Keywords: Humblement, je rends hommage à Pikku transport de vapeur d'eau, Arctique, Antarctique, réanalyse, radiosondage, cyclone moisture transport, Arctic, Antarctic, reanalysis, radiosounding, cyclone

J'aimerais remercier ma directrice de thèse, Olga Zolina, de m'avoir guidé pendant ces quatre années. Tout en sachant encadrer avec gentillesse ma tendance naturelle à la dispersion, elle m'a laissé deux libertés, ô combien précieuses en sciences : d'allier théorie et pratique et de suivre des fausses pistes.

En arrivant tout timide en conférence, je guettais de loin Sergey Gulev. Sa présence chaleureuse me laissait réconforté et je repartais bouillonnant de nouvelles idées. Je suis très reconnaissant envers les professeurs Brönnimann et Allan d'avoir accepté d'évaluer mon manuscrit, et ce dans des délais très brefs. De même, je suis honoré de compter dans mon jury Mme Masson-Delmotte et le professeur Koltermann. Également membre du jury, je tiens à remercier particulièrement Christophe Genthon qui m'a envoyé à l'autre bout du monde il y a deux ans et m'a introduit au laboratoire de glaciologie il y a quatre ans. C'est un merveilleux écosystème où se côtoient glaciologues, nivologues, chimistes, télédétecteurs, modélisateurs... et même un biologiste, qui se reconnaitra.

Transport de vapeur d'eau vers les hautes latitudes

Mécanismes et variabilité d'après réanalyses et radiosondages

Introduction

The Antarctic ice sheet north of 82 • S receives 171 kg m -2 of snowfall per year according to the satellite estimates of [START_REF] Palerme | How much snow falls on the Antarctic ice sheet?[END_REF] : this is equivalent to 6.4 mm of sea level.

Precipitation is also critical in forming the Arctic Ocean freshwater budget [START_REF] Serreze | The large-scale freshwater cycle of the Arctic[END_REF] and the surface mass balance of the Greenland ice sheet [START_REF] Ettema | Higher surface mass balance of the Greenland ice sheet revealed by high-resolution climate modeling[END_REF][START_REF] Burgess | A spatially calibrated model of annual accumulation rate on the Greenland Ice Sheet (1958-2007[END_REF]. In the Arctic, the net upwelling longwave surface radiation oscillated between ∼ 40 W m -2 under a clear sky and ∼ 0 W m -2 under moist and cloudy conditions at Ice Station SHEBA 1 during the polar night [START_REF] Stramler | Synoptically driven Arctic winter states[END_REF]. Indeed, the marginal greenhouse effect of water vapour is particularly strong in dry climates [START_REF] Curry | Water vapor feedback over the Arctic Ocean[END_REF].

The polar heat budgets are also affected by the release of latent heat during condensation and the subsequent clouds [START_REF] Solomon | Impact of latent heat release on polar climate[END_REF][START_REF] Curry | Overview of Arctic cloud and radiation characteristics[END_REF]. These different phenomena at either pole are all controlled by the transport of moisture from the mid to the high latitudes.

They illustrate the need for a detailed description of the atmospheric water fluxes to the polar regions by cross-referencing several sources, both reanalyses and observations. Once the present variability is established, the knowledge of the mechanisms responsible for the advection will enable to interpret and constrain current and future trends. It is the purpose of this thesis.

The effects of climate change are manifest in the Arctic : the surface temperature trend is twice as large as the global trend during the last few decades [START_REF] Polyakov | Observationally based assessment of polar amplification of global warming[END_REF][START_REF] Serreze | The emergence of surface-based Arctic amplification[END_REF][START_REF] Screen | The central role of diminishing sea ice in recent Arctic temperature amplification[END_REF][START_REF] Hartmann | Observations: Atmosphere and Surface, book section 2[END_REF]. The sea-ice extent in September has declined at a rate of 12.4% per decade from 1979 to 2010 with an associated reduction in ice thickness [START_REF] Stroeve | The Arctic's rapidly shrinking sea ice cover: a research synthesis[END_REF]. In Antarctica, the temperature and sea ice trends are more nuanced. The total Antarctic sea ice extent has increased by 1% per decade from 1979 to 2008 [START_REF] Cavalieri | Antarctic sea ice variability and trends, 1979-2006[END_REF] but these changes are compatible with rising oceanic and atmospheric temperatures [START_REF] Zhang | Increasing Antarctic sea ice under warming atmospheric and oceanic conditions[END_REF]. West Antarctica and the Peninsula are unmistakenly warming and the continent-wide near-surface temperature trend is positive [START_REF] Steig | Warming of the Antarctic ice-sheet surface since the 1957 International Geophysical Year[END_REF][START_REF] Bromwich | Central West Antarctica among the most rapidly warming regions on Earth[END_REF]. The results from the Coupled Model Intercomparison Project (CMIP5) indicate that the temperature tendencies at both poles will continue during the twenty-first century under different emission scenarios [START_REF] Collins | Long-term Climate Change: Projections, Commitments and Irreversibility, book section 12[END_REF].

1 Surface Heat Budget of the Arctic Ocean, from 1997 to 1998, in the Beaufort and Chukchi Seas Since relative humidity remains constant in climate model projections, specific humidity follows the Clausius-Clapeyron relation and should increase at a rate of 7% per degree Kelvin of warming [START_REF] Held | Robust responses of the hydrological cycle to global warming[END_REF][START_REF] Allan | Physically consistent responses of the global atmospheric hydrological cycle in models and observations[END_REF]. According to the authors, the moisture advection should increase in similar proportions, provided the winds do not change. This view is supported by model projections for the Arctic [START_REF] Bengtsson | The changing atmospheric water cycle in Polar Regions in a warmer climate[END_REF][START_REF] Hwang | Coupling between Arctic feedbacks and changes in poleward energy transport[END_REF] and the Antarctic [START_REF] Gregory | Ice-sheet contributions to future sea-level change[END_REF][START_REF] Krinner | Simulated Antarctic precipitation and surface mass balance at the end of the twentieth and twentyfirst centuries[END_REF]. In the Arctic, the retreat of the sea ice is a confounding factor : the intensification of the atmospheric water cycle may be driven by local evaporation over ice-free ocean rather than advection [START_REF] Bintanja | Future increases in Arctic precipitation linked to local evaporation and sea-ice retreat[END_REF][START_REF] Kopec | Influence of sea ice on Arctic precipitation[END_REF]. Through the direct radiative impact and indirect effect on clouds, the increasing amounts of moisture could themselves be a cause of the accelerated surface warming.

In situ observations of the components of the hydrological cycle are rare in the polar regions, particularly over the oceans and ice sheets. The sparse terrestrial station network, buoys, drifting ice stations and occasional scientific cruises do not provide the adequate temporal and spatial coverage for an explicit description of the regional climate and its evolution. Satellite data are indirect and subject to large uncertainties in the Arctic and Antarctic and may be limited in time by several years for specific instruments onboard specific satellites [START_REF] Groves | Moisture budget of the Arctic atmosphere from TOVS satellite data[END_REF][START_REF] Boisvert | Moisture flux changes and trends for the entire Arctic in 2003-2011 derived from EOS Aqua data[END_REF][START_REF] Palerme | How much snow falls on the Antarctic ice sheet?[END_REF].

Atmospheric reanalyses benefit from both in situ and remote sensing observations and likely constitute the most comprehensive source of information on polar hydrological budgets at present. However, neither precipitation nor evaporation is assimilated in global reanalyses : instead, they are computed based on model physics during the generation of the first guess field. As a result, these variables vary considerably across the datasets : for instance the net precipitation (precipitation minus evaporation) over global land areas varies by a factor of two between NCEP NCAR R1 and NCEP CFSR [START_REF] Trenberth | Atmospheric moisture transports from ocean to land and global energy flows in reanalyses[END_REF]. Moisture transport, however, is computed from wind and humidity, both of which are analysed, hence the results are more consistent among datasets. [START_REF] Trenberth | Atmospheric moisture transports from ocean to land and global energy flows in reanalyses[END_REF] reported only a 43% difference in moisture convergence over land between NCEP NCAR R1 and NCEP CFSR. For the Arctic, the difference between the moisture transport estimated by ERA 40 [START_REF] Jakobson | Atmospheric moisture budget in the Arctic based on the ERA-40 reanalysis[END_REF] and MERRA [START_REF] Cullather | The moisture budget of the polar atmosphere in MERRA[END_REF] is below 10%. Transport-based estimates of convergences also tend to be less affected by changes in the observation system unlike precipitation and evaporation. In MERRA for example, the transition from TOVS to ATOVS between 1998 and 2001 introduced a positive trend in global precipitation that is absent from the observational records [START_REF] Trenberth | Atmospheric moisture transports from ocean to land and global energy flows in reanalyses[END_REF].

Our work builds upon a number of previous studies evaluating moisture transport in reanalyses, starting with Genthon and [START_REF] Genthon | Convergence and disposal of energy and moisture on the Antarctic polar cap from ECMWF reanalyses and forecasts[END_REF] for Antarctica with ERA 15 and [START_REF] Cullather | The Atmospheric Hydrologic Cycle over the Arctic Basin from Reanalyses. Part I: Comparison with Observations and Previous Studies[END_REF] for the Arctic with NCEP NCAR R1 and ERA 15. [START_REF] Groves | Moisture budget of the Arctic atmosphere from TOVS satellite data[END_REF] are noteworthy for having decomposed the moisture flux into the monthly mean flow and transient eddy contributions, demonstrating the predominance of the latter, confirming the results of [START_REF] Peixóto | Physics of climate[END_REF]. In addition to this decomposition, we use the storm trajectories described in [START_REF] Gulev | Extratropical cyclone variability in the Northern Hemisphere winter from the NCEP/NCAR reanalysis data[END_REF]; [START_REF] Rudeva | Climatology of cyclone size characteristics and their changes during the cyclone life cycle[END_REF] and [START_REF] Tilinina | Comparing cyclone life cycle characteristics and their interannual variability in different reanalyses[END_REF] to evaluate the specific role of extratropical cyclones. [START_REF] Cullather | The moisture budget of the polar atmosphere in MERRA[END_REF] analysed the moisture budget of both polar regions as depicted in MERRA and included comparisons of evaporation and precipitation fields from ERA Interim and CFSR.

We extend the comparison to JRA 55 as well as the older reanalyses -NCEP NCAR R1, NCEP DOE R2 and JRA 25, all of which been continued up to 2013 (unlike ERA 40).

Besides evaporation and precipitation, we specifically focus on water vapour advection, as it is more stable and better suited to establish model-independent features of the hydrological cycle variability. This variable can also be validated against observations, namely radiosonde data. We are extending the earlier observational studies of [START_REF] Connolley | Atmospheric water-vapour transport to Antarctica inferred from radiosonde data[END_REF] and [START_REF] Serreze | Atmospheric water vapor characteristics at 70 • N[END_REF] that predated the widespread use of reanalyses.

The thesis is organized as follows. Chapter 1 describes the data sources, including their limitations, as well as the methods used to compute the moisture transports. Chapter 2 is dedicated to the Arctic, Chapter 3 to the Antarctic. These sections are subdivided into the analysis of the climatological spatial structure, of long-term moisture budgets, of the transport components due to the mean flow and transient eddies and of the seasonal cycle and interannual variability of the source terms. Finally, Chapter 4 offers some perspective on the methods used to distinguish between mean flow and transient eddies and revises the role of extratropical cyclones.

Chapter 1

Data and methods

Reanalyses

2 0 1 0 -0 1 -1 0 2 0 1 0 -0 1 -1 1 2 0 1 0 -0 1 -1 2 2 0 1 0 -0 1 -1 3 2 0 1 0 -0 1 -1 4 2 0 1 0 -0 1 -1 5 Numerical weather prediction models need to be initialised before any forecast can be made. This initial state, or analysis, should draw upon as many observations of the atmosphere as possible. Unfortunately, the observation network -ground stations, satellite tracks, buoys, aeroplane routes, etc.

-bears no relation with the model grid.

On first sight, a simple interpolation of the observations to the model grid seems the obvious solution. However, at synoptic scales, the variables governing the atmosphere -winds, pressure, temperature, etc.

-are tied, they rarely depart from quasiequilibria, like those defined by the quasigeostrophic equations. A careless interpolation will likely throw the modelled atmosphere off balance, leading to violent adjustments in the first hours of the forecast.

Instead of producing an analysis from scratch, weather forecasters take advantage of the last prediction, called the "background," which is already in equilibrium. It serves as a firstguess for the analysis. Figure 1.1 illustrates how the specific humidity at the South Pole was analysed on the 10 th of January, 2010, at 12 o'clock. A previous forecast, initialised twelve hours before, provides the background (blue dot). At noon, a weather balloon was launched from the South Pole station : its humidity measurements constitute the observations (red dot). The analysis (black dot) is a compromise between both sources of information.

Weather predictions centres frequently upgrade their models and data assimilation systems. Most conspicuously, when more powerful computers are acquired, the spatial resolution is increased. Such modifications prevent climatologists from using archived "operational" analyses to study global warming for instance : the abrupt or gradual improvements may lead to spurious shifts or trends in the temperature time series.

In "retrospective" analyses, or reanalyses, historical observations are processed with the same forecast model and data assimilation system. They provide a dynamically consistent view of the past state of the atmosphere that makes the best use of past observations. Nevertheless, the data input streams do change during the reanalysis period as new instruments are set up, drift or are replaced. Consequently, a trend or shift in the reanalysis data may reflect a modification in the observing system rather than a climatic phenomenon : trends derived from reanalysis data should therefore be treated with caution (Bengtsson et al., 2004a). New satellites are notorious for disrupting the continuity of the time series. This is particularly important for the polar regions, where the assimilation relies predominantly on remote sensing due to the scarcity of conventional observations. We used the output of seven global reanalyses (Table 1.1). Besides the increasing spatial resolution -from T62 in NCEP R1 to T382 in CFSR -the modern reanalyses distinguish themselves from the first generation by their improved model physics and data assimilation systems, especially regarding satellite observations. ERA Interim and JRA 55 both implement four-dimensional variational data assimilation (4D-Var)

1.1. Reanalyses to account for the observations' temporal distribution within the assimilation window. CFSR still relies on 3D-Var but with a refinement : "First Order Time interpolation to the Observation" (FOTO, Rancic et al. (2008)). CFSR also couples atmosphere, simplified ocean and sea ice models to generate the 6-hourly guess field. Unlike the other datasets, MERRA is based on finite volume dynamics. Its "Incremental Analysis Update" (IAU) scheme improves on 3D-Var to dampen the analysis increment. In IAU, a correction is applied to the forecast model gradually, limiting precipitation spin-up in particular. To explain this important phenomenon, we must first introduce the basic equations of the atmospheric water cycle.

