the whole Arctic is characterized by little consensus among CMIP5 models with only 2-4 models displaying negative trends.

In situ measurements

We have computed the SND trends reported by 422 snow stations in spring and autumn over 1979-2005 following the criteria explained in Chapter 3. Figure 5.12 provides a realistic overview of SND temporal evolution that has been used as a reference to evaluate models and reanalyses.

Note that we show all SND trends without considering their degree of statistical significance in order to include as many stations as possible to visualize the overall spatial SND trend pattern of Eurasia. During the melting season (Figure 5.12a), SND positive trends are located over the south of Western Eurasia and west of Lake Baikal of around 2-4 cm/dec . Decreasing trends are found south of the 90 • meridian (< 2 cm/dec) and between the Ob and Yenisei Rivers (∼4 cm/dec). Over Eastern Eurasia, snow stations are quite scarce, however a prevalence of weak negative trends can be distinguished. In the onset season (Figure 5.12b), the SND trends are weaker than in spring. SND trends are negative in central Siberia and in the coast of Barents Sea (-6 cm/dec). Positive trends are found over the south of Siberia around the 90 • meridian with values around +4-6 cm/dec.

Over the south of western Eurasia, increasing trends are dominant (+2 cm/dec) ; however, when moving to 30 • E parallel decreasing trend are found. Over the Far East, negative trends prevail over positive trends. The rest of CMIP5 ensemble underestimate the reference STD, with the lowest value found in CSIRO-Mk3-6-0 model. In autumn, the spread in CMIP5 models is also distinct.

Summary

The majority of models underestimate the amplitude of interannual variability. There are also four outliers among the models (NorESM1-ME and all versions of MIROCs), with considerably larger STDs than in observations.

• The interannual variability of SND is better captured by CMIP5 models compared to the other variables. In spring, JRA-55 and NOAAV2c agree in terms of STD and correlation whereas ERA20c displays lower STD but a significant correlation with JRA-55.

There are two models (MIROC-ESM-CHEM and MIROC5) that accurately reproduce the amplitude of interannual variability. The rest of CMIP5 ensemble underestimates the observed STD by a factor of two. Similar results are found for autumn, in particular, a good agreement between JRA-55 and NOAAV2C reanalyses, but an underestimation of STD is found in ERA20c. CMIP5 ensemble displays lower STD values than JRA-55, the models MIROC5, MIROC-ESM-CHEM and NorESM1-ME being the closest to the reference data set.

(ii) Seasonal trend analysis :

• Pan-Arctic SCE trends in spring across reference data sets present some discrepancies since the NCEP/CFSR reanalysis shows almost neutral and even increasing (in North America) values whereas NOAA CDR and NOAAV2c are in relatively good agreement, mainly for Eurasia. More than half of the ensemble models agree with NOAA CDR and NOAAV2, displaying a general decrease of spring SCE. In autumn, NOAA CDR displays an unrealistic positive trend being higher in Eurasia than in North America.

NCEP/CFSR and NOAAV2c display decreasing SCE trends and are in better agreement in North America, but both trends lack statistical significance. Overall almost all CMIP5 models are able to reproduce the pan-Arctic trends in autumn.

• Observed SWE trends over the Arctic lack statistical significance in both seasons. In spring, CMIP5 models report a large spread in SWE trends, namely in the North American sector. Over the Pan-Arctic, less than 30% of models display significant trends inside the range implied by CanSISE product. During the onset season, CMIP5 models show stronger than observed decreasing trends. As in spring, the spread is larger in North America. There are around three ensemble models approximating the SWE trend of CanSISE product in any Arctic subdomain and very few individual realizations ; but almost no trend is significant.

• The SND trends over the Arctic reported by the three reanalyses differ substantially.

ERA20c displays very weak trends in both seasons. During spring, the SND trend observed in JRA-55 is unrealistically strong in North America, one order of magnitude larger than the in situ measurements [START_REF] Brown | Arctic terrestrial snow cover[END_REF]. Compared to NOAAV2c reanalysis, CMIP5 models generally underestimate the magnitude of the SND trend all over the Arctic. In autumn, JRA-55 and NOAAV2c are in better agreement than in spring.

Nearly all models from the CMIP5 ensemble show weaker SND trends as evidenced by the multimodel mean being out of the observed range over the Pan-Arctic subdomains.

As for SWE trends, the spread in North American sector is quite large compared to Eurasia.

(iii) Spatial trend pattern :

• NOAAV2c SCE trends are very weak and only locally significant compared to NCEP/CFSR. The latter is in a good agreement with CMIP5 models, displaying decreasing trends over Western Eurasia (8-12 models) and over North America (4-8 models) and increasing trend over the north part of Eastern Eurasia (4-8 models). However, CMIP5 ensemble does not capture the observed positive trend over the Rocky Mountains. In autumn, models demonstrate practically everywhere more frequent negative than positive trends, which is in agreement with SCE trend pattern from NCEP/CFSR. However, mismatches occur in the Far East of Eurasia and along the West Coast of North America.

• SWE trends computed from CanSISE show very few locations with statistically significant trends in spring and autumn. The CMIP5 trends for spring form a pattern of primarily negative trends over North America and Western Eurasia, and primarily positive trends over Eastern Eurasia. During the onset season, in around 8 of the CMIP5 models, negative trends dominate, except over the Lena Delta.

• Assessment of SND in reanalyses shows that, in spring, ERA20c reports very weak trends whereas JRA-55 displays strong trends one order of magnitude larger ; in both cases, statistically significant trends are very local. NOAAV2c show significant SND decrease over central Canada, Scandinavia and east of Lake Baikal. The best agreement between CMIP5 models (8-12 models) is found in North America and, to a lesser degree in Western Eurasia. Over Eastern Eurasia, CMIP5 models (4-6 models) report positive SND trends ; so does the reference but without statistical significance. In autumn, NOAAV2c reports significant positive trends north of the Canadian Archipelago, east of the Yenisei River and south of the Lena River. Very few locations show decreasing significant trends such as north of the Laurentian Plateau, east of the Lake Baikal and south of the Ural Mountains. CMIP5 ensemble (8-12 models) displays primarily decreasing trends throughout the terrestrial Arctic, the best fit to the observations is found in the West Coast of North America. 2-4 models report positive trends over the south of the Lena catchment in agreement with NOAAV2c.

Chapter 6

Conclusions and perspectives

We have investigated snow characteristics in the Arctic during spring and autumn in the historical runs of CMIP5 climate models and in different observational data sets -various reanalyzes, a satellite-observed product, an observation-based ensemble product and in situ measurements. For the SCE and SND variables the period of study was 1979-2005 and for SWE the period was 1981-2005. The main characteristics of each individual model from the CMIP5 ensemble are indicated in tables (6.1,6.2,6.3,6.4) as well as of each reference data set (Table 6.5).

We identified three groups of CMIP5 models according to their representation of SCE : models broadly overestimating observational SCE (up to 60 p.p. regionally), models underestimating observed climatological SCE (the strongest differences between 40-50 p.p.) and those showing overestimation over the northern regions and underestimation in the southern regions of the Arctic.

Differences are especially marked in the melting season but also pronounced during autumn. For SWE, we identified a pan-Arctic overestimation in most CMIP5 models except for CSIRO-Mk3-6-0 and MPI-ESM-LR/P, who show either general underestimation or an east-west (underestimationoverestimation) pattern over Eurasia. Again, these patterns are most pronounced during the melting season, when positive biases may be of the same order as the mean values. Three groups of CMIP5 models can be identified with respect to SND : models displaying a large overestimation (up to 80 cm locally), models underestimating SND throughout the Arctic and finally, those exhibiting a general positive bias in Eurasia and a positive-negative bias pattern in the eastern-western part of North America. In autumn, differences are smaller than in spring and the pattern slightly changes.

We can distinguish three different groups : models showing a general negative bias, models with a strong positive bias centered in Eastern Eurasia and models generally overestimating the observed SND climatology. For the particular case of Eurasia, the comparison of CMIP5 models and SND reanalyses with snow stations reveals a clear overestimation in spring and an underestimation in autumn with respect to the in situ measurements.

The position of the snow margin is better captured by CMIP5 models in the spring season with the best agreement found in Eastern Eurasia and Western North America. During autumn, the CMIP5 ensemble identifies a considerable northward shift of the snow margin and the overall agreement only occurs in Central Siberia, whereas, there are only 4-6 out of 16 models matching the location of the observed snow margin.

The observed annual cycle of SCE is relatively well captured by CMIP5 models in autumn, but during the spring-summer season, most models tend to significantly underestimate SCE, especially over North America. At the same time, the annual cycle of SWE is largely positively biased with respect to observations in most CMIP5 models, indicating persistent snow in summer months, thus contradicting observations. The annual cycle of SND reported by CMIP5 models presents similar discrepancies with respect to observations as SWE annual cycle. The dispersion is remarkably high during the snow accumulation season notably in North America and Eastern Eurasia.

We found that spring SCE averaged over the whole terrestrial Arctic is generally underestimated by CMIP5 models, to the point where some models are 50% lower than observations. In autumn, there is better agreement with a slight tendency for overestimation. For SWE, there is a large inconsistency between CMIP5 models and an overestimation with respect to the observed reference, with only two out of sixteen models in accordance with the observations. The dispersion is smaller in autumn, however, the positive bias still exists. CMIP5 models show a general good agreement in SND in both seasons. However, the discrepancies between the different reanalyses are substantial.

We found that the interannual variability of all snow characteristics is significantly underestimated in most CMIP5 models compared to observations. The SWE variable shows the largest discrepancies among CMIP5 models regarding the amplitude of interannual variability. With respect to Pan-Arctic interdecadal variability, most CMIP5 models show weakly negative (partially significant) trends in SCE, mainly in spring. The spread in SWE trends in CMIP5 models is quite large, notably in North America in both seasons. Generally, CMIP5 models show slightly stronger than observed trends in spring and autumn that are statistically significant, which is not the case for the observational data set. With respect to SND, CMIP5 models report weaker trends than the observational reference and they are particularly inconsistent over North America.

Regionally, the CMIP5 ensemble captures relatively well the observational trend pattern in all snow characteristics in spring over Eurasia, but SWE and SND show no consistency with the regional trend patterns in autumn in both continents. However, the discrepancies found between the spatial pattern of observed trends in SCE and SND hampers to designate a reference data set for such a model evaluation.

In agreement with previous studies [START_REF] Brutel-Vuilmet | An analysis of present and future seasonal Northern Hemisphere land snow cover simulated by CMIP5 coupled climate models[END_REF][START_REF] Mudryk | Interpreting observed Northern Hemisphere snow trends with large ensembles of climate simulations[END_REF], we found that the SCE annual cycle is relatively well captured by CMIP5 models compared to the three different reference data sets used. Nevertheless, the significant overestimation and the large spread of SWE on the Northern Hemisphere reported by [START_REF] Roesch | Evaluation of surface albedo and snow cover in AR4 coupled climate models[END_REF] in the previous generation of models has not been reduced in CMIP5 models. Regional differences in snow cover duration in autumn [START_REF] Peng | Change in snow phenology and its potential feedback to temperature in the Northern Hemisphere over the last three decades[END_REF][START_REF] Brown | Arctic terrestrial snow cover[END_REF][START_REF] Liston | The changing cryosphere : Pan-Arctic snow trends (1979-2009)[END_REF] are the likely cause of the spatial differences in the position of the snow margin in the onset season in both reanalyses and models.

In spring, we have found that SCE discrepancies in CMIP5 models are located over the southern part of the Arctic, where temperature changes are substantial and may favor snow to recede. This is consistent with the inability of CMIP5 models to capture the temperature sensitivity of snow cover [START_REF] Fletcher | Using models and satellite observations to evaluate the strength of snow albedo feedback[END_REF][START_REF] Brutel-Vuilmet | An analysis of present and future seasonal Northern Hemisphere land snow cover simulated by CMIP5 coupled climate models[END_REF]Thackeray et al., 2016). Conversely, during the onset season, we have found a more spatially uniform pattern of SCE differences. In fact, snow onset is highly coupled with variability in regional precipitation and surface temperature, as both are need to initiate snow cover (Mudryk et al., 2017;Ye, 2019). The accumulation and persistence of snow are linked to atmospheric modes of variability such as North Atlantic Oscillation (NAO) and Arctic Oscillation (AO) [START_REF] Bamzai | Relationship between snow cover variability and Arctic Oscillation index on a hierarchy of time scales[END_REF]Cohen et al., 2012;[START_REF] Liu | Impact of declining Arctic sea ice on winter snowfall[END_REF]. This suggests that discrepancies found on the onset, as well as during the snow accumulation (December to February), are more related to atmospheric circulation rather than temperature.