We consider a volum of air δV delimited by infinitesimal increments in the three directions, δx, δy and δz. At synoptic scales, altitude and pressure are linked via the hydrostatic approximation : ρ dz = -dp/g with ρ the density, g the standard gravity and p the pressure.

The mass δm this volume contains can now be written δx δy δp/g without the density term, ρ. Let ω be the vertical wind component in pressure coordinates and u the horizontal wind.

In the absence of precipitation, the conservation of mass implies that the material derivative of δm be zero hence :

D δx δy Dt δp + δx δy D δp Dt = 0 (1.1) div u + ∂ ω ∂p = 0 (1.2)
In pressure coordinates, the equations of fluid mechanics simplify as if the fluid were incompressible.

The mass of water vapour the volum contains is : q δm with q the specific humidity.

The moisture content of this air parcel decreases when vapour precipitates and increases when condensed water evaporates. Such evaporation occurs either at the surface or in the atmosphere, as when a cloud dissipates. In other words :

D q δm Dt = (e -c) δm (1.3)
e and c are respectively the evaporation and condensation per unit mass. We use the conservation of mass equation in pressure coordinates to expand the material derivative :

∂q ∂t + div(q u) + ∂qω ∂p = e -c
(1.4) div(q u) is the divergence of the horizontal moisture flux. The term in ω vanishes if we integrate the local equation from the surface (pressure p s ) to the top of the atmosphere (pressure zero) :

∂ ∂t ps 0 q dp g + (P -E) = -div ps 0 q u dp g (1.5)
where E is the evaporation and P the precipitation, both per unit surface area.

The moisture budget of an atmospheric column can be analysed by evaluating either side of the moisture balance equation (Eq. 1.5). The first term on the left hand side, the precipitable water tendency, is typically negligible compared to the other terms for yearly time scales. The second term, P-E, or net precipitation, is computed by accumulating precipitation and evaporation during the generation of the model first guess. This is the so-called "physics output" method. NCEP NCAR R1, NCEP DOE R2, JRA25 and NCEP CFSR do not provide a ready-made evaporation product ; thus, we computed it from the latent heat flux using the skin temperature and snow and ice cover to determine the phase change enthalpy. The second method, referred to as the "aerological" method, evaluates the right hand side of Equation 1.5, the moisture flux convergence, which is based on analysed humidity and winds. The two methods yield different results : the moisture budget of the reanalyses is typically not closed (e.g. [START_REF] Trenberth | Atmospheric moisture transports from ocean to land and global energy flows in reanalyses[END_REF], [START_REF] Cullather | The moisture budget of the polar atmosphere in MERRA[END_REF]). The physics output method is more dependent on model physics and tends to be affected by changes in input data streams. The aerological method is more stable and its output in different reanalyses is more coherent [START_REF] Trenberth | Atmospheric moisture transports from ocean to land and global energy flows in reanalyses[END_REF].

Weather forecasters did not produce reanalyses with climatology in mind, at least not originally. The reanalyses were used to initialise "reforecasts" that served as benchmarks to evaluate their model and data assimilation schemes, as well as to study the impact of changes in the observation system. Reforecasts with lead times up to ten days are available for ERA Interim. In Figure 1.2, we plot the trajectories of the forecasted specific humidity at 600 hPa over the South Pole for different starting dates with colours varying from blue to red depending on the lead time. In this anecdotal example, the humidity at 600 hPa does not present any obvious tendency in the first hours of the model run. Does this hold over larger areas and for the whole 1979-2013 period ? For this purpose, we build climatologies with constant lead times to study how the worldwide water cycle is set in motion in ERA Interim (Figure 1.3,a). As reported by [START_REF] Kållberg | Forecast drift in ERA-Interim, European Centre for Medium Range Weather Forecasts[END_REF], precipitation undergoes a minor spin up in the first six hours of the forecast : a 7.8% increase. The atmosphere also has a slight tendency to dry up, particularly at lead times of 12 and 24 hours. We cannot account for the mismatch between evaporation, precipitation and the integrated water tendency (red we compute the precipitation : between 0 and 3 hours to be as close to the analysis as possible, or between 18 and 24 hours, when precipitation has stabilised ? There is no such ambiguity with moisture advection. The standard practice in other reanalyses is to archive the precipitation accumulated during the six first hours of the forecast : we followed this convention.

2 0 1 0 -0 1 -1 0 2 0 1 0 -0 1 -1 2 2 0 1 0 -0 1 -1 4 2 0 1 0 -0 1 -1 6 2 0 1 0 -0 1 -1 8 2 0 1 0 -0 1 -2 0 2 0 1 0 -0 1 -2 2 2 0 1 0 -0 1 -2 4 2 0 1 0 -0 1 -

Radiosoundings

To validate the characteristics of moisture transport derived from reanalyses, we compared them to observations, namely radiosoundings from the Integrated Global Radiosonde Archive (IGRA, [START_REF] Durre | Overview of the integrated global radiosonde archive[END_REF]). For the region north of 60 • N, seventy four sites were active throughout the satellite era from 1979 to 2013 (Figure 1.4). Thirty-nine sites are located on the coast including six on small islands. In Antarctica, there are only ten available sites, all but one on the coast of East Antarctica (Figure 1.5). The observation frequency ranges from once to twice daily, and corresponds to the synoptic times used in operational and retrospective analyses. Measurements are supposed to be available at least on certain standard levels, which are 1000, 850, 700, 500, 400, 300, 250 and 200 hPa in the troposphere.

IGRA does not constitute independent data : finding radiosoundings that are not assimilated in reanalyses is quite a challenge [START_REF] Francis | Validation of reanalysis upper-level winds in the Arctic with independent rawinsonde data[END_REF]. Nevertheless, radiosoundings are important to check the internal consistency of the data assimilation schemes. There may be conflicts between in situ and remote sensing sources as in [START_REF] Grant | Recent Arctic warming vertical structure contested[END_REF] or the observations may be overridden by the model. Radiosoundings also have their limitations particularly in dry and supersaturated conditions [START_REF] Connolley | Atmospheric water-vapour transport to Antarctica inferred from radiosonde data[END_REF][START_REF] Miloshevich | Absolute accuracy of water vapor measurements from six operational radiosonde types launched during awex-g and implications for airs validation[END_REF]. In certain cases, the assimilation procedure may be justified in giving them little weight.

Before being archived in IGRA, soundings pass a number of quality control checks. The pressure, temperature and geopotential height variables receive a particular attention. However, the specific humidity and winds, which are of special interest to us, did not undergo climatological checks in IGRA ; thus, we performed additional quality screens on these variables to filter out extremely high values. For this purpose, we used the median as an indicator of central tendency and the interquartile range (IQR) as a measure of spread. Means and standard deviations are overly sensitive to outliers and yield artificially high thresholds. We computed the medians and IQRs for each calendar month to account for the variability due to the annual cycle. After subjective examinations of unnatural shifts and outliers in the time series and vertical profiles, we chose to remove values lying outside the range of ± 4 IQR from the median. Because the IQR of a Gaussian distribution is 1.35 times its standard deviation, our criterion corresponds to approximately 5.4 σ. Although this threshold seems permissive, in the Arctic, it excludes 4.8% of the wind data and 5.5% of the humidity data. Additionally, we required the existence of values on at least five pressure levels before performing linear interpolations of the vertical profiles. Finally, we only considered stations with at least 85% of days with valid soundings over the entire period, which led us to discard 11 sites in the Arctic. Such a threshold would leave us with no data in Antarctica : in Chapter 3, we detail an ad hoc procedure to deal with the gaps in the observation records. ). The reanalyses were co-located in both time and space with the soundings in the second line but only in space in the third line.

To avoid a sampling bias, we only compared simultaneous observations and reanalysis values. The co-location of reanalysis data with radiosonde sites was performed via bilinear interpolation. In the Arctic, before we averaged a variable over the radiosonde sites, we first grouped the stations in eight 45 • longitudinal sectors. We averaged the variable within these longitudinal bands after which the averaging was applied over the bands. In this manner, the data-rich regions (such as Europe) are not given an unfair emphasis. We were also concerned that our filters would be biased against intense moisture events because they exclude exceptionally high values of humidity and wind. However, in Table 1.2, the mean meridional moisture fluxes in reanalyses over the radiosonde sites are only slightly reduced by the subsampling.

Computation of the fluxes

To calculate the moisture budget of a given region we integrate the moisture balance equation (Eq. 1.5). We must resort to finite differences to compute the divergence and this introduces an error, pointed out by [START_REF] Seager | Diagnostic Computation of Moisture Budgets in the ERA-Interim Reanalysis with Reference to Analysis of CMIP-Archived Atmospheric Model Data[END_REF]. ERA Interim happens to provide a vertically integrated moisture convergence product calculated in spectral space on model levels. Over Greenland, it deviates by 0.3% from the finite differences result ; even less over the Arctic Ocean. When we compute the water budget over a polar cap, say the region north of 70 • N, the divergence term simplifies to :

φ>70 • ps 0 div(q u) dp g ds = - π -π ps 0 qv dp g dλ (1.6)
where ds is a surface element, φ latitude, λ longitude and v the meridional wind.

Up to now, we have assumed that the transport of water took place exclusively in the gas phase. In the transition from Equation 1.4 to Equation 1.5, we implicitely assumed that the vertical integral of the condensation per unit mass was precipitation. Indeed, the condensed phases, liquid and frozen, only make a fraction of the total column water : 0.9% north of

60

• N and 1.5% south of 60 • S according to ERA-Interim. Few datasets provide the condensed water fraction on model levels and to our knowledge, no study has evaluated their impact on the water transport up to now (Table 1.3).

The condensed water fluxes are extremely variable from one dataset to the next. For the polar cap north of 70 Figure 1.9: Vertical profile of specific humidity at the South Pole on the 1 st of January, 2010. The dots materialize pressure levels, the horizontal lines correspond to the surface pressure numerical models use a different type of vertical coordinate. The conversion from "model levels" to "pressure levels" involves interpolation, a first source of error. What's more, the sea level pressure during an anticyclone may be higher than the first pressure level, 1000 hPa, hence the near surface information is lost. Conversely, the surface pressure over orography is bound to be lower than 1000 hPa : the pressure levels below the surface must be masked or filled with fictitious values. In Figure 1.8, the blue pressure levels intersect the grey profile of Greenland yet the lowest level does not make it to the sea. At the South Pole Station on the 1 st of January, 2010, the surface pressure was approximately 700 hPa : in some datasets, the specific humidity profile was extended to 1000 hPa using different conventions (Figure 1.9). Whenever possible, it is preferable to make the numerical vertical integrations on model levels. In the forecast models of the first generation reanalyses, the vertical is divided in σ-coordinates. σ is simply the ratio of the pressure at a given level to the surface pressure.

In NCEP NCAR R1 and NCEP DOE R2, σ ranges from 0.995 to 0.00273. If the surface pressure is 1000 hPa, this corresponds to 995 hPa for the first level and 2.73 hPa for the last. Whatever the surface elevation or the weather conditions, the σ-coordinates follow the terrain, just like the red curves in Figure 1.8. This ensures that the lowest layers of the atmosphere are properly represented in the model.

Unfortunately, σ-coordinates cannot do justice to the stratosphere -which is higly stratified as its name suggests -but pressure levels would be ideal. Starting with JRA 25, all the later reanalyses are produced on hybrid σ-pressure levels (so-called η levels), a compromise between the two systems. For any time t and location defined by latitude φ and longitude λ, [START_REF] Stepaniak | ERA-Interim Vertical Coordinate Conventions and Numerical Attributes[END_REF]. All the A k and B k are constants. The B k correspond to the σ variable, starting near 1 for the lowest levels and decreasing with altitude, eventually vanishing in the mid-stratosphere (pure pressure levels). The A k correspond to the pressure increments which are zero near the surface (pure σ-levels) but gradually set the pace as the altitude increases. The JRA 55 archive provides three dimensional data on η levels only : we used the preceding relation to convert it to pressure levels via linear interpolation.

the k th η level is defined as p k (φ, λ, t) = A k + B k p s (φ, λ, t)
The thickness of an η level is obtained using half levels, designated by half-integer indices : ∆p k = p k+.5 -p k-.5 . k ranges from 1 (the highest level) to K (closest to the surface). The vertical integral of any variable f (p) is then approximated by :

ps 0 f (p)dp ≈ N n=1 f (p)(A k+.5 -A k-.5 + (B k+.5 -B k-.5 ) • p s ) (1.7)
Ideally, the numerical vertical integrations should be made on model levels. For NCEP NCAR R1, NCEP DOE R2, NCEP CFSR and JRA 25, we only had specific humidities and winds on pressure levels, from p 0 = 1000 hPa to p N = 200 hPa (300 hPa for NCEP NCAR R1) ; above these levels, moisture concentrations become negligible. The value of the variable on the lowest pressure level above the ground was taken to be the value of the variable at the surface. Let p n 0 be that level. The vertical integral of any variable f (p) was approximated following the trapezoidal rule : We reorganise Equation 1.8 to make the weight given to each level more apparent.

ps 0 f (p)dp ≈ N -1 n=n 0 1 2 (f (p n+1 ) + f (p n ))(p n -p n+1 ) + f (p n 0 )(p s -p n 0 ) (1.
ps 0 f (p)dp ≈ f (p N ) p N -1 -p N 2 + N -1 n=n 0 +1 f (p n ) p n-1 -p n+1 2 +f (p n 0 ) p s - p n 0 +1 + p n 0 2 + + n 0 -1 n=0 f (p n ) • 0 (1.9)
To avoid the influence of fictitious underground values, we use these weights in our temporal and spatial averages, as in :

q(p n ) = 1 t 2 -t 1 t 2 t 1 q(p n , t) w n (t) dt t 2 t 1 w n (t) dt (1.10)
where p n is a given pressure level and the overbar signals a temporal average between times t 1 and t 2 .

To elucidate which time scales contribute most to the net moisture imports, we decompose the winds and humidity into mean and fluctuation (denoted by primes) using monthly averages to filter the synoptic transients as in [START_REF] Peixóto | Physics of climate[END_REF]. For a given location and altitude, the mean moisture flux breaks down into two terms, one due to transient eddies, the other to the mean flow :

qv = q , v , + qv (1.11)
Other applications of the Reynolds decomposition to the atmospheric moisture transport to the polar regions can be found in [START_REF] Groves | Moisture budget of the Arctic atmosphere from TOVS satellite data[END_REF], [START_REF] Oshima | Difference in seasonal variation of net precipitation between the Arctic and Antarctic regions[END_REF], [START_REF] Newman | Relative contributions of synoptic and low-frequency eddies to time-mean atmospheric moisture transport, including the role of atmospheric rivers[END_REF], [START_REF] Tsukernik | Atmospheric meridional moisture flux over the Southern Ocean: A story of the Amundsen Sea[END_REF] and Liu and Barnes (2015a), on individual datasets.

Following [START_REF] Peixóto | Physics of climate[END_REF], we introduce additional notations to refer to the zonal mean, [q], and the vertical mean on pressure levels, {q}, and the deviations therefrom, q • and q * . After vertical and zonal averaging of the meridional flux, we further decompose the mean flow term :

{[ qv]} = {[q , v , ]} + {[q * v * ]} +{[q] • [v] • } + {[q]}{[v]}
(1.12)

The first term on the right hand side groups the contribution of small-scale, short-lived, "transient eddies," including extratropical cyclones. The second term is the product of the zonal anomalies of the mean humidity and wind fields which are designated as "stationary eddies." For instance, in the North Atlantic at 70 • N, the air is particularly moist and the meridional wind is particularly strong compared to other longitudes. The third term on the right-hand side corresponds to the product of vertical anomalies in the zonally symmetric time mean humidity and wind fields, known as "vertical cells" by reference to the overturning circulations of the Hadley, Ferrel and polar cells. The fourth and last term should be zero because there is no net mass flux into a closed region on yearly time scales. We will test this assumption shortly.

Equation 1.12 involves the meridional wind averaged along time, longitude and over the full height of the atmosphere. For most reanalyses, our wind data is limited to an altitude of p N = 200 hPa, i.e. four fifths of the mass of the atmosphere. To cover the last fifth, we would need three times the current amount of vertical levels. Indeed, as shown in Table 1.1, we only use one third of the available levels, at least for the modern reanalyses. We can circumvent this problem by invoking the conservation of mass. We integrate Equation 1.2 over the polar cap north of latitude φ 0 on the horizontal, and between the top of the atmosphere (0 hPa) and p N on the vertical. Moist processes can be safely neglected at these altitudes.

p N 0 φ>φ 0 div u ds dp g + φ>φ 0 p N 0 ∂ω ∂p dp g ds = 0 (1.13) p N 0 2π 0 v(φ 0 ) dλ dp g = φ>φ 0 ω(p N ) ds (1.14)
The mean mass flux into the polar cap is therefore :

{[v]} • p N ps 2π 0 dλ dp g = p N ps 2π 0 v(φ 0 ) dλ dp g + φ>φ 0 ω(p N ) ds (1.15)
We will often be implicitely multiplying the terms of Equation 1.12 by the mean column mass along the domain boundary, to express the fluxes in units of kg m -1 s -1 . A further division by the surface of the domain considered yields units of kg m -2 s -1 , or in the case of water fluxes : mm s -1 . For south polar caps, the northward wind is replaced with the southward wind. For more complex domains like the Antarctic ice sheet, [.] will refer to averages along the boundary of the domain. In these cases, it is more convenient to write the first term on the right-hand side as a divergence.

We integrate Equation 1.2 over the polar cap, this time from the top of the atmosphere to the surface. At more humid altitudes, atmospheric mass may be lost in the form of net precipitation [START_REF] Trenberth | Atmospheric moisture transports from ocean to land and global energy flows in reanalyses[END_REF]. To put it concisely,

{[v]} -{[qv]} = 0 (1.16)
Let {[v nd ]} be the residual of this equation, "nd" standing for non-divergent. In practice, this residual term is not zero and it causes a non-physical advection of moisture (Table 1.5).

For wide domains, such as polar caps, the impact on the moisture budget is limited. The problem is more serious over the Greenland and Antarctic ice sheets, particularly in the first generation reanalyses.

Throughout this study, we used each reanalysis' output grid to perform all computations : Reynolds decomposition, vertical integrations, spatial averages, etc. When necessary for the comparison and as a last stage, we bilinearly interpolated the derived products on a common grid (0.5 • × 0.5 • latitude-longitude).

Region Reanalysis mass convergence moisture convergence moisture leak kg m -2 year -1 ). The font is red when the spurious moisture convergence represents more than 5% of the total.

{[v]} {[qv]} {[q]}{[v nd ]} • -90 • N NCEP NCAR R1 1.
Chapter 2

Moisture advection to the Arctic

Spatial structure

We now examine the Arctic atmospheric hydrological cycle as represented by the seven reanalyses studied, with an emphasis on moisture transport. Whenever possible, we compare the reanalyses to the radiosonde observations.

To the first order, the mean vertically integrated moisture fluxes north of 60 To evaluate the reliability of the moisture transport estimates in the reanalyses, we compared them to the IGRA radiosonde observations described in section 1. Considering climatological fluxes, the observed longitudinal pattern is broadly respected by the reanalyses (Figure 2.3,a). Aside from two outliers (Petchora station in the Northern Ural Mountains, and Narsarsuaq station in Greenland), correlations between moisture flux monthly anomalies in reanalyses and radiosoundings are higher than 0.85 (not shown). CFSR typically exhibits the best performance, followed by ERA Interim. JRA 25 often performs better than JRA 55 perhaps because the former relies more on satellite data.

Overall, the absolute moisture fluxes measured by radiosondes are lower than in the reanalyses regardless of whether the moisture is blowing north or south. The relative difference between the filtered observations and the subsampled ERA Interim is 10.2% when averaged over all radiosonde sites (Table 1.2). This difference is minimal in NCEP NCAR R1 (6.3%) and maximal in MERRA (13.2%). We sought an explanation in the representation of the The vertical pattern of correlation of reanalyses' moisture transport with IGRA's is more disconcerting (Figure 2.4,d). ERA Interim and CFSR systematically outmatch the other with values of approximately 0.9 for the bulk of the free troposphere. These reanalyses do not perform as well near the surface or the tropopause, but this is insignificant compared with the other reanalyses, which achieve coefficients superior to 0.8 only in the layer between 700 and 500 hPa. This result is perplexing given the high correlation with the IGRA soundings of the vertically integrated quantities in all datasets. Some datasets probably reject the radiosonde observations in the upper and higher troposphere but the data from the middle troposphere is sufficient to reconstruct a plausible albeit inaccurate vertical profile.

The specific humidity and meridional wind variables exhibit the same vertical correlation patterns as the moisture flux except in the upper troposphere : the wind in ERA Interim and CFSR remains highly correlated with the soundings even higher than 500 hPa (Figure 2.4, e and f).

Long-term moisture budgets

Table 2.1 and Figure 2.5 present the terms of the moisture budget in the different datasets for four regions : north of 70 • N, north of 60 • N, the Arctic Ocean and the Greenland ice sheet.

The mean moisture convergence through 70 • N is remarkably consistent between the seven reanalyses studied because they are constrained by common observations despite different model settings and resolutions. The minimum value (187 mm year -1 ) is given by JRA 25

and the maximum (203 mm year -1 ) by MERRA. In line with our findings in the previous section, the fluxes derived from radiosondes [START_REF] Serreze | Atmospheric water vapor characteristics at 70 • N[END_REF] or computed from satellite data [START_REF] Groves | Moisture budget of the Arctic atmosphere from TOVS satellite data[END_REF] tend to be lower than the reanalysis values. Estimates of precipitation and evaporation are more scattered among datasets ; net precipitation computed from model physics ranges from 95 mm year -1 (NCEP DOE R2) to 244 mm year -1

(NCEP CFSR). The interdataset standard deviation for net precipitation is 45 mm year -1 compared to 5.1 mm year -1 for transport.

Predictably, no reanalysis succeeds in closing the moisture budget, with the largest mismatch found in NCEP DOE R2, where the moisture convergence exceeds net precipitation by 52%. This mismatch is smaller in the other datasets (although still 34% for MERRA).

CFSR exhibits the most intense water cycle. Net precipitation is higher than the moisture convergence only in CFSR and JRA 55.

For the polar cap north of 60 We performed a similar budget analysis for the Arctic Ocean and the Greenland ice sheet.

Atmospheric moisture convergence represents an important source term in the Arctic freshwater budget impacting ocean stratification, convection, the intensity of the thermohaline circulation and the formation of sea ice [START_REF] Serreze | The large-scale freshwater cycle of the Arctic[END_REF]. For Greenland, net precipitation along with meltwater runnoff and blowing snow determine the surface mass balance of the ice sheet [START_REF] Ettema | Higher surface mass balance of the Greenland ice sheet revealed by high-resolution climate modeling[END_REF][START_REF] Burgess | A spatially calibrated model of annual accumulation rate on the Greenland Ice Sheet (1958-2007[END_REF]. Despite the warnings from Bengtsson et al. (2011), integrating fluxes on pressure levels has only a moderate impact on the results even over these complex domains (Table 1.4). The maximum relative error (3.8%) is found in MERRA over the Arctic Ocean. Even when applying the same time window ,

we were unable to reconcile our estimate of the moisture convergence over the Greenland ice sheet using MERRA (393 mm year -1 ) with that of [START_REF] Cullather | The moisture budget of the polar atmosphere in MERRA[END_REF] (459 mm year -1 ). This mismatch does not apply to precipitation and evaporation.

Role of the mean flow and transient eddies

We now turn to the analysis of the moisture transport into the Arctic using the decomposition given by Equation 1.11. The transient eddy flux is one order of magnitude weaker but is nearly exclusively meridional suggesting its dominant contribution to the poleward advection of moisture. However, the mean flow flux is not consistently zonal ; it has relatively small meridional components.

Given the large magnitude of the mean flux, it also contributes to the moisture advection toward or away from the Arctic. For example, approximately half of the total northward flux over the storm tracks is due to the mean flow component.

Over the Canadian archipelago and Strait of Denmark, the mean flow transport imparts a southward direction to the total transport, offsetting the effect of the transients. The explanation is found in [START_REF] Peixóto | Physics of climate[END_REF] and the standing wave pattern the authors identified in the mean tropopause winds. One of the two troughs is located East of the American continent implying southward winds over Canada and northward winds over the Baffin Bay and the Greenland Sea. Over Canada, these southward winds extend to the surface, so the mean flow flux in this region is also southward. Over the Strait of Denmark, the high northward winds advect a small amount of moisture compared to the southward surface winds associated with the Icelandic low, because the air is more humid near the surface. As a result, the vertically integrated mean flow flux is directed south between Greenland and Iceland.

To estimate the role of the transport components in different datasets, we apply the same decomposition (Equation 1.11) to all seven reanalyses for the meridional transport component at latitude 70 • N. Figure 2.7 illustrates that the contribution of the transient Table 2.2 presents the mean and standard deviation of all components of the decomposition from Equation 1.12 for the moisture flux at 70 • N.

[ qv]} {[q , v , ]} {[q * v * ]} {[q] • [v] • } {[q]}{[v nd ]} NCEP NCAR

Seasonal variability

The seasonal variability of the moisture advection into the Arctic is important because mid- The annual peak of moisture transport is more acute over the radiosonde sites and occurs in September (Figure 2.10, a). As noted previously, the observed fluxes are weaker than in the reanalyses, particularly in spring, summer and early autumn.

The maximum net precipitation lags by approximately one month with respect to the moisture convergence and is observed in August in all products, except for JRA 25, for which the maximum is observed in September. The reason for this lag is in part physical : during the warm season, the water holding capacity of an atmospheric column increases (Figure 2.9, red curve), limiting the potential for the imported and evaporated moisture to precipitate. However, a portion of the lag in Figure 2.9 can be interpreted as an artifact because the right and the left-hand sides of the moisture balance equation (Eq. 1.5) are computed independently. The water budget is thus unlikely to be closed, as indicated by the residual term in Figure 2.9 (light blue curve). The same applies to the energy budget ; for example, in MERRA the surface receives an excess of 11 W m -2 , which could lead to excessive latent heat fluxes [START_REF] Cullather | The moisture budget of the polar atmosphere in MERRA[END_REF]. Indeed, in MERRA and most datasets, the closure problem is most acute in late spring, when evaporation is the highest. In contrast, the reanalyses diagnosing the most precipitation (NCEP CFSR and JRA 55) err in the opposite direction in the wet period of August and September.

We further divided the transports into the two so-called "Arctic seasons" : January-February-March-April (JFMA) and July-August-September-October (JASO) suggested by [START_REF] Tilinina | New view of Arctic cyclone activity from the Arctic system reanalysis[END_REF] based on sea-ice concentrations. Figure 2.11 shows the longitudinal distribution of total moisture fluxes as well as the transient eddy part. The local maxima are well co-located in both seasons in the subpolar North Atlantic, the Labrador Sea and the Chukchi Sea. In these regions, the total summer fluxes are two to three times stronger compared to those in winter. This result also holds for the southward mean flow moisture flux over the Canadian Archipelago. The transient eddy fluxes in summer are also higher than in winter nearly everywhere, except for the Greenland Sea, where they are comparable.