With regard to snow tendencies, we have found that in both spring and autumn, CMIP5 snow characteristics display negative but weaker-than-observed trends, consistent to previous studies at North Hemispheric scale [START_REF] Brutel-Vuilmet | An analysis of present and future seasonal Northern Hemisphere land snow cover simulated by CMIP5 coupled climate models[END_REF][START_REF] Mudryk | Interpreting observed Northern Hemisphere snow trends with large ensembles of climate simulations[END_REF][START_REF] Connolly | Northern Hemisphere Snow-Cover Trends (1967-2018) : A Comparison between Climate Models and Observations[END_REF]. In addition, an interesting feature was that both CMIP5 and reference data sets report stronger trends in snow accumulation (SWE and SND) over North America than over Eurasia. This is consistent with the findings of [START_REF] Biancamaria | Satellitebased high latitude snow volume trend, variability and contribution to sea level over 1989/2006[END_REF] based on satellite data and [START_REF] Park | Analysis of satellite and model datasets for variability and trends in Arctic snow extent and depth, 1948-2006[END_REF] using both in situ data and an hydrological and biogeochemical model. In fact, [START_REF] Biancamaria | Satellitebased high latitude snow volume trend, variability and contribution to sea level over 1989/2006[END_REF] related this pattern of variations to a difference in regional climate conditions between both Arctic subdomains. Indeed, snow depth in Eurasia is linked to the Arctic Oscillation and Atlantic Multidecadal Oscillation (AMO) whereas in North America, snow depth accumulation is influenced by the Pacific North American (PNA) pattern and AMO. However, there exist some deficiencies in the reproductibility of these atmospheric modes in the CMIP5 ensemble [START_REF] Ning | NAO and PNA influences on winter temperature and precipitation over the eastern United States in CMIP5 GCMs[END_REF][START_REF] Davini | On the misinterpretation of the North Atlantic Oscillation in CMIP5 models[END_REF], which may make the reproduction of the snow-atmosphere coupling more difficult (e.g., [START_REF] Furtado | Eurasian snow cover variability and links to winter climate in the CMIP5 models[END_REF][START_REF] Gastineau | The Influence of Autumnal Eurasian Snow Cover on Climate and Its Link with Arctic Sea Ice Cover[END_REF]. We suggest that the mismatches found in snow accumulation, mainly in trends and the overall overestimation of SWE and SND throughout the snow season, can be linked to an inadequate representation of atmospheric internal variability and snow-atmosphere coupling. This is consistent with the low interannual variability found in CMIP5 models (Figures 5.1,5.2 and 5.3) and the internal limitations of CMIP5 models (Taylor et al., 2012). Our study highlights the need for a deeper understanding of atmospheric variability and snow in the CMIP5 ensemble and their relation to the dominant atmospheric circulation patterns of Northern Hemisphere (e.g. AO, NAO and PNA). Their role can be investigated with the help of EOF (Empirical Orthogonal Function) analysis following [START_REF] Popova | Winter snow depth variability over northern Eurasia in relation to recent References atmospheric circulation changes[END_REF].

We confirm that the October trend of NOAA CDR is an outlier compared to the other data sources, as previously reported [START_REF] Brown | Is Eurasian October snow cover extent increasing ?[END_REF][START_REF] Estilow | A long-term Northern Hemisphere snow cover extent data record for climate studies and monitoring[END_REF]. The discrepancies found in SND and SCE trends among the reference data sets encourages us to strongly recommend a multi-data set approach to evaluate snow characteristics in models. Using one single reference can induce to an incorrect model evaluation as it is sensitive to the choice of the reference data set (e.g., Gómez-Navarro et al., 2012). This is the case of [START_REF] Connolly | Northern Hemisphere Snow-Cover Trends (1967-2018) : A Comparison between Climate Models and Observations[END_REF] who identified an artificial bias in autumn SCE trends in CMIP5 models using only the NOAA CDR data set as reference, while in fact, it is the observation which is not realistic. When considering multiple data sets [START_REF] Mudryk | Characterization of Northern Hemisphere snow water equivalent datasets, 1981-2010[END_REF] or an ensemble product (CanSISE, Mudryk and Derksen, 2017), we can hope to overcome the limitations of individual data sets and get access to the real climate state.

Overall, the lack of agreement found among the ensemble of models in the spatial distribution of Arctic snow, as well as, in the reproductibility of snow trends questions the robustness of future projections (Hinzman et al., 2013). Climate projections cannot follow the pace of polar amplification and the associated snow-albedo feedback [START_REF] Derksen | Spring snow cover extent reductions in the 2008-2012 period exceeding climate model projections[END_REF][START_REF] Déry | Recent Northern Hemisphere snow cover extent trends and implications for the snow-albedo feedback[END_REF]Hernández-Henríquez et al., 2015;[START_REF] Qu | On the persistent spread in snow-albedo feedback[END_REF]. In the context of a warmer and wetter Arctic [START_REF] Screen | Exploring links between Arctic amplification and midlatitude weather[END_REF][START_REF] Bintanja | Future increases in Arctic precipitation linked to local evaporation and sea-ice retreat[END_REF], the future impact of snow on the surface albedo (Thackeray et al., 2018), circulations patterns [START_REF] Rydzik | Relationship between snow extent and midlatitude disturbance centers[END_REF], permafrost [START_REF] Biskaborn | Permafrost is warming at a global scale[END_REF] and water supply [START_REF] Mankin | The potential for snow to supply human water demand in the present and future[END_REF] among many other consequences [START_REF] Callaghan | Changing snow cover and its impacts[END_REF], should be consider as high priority. More targeted simulations of ESM-SnowMIP [START_REF] Krinner | ESM-SnowMIP : assessing snow models and quantifying snow-related climate feedbacks[END_REF] and the new generation of models [START_REF] Eyring | Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization[END_REF] will broaden our knowledge of snow-climate interactions and increase our confidence in future projections and mitigation scenarios in the context of polar amplification. We hope that our assessment of snow representation in CMIP5 models serve as a standard to evaluate the next generation of CMIP6 ensemble and also, to provide valuable information for climate community when using these snow-related variables from CMIP5 historical output. In this annex we show some exploratory results for snow cover from the two models' experiments described in [START_REF] Ogawa | Evaluating impacts of recent Arctic sea ice loss on the northern hemisphere winter climate change[END_REF].

A.2 Data

We have analyzed simulations of the recent 33 years displays the same horizontal resolution as CAM4, but a higher vertical resolution of 66 levels up to 0.000006 hPa, thus it is considered as "high top" model. Two different experiments were carried out to distinguish the impact of sea ice (SIC) and sea surface temperatures (SST). The experiments were repeated using different initial conditions to provide 20 member realizations for each of model.

Daily varying SIC is prescribed in both experiments. In the first experiment ("SST-SIC-EXP") daily varying SST conditions are prescribed, whereas daily climatological SST computed from the NOAA data is prescribed in the second experiment ("SIC-EXP" ). See [START_REF] Ogawa | Evaluating impacts of recent Arctic sea ice loss on the northern hemisphere winter climate change[END_REF] for further details of simulations and experiments. We analyzed the snow cover output (SCE) from these simulations. We restrict the domain to an ice-free land Arctic north of 50 • N. The mask from the coupled model CCSM4 [START_REF] Gent | The Community Climate System Model Version 4[END_REF], Table 2.1) has been applied considering only grid cells with more or equal to 50% of land fraction and less than 15% of permanent ice (Figure 3.3).

A.3 Results

A.3.1 Spatial distribution of snow cover

Differences in climatology between the four simulations are computed for winter (December-January-February), spring (March-April) and autumn (October-November) seasons for the period 4.17). We suggest that the inability to fully melt snow in summer in CAM4 and WACCM is due to the lack of coupling with a land surface model which controls the heat balance at the surface necessary for melting (Equation 2.1).

A.3.2 Seasonal trends of snow cover

A.4 Conclusions

We have analyzed the snow cover variable from two different modeling experiments using two atmospheric models CAM4 ("low-top") and WACCM ("high-top"). In the first experiment (SST-SIC-EXP) daily varying SIC and SST conditions were prescribed, whereas in the second experiment (SIC-EXP), SST was prescribed to daily climatology. Simulations expand from 1982 to 2014 and the seasons considered were winter (December-January-February), spring (March-April) and autumn(October-November).

We have found that climatological differences between both experiments, SST-SIC-EXP and SIC-EXP, are not statistically significant for any season. However, SCE climatology in "high-top"

(WACCM) and "low-top" (CAM4) differs significantly with the strongest discrepancies found in spring corresponding to the peak of maximum snow accumulation (Figure 4.18 and 4.19). The higher SCE climatology in WACCM than in CAM4 may be related to the ability of the "high-top" model to better capture stratosphere variability and thus, being able to accurately reproduce the frequency of stratospheric warming events. They are associated to cold air outbreaks [START_REF] Kolstad | The association between stratospheric weak polar vortex events and cold air outbreaks in the Northern Hemisphere[END_REF] and to increase of precipitation and moisture transport (Ziuliaeva et al. in preparation), thus providing favorable conditions for snowfall. This is consistent with [START_REF] Charlton-Perez | On the lack of stratospheric dynamical variability in low-top versions of the CMIP5 models[END_REF] who found that "low-top" models from CMIP5 ensemble strongly underestimate the frequencies of major sudden stratospheric warming events, reproducing less than half the frequency of events observed in the reanalysis data and in the "high-top" models. The next step would be to conduct a similar procedure for snowfall variable and to apply a regression analysis using September sea ice anomalies as in [START_REF] Ghatak | Simulated Siberian snow cover response to observed Arctic sea ice loss, 1979-2008[END_REF]. Another analysis to be conducted is to investigate the different patterns of variability from individual realizations (members) in both snow cover and snowfall as has already been presented by [START_REF] Ogawa | Evaluating impacts of recent Arctic sea ice loss on the northern hemisphere winter climate change[END_REF].

ARC-MarApr

Figure 1

 1 Figure 1.1 -(a) Map of high and low Arctic zones delineated according to the Circumpolar Arctic Vegetation Map (CAVM Team 2003). Tree line corresponding to the southern limit of Sub-Arctic zones (extracted from SWIPA (2017)). (b) Arctic domain defined north of 50 degrees latitude (in circle). The terrestrial ice-free Arctic (topographic in color) and the ocean and permanent ice areas (masked in white) are distinguished. Geographical features are labeled to facilitate the spatial description of snow characteristics in the text.

Figure 1 . 2 -

 12 Figure 1.2 -Surface air temperature climatology in (a) January and (b) July during 1979-2005 using NCEP/CFSR Reanalysis from ESRL (Earth System Research Laboratory) Monthly/Seasonal Climate Composites https://www.esrl.noaa.gov/psd/cgi-bin/data/composites/printpage.pl .

Figure 1 . 3 -

 13 Figure 1.3 -Schematic representation of the components of the Arctic Cryosphere and their associated observed changes caused by global warming (graphic extracted from SWIPA (2011) and has been adapted from an image created by the U.S. National Center for Atmospheric Research).

Figure 1 . 4 -

 14 Figure 1.4 -Time series of annual Arctic sea ice minimum since 1979 to present based on satellite observations. Data from : NSIDC/NASA (https://climate.nasa.gov/vital-signs/arctic-sea-ice/).

Figure 1 . 5 -

 15 Figure 1.5 -Mean annual snow cover duration over Arctic land areas from the NOAA IMS-24 daily snow cover analysis for the snow seasons 1998/99 to 2013/14. Extracted from SWIPA (2017).

Figure 1 . 6 -

 16 Figure 1.6 -Schematic illustration outlining the importance of snow on the strong temperature gradients occurring near the snow surface. The solid black line represents an idealized ground-snowatmosphere temperature profile. Source R. Brown and T. V. Callaghan. Extracted from Callaghan et al. (2011b).

Figure 2

 2 Figure 2.1 -(a) Schematic summary of CMIP5 long-term experiments. Upper hemisphere experiments are suitable for validation with observations or provide projections. Green fonts refer to simulations performed only by models with carbon cycle representations. (b) Schematic summary of CMIP5 decadal prediction integrations. Extracted from Taylor et al. (2012).

Figure 2 . 2 -

 22 Figure 2.2 -Time series of compatible emission rate (PgC yr -1 ) of fossil fuel emissions simulated by the CMIP5 ESMs for the four RCP scenarios. Dashed lines represent the historical estimates and emissions calculated by the Integrated Assessment Models (IAMs) used to define the RCP scenarios ; solid lines and shading show results from CMIP5 ESMs (model mean, with 1 standard deviation shaded). Extracted from Ciais et al. (2014).

Figure 2 . 3 -

 23 Figure 2.3 -Diagram of snow characteristics in general circulation models.

  conducted by the Japanese Meteorological Agency (JMA) ; extends back to 1958, coinciding with the establishment of the global radiosonde observing system. Snow depth is assimilated using snow stations data over the United States, Russia and Mongolia, which were supplied by UCAR (University Corporation for atmospheric research), RIHMI (Russian Research Institute of Hydrometeorological Information) and IMH (Institute of Meteorology and Hydrology), respectively.

  procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.2 Particular cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Ice-free land mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.4 From fraction to binary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5 Statistical analysis of snow characteristics . . . . . . . . . . . . . . . . . . 36 3.5.1 Test for differences of mean for paired samples . . . . . . . . . . . . . . . . 36 3.5.2 Statistical significance of linear trend . . . . . . . . . . . . . . . . . . . . . . 37 3.5.3 Taylor Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Figure 3 . 1 -

 31 Figure 3.1 -Example of weekly to monthly conversion used in NOAA CDR. The snow field of January 2018 (f) is the result of averaging the five weeks (a to e). Figures are extracted from https://climate.rutgers.edu/snowcover/.

Figure 3 . 2 -Figure 3 . 3 -

 3233 Figure 3.2 -Map of snow stations location and their classification depending on the percentage of gaps in the temporal record (in colors) for the period 1979-2005. The information about the coordinates and elevation of each station is described in http://meteo.ru/english/climate/snow.php.

Figure 3 .

 3 4 shows an example of the climatology of snow depth in March-April from the JRA-55 reanalysis in its original grid (Figure3.4a) and the resulting interpolation to snow locations (Figure3.4b). Note that there are some stations located overseas that show null values as they are out of the boundaries of snow land fields due to an ice-free land mask effect.

Figure 3 . 4 -

 34 Figure 3.4 -(a) Climatology of snow depth in March-April during 1979-2005 from the JRA-55 reanalysis. (b) Same climatology but interpolated into the snow station point locations.

Figure 3 . 5 -

 35 Figure 3.5 -Ice-free land mask for the Arctic domain (50 • N -90 • N) of each of CMIP5 models from Table 2.1.

Figure 3 . 6 -

 36 Figure 3.6 -Number of cells contained in the ice-free land Arctic domain (50 • N -90 • N) in each of CMIP5 models from Table 2.1.

Figure 3 .

 3 Figure 3.7 -Geometric relationship between the correlation coefficient R, the centered pattern RMS error E , and the standard deviations σ f and σ r of the test and reference fields, respectively Extracted from Taylor (2001).

Figure 4 .

 4 Figure 4.1 shows the climatology of snow cover for the melting (Figure 4.1a) and the onset (Figure 4.1b) seasons for the period 1979-2005 from the NCEP/CFSR reanalysis. In this section, we consider NCEP/CFSR as the reference for SCE evaluation in the models due to its high spatial

Figure 4 .

 4 Figure 4.1 -Climatology of snow cover extent in March-April (a) and October-November (b) from the NCEP/CFSR reanalysis over the period 1979-2005.

Figure 4 . 2 -

 42 Figure 4.2 -Differences for March-April (a) and October-November (b) snow cover climatology of NOAAV2c minus NCEP/CFSR. Only differences with p-values less than 0.01 from the t-Student test are shown.

Figure 4 .

 4 Figure 4.4a,e,i,j,k,l,m) show a general underestimation of SCE up to 60 p.p. over the whole terrestrial Arctic. In contrast, the models CCSM4, inmcm4, MRI-CGCM3 and NorESM1-M/ME(Figure 4.4c,h,n,o,p) demonstrate general overestimation of SCE over North America and Eastern Eurasia

(

  NCEP/CFSR] (Mar-Apr)

Figure 4 . 3 -

 43 Figure 4.3 -Difference of March-April snow cover climatology of each ensemble CMIP5 minus NCEP/CFSR. Only differences with p-values less than 0.01 from the t-Student test are shown.

Figure 4 .

 4 Figure 4.5 shows the position of the snow margin for spring (March-April) and autumn (October-November) for all the CMIP5 models and two reanalyses from 1979 to 2005. The position of the snow margin was defined as the 50% SCE contour. For both reanalyses, NOAAV2c and NCEP/CFSR, the snow margin position is computed directly by considering the contour of 50% SCE of the March-April and October-November climatologies for the period 1979-2005. We do not include NOAA CDR in this analysis because of the incompatibility between grid projections as mentioned in Chapter 2.

  NCEP/CFSR] (Oct-Nov)

Figure 4 . 4 -

 44 Figure 4.4 -Difference of October-November snow cover climatology of each ensemble CMIP5 minus NCEP/CFSR reanalysis. Only differences with p-values less than 0.01 from the t-Student test are shown.

Figure 4 .

 4 Figure 4.6 shows the climatology of Arctic SWE in the melting season (Figure 4.6a) and in the onset season (Figure 4.6b) during 1981-2005 derived from the CanSISE ensemble product. In March-April (Figure 4.6a), the areas with high SWE include the Kamchatka Peninsula and the region east of the Yenisei River, where SWE amounts to 300 kg m -2 . Also, high values of up to 210 kg m -2 are observed over the Ural and Kolyma Mountains as well as over Eastern Canada. The remaining part of the terrestrial Arctic is characterized by values around 50 kg m -2 . In October-November (Figure 4.6b), SWE values are smaller compared to spring. Maximum values of up to 100 kg m -2 are observed east of the Yenisei River. All over the Arctic, SWE is around 20 kg m -2 with larger values up to 60 kg m -2 over the Verkhoyansk, Chersky and Kolyma mountain ranges. White areas in Figure 4.6 correspond to the land ice mask of the CanSISE ensemble product visible

Figure 4 . 5 -

 45 Figure 4.5 -The position of the snow margin is defined as the contourline of 50% snow cover fraction averaged over 1979-2005 in the NCEP/CFSR and NOAAV2c reanalyses (purple and pink lines, respectively) for (a) March-April and (b) October-November. The colorbar shows the number of CMIP5 models that display an ensemble seasonal mean of snow cover fraction equal or superior to 50%.

Figure 4 .Figure 4 . 6 -

 446 Figure 4.7 shows the spatial patterns of differences in SWE spring climatology between CMIP5 models and CanSISE data for 1981-2005. There is an overall overestimation of SWE across nearly all CMIP5 models compared to the CanSISE ensemble product with differences ranging from 40 to 120 kg m -2 over most of Northern Eurasia and North America. Local underestimation up to -120kg m -2 is observed in the majority of models in the delta of the Yenisei River and is especially pronounced in GISS-E2-H/R, MIROC-ESM/-CHEM and MIROC-5(Figure 4.7f,g,i,j,k). This feature may result from the inability of models to capture the local cooling and moistening influence from the river that enhance the thickening of the snowpack. The pattern of underestimation of SWE

Figure 4 .

 4 Figure 4.7 -Difference of March-April snow water equivalent climatology of each CMIP5 model minus CanSISE Ensemble product over the period 1981-2005. Only differences with p-values less than 0.01 from the t-Student test are shown.

Figure 4 . 8 -

 48 Figure 4.8 -Difference of October-November snow water equivalent climatology of each CMIP5 model minus CanSISE Ensemble product over the period 1981-2005. Only differences with p-values less than 0.01 from the t-Student test are shown.

Figure 4 .

 4 Figure 4.9 shows the climatology of snow depth from the JRA-55 reanalysis during spring (Figure 4.9a) and autumn (Figure 4.9b) over the period 1979-2005. As expected, the snow depth spatial distribution in both seasons is very close to that of SWE (Figure 4.6) as the two variables represent snow accumulation on the ground and are directly related to each other (detailed explanation in Chapter 2). In spring (Figure 4.9a), the highest values of snow depth (up to 150 cm) are observed in the east coast of the Laurentian Plateau in Canada and on a more region to region basis, over the Pacific Coast of Alaska and the Kamchatka Peninsula. Other centers of high snow accumulation are located over the delta of the Yenisei River and over Scandinavia with values from 70 to 90 cm. There is a clear positive gradient of snow accumulation towards the north, mainly in Canada ; but also, from the continent to the ocean over the Pacific Coast of Eurasia. This last feature is related to the presence of the Kolyma and Chersky mountain ranges which act as natural barriers for moisture coming from the ocean. Consequently, they favor snow accumulation on the Pacific Ocean side (as long as temperatures are below freezing). During the onset season (Figure 4.9b), snow depth values are smaller than in spring since the snow season has just started and accumulation has not yet occurred. The maximum values are located in the delta of the Yenisei River reaching 35 cm. In addition, relatively high snow accumulation is found over the Canadian Archipelago, north of Alaska and in the Kolyma and Chersky mountain ranges with values around 20 cm.

Figure 4 . 9 -

 49 Figure 4.9 -Climatology of snow depth in March-April (a) and October-November (b) of the JRA-55 reanalysis over the period 1979-2005.

Figure 4 .

 4 Figure 4.10 -Difference of March-April (a,b) and October-November (c,d) snow depth climatology of the reanalyses ERA20c (a,c) and NOAAV2c (b,d) minus JRA-55 over the period 1979-2005. Only differences with p-values less than 0.01 from the t-Student test are shown.

Figure 4 .

 4 12a,c,m,n) still present a positive bias over the mountain ranges of the East Coast of North America and over the northern part of Eastern Eurasia with differences up to 45 cm, largely exceeding the observed snow depth climatology (Figure4.9b). The models GISS-E2-H/R (Figure4.12f,g) and MRI-CGCM3 (Figure4.12l) show a general positive bias, mainly across Eurasia with differences around 5-20 cm. These discrepancies may be related to an earlier onset of snow compared to the observations(Figure 4.19e). The rest of models (CanESM2, CNRM-CM5, CSIRO-Mk3-6-0, inmcm4, MIROCs ;

Figure 4 .

 4 Figure 4.12b,d,e,h,i,j,k) show a general SND underestimation over the terrestrial Arctic with an exception over the mountain ranges in the West Coast of North America, where positive bias is present in some models (CanESM2, CNRM-CM5, CSIRO-Mk3-6-0, inmcm4 ;Figure 4.12b,d,e,h).Both versions of NorESM1-M/ME display a strong overestimation up to 40 cm over the mountain ranges of Eastern Eurasia and over the West Coast of North America(Figure 4.12m,n). Similarly

Figure 4 .Figure 4 .

 44 Figure 4.11 -Difference of March-April snow depth climatology of each ensemble CMIP5 model minus JRA-55 over the period 1979-2005. Only differences with p-values less than 0.01 from the t-Student test are shown.

Figure 4 .Figure 4 .

 44 Figure 4.12 -Difference of October-November snow depth climatology of each ensemble CMIP5 model minus JRA-55 over the period 1979-2005. Only differences with p-values less than 0.01 from the t-Student test are shown.

Figure 4 .

 4 14). In spring(Figure 4.14a,b,c), the best agreement is found in JRA-55 over the eastern part of Eurasia with differences less than 10 cm in absolute value, whereas ERA20c and NOAAV2c display a positive bias of more than 45 cm, notably over the Kolyma Mountains.In central Siberia, around the 90 • E meridian, the NOAAV2c reanalysis shows the highest overestimation being up to 40-45 cm, followed by JRA-55 displaying differences up to 15 cm in the north and a stronger disagreement close to the Altai Mountain Range ; lastly, ERA20c displays smaller differences of 20 cm all along the 90 • E meridian. The western part of Eurasia is better reproduced by NOAAV2c with differences of 20 cm whereas in both ERA20c and JRA-55, the bias goes up to 40-45 cm north of 55 • N parallel. In autumn, both ERA20c and NOAAV2c present a relatively good agreement with snow data in Eastern Eurasia. They both present a slight overestimation in the Far East up to 20 cm and an underestimation over the south of Eastern Eurasia with values not exceeding 20 cm. JRA-55 shows a general underestimation of snow depth compared to the in situ measurements with maximum discrepancies in the basin of the Ob River (up to 45 cm). In western Eurasia, all reanalyses present a similar bias with small discrepancies of 15 cm in the south and larger ones northwards.

Figure 4 .

 4 Figure 4.14 -Difference of March-April (a,b,c) and October-November (d,e,f) snow depth climatologies of the ERA20c (a,d), JRA-55 (b,e) and NOAAV2c (c,f) reanalyses minus snow stations over the period 1979-2005. All the reanalyses have been converted to station locations by bilinear interpolation.

Figure 4 .

 4 Figure 4.16 shows a general underestimation of snow depth in CMIP5 model compared to the snow in situ data in autumn. However, these discrepancies are smaller in absolute magnitude than for the melting season. We can distinguish a recurrent pattern in the models bcc-csm1-1, CCSM4 and NorESM1-M/ME (Figure4.16a,c,m,n), which show higher than observed snow accumulation in the north of Eastern Eurasia and underestimation over the remaining land. To a lesser extent, this feature is also displayed by both versions of GISS-E2-H/R (Figure4.16f,g). There is a local overestimation in the south of central Siberia (bcc-csm-1, CanESM2, CNRM-CM5, GISS-E2-H/R, MRI-CGCM3, NorESM1-M/ME ;Figure 4.16a,b,d,f,g,l,m,n), which may be related to an associated effect of orographic precipitation close to the Altai mountain range.

  models, reanalyses and observations for different Arctic regions. Spatial average across different Arctic subdomains of climatological monthly means of SCE and SND were computed over the 1979-2005 period, and those of SWE over the 1981-2005. We applied for each CMIP5 model its own land-ice mask and the GISS-E2-R mask to the reanalyses (NCEP/CFSR, NOAAV2c, ERA20c, JRA-55) and CanSISE product. For the NOAA CDR data set (which has a binary land mask but

Figure 4 .

 4 Figure 4.17 shows that for the whole Arctic (Figure4.17a), the annual cycle of snow cover in both NCEP/CFSR and NOAAV2c is in good agreement with NOAA CDR with the largest differences not exceeding 10 p.p. . Between both reanalyses, the highest differences are only about 10 p.p. in May and they are observed in Eurasia. The multimodel mean generally reproduces the annual cycle compared to NOAA CDR with the largest discrepancies of up to 25 p.p. in October and November.

Figure 4 .

 4 Figure 4.15 -Difference of March-April snow depth climatology of each ensemble CMIP5 model snow stations over the period 1979-2005. CMIP5 models have been converted to station locations by bilinear interpolation.

Figure 4 .

 4 Figure 4.16 -Difference of October-November snow depth climatology of each ensemble CMIP5 model snow stations over the period 1979-2005. CMIP5 models have been converted to station locations by bilinear interpolation.

  18) is characterized by a relatively stronger spread across the models and larger deviations from observations. There is a definite overestimation of SWE in CMIP5 models with respect to the CanSISE product. The multimodel mean shows a positive bias all along the annual cycle with the largest overestimation during March-May when differences for the whole Arctic amount to 40 kg m -2 (Figure 4.18a) reaching 65 kg m -2 in North America (Figure 4.18c) and 30 kg m -2 in Eurasia (Figure 4.18b), more specifically over the eastern part (Figure 4.18e). Considering the whole Arctic (Figure 4.18b), the largest differences are observed during the melting season, from March to June, reaching 20-30 kg m -2 . Among CMIP5 models, the greatest SWE overestimation is in excess of 100 kg m -2 and occurs in April for MRI-CGCM3 (Figure 4.18a). The differences are larger over North America (Figure 4.18b) than over Eurasia (Figure 4.18c). Notably, there are three models (CSIRO-Mk3-6-0 and both versions of MPI-ESM-LR/P) that match fairly well the annual cycle of the CanSISE product for the whole Arctic and demonstrate differences in SWE from -10 kg m -2 to +20 kg m -2 . For the period from August to September, when CanSISE is characterized by complete snow melt in the Arctic (Figure 4.18a),

Figure 4 .