Likely, this results from the higher moisture in summer and the intensified storm activity over Northern Eurasia and the Eastern Arctic. [START_REF] Serreze | The emergence of surface-based Arctic amplification[END_REF] and [START_REF] Tilinina | Comparing cyclone life cycle characteristics and their interannual variability in different reanalyses[END_REF] demonstrated an intensification of cyclone activity over Northern Eurasia and Canada in summer that increases the advection of moistened air, leading to a doubling of the moisture transports over these regions.

Interannual variability

We also analysed how consistently the reanalyses reproduce the interannual variability of the Arctic moisture budget. The spread between reanalyses for the moisture transports is smaller than the interannual variability (Figure 2.12, a). As a result, the transport-based estimates of moisture convergence present common interannual variability patterns, such as a decade long decline starting in 1989. During this period, the total transports decreased statistically significantly by 12 (ERA Interim) to 15% (JRA 25). We computed linear trends The time series of the moisture budget components confirm the disparity in evaporation and precipitation estimates as opposed to the transport products (Figure 2.13, e, f and g).

Precipitation and evaporation are on the rise with the strongest signals identified in NCEP DOE R2 for evaporation (9.7% per decade) and in JRA55 for evaporation also (4.6% per decade). The reanalyses disagree as to the sign of the net precipitation change. Unlike the two JRA, most report an increase, with statistical significance in MERRA. A joint consideration of changes in the total meridional moisture transport and precipitable water reveals an apparent paradox. On the one hand, neither observations nor reanalyses report any significant change in northward moisture fluxes (Figure 2.13, i). On the other hand, precipitable water has increased unambiguously in all datasets (panel j).

) (f) (f) (f) (f) (f) (f) (f) 100
) (h) (h) (h) (h) (h) (h) (h)
The increases in specific humidity have therefore not translated into corresponding increases in moisture fluxes. This goes against the widespread argument that the poleward moisture fluxes should strengthen in a warmer climate -it vindicates the opposing thesis, that the intensification of the hydrological cycle is driven locally by evaporation [START_REF] Bintanja | Future increases in Arctic precipitation linked to local evaporation and sea-ice retreat[END_REF].

Given that moisture fluxes depend on both humidity and wind, a reasonable question comes : could changes in winds compensate the moistening ? To solve this conundrum, we introduce a more compact decomposition of the mean moisture fluxes through 70 • N :

{[ qv]} = {[q , * • v , * • ]} + {[q]}{[v]} (2.1)
where q

, * • = q -{[q]} and v , * • = v -{[v]} i.e.
anomalies relative to the vertical, zonal and monthly mean. The first term on the right-hand side is the covariance between the specific humidity and meridional wind. The second term is small as shown in Table 2.2 and we ignore it. We represent the covariance as the product of the standard deviation of the humidity and wind and their mutual correlation.

{[ qv]} = σ t,λ,p q σ t,λ,p v corr t,λ,p (q, v) (2.2)
The evolution of the three factors over time is plotted in Figure 2.14.

[ qv]/(σ t,λ,p q σ t,λ,p v)
The standard deviation of the humidity increased in all datasets from 7.5% (JRA 25) to 12.9% (MERRA), with statistical significance in NCEP NCAR R1, JRA 25, ERA Interim and JRA55 (Figure 2.14, a). The variance in humidity can be written as the sum of the temporal variance, the zonal variance and the vertical variance in much the same manner as the moisture flux in Equation 1.12.

σ 2 t,λ,p q = {[σ 2 t q]} + [σ 2 λ q] + σ 2 p [q] (2.
3)

The first term on the right-hand side, the temporal variability, only contributes slightly to the increase in the total variance (6-16%, depending on the reanalysis). The second and third terms represent the spatial variability, in both longitude and height. The saturation specific humidity depends exponentially on temperature through the Clausius-Clapeyron relation.

If the atmosphere warms homogeneously and the relative humidity remains constant, the humid regions moisten faster than the dry regions. For example, the humidity contrast between the surface and the higher troposphere becomes sharper : σ 2 p [q] comprises 83-89% of the increase in the total variance. The contribution of the zonal variance is considerably smaller (-3-7%).

The standard deviation of the meridional wind stayed approximately stable, with a slight decrease in some reanalyses that was never statistically significant (Figure 2.14,b). The correlation between wind and humidity decreased significantly in all dataset but one (NCEP DOE R2) as shown in Figure 2.14 (c), which led to the slight decrease in the moisture flux (Figure 2.14, d) in spite of the moistening. The increasing humidity did not result in stronger moisture fluxes because the moisture and wind variations in space and time do not correspond as well as in previous periods.

Figure 2.15 (a) shows that the moisture flux has decreased below 700 hPa and increased moderately above. To explain this, we consider the correlation between meridional wind speed and humidity to determine which levels have contributed most to the corr t,λ,p (q, v) statistic. We introduce a normalized flux : [ qv]/(σ t,λ,p q σ t,λ,p v) ; its vertical integral is exactly corr t,λ,p (q, v) according to Equation 2.3. The normalized flux has decreased particularly near the surface, between 950 and 850 hPa depending on the reanalysis (Figure 2.15, b). At these altitudes, the prevailing wind blows south, as part of the lower branch of the polar cell. However, this is only part of the explanation because the moisture transport due to the polar cell has not changed significantly (Figure 2.13, c).

The link between increases in moisture and transports is therefore not straightforward.

The analysis of trends is impeded by strong interannual variability dominating the long-term tendencies. At the same time, climate models consistently project an increase in the moisture fluxes to the Arctic for the 21st century e.g. [START_REF] Hwang | Coupling between Arctic feedbacks and changes in poleward energy transport[END_REF]. The departure from the simple Clausius-Clapeyron scaling of the moisture fluxes could be a transitory phenomenon that would lapse when the global warming signal becomes stronger.

Chapter 3

Moisture advection to Antarctica

Spatial variability

In terms of observation density, a quick glance at Figures 1.4 Polar orbiting satellites offer a good coverage of the continent but are handicapped by the resemblance between clouds and the frozen surface, the uncertainty in the snow emissivity estimates and the strong temperature inversions [START_REF] Bouchard | Enhancements of satellite data assimilation over Antarctica[END_REF]. Consequently, we should expect a heavier reliance on the model first guess in the reanalyses and larger disagreements than in the Arctic even for analysed fields such as moisture and winds.

Over the Southern Ocean, the climatological moisture fluxes in ERA Interim (Figure 3.1, a) are dominated by the circumpolar westerlies with magnitudes in the order of 100 kg m -1 s -1 . The orographic precipitation over the Antarctic Peninsula leads to a depletion of moisture : the fluxes are halved on the leeward side. The polar vortex is centered on the Ross ice shelf (150 • W-160 • E) rather than on the South Pole, as explained in [START_REF] King | Antarctic meteorology and climatology[END_REF]. The asymmetry in the prevailing winds causes significant advection to West Antarctica. Surprisingly, the fluxes do not immediately decrease as they move inland, despite the ice sheet's mean altitude of 850 m (Figure 3.1, b).

The moisture flux to East Antarctica is controlled by the circumpolar trough, a feature also described in [START_REF] King | Antarctic meteorology and climatology[END_REF]. This belt of low pressure and high cyclone activity is located at an average latitude of 66 • S with variations according to seasons. The mean winds inferred from Buys Ballot's law change from westerlies on the equatorward side of the trough, to easterlies on the poleward side. The change of direction causes some advection inland depending on the configuration of the coast. The trough off the coast of East Antarctica is actually subdivided into two low pressure regions, one at 20 • E, the other at 90 • E. Each is the center of a cyclonic circulation whose eastern branch works to advect moisture southward.

The reanalyses disagree on the magnitude of the fluxes due to the circumpolar westerlies On the other hand, NCEP CFSR, whose spectral resolution is the highest (T382), shows stronger offshore fluxes at these locations than ERA Interim, MERRA and JRA 55.

The inter-dataset spread of the southward moisture flux is variable depending on the coastal radiosonde sites (Figure 3.3) : small for homogeneous coastal conditions, but large near valleys acting like funnels for the wind. Syowa Station (69 • S, 39 E). Compared with the Arctic, the reanalyses are still highly correlated with the observations although the coefficients are more spread out : from 0.75 to practically 1. CFSR is still the closest to the radiosondes, followed closely by ERA Interim. Our most recent dataset, JRA 55, often performs the worst.

Just like in the Arctic, the observed precipitable water content is higher than in the reanalyses (Figure 3.3,b). Given the low amounts, the range between the most dry and the most humid dataset amounts to approximately one fourth of the mean value. The dispersion of southward wind speeds at 850 hPa is even greater. The coarser the grid, the more the reanalysis is biased towards offshore northward winds. We suggest that the stations are not representative of their surroundings, because they were generally built in places sheltered from the winds. Only the high resolution datasets can represent both the katabatic outflow and the relative haven of the station. Unlike the Arctic, the direction of the wind at 850 hPa corresponds to the direction of the moisture fluxes : the mean flow flux may be comparable in magnitude to the transient eddies.

The vertically integrated moisture flux is the product of two competing phenomena according to the vertical profiles in Figure 3.4. Near the surface, moisture is exported to the north but higher up, it is imported south. CFSR and JRA 55 reproduce the observed height where the fluxes change sign, at 950 hPa. The two first NCEP reanalyses see it at 750 hPa, JRA 25 at 850 hPa. As a consequence, they overestimate the near-surface northward fluxes and underestimate the upper-air southward fluxes. Specific humidity is not quite as consistent between reanalyses and observations than in the Arctic. The datasets diverge at the surface. As observed, there is a humidity inversion in MERRA and JRA55, but it is too deep and too strong. Conversely, the three NCEP reanalyses (R1, R2, CFSR) are all too moist. Figure 3 reach a maximum of correlation at a lower altitude than in the Arctic, by 100 hPa.

Conventional snow gauges cannot discriminate between precipitation and blowing snow, a frequent phenomenon on the coast, nor can they measure the tenuous snowfall in the interior of the continent [START_REF] Bromwich | An Assessment of Precipitation Changes over Antarctica and the Southern Ocean since 1989 in Contemporary Global Reanalyses*[END_REF]. The accumulation datasets of [START_REF] Arthern | Antarctic snow accumulation mapped using polarization of 4.3-cm wavelength microwave emission[END_REF] and [START_REF] Favier | An updated and quality controlled surface mass balance dataset for Antarctica[END_REF] rely mainly on stake measurements, on the identification of reference horizons in ice cores, and, in the case of [START_REF] Arthern | Antarctic snow accumulation mapped using polarization of 4.3-cm wavelength microwave emission[END_REF], on satellite microwave observations to interpolate between in situ measurements. From August 2006 to April 2011, CloudSat offered direct measurements of Antarctic precipitation. The spaceborne radar measured the reflectivity of clouds and precipitating particles and was able to detect the occurrence and rate of snowfall [START_REF] Palerme | How much snow falls on the Antarctic ice sheet?[END_REF]. We reproduce the CloudSat and ERA Interim snowfall estimates (Figure 3.5, a and b). The footprint of CloudSat is relatively narrow and its orbit never goes further south than 82 • S. As a result, there is no data for higher latitudes. We followed the same conventions to plot ERA Interim's convergence of atmospheric water product (all three phases) in panel (c).

Tsukernik and Lynch

Long-term moisture budgets

With fewer observations to constrain the analysed fields, we cannot expect to find a similar agreement between datasets in the Antarctic as in the Arctic. On the other hand, the analysis increment should be reduced due to the smaller amount of new information to accomodate.

This is indeed what the figures in Table 3.1 suggest. Unlike the Arctic, precipitation is generally higher than evaporation plus advection, but only by 25% in the worst case (JRA 25 over the Antarctic Plateau). This can be be seen in Figure 3.6 by comparing the left and right bar of each reanalysis. The evaporation in NCEP NCAR R1 is unrealistically large [START_REF] Hines | Surface Energy Balance of the NCEP MRF and NCEP-NCAR Reanalysis in Antarctic Latitudes during FROST*[END_REF] and still excessive in NCEP DOE R2 [START_REF] Bromwich | An Assessment of Precipitation Changes over Antarctica and the Southern Ocean since 1989 in Contemporary Global Reanalyses*[END_REF]. In the latest reanalyses, it is barely positive, with net sublimation in JRA 55.

The 60 • S latitude circle covers only ocean ; the Antarctic Plateau covers only land.

The 70 • S parallel briefly crosses the Antarctic Peninsula and intersects large swaths of East Antarctica so it could count as "piecewise homogeneous" terrain. On the boundaries of the ice sheet however, the moisture fluxes experience substantial changes of magnitude and direction over short distances. This translates in the ratio of the inter-dataset standard deviation to the inter-dataset mean : 4 % at 60 • S, 3% at 70 • S, 11% for the ice sheet and 7% for the plateau despite its radical climate.

CloudSat does not reach latitudes south of 82 • S, which justified a separate table, adapted from [START_REF] Palerme | How much snow falls on the Antarctic ice sheet?[END_REF]. The different variables are close to one another over the whole ice sheet. The difference between net precipitation and atmospheric water convergence is of the same order of magnitude as the liquid precipitation (∼ 10 mm year -1 ).

Role of the mean flow and transient eddies

From Figure 3.7 (a), the mean flow fluxes correspond to the circumpolar westerlies. Their magnitude weakens at longitude 0 • and 90 [START_REF] Genthon | Convergence and disposal of energy and moisture on the Antarctic polar cap from ECMWF reanalyses and forecasts[END_REF]) 1979[START_REF] Connolley | Atmospheric water-vapour transport to Antarctica inferred from radiosonde data[END_REF][START_REF] Cullather | The moisture budget of the polar atmosphere in MERRA[END_REF]) 1979-2005 198 (14) We decompose the mean flow term into stationary eddies, vertical cells and a residual, 1.11, semitransparent bars ; all bars start at zero) in the seven reanalyses . Each set of bars correspond to the average over 45-degree longitudinal bands, defined in the map in the lower panel.

according to Equation 1.12. The result on latitude circles is displayed in Figure 3.9 (a) and is similar to the profile found in [START_REF] Tsukernik | Atmospheric meridional moisture flux over the Southern Ocean: A story of the Amundsen Sea[END_REF] In this particular case, the Reynolds decomposition was performed after the interpolation.