 4 Figure 4.17 -Annual cycle of snow cover extent for CMIP5 models, the multimodel mean, reanalyses (NCEP/CFSR and NOAAV2c) and satellite-based NOAA CDR product over the ice-free land Arctic and subdomains computed from 1979 to 2005.

Figure 4 .

 4 Figure 4.19 shows the annual cycle of snow depth over the Arctic and its subdomains for the period 1979-2005. It is characterized by a large spread similar to that of the annual cycle of SWE (Figure 4.18). The dispersion is more remarkable during the snow season (from December to June)

Figure 4 .

 4 Figure 4.18 -Annual cycle of snow water equivalent for CMIP5 models, the multimodel mean and CanSISE ensemble over the ice-free land Arctic and subdomains computed from 1981 to 2005.

Figure 4 .

 4 Figure 4.19 -Annual cycle of snow depth for CMIP5 models, the multimodel mean and reanalyses (ERA20c, JRA-55 and NOAAV2c) over the ice-free land Arctic and subdomains computed from 1979 to 2005.

Figure 4 .

 4 Figure 4.20 -Quantile statistics of the spatial average of snow cover for the CMIP5 models and the multimodel mean, the reanalyses (NCEP/CFSR and NOAAV2c) and the satellite data NOAA CDR for March-April (a) and October-November (b) over the terrestrial Arctic during 1979-2005.

Figure 4 .

 4 Figure 4.21 exhibits a general overestimation of SWE in CMIP5 models since the multimodel mean amounts to a value of 99 kg m -2 whereas the CanSISE product displays 59 kg m -2 . This feature was already manifested in Figure 4.7. The exception is CSIRO-Mk3-6-0(e) who shows the lowest average of 33 kg m -2 . The models MPI-ESM-LR/P(l,m) capture the SWE average of the whole Arctic accurately (64 kg m -2 , 50 kg m -2 ), however, this is the result of compensating errors (Figure 4.7l,m) : the positive/negative biases in east/west Eurasia and north/south of North America cancel out in the spatial mean. It is not surprising from Figure 4.18 that MRI-CGCM3(n)shows the highest value of SWE in spring at 148 kg m -2 , that is 60% more that the reference. During the onset season (Figure4.21b), CMIP5 models are in a better agreement with the CanSISE product, with values ranging from 40 to 60 kg m -2 in the majority of models, which is consistent with a multimodel mean of 52 kg m -2 and a SWE mean of 40 kg m -2 in CanSISE. As in spring,

Figure 4 .

 4 Figure 4.21 -Quantile statistics of the spatial average of snow water equivalent for the CMIP5 models and the multimodel mean, the CanSISE ensemble product for March-April(a) and October-November (b) over the terrestrial Arctic during 1981-2005

  a b c d e f g h i j k n o p q r s

Figure 4 .

 4 Figure 4.22 -Quantile statistics of the spatial average of snow depth for the CMIP5 models and the multimodel mean and the reanalyses (ERA20c, JRA-55 and NOAAV2c) for March-April (a) and October-November (b) over the terrestrial Arctic during 1979-2005.

  ,

  in the Arctic during spring and autumn in the historical runs of CMIP5 climate models and in different observational data sets -various reanalyses, one satellite-based product, an observation-based ensemble product and in situ measurements. For SCE and SND variables, the period of study was 1979-2005 and for SWE the period was 1981-2005. (i) Climatology : • We have found that NOAAV2c displays higher SCE values than NCEP/CFSR in spring and autumn climatologies, they are nonetheless in relatively good agreement. The only discrepancies are located above the Eurasian Dry Land Band (EDLB, Groisman et al., 2018) in Siberia and over the Rocky Mountains in spring and, in autumn, all over the terrestrial Arctic (but smaller in magnitude). CMIP5 models show three different patterns of SCE differences compared to NCEP/CFSR. The first group (bcc-csm1-1, CSIRO-Mk3-6-0 and MPI-ESM-LR/P) generally underestimates SCE, mainly in the south part of Eastern Eurasia. The second group (CanESM2, MIROC-ESM/-CHEM and MRI-CGCM3) displays a broad positive bias over the Rocky Mountains and a negative bias over the southern edge of Western Eurasia. The third group (CNRM-CM5, GISS-E2-H/R and MIROC5) is prone to underestimation in the north and overestimation in the south part of the Arctic. Lastly, the smallest significant differences are found for CCSM4 and NorESM1-M/ME with a negative bias over Western Eurasia and Eastern Canada whereas the south of Eastern Eurasia and Western Canada are characterized by a small positive bias. In autumn, 7 out of 16 models (bcc-csm1-1, CSIRO-Mk3-6-0, the MIROC and MPI versions) show a general underestimation of SCE over the whole terrestrial Arctic. In contrast, five other models (CCSM4, inmcm4, MRI-CGCM3 and NorESM1-M/ME) display a general overestimation, more marked over Eastern Eurasia and North America. GISS-E2-H/R presents a bias dipole with positive bias over Western Eurasia and Eastern Canada and a negative bias over Eastern Eurasia and Western Canada. The remaining models (CanESM2 and CNRM-CM5) show less significant SCE differences, and are generally the closest to observations

Figure 5 .

 5 Figure 5.1 -Taylor diagram used in the evaluation of SCE time series over the Arctic in March-April (a) and in October-November (b) in CMIP5 models (a-p letters). The NCEP/CFSR (Q) and NOAAV2c (R) reanalyses are included versus the satellite-based NOAA CDR (black star). The radial distance to the origin indicates the standard deviation, the centered root-mean-squared error (RMS) is the distance to the reference point (star in x-axis) and the azimuth gives the correlation coefficient R.

Figure 5 . 2 -

 52 Figure 5.2 -Taylor diagram used in the evaluation of SWE time series over the Arctic in March-April (a) and in October-November (b) in CMIP5 models (a-p letters). CanSISE Ensemble product is used as reference (black star). The radial distance to the origin indicates the standard deviation, the centered root-mean-squared error (RMS) is the distance to the reference point (star in x-axis) and the azimuth gives the correlation coefficient R.

Figure 5 . 3 -

 53 Figure 5.3 -Taylor diagram used in the evaluation of SND time series over the Arctic in March-April (a) and in October-November (b) in CMIP5 models(a-p letters). ERA20c (Q) and NOAAV2c (R) reanalyses are included versus the JRA-55 reanalysis (black star) considered here as reference.The radial distance to the origin indicates the standard deviation, the centered root-mean-squared error (RMS) is the distance to the reference point (star in x-axis) and the azimuth gives the correlation coefficient R.

Figure 5 . 4 -

 54 Figure 5.4 -SCE trend in March-April (top row) and October-November (bottom row) during 1979-2005 for the Arctic (a,c) and the subdomains of Eurasia (b,d) and North America (d,f). Trends are computed for each individual model realization (circle), the ensemble model mean (diamond) and the multimodel mean (black square). NCEP/CFSR and NOAAV2c and NOAA CDR are shown in horizontal lines. Shaded regions indicate the ±1 standard error of the trend in the reference data set. Filled markers indicates statistical significance at the 90% of confidence level (t-test). See text or tables in Annex B for statistical significance of the SCE trends in the reference data sets.

Figure 5 . 5 -

 55 Figure 5.5 -SWE trend in March-April (top row) and October-November (bottom row) during 1981-2005 for the Arctic (a,c) and the subdomains of Eurasia (b,d) and North America (d,f). Trends are computed for each individual model realization (circle), the ensemble model mean (diamond) and the multimodel mean (black square). Shaded regions indicate the ±1 standard error of the trend in the CanSISE product. Filled markers indicated statistical significance at 90% of confidence level (t-test). See text or tables in Annex B for statistical significance of the SWE trends in the CanSISE product.

Figure 5 .

 5 Figure 5.6 -SND trend in March-April (top row) and October-November (bottom row) during 1979-2005 for the Arctic (a,c) and the subdomains of Eurasia (b,d) and North America (d,f). Trends are computed for each individual model realization (circle), the ensemble model mean (diamond) and the multimodel mean (black square). ERA20c, JRA-55 and NOAAV2c trends are indicated in horizontal lines. Shaded regions indicate the ±1 standard error of the trend in the reference data set. Filled markers indicated statistical significance at 90% of confidence level (t-test). See text or tables in Annex B for statistical significance of the SND trends in the reference data sets.

Figure 5

 5 Figure 5.7 -Spatial SCE trend in March-April (a) and October-November (b) from the NOAAV2c reanalysis during the period 1979-2005. Statistically significant trends at 90% confidence level from the t-Student are hatched.

  of NCEP/CFSR(Figure 5.8b,d) since NOAAV2c reanalysis shows very weak insignificant trends (Figure5.7). NOAAV2c shows a localized significant decrease in SCE over Scandinavia of almost 8 cm/dec in spring (Figure5.7a). During the onset season (Figure5.7a), the areas with a positive significant SCE trend are located east of the Yenisei River (up to 4 cm/dec) and east of the Lake Baikal (around 10 cm/dec).

Figure 5 .

 5 Figure 5.8b shows NCEP/CFSR trend pattern in SCE in spring. NCEP/CFSR exhibits significant positive trend over the eastern part of Siberia with a maximum up to +12%/dec observed east of the Lake Baikal. Positive SCE trends of +10-12%/dec are also observed over the mountain regions of the western part of North America. Most of Eastern Europe is characterized by significantly negative trends, amounting to -12%/dec over Eastern Scandinavia and south of the Ural

Figure 5 .

 5 9d), SWE in the CanSISE product demonstrates negative trends over northwestern Canada and the south part of Eastern Eurasia and locally positive trends over Northern Eurasia along the coast of the Arctic Ocean. In spring most models report primarily negative trends in SWE over Eastern Eurasia and primarily positive tendencies over Northern Siberia. In autumn (Figure 5.9c), the model ensemble reports negative trends nearly everywhere, with around 8 models showing downward SWE changes in North America and Western Eurasia. Eastern Eurasia is characterized by little consensus among CMIP5 models with estimates showing mostly insignificant trends and less than 4 models out of 16 demonstrating statistically significant trends.

Figure 5

 5 Figure 5.8 -(a,c) Number of CMIP5 models displaying a positive/negative SCE trend in March-April (a) and in October-November (c) during 1979-2005. Only SCE trends statistically significant at the 80% confidence level (t-Student test) are counted.(b,d) Spatial trend of SCE trend (%/dec) from NCEP/CFSR reanalysis in March-April(b) and October-November(d) during 1979-2005. Hatched regions indicate SCE trends statistically significant at the 90% confidence level (t-Student test).

Figure 5

 5 Figure 5.9 -(a,c) Number of CMIP5 models displaying a positive/negative SWE trend in March-April (a) and October-November (c) during 1981-2005.Only SWE trends statistically significant at the 80% confidence level (t-Student test). (b,d) Spatial trend of SWE trend (kg m -2 )/dec) in March-April (b) and October-November (d) during 1981-2005 of CanSISE ensemble product. Hatched regions indicate SWE trends statistically significant at the 90% confidence level (t-Student test).

Figure 5 .

 5 10a), ERA20c shows localized statistical significance over the east of the Canadian Archipelago and east of the Yenisei River, displaying increasing trends of less than + 1.5 cm/dec. Negative significant trends are located over Scandinavia with values as low as -2 cm/dec. During the onset season (Figure5.10b), ERA20c displays a similar pattern of SND trend but twice smaller in magnitude than in spring. Two other regions, the south of Western Eurasia and west side of the Lake Baikal, show statistical significance, with decreasing trends of less than -1.0 cm/dec. The SND trends estimates in both seasons are very weak compared to the in situ data (Figure5.12a ;

Figure 5 .

 5 Figure 5.10 -Spatial SND trend in March-April (a,c) and October-November (b,d) from 1979-2005 from ERA20c (a,c) and JRA-55 (b,d) reanalyses. Statistical significant trends at the 90% confidence level from t-Student are hatched.

Figure 5 .

 5 Figure 5.11 -(a,c) Number of CMIP5 models displaying a positive/negative SND trend in March-April (a) and in October-November (c) during 1979-2005. Only SND trends statistically significant at the 80% confidence level (t-Student test).(b,d) Spatial trend of SND trend (%/dec) from NOAAV2c reanalysis in March-April(b) and October-November(d) during 1979-2005. Hatched regions indicate SND trends statistically significant at the 90% confidence level (t-Student test).

Figure 5 .

 5 Figure 5.12 -Snow depth trends from snow stations in March-April (a) and October-November (b) from 1979-2005.

  Characteristics of snow interannual variability and seasonal trends have been studied in spring and autumn across CMIP5 models and in different data sets -reanalyses, satellite-based products and in situ measurements. The period of study was from 1979 to 2005 for SCE and SND and from 1981 to 2005 for SWE.(i) Interannual variability :• Regarding SCE interannual variability, we have found that the reanalyses NCEP/CFSR and NOAAV2c are in good agreement with NOAA CDR in spring. However, most of CMIP5 ensemble underestimates the amplitude of interannual variability, being twice as small as in observations. During autumn, discrepancies are large between the reference data sets since NOAAV2c displays smaller standard deviation (STD) than NCEP/CFSR and NOAA CDR ; as well as CMIP5 models that still underestimate the amplitude of interannual variability. In addition, both reanalyses correlates negatively with NOAA CDR.• SWE interannual variability is characterized by a large spread in both seasons. In terms of spring STD, three models (CCSM4, MIROC-ESM and MPI-ESM-P) agree with the CanSISE product. Four other models (MIROC5, inmcm4 and NorESM1-ME, MIROC-ESM-CHEM) show larger amplitude of interannual variability than CanSISE product.

FigureFigure A. 2 -

 2 Figure A.1 -Difference of snow cover climatology (1982-2014) of December-January-February (a,d), March-April (b,e) and October-November (c,f) of WACCM minus CAM4 atmospheric model simulations of SST-SIC-EXP (a,b,c) and SIC-EXP (d,e,f) experiments. Only differences with pvalues less than 0.10 from the t-Student test are shown.

Figure A. 3

 3 Figure A.3 shows the quantile statistics of spatial SCE averaged over the land Arctic during the period 1982-2014 for winter (December-January-February), spring (March-April) and autumn (October-November) seasons. It is difficult to make a clear separation across the simulations as discrepancies in SCE average are almost negligible being less than 2 p.p. for all considered seasons.As expected, we found that the amplitude of interannual variability is slightly larger in simulations from SST-SIC-EXP, where both SST and SIC are prescribed with daily variations, than in simulation from SIC-EXP, where SST are set to daily climatology (IQRs inFigure A.3).

Figure A. 3 -

 3 Figure A.3 -Quantile statistics of the spatial average for snow cover of simulations from SST-SIC-EXP and SIC-EXP from CAM4 "low-top" and WACCM "high-top" atmospheric models for winter DJF (a), March-April (b) and October-November (c) over the land Arctic during 1982-2014. Horizontal line represents the spatial average, filled rectangle is the interquartil range (IQR) from Q1 (25th percentile) to Q3 (75th percentile). The IQR provides information about the amplitude of snow interannual variability.

Figure A. 4

 4 Figure A.4 shows the time series of Arctic SCE average from the four simulations for three seasons during 1982-2014. As seen in figure A.1 and A.3, simulations using WACCM atmospheric model have systematically larger SCE throughout the period. During winter, SCE time series shows the lowest amplitude of interannual variability, whereas in spring larger variations are observed.

Figure A. 4 -

 4 Figure A.4 -Time series of Arctic snow cover (1982-2014) of simulations from EXP1 and EXP2 from CAM4 ("low-top") and WACCM ("high-top") atmospheric models in December-January-February (a), March-April (b) and October-November (c).

Figure A. 5 -

 5 Figure A.5 -Snow cover trends of Arctic snow cover of simulations from SST-SIC-EXP and SIC-EXP from CAM4 ("low-top") and WACCM ("high-top") atmospheric models in December-January-February (a), March-April (b) and October-November (c). All SCE trends are statistically significant at the 90% confidence level from the t-Student test.

Figure A. 6 FigureFigure

 6 Figure A.6 shows the spatial patterns of SCE trends. For the first experiment SST-SIC-EXP, snow cover trends in winter are significantly weaker compared to the other seasons (Figure A.5a,b). Slightly positive SCE trends are located in central-east Eurasia and Northern Canada with values less than 1%/dec in both models (Figure A.5a,b). In spring, simulations from CAM4 and WACCM show decreasing significant SCE trends (at the 90% confidence level) over the western and southern part of Eurasia up to 4%/dec over Scandinavia (Figure A.6c,d). Positive significant SCE trends are found locally in central Canada in CAM4, but are not significant in WACCM. During the onset season (Figure A.6e,f), SCE decreasing trends cover almost the whole land Arctic, except over the east part of North America. Maxima SCE trends are located in Scandinavia with values up to 5%/dec. Regarding the second experiment SIC-EXP, winter SCE trends performed are almost indistinguishable from SST-SIC-EXP (Figure A.7a,b). In contrast, for spring and autumn, we have found that SCE trends reported in simulations from SIC-EXP are not statistically significant(Figure A.7c,d,e,f). Significant trends only appear locally in some parts of Western Eurasia in WACCM with values of 2%/dec in spring(Figure A.7a,b). In autumn(Figure A.7c,d), SCE trends of less than 1.5%/dec are located over the Canadian Archipelago and central Siberia.

  SCE annual cycle is almost indistinguishable across all simulations. It is interesting that, in all cases, the simulations are not able to melt snow in summer displaying values of 10-15% during July-August, whereas the coupled model CCSM4 reproduces accurately the observed SCE annual cycle (Figure4.17). This is likely due to absence of a land surface model which is crucial for the heat balance at the surface necessary for melting (M e in Equation2.1).[START_REF] Ogawa | Evaluating impacts of recent Arctic sea ice loss on the northern hemisphere winter climate change[END_REF] did not observe any significant cooling trend in 2 m temperature over Siberia, neither SST-SIC-EXP nor SIC-EXP ; instead, SST-SIC-EXP displayed a strong warming trend during 1982-2014 (∼ 0.5 • C/dec). The connection to the temperature trends found in[START_REF] Ogawa | Evaluating impacts of recent Arctic sea ice loss on the northern hemisphere winter climate change[END_REF] may be related with the negative SCE trends displayed in spring(Figure A.6), that is, the warming found in SST-SIC-EXP in winter may promote an early melt in spring.

  Arctic climate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Spatial and temporal resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.1 General procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

	Introduction	1
	1.1 Methodology	27
	3.1

1.2 Snow and climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Snow formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Snow properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Arctic amplification and its influence on snow . . . . . . . . . . . . . . . . . . . . . . 8 1.4 PhD rationale : Snow representation and objectives . . . . . . . . . . . . . . . . . . . 10 Data 13 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 General Circulation Models (GCMs) . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1 Coupled Model Intercomparison Project 5 : CMIP5 . . . . . . . . . . . . . . . 14 2.2.2 Snow Variables in CMIP5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.1 Snow Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.2 NOAA CDR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.3 CanSISE Ensemble Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.4 Reanalyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.2 Particular cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Ice-free land mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

  Coupled Model Intercomparison Project 5 : CMIP5 . . . . . . . . . . . . . . 14 2.2.2 Snow Variables in CMIP5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.1 Snow Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 General Circulation Models (GCMs) . . . . . . . . . . . . . . . . . . . . . 14 2.2.1 2.3.2 NOAA CDR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.3 CanSISE Ensemble Product . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.4 Reanalyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2.1 Coupled Model Intercomparison Project 5 : CMIP5

As a part of the World Climate Research Program (WCRP), CMIP5 (Taylor et al., 2012, Coupled Model Intercomparison Project Phase 5

Modeling Center (Institut ID) Resolution Nb members

	Reference	bcc-csm1-1 Beijing Climate Center, China Meteorological Administra-2.8 • × 2.8 • 3 Wu et al. (2013)	tion (BCC)	CanESM2 Canadian Center for Climate Modeling and Analysis 2.8 • × 2.8 • 5 Arora et al. (2011)	(CCCMA)	CCSM4 National Center for Atmospheric Research (NCAR) 0.9 • × 1.2 • 8 Gent et al. (2011)	CNRM-CM5 Centre National de Recherches Météorologiques/Centre Eu-1.4 • × 1.4 • 10 Voldoire et al. (2012)	ropéen de Recherche et Formation Avancée en Calcul Scien-	tifique (CNRM-CERFACS)	CSIRO-Mk3-6-0 Commonwealth Scientific and Industrial Research Organiza-1.8 • × 1.8 • 10 Collier et al. (2011)	tion in collaboration with Queensland Climate Change Cen-	ter of Excellence (CSIRO-QCCCE)	GISS-E2-H NASA Goddard Institute for Space Studies (NASA GISS) 2.0 • × 2.5 • 6 Schmidt et al. (2006)	GISS-E2-R 6 Schmidt et al. (2006)	inmcm4 Institute for Numerical Mathematics (INM) 1.5 • × 2.0 • 1 Volodin et al. (2010)	MIROC-ESM-CHEM Japan Agency for Marine-Earth Science and Technology, At-2.8 • × 2.8 • 1 Watanabe et al. (2011)	mosphere and Ocean Research Institute (The University of	Tokyo), and National Institute for Environmental Studies	(MIROC)	MIROC-ESM 2.8 • × 2.8 • 3 Watanabe et al. (2011)	MIROC5 1.4 • × 1.4 • 5 Watanabe et al. (2010)	MPI-ESM-LR Max Planck Institute for Meteorology (MPI-M) 1.8 • × 1.8 • 3 Giorgetta et al. (2013)	MPI-ESM-P 2 Giorgetta et al. (2013)	MRI-CGCM3 Meteorological Research Institute (MRI) 1.1 • × 1.1 • 5 Yukimoto et al. (2012)	NorESM1-M Norwegian Climate Center (NCC) 1.8 • × 2.5 • 3 Bentsen et al. (2013)	NorESM1-ME 2 Bentsen et al. (2013)	Table 2.1 -CMIP5 models, modeling center and institute acronym (https://cmip.llnl.gov/cmip5/), resolution and number of ensemble	members considered.

Table 2 .

 2

	Data set	Spatial Resolution Time coverage	References
	Snow Stations (SND)	In situ	1881-2013	Bulygina et al. (2011)
	NOAA CDR (SCE)	∼ 190.5km × 190.5km	1966 -Present	Robinson et al. (1993)
	CanSISE (SWE)	1.0 • × 1.0 •	1981-2010	Mudryk and Derksen (2017)
	NOAAV2c (SCE ; SND)	2.0 • × 1.75 •	1851-2012	Compo et al. (2011)
	NCEP/CFSR(SCE)	0.5 • × 0.5 •	1979-Present	Saha et al. (2010)
	JRA 55 (SND)	0.5625 • × 0.5625 •	1958-Present	Kobayashi et al. (2015)
	ERA20c (SND)	1.125 • × 1.125 •	1900-2010	Poli et al. (2016)

is the first atmospheric reanalysis from ECMWF (European Centre for Medium-Range Weather Forecasts) from 1900 to 2010. It assimilates observation of surface pressure and surface marine winds. The temporal resolution of the snow depth variable is 6-hourly. It is a coupled atmosphere/land-surface/ocean-waves model with 91 atmospheric levels (from surface to 0.01 hPa) and 4 soil layers. The horizontal spatial resolution is approximately 1.125 • × 1.125 • (spectral truncation T159). We used snow depth from this reanalysis which is available for download at https://apps.ecmwf.int/datasets/data/ era20c-ofa/. 2 -Major characteristics of observational data sets compared in this study.

Table 3 .

 3

		Standard name	Long name (Units)	Comment	Criteria of
					masking
	sftlf	land area fraction	Land Area Fraction (%)		< 50%
	sftgif	land ice area fraction Fraction of Grid Cell	(fraction of grid	>15%
			Covered with Glacier	cell occupied by
			(%)	"permanent ice"
				(i.e., glaciers)

3 -Criteria of ice-free land mask in CMIP5 models. Definition of variables extracted from the document "CMIP5 output metadata requirements.pdf" from https://cmip.llnl.gov/ cmip5/docs/.

Table 3 .

 3 4 -Criteria of conversion from snow fraction to binary.

	Bin	Bin	Bin	Bin
	Member 1	Member 2	Member 3	Ensemble Mean

3 Quantile statistics of the spatial average

  Snow cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.2 Snow water equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.1 Climatology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.1 4.1.3 Snow depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2 Annual Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2.1 Snow cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2.2 Snow water equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2.3 Snow depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.. . . . . . . . . . . . . . . . . . . 69 4.3.1 Snow cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3.2 Snow water equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.3.3 Snow depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

  Northern Alaska, the Canadian Archipelago and the northern part of Eastern Eurasia. Over North America, high values of SCE are observed in the Brooks mountain range in Alaska, in the Mackenzie Mountains in the northwest of Canada and over the Canadian Archipelago. In the Rocky Mountains in Western Canada, SCE values are around 50%. Over Eurasia, the maximum of SCE is observed First, we assess the differences of climatology between both reanalyses, NCEP/CFSR and NOAAV2c, for spring and autumn from 1979 to 2005 (Figure4.2). In March-April (Figure4.2a), there is a good agreement over north central and far eastern Siberia as well as over east central Canada and over the Canadian Archipelago. By contrast, the mismatch occurs above the Eurasian Dry Land Band(EDLB, Groisman et al., 2018) in Siberia with differences up to 50 p.p. 1 SCE east of the Lake Baikal. Additionally, NOAAV2c displays excess of SCE compared to NCEP/CFSR over the Rocky Mountains reaching 60 p.p. values. This local strong disagreement is likely due to a better resolved topography in NCEP/CFSR which makes it more sensitive to temperature changes that reduce SCE earlier in the season than NOAAV2c. In Scandinavia, differences are reversed and NCEP/CFSR estimates a slightly larger SCE than NOAAV2c but only by about 15 p.p. and very locally. Averaged over each of the subdomains NOAAV2c displays overestiamation by 6 p.p. For example, if the model displays 80 % of SCE and the reanalysis, 30 % SCE, the difference is 50 p.p. not 50 % as this can induce to wrongly state that the model is doubling the value of the reanalysis.

	Differences of climatology
	csm1-1,
	CSIRO-Mk3-6-0 and both versions of MPI-ESM-LR/P ; Figure 4.3a,e,l,m) generally underestimates
	snow cover compared to NCEP/CFSR by almost 50 p.p. with the largest differences observed in the
	southern part of Western Eurasia. The second group (CanESM2, MIROC-ESM/-CHEM and MRI-

. In the southern part of Western Eurasia, snow has almost melted with SCE being around 15% whereas in Scandinavia, SCE values of 80-100% are observed northern of 60 • N. Over North America, the decrease in SCE from north to south is more pronounced than over Eurasia in both seasons.