The zonal mean [ • ] is replaced with the average along the boundary. Unsurprisingly, the transient eddies blow moisture inland at all altitudes, with a maximum around 750 hPa. We interpret the stationary eddy and the vertical cell profiles as the effect of katabatic winds. Some locations on the coast at the mouth of valleys drain more dry, inland air than the rest, which implies anomalous mean humidities q * and offshore winds v * , in other words, stationary eddies. The katabatic winds occur near the surface so they show up as vertical anomalies too : both [q] • and [v] • , i.e. the polar cell. As we saw over the radiosonde sites, the katabatic layer is deeper in the old reanalyses. The lower branch of the vertical cell is weaker in MERRA but we believe this is an artefact. The underground pressure levels are already masked in the MERRA archives, more conservatively than by our own procedure : part of the katabatic layer is masked. The vertical cell imports very dry air from the mid-latitudes higher than 500 hPa, actually higher still than our last level, 200 hPa. We accounted for the subsequent subsidence in our mass budget calculations. Table 3.3 summarises the contribution of each flux component to the moisture convergence over the Antarctic ice sheet. The figures must be taken with a grain of salt : the domain boundaries have been smoothed and we performed the interpolation before computing averages and anomalies.

Seasonal variability

The seasonal cycle of moisture convergence and net precipitation is not as pronounced as in the Arctic because the precipitable water content does not vary as much [START_REF] Oshima | Difference in seasonal variation of net precipitation between the Arctic and Antarctic regions[END_REF]. Instead, the winter maximum is due to the stronger cyclone activity despite the low humidity. This pattern is reproduced by all the reanalyses (Figure 3.10).

The convergence is highest in March (∼ 15 mm month -1 in the modern datasets) and then settles on a plateau throughout autumn and winter. Spring sees a short-lived drop in total transient eddies stationary eddies vertical cell residual Reanalysis 12) 67 ( 7) -105 ( 7) -1.6 (0.0) MERRA 218 ( 14) 184 ( 10) 62 (8) -86 (8) -0.3 (0.0) JRA 55 215 ( 14) 199 ( 14) 69 ( 7) -114 (9) -4.2 (0.0) Table 3.3: Long-term averaged components of the moisture convergence on the Antarctic ice sheet (mm year -1 ) according to Equation 1.12. {[v nd ]} is the residual of Equation 1.16. Values in brackets are the interannual standard deviations.

{[ qv]} {[q , v , ]} {[q * v * ]} {[q] • [v] • } {[q]}{[v nd ]} NCEP NCAR R1
convergence, caused mainly by increased evaporation and decreased mean flow fluxes. There is no appreciable precipitable water tendency, at least not of similar magnitude as the other terms of the moisture budget.

The radiosondes sites only sample a small part of the domain boundary. The cycle of moisture advection averaged over the stations has little in common with the cycle for the whole ice sheet (Figure 3.11). Instead of a plateau, the late autumn and winter seasons are interrupted by weaker months, in May and September. The precipitable water content follows the expected cycle : a sharp maximum in January (3 mm in observations) and dry values (below 1.5 mm) for the whole winter. The interior of the continent is even drier : this is why there was no visible annual variation in water content in Figure 3.10.

The spatial distribution of moisture fluxes shows no consistent behaviour among sectors between summer and winter (Figure 3.12). Over West Antarctica, the dramatic winter increase was mainly due to the mean flow, whereas it decreased over the Peninsula. East Antarctica remains quite unchanged except in Wilkes Land, which sees an approximate 50% increase of both the mean flow and transient eddy components.

Interannual variability

The interannual variability of precipitation in Antarctica has been treated extensively in [START_REF] Bromwich | An Assessment of Precipitation Changes over Antarctica and the Southern Ocean since 1989 in Contemporary Global Reanalyses*[END_REF] and [START_REF] Nicolas | Precipitation changes in high southern latitudes from global reanalyses: A cautionary tale[END_REF]. The former article has a telling title "Precipitation Changes in High Southern Latitudes from Global Reanalyses: A Cautionary Tale" : the trends were largely spurious according to the authors. Even the modern reanalyses were affected by artefacts : MERRA (and CFSR to a lesser extent) by the in- We nonetheless display the time series for all the terms of the moisture budget (Figure 3.13) with our usual emphasis on moisture transport (first column). [START_REF] Bromwich | An Assessment of Precipitation Changes over Antarctica and the Southern Ocean since 1989 in Contemporary Global Reanalyses*[END_REF] and [START_REF] Nicolas | Precipitation changes in high southern latitudes from global reanalyses: A cautionary tale[END_REF] had excluded NCEP NCAR R1 (understandably), ERA Interim only extended to 1989 and JRA 55 was not yet released. However, we cannot escape the conclusion of the authors. Our time series share the same ambiguity : the observed patterns of interannual variability cannot be interpreted as real world phenomena with any confidence. The inter-dataset spread is greater than the interannual variability even for the moisture convergence variable.

As far as we know, radiosondes were only used to build moisture flux climatologies as in [START_REF] Connolley | Atmospheric water-vapour transport to Antarctica inferred from radiosonde data[END_REF] or [START_REF] Cullather | Spatial and Temporal Variability of Antarctic Precipitation from Atmospheric Methods*[END_REF]. With longer records, we hope to exploit trends as well. The threshold we applied to the Arctic stations -at least 85% of valid days -is too demanding for Antarctica. There are fewer radiosonde launches and those few observations are more likely to be filtered by our quality checks. Figure 3.14 summarises the data availability at the nine IGRA stations on the coast active from 1979 to 2013. Before the 1990s, it looks as though several stations did not run a radiosonde program at all. In fact they did, but only in summer, or the launches were irregular and error-ridden. We cannot 1.12. Time series of the terms of the moisture budget for the said region : net precipitation or P-E via the physics output method (e), precipitation (f), evaporation (g) and the residual, i.e. the difference between the physics output and the aerological methods (h). The regression line of the variable is drawn (in dashes) if its trend is statistically significant at the 95% level (Student t-test). build a time series by simply averaging the stations operational at a given time : in the 1990s, we can expect an artificial jump when new stations are taken into account. We rather compute anomalies per synoptic time, month and station and we average the anomalies, by analogy with worldwide surface temperature datasets e.g. [START_REF] Jones | Hemispheric surface air temperature variations: a reanalysis and an update to 1993[END_REF].

) (f) (f) (f) (f) (f) (f) (f)
Once we correct for the spatial heterogeneity of the data, we find statistically significant increases of the southward moisture transport (Figure 3.15, a). Except for Mirnyj and Mc-Murdo, all stations report increases, with significance in the case of Halley, Syowa and Casey.

Such trends were anticipated from climate model projections [START_REF] Gregory | Ice-sheet contributions to future sea-level change[END_REF][START_REF] Krinner | Simulated Antarctic precipitation and surface mass balance at the end of the twentieth and twentyfirst centuries[END_REF] but not observed [START_REF] Monaghan | Insignificant change in Antarctic snowfall since the International Geophysical Year[END_REF][START_REF] Bromwich | An Assessment of Precipitation Changes over Antarctica and the Southern Ocean since 1989 in Contemporary Global Reanalyses*[END_REF]. We must nevertheless issue three caveats. First, the spatial and temporal representativity of our result is questionable. Second, the radiosonde time series can be affected by changes in instruments and practices. Third, the trend is not the product of additional moisture, the expected mechanism. Indeed, the precipitable water content has not changed over the same period (Figure 3.15, b). The transient eddy component has increased but not significantly.

The remainder of the trend is therefore due to a weakening of the mean flow, which was not predicted by climate models as far as we know.

To conclude, trends in the Antarctic are as surprising as in the Arctic. In both regions, the moisture fluxes were expected to increase because of additional humidity. The humidity in the Arctic did rise, but not the fluxes because of unfavourable winds. The Antarctic stayed as dry but the moisture convergence increased due to weaker equatorward mean winds and stronger poleward transient eddy fluxes. Chapter 4

The role of cyclones in moisture advection

Temporal scale decompositions

The two previous chapters have shown the predominant contribution of transient eddies to the moisture transport to the high latitudes : 90-92% at 70 • N, 84-145% to the (smoothed)

Antarctic ice sheet. Now we would like to delve deeper into the meaning of this statistic.

How dependent is it on the choice of a temporal threshold ? How does it compare to spectral methods ?

Our original purpose was to identify the mechanisms responsible for moisture advection : we wanted to know which time scales contributed the most to the transports. Let [0, A] be the period of study, in our case 35 years and qv the mean moisture flux at a given location and altitude. a = A/N is a shorter time scale e.g. a month, and N the number of months in period A. What is the contribution of time scales shorter than a to qv ?

By analogy with fluid mechanics, the Reynolds decomposition lends itself to the study of turbulence on synoptic scales. For a given month n ∈ 0, N , we divide any variable, say q, into its monthly mean and monthly anomaly : q = q n + q , where q n = 1 a (n+1)a na q dt and q , = q -q n (4.1)

Since q and v are correlated, the mean of their product is not the product of their means but qv n = q n v n + q , v , n . The remaining term is the "eddy" flux :

q , v , n = 1 a (n+1)a na (q -q n )(v -v n ) dt (4.2)
We now average the monthly decompositions over the whole period :

qv n = 1 N N -1 n=0 qv n (4.3)
This yields the complete Reynolds decomposition : qv n = q n v n + q , v , n which separates the contribution by time scales longer than a month from those shorter than a month. We can also expand q and v in their respective Fourier series, as in q = j∈Z q j e j with e j = e 2πijt/A (4.4) i is the imaginary unit and Z the set of integers, positive and negative. The product of q and v breaks down into : qv = j,k∈Z 2 q j v k e j+k (4.5)

Since e j = δ j0 , it follows that :

qv = j∈N f j with f j =        q 0 v 0 if j = 0.
q j v -j + q -j v j otherwise. We would like to relate the "mean flow" term of the Reynolds decompostion, q n v n , to the Fourier series. After a number of calculations, detailed in the appendix, we came up with the following approximation.

q n v n ≈ j ∈ Z q j v -j sinc 2 (πj/N ) (4.7)
The cardinal sine function is reminiscent of the effect of convoluting a signal with a rectangular window i.e. a moving average.

Q(t) = 1 a t+a/2 t-a/2 q(τ ) dτ = q 0 + j ∈ Z* q j [e j ] t+a/2 t-a/2 = j ∈ Z q j sinc(πj/N ) e j (t) (4.8)
We multiply Q by V :

Q(t) V (t) = k, j ∈ Z
q j v k sinc(πj/N ) sinc(πk/N ) e j+k (t) (4.9)

Averaging over [0, A] yields the same result as q n v n .

We perform several Reynold decompositions of the meridional moisture flux at 70 to the total is summed, up to a certain temporal threshold given by the horizontal axis. The negative contribution of the annual cycle shows up as a small drop in the green curve ; it is absent from the two others. From Equation 4.7, it was unlikely that Fourier and Reynolds decompositions would yield similar results. The overall aspect is similar but the Fourier distribution is shifted towards the longer frequencies. As expected, the output from moving averages (computed using Fourier coefficients) cannot be distinguished from the Reynolds decomposition. Using these two methods, we find the familiar 92% figure for a time scale of a month. The Fourier decomposition gives a mere 76%. Unfortunately, there is no reason to trust one method more than the other. Though they disagree on the details, they do paint a similar picture : scales shorter than a month dominate the moisture advection to the Arctic. These formal decomposition methods have done good service but their physical meaning is not clear. To move further, we need methods more discriminative of the actual meteorological mechanism at play.

Contribution of individual cyclones

The term "transient eddies" is suggestive of cyclones. Several authors, ourselves included, have implied the connection. For example, [START_REF] Karoly | Meteorology of the southern hemisphere[END_REF] talks of "synoptic-scale cyclones (also known as transient eddies)." Indeed, extratropical cyclones make good suspects : they occur on the right time scales and they generate meridional winds that put the middle and the high latitudes into contact, leading to transports of moisture and heat. [START_REF] Sorteberg | Seasonal cyclone variability at 70 • N and its impact on moisture transport into the Arctic[END_REF] demonstrated that cyclone activity and moisture transport were significantly correlated in the Arctic.

Extratropical cyclone were formerly known as barometric depressions i.e. minima of the sea level pressure (SLP) fields. We defined transient eddy fluxes as q , v , ; likewise, we define high frequency variations of the SLP as p , 0 p , 0 . Before the advent of tracking methods, this is how storm tracks were located (e.g. [START_REF] Rogers | North Atlantic storm track variability and its association to the North Atlantic Oscillation and climate variability of northern Europe[END_REF]). Using six-hourly fields instead of monthly averages, one can follow individual cyclones : designated features can be traced on gridded fields from one time step to the next [START_REF] Hodges | A general-method for tracking analysis and its application to meteorological data[END_REF]. The identification criteria varies from method to method. The cyclone trajectories of the Institute of Oceanolgy, Russian Academy of Science, which we use, rely on SLP minima [START_REF] Gulev | Extratropical cyclone variability in the Northern Hemisphere winter from the NCEP/NCAR reanalysis data[END_REF][START_REF] Rudeva | Climatology of cyclone size characteristics and their changes during the cyclone life cycle[END_REF][START_REF] Tilinina | Comparing cyclone life cycle characteristics and their interannual variability in different reanalyses[END_REF] but [START_REF] Sorteberg | Seasonal cyclone variability at 70 • N and its impact on moisture transport into the Arctic[END_REF] tracked maxima of the 850 hPa vorticity. An example of a so-called spaghetti plot is shown in 2) and another 7.5% failed steps (3.1) or (4.1). Surprisingly, the remaining cyclones have contributed to both negative (39%) and positive (61%) net fluxes with a mean of +28 • 10 6 kg s -1 (Figure 4.6, a). The positive tail is quite heavy : the top decile contributed to 75% of the mean. The figure drops to 35% if we only consider cyclones making a positive net contribution. The importance of extreme atmospheric transport events has already been underlined by [START_REF] Messori | On the sporadic nature of meridional heat transport by transient eddies[END_REF] for heat and [START_REF] Woods | Large-scale circulation associated with moisture intrusions into the Arctic during winter[END_REF] for moisture.