In October-November (Figure

4

.1b), the maximum SCE (from 80% to 100%) is observed over over the northern part of Eastern Siberia with maxima of 90% to 100% over the Verkhoyansk, Chersky and Kolyma mountain ranges.

in Eurasia and by 8 p.p. in North America in comparison with NCEP/CFSR (Tables

B.2 and B

.3, respectively)

. During the onset season (Figure

4

.2b), NOAAV2c shows larger values of SCE than NCEP/CFSR over the whole terrestrial Arctic. Over North America differences are greater than in Eurasia, being of 15-20 p.p. in the southern part and 30-40 p.p. over the Canadian Archipelago ; however, averaged over North America, the discrepancy is only 12 p.p.

(Table B.6

). Differences across Eurasia cover the continent uniformly with NOAAV2c displaying less than 15 p.p. SCE exceeding NCEP/CFSR. On average the difference between both reanalyses over Eurasia is equal to 8 p.p.

SCE (Table

B

.5). Overall, both reanalyses agree on the representation of SCE during the melting and onset seasons.

We now turn to the evaluation of snow cover climatology across the ensemble of CMIP5 models (Table

2

.1) in the mid-seasons during the present period from 1979 to 2005. Figure 4.3 shows the differences between March-April SCE climatology in each of the selected CMIP5 models minus the NCEP/CFSR reanalysis. We can separate all models by three groups. The first group (bcc-1. The arithmetic difference of two percentages is expressed in percentage points or percent points [pp] or [p.p.].

2 Seasonal trend analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

  Snow cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.1.2 Snow water equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.1.3 Snow depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.5.2.1 Snow cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.2.2 Snow water equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2.3 Snow depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.

	5.1 Interannual variability of snow characteristics . . . . . . . . . . . . . . . 79
	5.1.1

3 Spatial trend pattern

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.3.1 Snow cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3.2 Snow water equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.3 Snow depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Table 6 .

 6 1 -Main characteristics of the spatial structure and temporal variability of snow representation in individual CMIP5 models. * Dipole Pattern : Overestimation over Western North America and Eastern Eurasia and underestimation over Eastern North America and Western Eurasia. "MA" and "ON" refer to March-April and October-November. The abbreviations for the Arctic and its subdomains are indicated in Table1.1.dynamics could have played a major role in the observed wintertime Siberian temperature trends.

  from two atmospheric circulations models forced by prescribed sea surface temperature (SST) and sea ice concentration (SIC) from National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation 1/ Degree Daily Surface Temperature Analysis version 2, AVHRR-only product[START_REF] Reynolds | Daily high-resolution-blended analyses for sea surface temperature[END_REF] http://www.ncdc.noaa.gov/sst/index.php). The first atmospheric model employed is the Community Atmosphere Model (CAM4,[START_REF] Neale | The mean climate of the Community Atmosphere Model (CAM4) in forced SST and fully coupled experiments[END_REF] with a horizontal resolution of 0.9 • × 1.25 • and 26 vertical levels from surface to 3 hPa. We refer to it as "low top" model and it is the atmospheric component of the general circulation model of CCSM4(Gent et al., 2011, Table 2.1). The second model is the Whole Atmosphere Community Climate Model (WACCM,[START_REF] Marsh | Climate change from 1850 to 2005 simulated in CESM1 (WACCM)[END_REF] and it

Table A

 A -0.31 ± 0.10%/dec in experiment SIC-EXP. While stronger significant SCE trends are found in SST-SIC-EXP of -0.51 ± 0.16%/dec and -0.55 ± 0.16%/dec in CAM4 and WACCM, respectively. 05%/dec in WACCM. From the larger discrepancies of SCE trends in autumn compared to the other seasons we can conclude that the onset of snow cover is more affected by summer sea ice reduction than the snow accumulation (winter) or melting snow seasons (spring).

	The differences in autumn SCE trends between both experiments are larger than in spring
	(Figure A.5c). In SST-SIC-EXP, both models shows stronger trends of -0.60 ± 0.08%/dec and
	-0.55 ± 0.10%/dec close to the SCE trends displayed by CCSM4 (-0.89 ± 0.12%/dec) but for
	1979-2005. By contrast, SIC-EXP displays weaker trends of -0.16 ± 0.06%/dec in CAM4 and
	-0.16 ± 0.
	.1), SCE trends are weaker compared to the other seasons. Stronger
	trends are displayed by simulations from SST-SIC-EXP experiment showing -0.17 ± 0.07%/dec and
	-0.18 ± 0.07%/dec using CAM4 and WACCM, respectively. Weaker,but still significant, trends are

found in SIC-EXP being of -0.07 ± 0.04%/dec in CAM4 and -0.09 ± 0.04%/dec in WACCM. In spring

(Figure A.5b,Table A.2)

, SCE trends from CAM4 and WACCM are -0.30 ± 0.11%/dec and

Table A .

 A ). All SCE trends are statistically significant at the 90% confidence level from the t-Student test.

			ARC Mar-Apr
	Model and experiment	µ [%]	σ µ [%]	T [%/dec] σ T [%/dec] p-value
	CAM4 SST-SIC-EXP	63.18	1.00	-0.51	0.16	0.004
	WACCM SST-SIC-EXP 64.79	1.00	-0.55	0.16	0.002
	CAM4 SIC-EXP	63.51	0.65	-0.30	0.11	0.011
	WACCM SIC-EXP	65.14	0.61	-0.31	0.10	0.005
	Table A.2 -Spring (March-April) Arctic SCE mean (i.e., µ), standard deviation (i.e., σ µ ), trend
	(i.e., T), standard error (i.e., σ T ) and p-value from the trend (1982-2014) from SST-SIC-EXP and
	SIC-EXP simulations using CAM4 and WACCM atmospheric models.
			ARC Oct-Nov
	Model and experiment	µ [%]	σ µ [%]	T [%/dec] σ T [%/dec] p-value
	CAM4 SST-SIC-EXP	84.43	0.73	0.60	0.08	e-08
	WACCM SST-SIC-EXP 85.42	0.74	-0.55	0.10	e-06
	CAM4 SIC-EXP	84.66	0.35	-0.16	0.06	0.013
	WACCM SIC-EXP	85.71	0.32	-0.16	0.05	0.0037
			ARC DJF
	Model and experiment	µ [%]	σ µ [%]	T [%/dec] σ T [%/dec] p-value
	CAM4 SST-SIC-EXP	90.33	0.37	-0.17	0.07	0.02
	WACCM SST-SIC-EXP 91.27	0.38	-0.18	0.07	0.01
	CAM4 SIC-EXP	90.37	0.20	-0.07	0.04	0.09
	WACCM SIC-EXP	91.40	0.20	-0.09	0.04	0.02

Table

A

.1 -Winter (December-January-February) Arctic SCE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend (1982-2014) from SST-SIC-EXP and SIC-EXP simulations using CAM4 and WACCM atmospheric models. 3 -Autumn (October-November) Arctic SCE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend (1982-2014) from SST-SIC-EXP and SIC-EXP simulations using CAM4 and WACCM atmospheric models.

  TableB.1 -Spring (March-April) Arctic SCE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1979-2005.TableB.2 -Spring (March-April) Eurasian subdomain SCE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e.,σ T ) and p-value from the trend for the period 1979-2005.TableB. North American subdomain SCE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e.,σ T ) and p-value from the trend for the period 1979-2005.TableB.4 -Autumn (October-November) Arctic SCE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e.,σ T ) and p-value from the trend for the period 1979-2005.TableB.5 -Autumn (October-November) Eurasian subdomain SCE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e.,σ T ) and p-value from the trend for the period 1979-2005.TableB.6 -Autumn (October-November) North American subdomain SCE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1979-2005.TableB.7 -Spring (March-April) Arctic SWE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1981-2005.TableB.9 -Spring (March-April) North American subdomain SWE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1981-2005.TableB.11 -Autumn (October-November) Eurasian subdomain SWE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1981-2005.TableB.12 -Autumn (October-November) North American SWE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1981-2005.TableB.14 -Spring (March-April) Eurasian subdomain SND mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1979-2005.TableB.15 -Spring (March-April) North American subdomain SND mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1979-2005.TableB.17 -Autumn (October-November) Eurasian subdomain SND mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1979-2005.TableB.18 -Autumn (October-November) North American SND mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period1979-2005.