The mode of the distribution is zero : the most common case is cyclones having no effect at all. Was the tracking scheme particularly sensitive to weak cyclones or were these cyclones actually vigorous, but with compensating cold and warm sectors ? This time, we take the absolute value of the meridional moisture flux before we perform the integration between the western and eastern boundaries of the cyclone (Figure 4.6,b). The first hypothesis was correct : most cyclones have a weak effect on the meridional moisture fluxes. The cyclones with no effect whatsoever are nonetheless rare. It would be interesting to apply the algorithm to random "pseudo-cyclones" to see if the tracking scheme is prone to false positive errors. Conversely, we could restrict ourselves to deep cyclones only and see if they are indeed responsible for the extreme transport events.

Contribution of all cyclones

The 24 225 cyclones we examined in the previous section are only a small subset of the cyclones that contribute to the moisture transport at 70 • N. Intuitively, the further the cyclone center is from 70 • N, the smaller his influence on the transport at 70 • N. Its signature on the moisture flux field will likely be indistinguishable from noise, especially to our algorithm. λ. When a cyclone is present at latitude φ, a point at 70 • N and λ degrees of longitude to the east of the cyclone experiences on average the meridional moisture flux symbolized by that colour. For example, a cyclone located between 50 • N and 80 • N is likely to affect the fluxes at 70 • N. Points at 70 • N less than 45 • of longitude to the east of the cyclone would be located in its warm sector. They would therefore experience northward fluxes under those conditions. Points at 70 • N located less than 45 • of longitude to the west of the cyclone would find themselves in its cold sector where on average moisture fluxes would be negative. This is the explanation for the blue and red patterns on either side of the prime meridian : they represent the influence of the cold and warm sectors of cyclones. Points at 70 • N that are more than 45 • degrees of longitude to the east or to the west of the cyclone are unaffected by its presence. This is also true when the cyclone is located below 50 • N : the fluxes at 70 • N are independent of his presence.

We are now tempted to apply the attribution algorithm defined in the previous section on the composited profiles (green contour on Figure 4.8). Qualitatively, the objective boundaries make sense though they look spread-out. Quantitatively, the fluxes inside the boundary amount to 15.7 kg m -1 s -1 . The total fluxes, both inside and outside, amount to an improbable 90.2 kg m -1 s -1 when we would expect no more than the average moisture fluxes through 70 • N, 6.9 kg m -1 s -1 .

Cyclones are an ubiquitous phenomenon : we must partition the 70 • N profile or we will be attributing the same flux to several cyclones. The instructions in italics share the profile among the closest cyclones to avoid double-counts. The pink background colour has been replaced with white (zero fluxes) in Figure 4.8, (b). The green contour is more narrow ; it encloses 6.1 kg m -1 s -1 . The regions outside the boundary weigh 0.8 kg m -1 s -1 and the whole is 6.9 kg m -1 s -1 . From these calculations, cyclones are responsible for 89% of the advection through 70 • N, which is not far from the share of transient eddies according to the Reynolds decomposition (92%).

Actually, we have come up with a tool rather than a final result. We merely showed that most of the moisture flux occurred in the neighbourhood of a cyclones. Now, as we said, cyclones are a very frequent phenomenon. The 89% of moisture fluxes we attributed to cyclones were due to 78% of longitudes and time steps. Put this way, the proximity to a cyclone is not a good predictor of above average fluxes.

In designing the algorithm, we guessed that cyclones far from 70 • N would have no effect on the moisture fluxes at 70 • N so we stratified the cyclones by latitude. We know from the previous section that even among the cyclones crossing 70 • N, most have little effect on the moisture flux. We would like to extend the stratification to an index of the cyclone's strength. For instance, [START_REF] Sorteberg | Seasonal cyclone variability at 70 • N and its impact on moisture transport into the Arctic[END_REF] did not just correlate the number of cyclones with the moisture fluxes : they correlated the accumulated cyclone central vorticities at 850 hPa with the moisture fluxes. We decide to sort the cyclones by their central SLP and to divide them into deciles, which we divide into even smaller bins depending on the latitude of the cyclone. For each SLP-latitude bin, we build composites of the storm-centered 70 • N meridional moisture flux profile, excluding locations on the parallel that are closer to some other cyclone. We then apply the attribution algorithm to the composites of each SLP-latitude bin. Finally, we sum the contributions from the bins of matching SLP and plot the share of each decile (Figure 4.9). Unsurprisingly, the deeper the cyclone, the stronger the fluxes (red line) and the more longitudes it affects (blue line).

The first decile is responsible for 30% of the mean fluxes. By the fourth decile, the fraction of fluxes due to cyclones is the same as the fraction of 70 • N they affect. Cyclones belonging to the remaining deciles bring about below average fluxes. A minority of deep cyclones is therefore associated with the majority of the moisture transport to the Arctic. To do so, we should exploit both the harmonic analysis of Section 4.1 and the cyclone trajectories of Sections 4.2 and 4.3. Using wavelets, the fluxes can be expressed as the sum of basic functions representing the different scales at work. Unlike Fourier harmonics, these functions have a compact support and are thus localised in time and space : they can be assigned to specific cyclones. With wavelets, we would able to share the credit between the large scale flow and the embedded cyclones.

reanalyses. They more than compensate the disposal of moisture by the mean flow. Instead of the reanalyses, prone to artefacts, we looked to radiosonde observations for indications of the interannual variability. In spite of an unchanged precipitable water content, the southward moisture transport has increased significantly, due to a weakening of the mean flow and stronger transient eddy fluxes. When analysing trends, the Reynolds decomposition reminds that the total fluxes do not depend on the average humidity only but also on the mean winds and, more importantly, on both variables' second order moments.

In order make its physical interpretation clearer, we began by reframing the Reynolds decomposition in the broader context of harmonic analysis. In the case of moisture transport through 70 • N, the two methods are slightly different quantitatively but both agree that the lion's share occurs on time scales shorter than a month. We questioned the identification of transient eddies with extratropical cyclones by computing an independent estimate of cyclones' contribution to moisture transport. The percentage is remarkably close to the Reynolds' estimate : 89% and 92% respectively. However, cyclones are commonplace and most of them cause very little advection. On the other hand, the deepest ten percent are responsible for 30% of the moisture fluxes through 70 • N.

Although transient eddies dominate moisture advection to the polar regions, several studies have shown how dependent they are on larger temporal and spatial scale patterns. Sorteberg and Walsh (2008) demonstrated that cyclones entering the Arctic are largely responsible for the poleward moisture advection but they also noted that the number of cyclones passing over the Greenland Sea depends on large scale circulation patterns, as reported earlier by [START_REF] Tsukernik | Characteristics of winter cyclone activity in the northern North Atlantic: Insights from observations and regional modeling[END_REF]. [START_REF] Woods | Large-scale circulation associated with moisture intrusions into the Arctic during winter[END_REF] also argued along these lines, positing that blocking high pressure systems steer cyclones towards the pole and lead to intense moisture intrusions. In this respect, further analysis should be conducted to clarify the interplay between transient eddies and the large-scale flow, relying on a detailed analysis of cyclone activity [START_REF] Tilinina | Comparing cyclone life cycle characteristics and their interannual variability in different reanalyses[END_REF][START_REF] Tilinina | New view of Arctic cyclone activity from the Arctic system reanalysis[END_REF] which may be combined with a wavelet decomposition of the fluxes.

Similar studies with refined diagnostics can be extended to regional and long-term reanalyses. A natural choice would be the recent Arctic System Reanalysis [START_REF] Bromwich | A comparison of the regional Arctic System Reanalysis and the global ERA-Interim Reanalysis for the Arctic[END_REF], which was produced with a high-resolution version of the non-hydrostatic Polar Weather Research and Forecast model and assimilated more data regionally than the global reanalyses.

To understand the Arctic hydrological cycle on multidecadal time scales, it is also important to examine reanalyses not limited to the satellite era, such as NOAA ESRL 20 th Century Reanalysis [START_REF] Compo | The twentieth century reanalysis project[END_REF], ERA 20C (Hersbach et al., 2015a) and ERA CLIM (Hersbach et al., 2015b). The analysis of moisture transports in these products would enable an understanding of the mechanisms steering the Arctic hydrological cycle during the time of the so-called early twentieth century Arctic warming (Bengtsson et al., 2004b;[START_REF] Brönnimann | Early twentieth-century warming[END_REF][START_REF] Yamanouchi | Early 20th century warming in the Arctic: A review[END_REF].

Our assessement for both polar regions should serve as a standard to evaluate the historical runs of the CMIP5 ensemble of climate models and to clarify the extent to which they reproduce the features of the polar hydrological cycle and their changes in a warming climate. Existing assessments of climate model projections of the Arctic hydrological cycle [START_REF] Kattsov | Twentieth-century trends of Arctic precipitation from observational data and a climate model simulation[END_REF][START_REF] Kattsov | Simulation and projection of Arctic freshwater budget components by the IPCC AR4 global climate models[END_REF][START_REF] Rawlins | Analysis of the Arctic system for freshwater cycle intensification: Observations and expectations[END_REF] and of the Antarctic surface mass balance [START_REF] Gregory | Ice-sheet contributions to future sea-level change[END_REF][START_REF] Krinner | Simulated Antarctic precipitation and surface mass balance at the end of the twentieth and twentyfirst centuries[END_REF]

Relating Reynolds and Fourier decompositions

We would like to relate the "mean flow" term of the Reynolds decompostion, q n v n , to the |j|≤N q j v -j term of the Fourier series. N is the ratio between the length of the time series, A, and the shorter time scale, a.

First we split the variables in long term mean and fluctuation e.g. q = q + (qq).

For a given month, the product of the means can be written as :

q n v n = qv + q v -v n + q -q n v + q -q n v -v n
When we average the monthly means of a variable X over all months, Chasles' relation ensures that : X n = X. Accordingly :

q n v n = qv + q v -v + q -q v + q -q n v -v n q -q and v -v go to zero so the second and third right hand side terms vanish.

We will now tackle the last term bit by bit, using the Fourier decomposition q = j∈Z q j e j with e j = e 2πijt/A to take advantage of the nice properties of the exponential function :

q -q n = 1 a (n+1)a na j∈Z*
q j e j dt = 1 a j∈Z* q j A 2πij e j (n+1)a na = j∈Z* N q j 2πij (e j (a) -1) (e j (a)) n

Combining both factors, we obtain :

q -q n v -v n = j,k∈Z* N q j 2πij
N v k 2πik (e j (a) -1) (e k (a) -1) (e j+k (a)) n

Finally we average over all months in [0, A]. We change the order of summation : As it happens, e j+k (a) N = e 2πi(j+k) which is one, j + k being an integer, therefore the sum is zero.

q -q n v -v n = 1 N j,k∈Z* N q j 2πij N v k 2πik (
• If there exists an integer p such that j + k = N p, then e j+k (a) = e 2πip , which is one.

Therefore :

N -1 n=0 (e j+k (a)) n = N It follows that :

q -q n v -v n = j∈Z* p∈Z N q j 2πij N v N p-j 2πi(N p -j)
(e j (a) -1) (e -j (a) -1)

We now reorganise the exponentials and the denominators into sinc functions and include the product of the means, qv = q 0 v 0 :

q n v n = j∈Z p∈Z
(-1) q j v -j sinc π j N sinc π N p -j N

For well-behaved functions, the Fourier coefficents q j and v j tends towards 0 with increasing indices. Unless p = 0, either q j or v N p-j will likely be negligible.

Consequently, we propose the following approximation for the mean flow term :

q n v n ≈ j∈Z q j v -j sinc 2 (πj/N )

Figure 1

 1 Figure 1.1: Assimilation of specific humidity at 600 hPa over the South Pole based on ERA Interim data and radiosoundings

Figure 1 . 2 :

 12 Figure 1.2: Ten day ERA Interim reforecasts for specific humidity at 600 hPa over the South Pole.

Figure 1

 1 Figure 1.3: Spin-up of the ERA Interim water cycle for the entire atmosphere (a), the polar cap north of 70 • N (b) and the Antarctic ice sheet (c).

Figure 1 . 4 :

 14 Figure 1.4: Arctic radiosonde launch sites active from 1979 to 2013 with the proportion of missing daily values (pie charts). Rejected sites are semi-transparent.

Figure 1 . 5 :

 15 Figure 1.5: Same as Figure 1.4 but for the Antarctic. No rejection threshold was applied.

Figure 1

 1 Figure 1.6: Arctic domains : the polar caps north of 60 • N, 70 • N, the Arctic Ocean defined in Serreze et al. (2006) and the Greenland ice sheet defined in Cullather and Bosilovich (2011).

Figure 1

 1 Figure 1.7: Antarctic domains : the polar caps south of 60 • S, 70 • S, the Antarctic ice sheet (smoothed boundary in red, excludes ice shelves) and plateau (elevation > 2250 m), as in Palerme et al. (2014).

  N in ERA Interim follow an eastward zonally symmetric flow with magnitudes of approximately 25 kg m -1 s -1 (Figure 2.1, a). The magnitudes decrease with latitude following the decreasing temperature and humidity, from 70 kg m -1 s -1 over Northern Europe to zero over the central Arctic. Deviations occur from the zonal pattern, particularly in the northern North Atlantic as shown in Figure 2.1 (b). Transport over the Denmark Strait is clearly influenced by the cyclonic circulation associated with the Icelandic Low. Over the Norwegian Sea, the transport is the most intense (more than 80 kg m -1 s -1 ) and exhibits a definite northward component. Over Alaska and the Bering Strait, the transport is weaker in magnitude (approximately 50 kg m -1 s -1 ) but is directed straight towards the North Pole ; the same holds for the Labrador Sea and the Davis Strait.The other datasets correspond well with the broad features of this climatology. As shown in Figure2.1 (c), the differences between the mean moisture transport in ERA Interim and in the other reanalyses are on the order of 10 kg m -1 s -1 , constituting approximately one fifth to one fourth of the mean transport magnitude. The differences in model resolution are likely the reason for the larger spread over regions with complex orography such as Alaska, Scandinavia and Greenland. The first generation datasets, NCEP NCAR R1 and NCEP DOE R2 (turquoise and orange arrows in Figure2.1, c and d), are often in disagreement with the other reanalyses in these areas. Their relatively coarse resolution (T62, 2.5 • ) does not allow fine-scale features to be adequately captured, such as off the southwestern shore of Greenland. In the higher resolution versions of Figure2.1 (not shown here), the ensemble spread was not appreciably reduced in the vicinity of the radiosonde sites.The longitude distribution of moisture transports at 70 • N confirms the consensus among

Figure 2

 2 Figure 2.1: Time-averaged (1979-2013) vertically integrated moisture flux north of 60 • N in ERA-Interim (a) and, with the same arrow scale, a zoom on the northern North Atlantic (b). Panels (c) and (d) show the differences in vertically integrated moisture flux between the other 6 reanalyses and ERA-Interim (same arrow scales).