				ARC-MarApr NAm-MarApr NAm-OctNov NAm-MarApr
		µ	µ	µ µ	σ µ σ µ	σ µ σ µ	T T	T T	σ T	σ T	p-value p-value p-value p-value σ T σ T
	Data sets Data sets Data sets Data sets	[kg m -2 ] [kg m -2 ] [kg m -2 ] [cm]	[kg m -2 ] [kg m -2 ] [kg m -2 ] [cm]	[kg m -2 /dec] [kg m -2 /dec] [kg m -2 /dec] [kg m -2 /dec] [kg m -2 /dec] [kg m -2 /dec] [cm / dec] [cm/ dec]
	bcc-csm1-1 bcc-csm1-1 bcc-csm1-1 bcc-csm1-1	84.98 113.98 59.54 37.41	3.87 2.73 8.06 3.41	-0.76 -2.36 -2.62 -1.12	1.11 0.66	2.28 0.82 0.10	0.50	0.31 0.00
	CanESM2 CanESM2 CanESM2 CanESM2	107.50 142.52 59.69 40.51	3.80 1.76 7.11 3.79	-2.97 -4.22 -3.08 -1.09	0.91 0.40	1.86 0.89 0.01	0.00	0.03 0.00
	CCSM4 CCSM4 CCSM4 CCSM4	127.64 156.65 68.70 48.16	4.28 1.98 6.51 3.47	-3.23 -4.51 -3.54 -1.45	1.04 0.42	1.63 0.68 0.00	0.00	0.01 0.00
	CNRM-CM5 CNRM-CM5 CNRM-CM5 CNRM-CM5	131.28 159.44 58.65 53.56	2.67 1.42 4.20 2.62	-2.86 -4.28 -2.95 -1.40	0.49 0.23	0.82 0.44 0.00	0.00	0.00 0.00
	CSIRO-Mk3-6-0 CSIRO-Mk3-6-0 CSIRO-Mk3-6-0 CSIRO-Mk3-6-0	32.82 39.61 39.91 16.27	1.16 0.73 1.88 1.62	-1.22 -1.35 -0.98 -0.42	0.22 0.17	0.47 0.42 0.02	0.00	0.01 0.03
	GISS-E2-H GISS-E2-H GISS-E2-H GISS-E2-H	108.44 115.97 56.73 34.28	3.82 1.75 6.01 2.22	-3.55 -6.06 -1.40 -1.58	0.82 0.32	1.19 0.57 0.00	0.00	0.00 0.02
	GISS-E2-R GISS-E2-R GISS-E2-R GISS-E2-R	105.47 108.71 51.20 34.91	3.27 1.33 4.58 2.28	-1.91 -2.91 -1.62 -0.98	0.86 0.28	1.18 0.57 0.00	0.04	0.02 0.01
	inmcm4 inmcm4 inmcm4 inmcm4	72.89 81.47 50.11 16.64	6.60 11.83 5.72 1.84	1.26 0.35 1.60 4.65	1.89 0.47	3.28 1.62 0.45	0.51	0.17 0.33
	µ [%] 43.65 65.66 57.43 64.64 37.23 58.84 58.14 44.97 62.92 MIROC-ESM-CHEM 61.63 Data sets bcc-csm1-1 CanESM2 CCSM4 CNRM-CM5 CSIRO-Mk3-6-0 GISS-E2-H GISS-E2-R inmcm4 MIROC-ESM MIROC5 65.42 MPI-ESM-LR 39.38 MPI-ESM-P 33.92 MRI-CGCM3 69.69 NorESM1-M 57.69 NorESM1-ME 59.13 NCEP/CFSR 80.43 NOAAV2c 85.14 NOAA CDR 85.11 CMIP5 55.02 Data sets [%] µ bcc-csm1-1 38.12 CanESM2 64.07 CCSM4 51.99 CNRM-CM5 62.40 CSIRO-Mk3-6-0 36.23 GISS-E2-H 59.18 GISS-E2-R 58.47 inmcm4 46.47 MIROC-ESM 61.54 MIROC-ESM-CHEM 61.58 MIROC5 62.51 MPI-ESM-LR 36.66 MPI-ESM-P 33.19 MRI-CGCM3 64.10 NorESM1-M 54.42 NorESM1-ME 55.27 NCEP/CFSR 77.46 NOAAV2c 82.17 NOAA CDR 82.25 CMIP5 52.89 NAm-MarApr σ µ [%] 1.44 1.43 1.41 1.10 1.02 1.41 1.26 2.67 3.67 2.10 1.50 1.38 1.83 1.06 1.61 1.62 2.31 2.44 2.83 1.00 EURA-MarApr T [%/dec] [%/dec] σ T -1.11 0.30 -1.51 0.21 -1.44 0.22 -1.22 0.14 -1.04 0.16 -1.39 0.23 -1.05 0.25 0.28 0.68 -2.28 0.83 -1.87 0.39 -1.59 0.22 -0.58 0.34 -0.77 0.44 -0.22 0.27 -1.20 0.34 -0.54 0.40 0.41 0.59 -1.21 0.58 -1.26 0.68 -1.10 0.13 σ µ T [%] [%/dec] [%/dec] p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.68 0.01 0.00 0.00 0.10 0.09 0.41 0.00 0.19 0.50 0.05 0.08 0.00 σ T p-value 2.10 -0.85 0.51 0.11 1.65 -1.70 0.25 0.00 1.78 -1.60 0.33 0.00 1.25 -1.26 0.20 0.00 1.13 -1.10 0.19 0.00 1.12 -0.97 0.21 0.00 1.33 -0.93 0.29 0.00 3.99 0.40 1.02 0.70 3.91 -1.28 0.97 0.20 2.61 -2.27 0.49 0.00 1.83 -2.04 0.23 0.00 1.87 -0.64 0.46 0.18 3.02 -0.57 0.77 0.47 1.38 -0.02 0.35 0.95 2.12 -1.04 0.50 0.05 2.24 -0.22 0.57 0.70 3.20 0.03 0.82 0.97 3.73 -1.42 0.91 0.13 3.94 -1.79 0.95 0.07 1.03 -1.01 0.17 0.00 µ σ µ T σ T p-value Data sets [%] [%] [%/dec] [%/dec] bcc-csm1-1 51.80 2.41 -1.49 0.54 0.01 CanESM2 67.56 1.65 -1.28 0.34 0.00 CCSM4 64.11 1.79 -1.26 0.39 0.00 CNRM-CM5 67.51 1.16 -1.16 0.19 0.00 CSIRO-Mk3-6-0 38.56 1.22 -0.97 0.25 0.00 GISS-E2-H 58.39 2.11 -1.96 0.37 0.00 GISS-E2-R 57.68 1.48 -1.21 0.29 0.00 inmcm4 43.09 3.72 0.14 0.95 0.88 MIROC-ESM 65.09 5.66 -3.84 1.23 0.00 MIROC-ESM-CHEM 61.72 2.65 -1.26 0.63 0.06 MIROC5 68.46 1.81 -1.12 0.41 0.01 MPI-ESM-LR 43.47 2.21 -0.48 0.56 0.40 MPI-ESM-P 35.01 2.67 -1.08 0.65 0.11 MRI-CGCM3 76.49 1.08 -0.47 0.26 0.08 NorESM1-M 61.95 2.61 -1.41 0.61 0.03 NorESM1-ME 64.15 2.84 -0.96 0.70 0.18 NCEP/CFSR 83.80 2.91 0.83 0.73 0.27 NOAAV2c 89.82 2.83 -0.87 0.71 0.23 NOAA CDR 90.13 2.96 -0.33 0.76 0.67 CMIP5 57.81 1.13 -1.24 0.15 0.00 EURA-OctNov NAm-OctNov MIROC-ESM 104.07 10.05 -5.76 2.65 MIROC-ESM 110.39 17.20 -12.41 4.25 MIROC-ESM 51.73 6.60 -5.04 1.59 MIROC-ESM 37.47 5.60 -2.77 1.33 0.05 ARC-OctNov µ σ µ T σ T p-value Data sets [%] [%] [%/dec] [%/dec] bcc-csm1-1 59.16 1.15 -0.98 0.22 µ σ µ T σ T p-value Data sets [%] [%] [%/dec] [%/dec] bcc-csm1-1 56.68 1.37 -0.79 0.31 0.02 µ σ µ T p-value MIROC-ESM-CHEM 100.40 4.37 -3.93 0.96 MIROC-ESM-CHEM 101.60 6.90 -5.12 1.68 EURA-OctNov MIROC-ESM-CHEM 51.67 3.76 -4.33 0.61 EURA-MarApr MIROC-ESM-CHEM 34.79 2.21 -1.18 0.52 0.03 EURA-OctNov NAm-OctNov σ T Data sets [%] [%] [%/dec] [%/dec] bcc-csm1-1 62.81 1.34 -1.26 0.24 0.00 MIROC5 112.21 6.47 -8.02 0.84 MPI-ESM-LR 64.39 2.78 -0.49 0.80 MIROC5 131.41 10.84 -12.80 1.64 MPI-ESM-LR 72.23 4.46 0.53 1.28 µ σ µ T σ T Data sets [kg m -2 ] [kg m -2 ] [kg m -2 /dec] [kg m -2 /dec] MIROC5 64.33 9.72 -12.47 1.06 MPI-ESM-LR 39.86 2.56 -0.49 0.73 µ σ µ T σ T p-value Data sets [cm] [cm] [cm / dec] [cm/ dec] MIROC5 44.97 3.84 -4.33 0.47 0.00 MRI-CGCM3 47.37 1.48 -0.37 0.37 µ σ µ T σ T p-value µ σ µ T p-value 0.04 0.00 0.00 0.54 p-value 0.01 0.00 0.01 0.00 0.00 0.68 0.00 0.51 σ T 0.33 Data sets [cm] [cm] [cm / dec] [cm/ dec] Data sets [cm] [cm] [cm / dec] [cm/ dec] 0.00 CanESM2 69.97 1.03 -0.68 0.23 CanESM2 69.33 1.37 -0.14 0.35 0.69 CanESM2 70.74 1.70 -1.32 0.35 0.00 MPI-ESM-P 50.91 4.30 -2.75 1.10 0.02 MPI-ESM-P 54.36 6.53 -3.91 1.70 0.03 bcc-csm1-1 42.93 1.96 -0.59 0.55 0.30 MPI-ESM-P 37.43 3.12 -0.61 0.89 0.50 bcc-csm1-1 23.76 1.78 -0.21 0.45 0.65 NorESM1-M 43.83 3.10 -2.01 0.69 0.01 bcc-csm1-1 24.24 1.15 -0.62 0.27 0.03 bcc-csm1-1 29.90 1.54 -1.17 0.32 0.00 0.01 CCSM4 81.12 0.84 -0.89 0.12 CCSM4 78.46 1.07 -0.83 0.22 0.00 CCSM4 84.38 1.10 -0.97 0.21 0.00 MRI-CGCM3 147.91 3.64 -0.85 1.04 0.42 MRI-CGCM3 185.43 5.50 0.57 1.59 0.72 CanESM2 36.13 1.59 0.44 0.45 0.34 MRI-CGCM3 73.86 2.48 1.38 0.66 0.05 CanESM2 25.99 1.12 -0.96 0.21 0.00 NorESM1-ME 48.64 3.06 -1.48 0.73 0.05 CanESM2 13.53 0.52 -0.02 0.13 0.89 CanESM2 19.34 1.19 -0.92 0.25 0.00 0.00 CNRM-CM5 64.31 0.92 -0.93 0.15 CNRM-CM5 64.33 1.04 -0.82 0.21 0.00 CNRM-CM5 64.29 1.15 -1.07 0.20 0.00 NorESM1-M 111.10 5.52 -4.59 1.28 0.00 NorESM1-M 137.01 9.52 -5.12 2.54 0.06 CCSM4 49.93 1.53 -0.93 0.40 0.03 NorESM1-M 100.71 4.13 -1.40 1.16 0.24 CCSM4 34.88 1.46 -0.94 0.32 0.01 ERA20c 31.27 1.05 -0.43 0.26 0.11 CCSM4 26.73 0.75 -0.43 0.17 0.02 CCSM4 32.58 1.40 -1.28 0.25 0.00 0.00 CSIRO-Mk3-6-0 56.72 0.74 -0.55 0.16 CSIRO-Mk3-6-0 57.78 0.90 -0.45 0.21 0.05 CSIRO-Mk3-6-0 55.33 0.83 -0.69 0.16 0.00 NorESM1-ME 127.63 6.23 -3.96 1.60 0.02 NorESM1-ME 160.18 11.77 -8.20 2.94 0.01 CNRM-CM5 47.67 1.16 -0.71 0.30 0.03 NorESM1-ME 79.45 7.08 -7.12 1.41 0.00 CNRM-CM5 37.40 0.90 -0.67 0.19 0.00 JRA-55 38.28 8.56 -7.43 1.62 0.00 CNRM-CM5 16.98 0.43 -0.29 0.09 0.01 CNRM-CM5 20.75 0.89 -0.93 0.14 0.00 0.00 GISS-E2-H 71.77 0.82 -0.55 0.18 GISS-E2-H 72.30 0.94 -0.46 0.22 0.05 GISS-E2-H 71.06 0.97 -0.67 0.21 0.00 CanSISE 58.84 4.39 -1.09 1.25 0.39 CanSISE 58.57 7.08 -1.67 2.02 0.42 CSIRO-Mk3-6-0 32.90 0.98 -0.14 0.28 0.62 CanSISE 39.07 4.38 -0.70 1.26 0.58 CSIRO-Mk3-6-0 11.68 0.44 -0.32 0.09 0.00 NOAAV2c 44.76 6.06 -1.88 1.51 0.22 CSIRO-Mk3-6-0 13.35 0.39 0.00 0.10 0.97 CSIRO-Mk3-6-0 16.01 0.64 -0.39 0.14 0.01 0.01 GISS-E2-R 68.53 1.09 -0.94 0.21 GISS-E2-R 70.01 1.24 -1.00 0.25 0.00 GISS-E2-R 66.53 1.12 -0.86 0.23 0.00 CMIP5 99.35 2.38 -2.85 0.34 0.00 CMIP5 116.93 3.60 -4.22 0.56 0.00 GISS-E2-H 54.53 1.79 -0.21 0.52 0.69 CMIP5 58.97 2.23 -2.79 0.28 0.00 GISS-E2-H 33.24 1.12 -0.62 0.26 0.03 CMIP5 38.49 1.27 -1.42 0.16 0.00 GISS-E2-H 24.52 0.55 -0.26 0.13 0.05 GISS-E2-H 23.35 1.01 -0.74 0.21 0.00 0.00 inmcm4 77.27 1.12 0.23 0.29 inmcm4 80.65 2.42 1.25 0.57 0.04 inmcm4 73.04 1.78 -1.05 0.41 0.02 GISS-E2-R 53.60 2.07 -0.89 0.57 0.13 GISS-E2-R 33.64 1.04 -0.38 0.25 0.15 GISS-E2-R 24.60 0.80 -0.50 0.18 0.01 GISS-E2-R 22.61 0.82 -0.54 0.18 0.01 0.43 MIROC-ESM 60.16 2.96 -1.48 0.70 MIROC-ESM 58.77 3.52 -1.03 0.88 0.25 MIROC-ESM 62.33 3.73 -2.18 0.85 0.02 inmcm4 44.91 3.48 1.12 0.98 0.27 inmcm4 16.84 1.68 0.01 0.43 0.99 inmcm4 17.40 0.91 0.40 0.22 0.08 inmcm4 16.72 1.32 0.09 0.34 0.78 0.04 MIROC-ESM-CHEM 60.06 1.60 -1.05 0.35 MIROC-ESM-CHEM 58.72 1.62 -0.48 0.41 0.24 MIROC-ESM-CHEM 62.16 2.04 -1.93 0.35 0.00 MIROC-ESM 46.13 4.81 -0.72 1.38 0.61 MIROC-ESM 34.45 3.78 -0.84 0.96 0.39 MIROC-ESM 15.71 1.56 -0.25 0.40 0.54 MIROC-ESM 17.67 2.27 -1.46 0.50 0.01 0.01 MIROC5 55.33 1.12 -1.12 0.18 MIROC5 54.36 0.99 -0.45 0.24 0.07 MIROC5 56.36 1.84 -1.83 0.30 0.00 EURA-MarApr MIROC-ESM-CHEM 46.35 2.21 -0.79 0.62 0.21 MIROC-ESM-CHEM 34.17 1.53 -1.02 0.34 0.01 MIROC-ESM-CHEM 15.74 0.78 -0.23 0.20 0.25 MIROC-ESM-CHEM 17.71 1.27 -1.35 0.18 0.00 0.00 MPI-ESM-LR 61.08 1.24 -0.49 0.30 0.12 MPI-ESM-P 59.99 1.86 -0.77 0.45 0.10 MRI-CGCM3 84.91 0.64 -0.13 0.16 MPI-ESM-LR 58.85 1.47 -0.34 0.37 0.37 MPI-ESM-P 58.10 2.52 -0.86 0.62 0.18 MRI-CGCM3 84.31 1.05 -0.07 0.27 0.81 MPI-ESM-LR 64.42 1.38 -0.71 0.32 0.04 MPI-ESM-P 62.84 2.52 -0.62 0.64 0.33 MRI-CGCM3 85.65 0.61 -0.21 0.15 0.18 µ σ µ T p-value ARC-OctNov MIROC5 44.96 1.23 -0.34 0.35 0.34 ARC-MarApr MIROC5 32.36 1.18 -1.03 0.22 0.00 ARC-OctNov MIROC5 15.44 0.45 -0.23 0.11 0.04 MIROC5 22.48 3.53 -4.22 0.33 0.00 σ T Data sets [kg m -2 ] [kg m -2 ] [kg m -2 /dec] [kg m -2 /dec] bcc-csm1-1 65.32 5.12 0.33 1.48 0.82 µ σ µ T σ T p-value Data sets [kg m -2 ] [kg m -2 ] [kg m -2 /dec] [kg m -2 /dec] MPI-ESM-LR 37.99 2.14 -1.13 0.57 0.06 MPI-ESM-P 36.43 2.59 -1.64 0.67 0.02 µ σ µ T σ T p-value Data sets [cm] [cm] [cm / dec] [cm/ dec] MRI-CGCM3 32.16 1.14 -0.24 0.29 0.41 NorESM1-M 34.97 1.72 -1.02 0.39 0.02 µ σ µ T p-value MRI-CGCM3 21.34 0.52 -0.28 0.12 0.03 MRI-CGCM3 25.95 0.75 0.03 0.19 0.89 σ T Data sets [cm] [cm] [cm / dec] [cm/ dec] NorESM1-M 25.35 1.35 -0.87 0.30 0.01 NorESM1-M 30.42 1.44 -0.70 0.34 0.05 0.43 NorESM1-M 80.10 1.22 -0.79 0.27 NorESM1-M 78.29 1.94 -0.98 0.46 0.04 NorESM1-M 82.45 1.19 -0.54 0.29 0.07 CanESM2 85.13 2.99 -2.16 0.74 0.01 bcc-csm1-1 49.64 2.03 -1.41 0.51 0.01 MRI-CGCM3 54.23 1.67 -0.75 0.46 0.11 bcc-csm1-1 29.27 1.35 -0.58 0.33 0.09 NorESM1-ME 35.59 1.88 -0.07 0.48 0.88 bcc-csm1-1 26.52 1.06 -0.84 0.21 0.00 NorESM1-ME 25.67 1.11 -0.63 0.26 0.02 NorESM1-ME 33.29 2.23 -1.65 0.47 0.00 0.01 NorESM1-ME 80.57 0.95 -0.45 0.23 NorESM1-ME 78.43 1.38 -0.16 0.35 0.65 NorESM1-ME 83.36 1.35 -0.82 0.31 0.01 CCSM4 103.82 4.53 -2.17 1.23 0.09 CanESM2 45.32 1.57 -0.93 0.41 0.03 NorESM1-M 61.11 3.18 -2.69 0.73 0.00 CanESM2 32.59 1.21 -1.02 0.24 0.00 ERA20c 8.66 0.65 -0.19 0.16 0.25 CanESM2 16.17 0.58 -0.43 0.12 0.00 ERA20c 4.86 0.35 -0.09 0.09 0.30 ERA20c 24.02 0.55 -0.10 0.14 0.49 0.06 NCEP/CFSR 56.20 4.66 -1.61 1.15 NCEP/CFSR 53.51 5.61 -1.84 1.39 0.20 NCEP/CFSR 59.26 4.78 -1.35 1.20 0.27 CNRM-CM5 109.22 2.52 -1.75 0.63 0.01 CCSM4 58.40 2.03 -2.11 0.39 0.00 NorESM1-ME 48.39 2.96 -2.26 0.71 0.00 CCSM4 40.87 1.38 -1.17 0.27 0.00 JRA-55 21.98 2.21 -0.76 0.55 0.18 CCSM4 29.37 0.88 -0.81 0.16 0.00 JRA-55 20.36 1.76 -0.89 0.42 0.04 JRA-55 26.65 4.85 -2.49 1.14 0.04 0.18 NOAAV2c 62.38 2.36 -0.76 0.59 NOAAV2c 60.46 3.11 -0.36 0.80 0.65 NOAAV2c 65.40 4.02 -1.38 1.00 0.18 CSIRO-Mk3-6-0 27.68 1.07 -1.13 0.20 0.00 CNRM-CM5 52.49 1.54 -1.69 0.27 0.00 CanSISE 41.27 2.76 -0.59 0.79 0.47 CNRM-CM5 44.50 0.95 -0.99 0.14 0.00 NOAAV2c 36.07 3.90 -1.64 0.95 0.10 CNRM-CM5 18.64 0.54 -0.57 0.08 0.00 NOAAV2c 35.35 2.39 -0.50 0.61 0.42 NOAAV2c 39.75 4.54 -1.52 1.12 0.19 0.21 NOAA CDR 66.88 4.37 3.29 0.91 CMIP5 68.19 0.72 -0.72 0.12 0.00 CMIP5 67.46 0.66 -0.48 0.14 0.00 CMIP5 69.23 0.96 -1.05 0.13 GISS-E2-R 103.26 3.45 -1.23 0.96 0.22 GISS-E2-H 55.45 1.53 -0.71 0.42 0.10 GISS-E2-H 33.68 1.11 -1.02 0.20 0.00 GISS-E2-H 24.02 0.60 -0.46 0.12 0.00 0.00 0.00 NOAA CDR 64.11 4.81 3.67 0.99 0.00 NOAA CDR 71.73 5.00 2.62 1.17 0.03 GISS-E2-H 103.00 3.71 -1.74 1.01 0.10 CSIRO-Mk3-6-0 35.91 0.87 -0.50 0.23 0.04 CMIP5 46.14 0.87 -0.77 0.19 0.00 CSIRO-Mk3-6-0 13.65 0.45 -0.37 0.09 0.00 CMIP5 30.08 0.67 -0.59 0.13 0.00 CSIRO-Mk3-6-0 14.49 0.35 -0.16 0.08 0.06 CMIP5 20.04 0.36 -0.30 0.07 0.00 CMIP5 23.49 0.91 -1.09 0.09 0.00
	inmcm4 GISS-E2-R GISS-E2-R GISS-E2-R	66.03 52.63 34.18 23.76	8.23 1.88 0.99 0.71	-1.45 -1.19 -0.63 -0.51	0.22 0.15	2.36 0.48 0.01 0.00	0.55 0.02
	MIROC-ESM inmcm4 inmcm4 inmcm4	100.04 47.22 16.75 17.10	11.45 3.56 1.18 0.84	-1.52 1.33 0.16 0.26	0.30 0.21	3.30 0.99 0.60 0.22	0.65 0.19
	MIROC-ESM-CHEM MIROC-ESM MIROC-ESM MIROC-ESM	99.63 48.31 35.62 16.47	4.64 4.22 3.25 1.40	-3.17 -2.40 -1.59 -0.72	0.77 0.33	1.17 1.11 0.05 0.04	0.01 0.04
	MIROC5 MIROC-ESM-CHEM 93.87 48.42 MIROC-ESM-CHEM 34.41 MIROC-ESM-CHEM 16.51	3.51 2.41 1.41 0.82	-3.45 -2.17 -1.08 -0.67	0.29 0.16	0.71 0.53 0.00 0.00	0.00 0.00
	MPI-ESM-LR MIROC5 MIROC5 MIROC5	58.05 54.42 38.52 18.88	3.69 4.91 2.28 1.83	-1.32 -6.27 -2.64 -2.18	0.25 0.18	1.03 0.56 0.00 0.00	0.21 0.00
	MPI-ESM-P MPI-ESM-LR MRI-CGCM3 MRI-CGCM3	48.12 38.83 39.02 23.42	6.42 1.87 0.90 0.46	-1.81 -0.84 -0.30 -0.14	0.22 0.11	1.82 0.51 0.19 0.23	0.33 0.11
	MRI-CGCM3 MPI-ESM-P NorESM1-M NorESM1-M	117.09 36.88 38.82 27.55	4.46 2.18 1.71 1.07	-2.02 -1.18 -1.45 -0.80	0.33 0.22	1.22 0.58 0.00 0.00	0.11 0.05
	NorESM1-M MRI-CGCM3 NorESM1-ME NorESM1-ME	91.23 63.08 41.25 28.98	6.03 1.42 1.65 1.32	-4.19 0.21 -0.68 -1.07	0.40 0.26	1.51 0.41 0.10 0.00	0.01 0.61
	NorESM1-ME NorESM1-M ERA20c ERA20c	102.68 78.30 18.27 13.00	6.05 2.67 0.58 0.33	-0.70 -2.13 -0.29 -0.09	0.14 0.08	1.74 0.63 0.04 0.26	0.69 0.00
	CanSISE NorESM1-ME JRA-55 JRA-55	59.03 61.87 29.44 23.23	5.37 4.17 4.09 2.40	-0.69 -4.37 -3.81 -1.62	0.72 0.53	1.55 0.79 0.00 0.00	0.66 0.00
	CMIP5 CanSISE NOAAV2c NOAAV2c	85.89 40.36 39.45 37.06	2.01 2.65 3.51 2.60	-1.84 -0.63 -1.74 -0.89	0.83 0.64	0.44 0.76 0.05 0.18	0.00 0.41
	CMIP5 CMIP5 CMIP5	51.70 33.80 21.56	1.35 0.84 0.57	-1.65 -0.95 -0.65	0.10 0.07	0.18 0.00 0.00	0.00