Figure 2 . 3 :

 23 Figure 2.3: Climatological vertically integrated meridional moisture flux derived from reanalyses and radiosoundings (1979-2013) at the location of the radiosonde stations (a), idem for precipitable water (b) and for the meridional wind at 850 hPa (c). Panel (d) gives the location of the radiosonde stations.

Figure 2 . 4 :

 24 Figure2.4: Mean vertical profiles of the seven reanalyses co-located with the selected radiosonde sites and averaged over all these sites for the meridional moisture flux (a), specific humidity (b) and meridional wind (c). The lower panels show the correlations between the said variables in reanalyses and in the radiosoundings.

Figure 2

 2 Figure 2.5: Histogram of the long-term averaged (1979-2013) moisture budget terms (mm year -1 ) for the polar caps north of 70 • N and north of 60 • N, the Arctic Ocean and the Greenland ice sheet.

  Figure 2.6 shows the climatological mean moisture transport due to the mean flow and transient eddies as represented in ERA Interim. Driven by the westerly winds, the mean flow is largely responsible for the zonal component of the total transport.

Figure 2

 2 Figure 2.6: Reynolds decomposition (Equation 1.11) of the moisture fluxes in ERA-Interim : north of 60 • N (a) and with the same arrow scale, a zoom on the northern North Atlantic (b).

Figure 2

 2 Figure 2.7: Longitudinal distribution of the vertically integrated total moisture transport at 70 • N (solid bars) and its transient eddy component (from Equation 1.11, semi-transparent bars ; all bars start from zero) in the seven reanalyses. Each set of bars correspond to the average over 45-degree longitudinal bands, defined in the map in the lower panel.

  latitude and subpolar stormtracks and atmospheric humidity undergo significant changes throughout the year. The seasonal march of net precipitation over the Arctic is pronounced because precipitation and evaporation are strongly dependent on the seasonal variations in sea ice extent. All reanalyses show a similar seasonal behaviour of moisture convergence north of 70 • N (Figure 2.9). The maximum of moisture convergence (∼ 25 mm month -1 ) is observed in July in all reanalyses except for NCEP NCAR R1 and NCEP DOE R2 which lag by one month compared to the other products. A winter minimum of about 12 mm month -1 is observed from December to March. The moisture transport component associated with transient eddies accounts for nearly the entire moisture convergence, providing up to 90% in winter and summer and up to 100% in the interseasons.

Figure 2 .Figure 2 . 9 :Figure 2

 2292 Figure 2.10 (b) shows the annual cycle of precipitable water over the chosen radiosonde locations, which reaches a maximum in July, two months before the peak in moisture trans-

)

  Figure 2.11: Same as Figure 2.7 but for the Arctic winter season (JFMA, panel a) and the Arctic summer season (JASO, panel b).

  with different time windows to evaluate how robust these patterns were. Unlike MERRA (Figure 2.12, b), the significance of the trends in ERA Interim (panel c) is very sensitive to the starting year of the record : 1989 was a year of exceptionally strong fluxes. The impact of 1989 is evident in all reanalyses with the exception of MERRA. Over the 1979-2013 period, the trends in moisture transport are not statistically different from zero. The Reynolds decomposition of the moisture flux gives some insight into the post-1989 decline. During this period, the transient eddy fluxes remained constant (Figure 2.13, a) but the contribution of stationary eddies and the polar cell dropped (panels b and c). The transport by the mean flow was responsible for the weakening of the meridional total moisture flux : by the turn of the millennium, transient eddies provided all of the moisture transport (panel d).

Figure 2 .

 2 Figure 2.12: Time series of the mean meridional moisture flux through 70 • N in all reanalyses (a). Slope of the linear trend for the said variable for MERRA (b) and ERA Interim (a) for different time windows. Statistical significance is denoted by hatches.

Figure 2

 2 Figure 2.13: Time series of moisture convergence to the polar cap north of 70 • N via the aerological method decomposed into the transient eddy part (a), the stationary eddy part (b) and the vertical cell (c) according to Equation1.12. Panel (d) shows the transient eddy part divided by the total flux. Time series of the terms of the moisture budget for the said region : net precipitation or P-E via the physics output method (e), precipitation (f), evaporation (g) and the residual, i.e. the difference between the physics output and the aerological methods (h). Panel (i) on the lower left displays the meridional moisture flux in reanalyses and radiosondes averaged over all selected stations whereas panel (j) on the right does the same for the precipitable water variable. The regression line of the variable is drawn (in dashes) if its trend is statistically significant at the 95% level (Student t-test).

Figure 2 .

 2 Figure 2.13 (i) and (j) show the comparison between reanalyses and IGRA data for meridional moisture fluxes and precipitable water, respectively. The radiosoundings indicate weaker moisture transport in the 1980s than the reanalyses but after 1989, the different transport estimates are highly consistent. Changes in precipitable water content are also very consistent across datasets, showing upward trends ranging from 5.0 to 9.8% over the 35-year period, with statistical significance at the 95% level.

Figure 2 Figure 2

 22 Figure 2.14: The covariance of meridional wind and specific humidity at 70 • N decomposed into : the standard deviation of specific humidity (a), the standard deviation of meridional wind (b) and the correlation between both variables (c) according to Equation 2.2. Time series of the vertically integrated moisture flux through 70 • N can be found in panel (d). Regression lines are drawn (in dashes) if the trends are statistically significant.

  and 1.5 shows that, of the two polar regions, the Antarctic is the poor relation. Ongoing long-term upper-air measurements are limited to the coast of East Antarctica and the South Pole station. Inland, the radiosonde program at Vostok Station stopped in 1992 ; at Dome C, winter-overs started in 2005 only.

Figure 3 . 1 :

 31 Figure 3.1: Mean vertically integrated moisture flux south of 60 • S in ERA-Interim (a) and, with twice the arrow scale, a zoom on just the ice sheet (b). Panel (c) shows the differences in vertically integrated moisture flux between the other 6 reanalyses and ERA-Interim, idem for panel (d) with twice the scale on just the ice sheet.

Figure 3 . 3 :Figure 3

 333 Figure 3.3: Estimates of the vertically integrated meridional moisture flux derived from reanalyses and radiosoundings at the location of the coastal radiosonde stations (a), idem for precipitable water (b) and for the meridional wind at 850 hPa (c). Panel (d) gives the location of the radiosonde stations

  (2013) suggested to use moisture convergence over Antarctica as a proxy for accumulation. Moisture fluxes are observed more reliably outside the domain whereas net precipitation is computed by the model using different and potentially inappropriate parameterisations. The convergence product has one drawback : even in spectral space and on model levels, its computation generates numerical artefacts. In East Antartica, some spatial patterns are suspiciously aligned along meridians (this would not affect continent-wide averages). Unlike snowfall, the convergence can sometimes be negative : net sublimation occurs in the vicinity of the McMurdo Dry Valleys (77 • S, 162 • E), on the Lambert Glacier and on the plateau, even if the former may be artefacts. The strong convergence over the Antarctic Peninsula is shifted towards the West compared with the satellite snowfall. ERA Interim's snowfall is everywhere below 1500 mm per year whereas the convergence may be greater than 2000 mm per year. The difference is due to liquid precipitation and the analysis increment.

Figure 3 . 5 :Figure 3

 353 Figure 3.5: Mean snowfall rate from August 2006 to April 2011 according to CloudSat (a) and ERA Interim (b). These two panels are reproduced from Palerme et al. (2014). Mean convergence of atmospheric water -vapour and condensate -in ERA Interim, for the same time window and colour scale (c).

Figure 3

 3 Figure 3.7: Reynolds decomposition (Equation 1.11) of the moisture fluxes in ERA-Interim : south of 60 • S (a) and with twice the arrow scale, just on the Antarctic ice sheet (b).

  8: Distribution of the vertically integrated total moisture transport along the boundary of the Antarctic ice sheet and its transient eddy component (from Equation

  . Given their preferred meridional orientation, transient eddies are responsible for most of the southward moisture flux : around 90% at 70 • S (Figure 3.9, b). The stationary eddies are considerably weaker, despite the moisture contrasts along the latitude circles intersecting the coast (mostly between 65 and 80 • S). The polar cell is of comparable magnitude : it advects moisture away from the pole south of 65 • S.

Figure 3

 3 Figure 3.9, (c) shows data interpolated along the smoothed boundary of the ice sheet.

  Figure 3.9: Meridional distribution in absolute (a) and relative values (b) of the different terms of the Reynolds decomposition (Equation 1.12) of the southward moisture flux and their vertical profiles along the coast of the Antarctic ice sheet (c).

Figure 3 .Figure 3

 33 Figure 3.10: Seasonal cycle of the moisture budget for the Antarctic ice sheet. The residual term is equal to net precipitation minus convergence minus the rate of change of precipitable water.

  12: Same as Figure 3.8 but for summer (DJF, panel a) and winter (JJA, panel b). troduction of AMSU in the late 1990s, ERA Interim by the increased assimilation of SSM/I radiances between 1992 and 2005 when the mission was ended.

Figure 3

 3 Figure 3.13: Time series of moisture convergence to the Antarctic ice sheet via the aerological method (a). On the smoothed boundary, the fluxes were decomposed into the transient eddy part (b), the stationary eddy part (c) and the vertical cell (c) according to Equation1.12. Time series of the terms of the moisture budget for the said region : net precipitation or P-E via the physics output method (e), precipitation (f), evaporation (g) and the residual, i.e. the difference between the physics output and the aerological methods (h). The regression line of the variable is drawn (in dashes) if its trend is statistically significant at the 95% level (Student t-test).

Figure 3

 3 Figure 3.14: Average time of the radiosonde launch at the nine IGRA coastal stations. A station is considered to have regular observations at a given hour (midnight or midday) if it has more than 50% of valid soundings for this time of the day. 'None' refers to an absence of regular soundings.

Figure 3

 3 Figure3.15: Anomalies of the southward moisture flux averaged over the IGRA coastal stations (a) ; idem with precipitable water. A regression line is drawn (in dashes) if the trend is statistically significant at the 95% level (Student t-test).

Figure 4

 4 Figure 4.1: Periodogram of the mean moisture flux at 70 • N for the period 1979-2013 from ERA Interim. The linear scale spectrum has been divided by d log 10 j dj to account for the logarthmic scale.

N

  is the set of postive integers. The terms with indices lower or equal to N correspond to periods of a month or more, those with indices higher than N correspond to periods less than a month, miroring the Reynolds decomposition. We average Equation 4.6 over the 70 • N parallel using the time averaged weights from Equation 1.10.

  Figure 4.1 shows each time scale's share of the total moisture flux at 70 • N. The periodogram peaks between one month and one week, which is consistent with the return time of cyclones. Interestingly, the annual cycles of humidity and meridional wind are anticorrelated.

  • N with temporal cutoffs ranging from 35 years to 6 hours and compute the mean flow contribution to the total fluxes (Figure 4.2). The output of the Fourier decomposition and cardinal sine formula (Equation 4.7) are plotted alongside. This time, the spectrum in Figure 4.1 is displayed as a cumulative distribution function rather than a density. Each coefficient's contribution

Figure 4

 4 Figure 4.2: Relative contribution of the mean flow to the moisture transports through 70 • N depending on the time scale defining mean flow and transient eddies and the method chosen : Reynolds, Fourier or the cardinal sine formula ; based on ERA Interim fluxes for the 1979-2013 period.

  Figure 4.3 (a).The SLP fields used by the algorithm are from ERA Interim.

  Figure 4.3 (b) reveals the two main storm tracks : in the North Atlantic and North Pacific, as well as other regions of cyclonic activity : the Baffin Bay and Northern Eurasia. Some of these regions overlap with the areas of intense transient eddy fluxes in Figure 2.6. Over the whole archive, we isolate the cyclones crossing the 70 • N parallel. Figure 4.4 shows storm-centered composites of several fields in the vicinity of these cyclones at the time of the crossing. The moisture flux vector field (arrows) is arranged in an eddy pattern centered on the cyclone center, superimposed on the mean westerly circulation. The magnitude of the zonal flux decreases with the latitude, along with the integrated water content (coloured contours). The northward flux to the east of the cyclone feeds on the warm and moist mid-latitude air whereas to the west of the cyclone, the southward flux advects cold and dry Arctic air. The zonal patern of integrated water vapour is subsequently deformed by the eddy revealing the cold and warm sectors of the cyclone and a closed contour of especially moist air near the cyclone center. The meridional moisture fluxes are maximal at

Figure 4

 4 Figure 4.3: The trajectories of the first 50 cyclones of 1979 according to the IORAS algorithm running on ERA Interim SLP fields (a). With the same method and data from 1979 to 2013 : map of cyclone frequencies i.e. percentage of the time at least one cyclone was within 500 km of ny point.

Figure 4 . 4 :

 44 Figure 4.4: Storm centered composites of precipitable water (coloured contours), moisture fluxes (arows) and moisture convergence (black contours : solid if positive, dashed if negative) using IORAS tracks and ERA Interim fields. The composited cyclones were crossing the 70 • N parallel at all longitudes ; the coastlines for longitude 0 • were drawn to give a sense of scale.

  Figure 4.5: Example of our flux attribution algorithm on a cyclone crossing the 70 • N parallel (2008/02/21). The top panel shows the meridional moisture flux at 70 • (red curve) and the band-passed version on which the algorithm operates (blue curve). Below is a map displaying the fluxes in the neighbourhood of the cyclone. The purple and orange points signal the western and eastern boundaries of the cyclone.