Table

B

.8 -Spring (March-April) Eurasian subdomain SWE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1981-2005.

Table

B

.10 -Autumn (October-November) Arctic SWE mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1981-2005.

Table

B

.13 -Spring (March-April) Arctic SND mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period 1979-2005.

Table

B

.16 -Autumn (October-November) Arctic SND mean (i.e., µ), standard deviation (i.e., σ µ ), trend (i.e., T), standard error (i.e., σ T ) and p-value from the trend for the period

1979-2005.

Remerciements

of Advances in Modeling Earth Systems, 5(3), 572-597.

Gómez-Navarro, J., Montávez, J., Jerez, S., Jiménez-Guerrero, P., and Zorita, E. (2012). What is the role of the observational dataset in the evaluation and scoring of climate models ? Geophysical Research Letters, 39(24). Gouttevin, I., Menegoz, M., Dominé, F., Krinner, G., Koven, C., Ciais, P., Tarnocai, C., and Boike, J. (2012). How the insulating properties of snow affect soil carbon distribution in the continental pan-Arctic area. Journal of Geophysical Research : Biogeosciences, 117(G2), n/a-n/a. Groisman, P. and Davies, T. (2001). Snow cover and the climate system Snow Ecology ed HG Jones, JW Pomeroy, DA Walker and RW Hoham. Groisman, P., Shugart, H., Kicklighter, D., Henebry, G., Tchebakova, N., Maksyutov, S., Monier, E., Gutman, G., Gulev, S., Qi, J., et al. (2017). Northern Eurasia Future Initiative (NEFI) : facing the challenges and pathways of global change in the twenty-first century. Progress in Earth and Planetary Science, 4(1), 41. Groisman, P., Bulygina, O., Henebry, G., Speranskaya, N., Shiklomanov, A., Chen, Y., Tchebakova, N., Parfenova, E., Tilinina, N., Zolina, O., et al. (2018). Dryland belt of Northern Eurasia : contemporary environmental changes and their consequences. Environmental Research Letters, 13(11), 115008. Groisman, P. Y., Karl, T. R., Knight, R. W., and Stenchikov, G. L. (1994). Changes of snow cover, temperature, and radiative heat balance over the Northern Hemisphere. Journal of Climate, 7(11), 1633-1656. Henderson, G. R., Peings, Y., Furtado, J. C., and Kushner, P. J. (2018). Snow-atmosphere coupling in the Northern Hemisphere. Nature Climate Change, page 1. Hernández-Henríquez, M. A., Déry, S. J., and Derksen, C. (2015). Polar amplification and elevationdependence in trends of Northern Hemisphere snow cover extent, 1971-2014. Environmental Research Letters, 10(4), 044010. Hinzman, L. D., Deal, C. J., McGuire, A. D., Mernild, S. H., Polyakov, I. V., and Walsh, J. E. (2013).

Trajectory of the Arctic as an integrated system. Ecological Applications, 23(8), 1837-1868.

Annexe A

GREENICE Experiments

At the beginning of my 2nd

A.1 Introduction

Arctic sea ice extent has declined significantly under recent global warming (e.g., Comiso et al., 2008;[START_REF] Cavalieri | Arctic sea ice variability and trends, 1979-2010[END_REF][START_REF] Serreze | Processes and impacts of Arctic amplification : A research synthesis[END_REF] with a direct impact on the climate system [START_REF] Vihma | Effects of Arctic Sea Ice Decline on Weather and Climate : A Review[END_REF][START_REF] Gao | Arctic sea ice and Eurasian climate : a review[END_REF][START_REF] Koenigk | Impact of Arctic sea ice variations on winter temperature anomalies in northern hemispheric land areas[END_REF]. Particular attention has been paid to the influence of sea ice reduction in the Barents-Kara Seas region onto the wintertime cooling trend over the Eurasian continent, the so-called "Warm Arctic, Cold Continents" teleconnection pattern (e.g., Cohen et al., 2013;[START_REF] Inoue | The role of Barents Sea ice in the wintertime cyclone track and emergence of a warm-Arctic cold-Siberian anomaly[END_REF][START_REF] Mori | Robust Arctic sea-ice influence on the frequent Eurasian cold winters in past decades[END_REF][START_REF] Wegmann | Warm Arctic-cold Siberia : comparing the recent and the early 20th-century Arctic warmings[END_REF]. Concomitantly, observational and modeling studies have associated sea ice reduction over the Eastern Arctic with increase in snowfall over Siberia [START_REF] Deser | The seasonal atmospheric response to projected Arctic sea ice loss in the late twenty-first century[END_REF][START_REF] Orsolini | On the potential impact of the stratosphere upon seasonal dynamical hindcasts of the North Atlantic Oscillation : a pilot study[END_REF]Cohen et al., 2012Cohen et al., , 2013;;[START_REF] Ghatak | Simulated Siberian snow cover response to observed Arctic sea ice loss, 1979-2008[END_REF][START_REF] Liu | Impact of declining Arctic sea ice on winter snowfall[END_REF][START_REF] Li | Autumn sea ice cover, winter Northern Hemisphere annular mode, and winter precipitation in Eurasia[END_REF][START_REF] Wegmann | Arctic moisture source for Eurasian snow cover variations in autumn[END_REF]. However, the processes underlying both teleconnections are still unclear (e.g., [START_REF] Wegmann | Warm Arctic-cold Siberia : comparing the recent and the early 20th-century Arctic warmings[END_REF]. Ogawa Takala, M., Luojus, K., Pulliainen, J., Derksen, C., Lemmetyinen, J., Kärnä, J.-P., Koskinen, J., and Bojkov, B. (2011) Zhang, T., Wang, T., Krinner, G., Wang, X., Gasser, T., Peng, S., Piao, S., and Yao, T. (2019).

The weakening relationship between Eurasian spring snow cover and Indian summer monsoon rainfall. Science Advances, 5(3), eaau8932.

Zhong, X., Zhang, T., Kang, S., Wang, K., Zheng, L., Hu, Y., and Wang, H. (2018). Spatiotemporal variability of snow depth across the Eurasian continent from 1966 to 2012. The Cryosphere, 12(1),