Figure 4

 4 Figure 4.6: Distributions of fluxes due to cyclones crossing the 70 • N parallel during the 1979-2013 period from ERA Interim data.

Figure 4

 4 Figure 4.5 (a). The compositing removed the noise that prevented the attribution algorithm from functioning : the composites can be fed into the algorithm without fear of rejection. On the downside, we can no longer attribute a flux to a single cyclone. The compositing procedure is illustrated by Figure 4.7. For each time step in the 1979-2013 period,

Figure 4

 4 Figure 4.8 (a) shows the output of the algorithm without the instructions in italics. Let us interpret the meaning of the blue-white-red colour at a given latitude φ and longitude

Figure 4 . 7 :

 47 Figure 4.7: The four steps of the cyclone compositing algorithm, applied to the 1 st of January 1979. The green points locate the cyclones. The bold lines in panel (b) define each cyclone's closest neighbours.

Figure 4 . 8 :

 48 Figure 4.8: Output of the flux attribution algorithm on the profile composites without partitioning the fluxes between cyclones (a) and with a division of the fluxes between the closest cyclones (b).

Figure 4 . 9 :

 49 Figure 4.9: Share of moisture fluxes due to cyclones depending on their strength, using the central SLP to sort them into deciles.

  mainly cover evaporation, precipitation and runoff. These assessments will benefit from estimates of moisture advection, which shed additional light on the mechanisms of change and the model capacity to represent these mechanisms. 2.2 Longitudinal distribution of the climatological vertically integrated meridional moisture flux at 70 • N in different reanalyses (1979-2013). The grey shaded bands indicate the ranges corresponding to plus or minus one interannual standard deviation from the mean. . . . . . . . . . . . . . . . . . . . . . . . 2.3 Climatological vertically integrated meridional moisture flux derived from reanalyses and radiosoundings (1979-2013) at the location of the radiosonde stations (a), idem for precipitable water (b) and for the meridional wind at 850 hPa (c). Panel (d) gives the location of the radiosonde stations. . . . . . 2.4 Mean vertical profiles of the seven reanalyses co-located with the selected radiosonde sites and averaged over all these sites for the meridional moisture flux (a), specific humidity (b) and meridional wind (c). The lower panels show the correlations between the said variables in reanalyses and in the radiosoundings. 2.5 Histogram of the long-term averaged (1979-2013) moisture budget terms (mm year -1 ) for the polar caps north of 70 • N and north of 60 • N, the Arctic Ocean and the Greenland ice sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Reynolds decomposition (Equation 1.11) of the moisture fluxes in ERA-Interim : north of 60 • N (a) and with the same arrow scale, a zoom on the northern North Atlantic (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Longitudinal distribution of the vertically integrated total moisture transport at 70 • N (solid bars) and its transient eddy component (from Equation 1.11, semi-transparent bars ; all bars start from zero) in the seven reanalyses. Each set of bars correspond to the average over 45-degree longitudinal bands, defined in the map in the lower panel. . . . . . . . . . . . . . . . . . . . . . . . 2.8 Meridional distribution in absolute (a) and relative values (b) of the different terms of the Reynolds decomposition (Equation 1.12) of the meridional moisture flux and their vertical profiles at 70 • N (c). . . . . . . . . . . . . . . 2.9 Seasonal cycle of the moisture budget for the polar cap north of 70 • N. The residual term is equal to net precipitation minus convergence minus the rate of change of precipitable water. . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Annual cycle of the meridional moisture flux (a) and of precipitable water (b) in reanalyses and IGRA, averaged over all the radiosonde sites. . . . . . . . . 2.11 Same as Figure 2.7 but for the Arctic winter season (JFMA, panel a) and the Arctic summer season (JASO, panel b). . . . . . . . . . . . . . . . . . . . . . 2.12 Time series of the mean meridional moisture flux through 70 • N in all reanalyses (a). Slope of the linear trend for the said variable for MERRA (b) and ERA Interim (a) for different time windows. Statistical significance is denoted by hatches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13 Time series of moisture convergence to the polar cap north of 70 • N via the aerological method decomposed into the transient eddy part (a), the stationary eddy part (b) and the vertical cell (c) according to Equation 1.12. Panel (d) shows the transient eddy part divided by the total flux. Time series of the terms of the moisture budget for the said region : net precipitation or P-E via the physics output method (e), precipitation (f), evaporation (g) and the residual, i.e. the difference between the physics output and the aerological methods (h). Panel (i) on the lower left displays the meridional moisture flux in reanalyses and radiosondes averaged over all selected stations whereas panel (j) on the right does the same for the precipitable water variable. The regression line of the variable is drawn (in dashes) if its trend is statistically significant at the 95% level (Student t-test). . . . . . . . . . . . . . . . . . . 2.14 The covariance of meridional wind and specific humidity at 70 • N decomposed into : the standard deviation of specific humidity (a), the standard deviation of meridional wind (b) and the correlation between both variables (c) according to Equation 2.2. Time series of the vertically integrated moisture flux through 70 • N can be found in panel (d). Regression lines are drawn (in dashes) if the trends are statistically significant. . . . . . . . . . . . . . . . . . . . . . . . . 2.15 Vertical profile of the trend in meridional moisture flux at 70 • N (a). Bold lines correspond to statistically significant trends. Vertical profile of the trend in normalized moisture flux (b). The normalized flux is defined as [ qv]/(σ t,λ,p q σ t,λ,p v) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Mean vertically integrated moisture flux south of 60 • S in ERA-Interim (a) and, with twice the arrow scale, a zoom on just the ice sheet (b). Panel (c) shows the differences in vertically integrated moisture flux between the other 6 reanalyses and ERA-Interim, idem for panel (d) with twice the scale on just the ice sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Distribution of the mean meridional vertically integrated moisture flux on the boundary of the Antarctic ice sheet in different reanalyses. The grey shaded bands indicate the ranges corresponding to plus or minus one interannual standard deviation from the mean. . . . . . . . . . . . . . . . . . . . . . . . 3.3 Estimates of the vertically integrated meridional moisture flux derived from reanalyses and radiosoundings at the location of the coastal radiosonde stations (a), idem for precipitable water (b) and for the meridional wind at 850 hPa (c). Panel (d) gives the location of the radiosonde stations . . . . . . . . 3.4 Time-averaged (1979-2013) vertical profiles of the seven reanalyses co-located with the coastal radiosonde sites and averaged over all these sites for the meridional moisture flux (a), specific humidity (b) and meridional wind. The lower panels show the correlations between the said variables in reanalyses and in the radiosoundings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Mean snowfall rate from August 2006 to April 2011 according to CloudSat (a) and ERA Interim (b). These two panels are reproduced from Palerme et al. (2014). Mean convergence of atmospheric water -vapour and condensate -in ERA Interim, for the same time window and colour scale (c). . . . . . . . . . 3.6 Histogram of the long-term averaged (1979-2013) moisture budget terms (mm year -1 ) for the polar caps south of 60 • S, 70 • S and the Antarctic ice sheet and plateau. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Reynolds decomposition (Equation 1.11) of the moisture fluxes in ERA-Interim : south of 60 • S (a) and with twice the arrow scale, just on the Antarctic ice sheet (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Distribution of the vertically integrated total moisture transport along the boundary of the Antarctic ice sheet and its transient eddy component (from Equation 1.11, semi-transparent bars ; all bars start at zero) in the seven reanalyses (1979-2013). Each set of bars correspond to the average over 45degree longitudinal bands, defined in the map in the lower panel. . . . . . . . 3.9 Meridional distribution in absolute (a) and relative values (b) of the different terms of the Reynolds decomposition (Equation 1.12) of the southward moisture flux and their vertical profiles along the coast of the Antarctic ice sheet (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 Seasonal cycle of the moisture budget for the Antarctic ice sheet. The residual term is equal to net precipitation minus convergence minus the rate of change of precipitable water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Annual cycle of the meridional moisture flux (a) and of precipitable water (b) in reanalyses and IGRA, averaged over all the radiosonde sites. . . . . . . . . 3.12 Same as Figure 3.8 but for summer (DJF, panel a) and winter (JJA, panel b). 3.13 Time series of moisture convergence to the Antarctic ice sheet via the aerological method (a). On the smoothed boundary, the fluxes were decomposed into the transient eddy part (b), the stationary eddy part (c) and the vertical cell (c) according to Equation1.12. Time series of the terms of the moisture budget for the said region : net precipitation or P-E via the physics output method (e), precipitation (f), evaporation (g) and the residual, i.e. the difference between the physics output and the aerological methods (h). The regression line of the variable is drawn (in dashes) if its trend is statistically significant at the 95% level (Student t-test). . . . . . . . . . . . . . . . . . . 3.14 Average time of the radiosonde launch at the nine IGRA coastal stations. A station is considered to have regular observations at a given hour (midnight or midday) if it has more than 50% of valid soundings for this time of the day. 'None' refers to an absence of regular soundings. . . . . . . . . . . . . . . . . 3.15 Anomalies of the southward moisture flux averaged over the IGRA coastal stations (a) ; idem with precipitable water. A regression line is drawn (in dashes) if the trend is statistically significant at the 95% level (Student t-test). 4.1 Periodogram of the mean moisture flux at 70 • N for the period 1979-2013 from ERA Interim. The linear scale spectrum has been divided by d log 10 j dj to account for the logarthmic scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Relative contribution of the mean flow to the moisture transports through 70 • N depending on the time scale defining mean flow and transient eddies and the method chosen : Reynolds, Fourier or the cardinal sine formula ; based on ERA Interim fluxes for the 1979-2013 period. . . . . . . . . . . . . 4.3 The trajectories of the first 50 cyclones of 1979 according to the IORAS algorithm running on ERA Interim SLP fields (a). With the same method and data from 1979 to 2013 : map of cyclone frequencies i.e. percentage of the time at least one cyclone was within 500 km of ny point. . . . . . . . . . . . 4.4 Storm centered composites of precipitable water (coloured contours), moisture fluxes (arows) and moisture convergence (black contours : solid if positive, dashed if negative) using IORAS tracks and ERA Interim fields (1979-2013). The composited cyclones were crossing the 70 • N parallel at all longitudes ; the coastlines for longitude 0 • were drawn to give a sense of scale. . . . . . . 4.5 Example of our flux attribution algorithm on a cyclone crossing the 70 • N parallel (2008/02/21). The top panel shows the meridional moisture flux at 70 • (red curve) and the band-passed version on which the algorithm operates (blue curve). Below is a map displaying the fluxes in the neighbourhood of the cyclone. The purple and orange points signal the western and eastern boundaries of the cyclone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Distributions of fluxes due to cyclones crossing the 70 • N parallel during the 1979-2013 period from ERA Interim data. . . . . . . . . . . . . . . . . . . . 4.7 The four steps of the cyclone compositing algorithm, applied to the 1 st of January 1979. The green points locate the cyclones. The bold lines in panel (b) define each cyclone's closest neighbours. . . . . . . . . . . . . . . . . . . 4.8 Output of the flux attribution algorithm on the profile composites without partitioning the fluxes between cyclones (a) and with a division of the fluxes between the closest cyclones (b). . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Share of moisture fluxes due to cyclones depending on their strength, using the central SLP to sort them into deciles. . . . . . . . . . . . . . . . . . . . .

•

  e j (a) -1) (e k (a) -1) N -1 n=0 (e j+k (a)) n 106 If (j + k)/N ∈ Z, the e j+k (a) n or (e 2πi(j+k)/N ) n for n ∈ [[1, N ]] constitute a geometric series whose sum is : N -1 n=0 (e j+k (a)) n = e j+k (a) N -1 e j+k (a) -1

Table 1 .

 1 2: Mean meridional moisture flux averaged over all radiosonde sites in reanalyses and IGRA (kg m -1 s -1

	Dataset	NCAR R1 DOE R2 JRA 25 ERA I CFSR MERRA JRA 55 IGRA
	subsampled	9.31	9.47	9.52	9.66	9.33	9.92	9.47	8.76
	unsampled	10.04	10.11	9.68	9.67	9.48	10.26	9.71

Table 2 .

 2 1: Long-term averaged moisture budget terms (mm year -1 ) for the polar caps north of 70 • N and north of 60 • N, the Arctic Ocean and the Greenland ice sheet : T refers to the total poleward moisture transport, P to precipitation and E to evaporation. Values in brackets are the interannual standard deviations. This table is adapted from[START_REF] Cullather | The moisture budget of the polar atmosphere in MERRA[END_REF].

Table 2 .

 2 2: Long-term averaged components of the moisture convergence north of 70 • N (mm year -1 ) according to Equation1.12. {[ v nd ]} is the residual of Equation1.16. Values in brackets are the interannual standard deviations.

	R1 192 (14)	176 (10)	40 (9)	-26 (7)	0.8 (0.0)
	NCEP DOE R2	199 (14)	178 (10)	45 (10)	-24 (8)	0.2 (0.0)
	JRA 25	187 (14)	167 (9)	40 (9)	-22 (7)	2.1 (0.0)
	ERA Interim	196 (13)	180 (11)	40 (9)	-23 (6)	-1.3 (0.0)
	NCEP CFSR	192 (15)	176 (11)	40 (10)	-22 (6)	-2.4 (0.0)
	MERRA	200 (14)	183 (11)	42 (10)	-30 (7)	0.4 (0.0)
	JRA 55	193 (14)	173 (10)	41 (10)	-25 (8)	0.2 (0.0)

  • E) and Davis Station (68 • S, 77 • E) are both located near glacier outlets (Shirase and Lambert Glaciers, respectively) nested in such valleys. CFSR is paradoxical : it is either the closest to the radiosonde observations, or the furthest (at Halley Station, 75 • S, 26 • W and McMurdo Station, 77 • S, 166

Table 3

 3

	variable	source	ice sheet altitude >2250 m altitude <2250 m
	snow accumulation Arthern et al. (2006)	163	81	243
	snowfall	Palerme et al. (2014)	171	36	303
	snowfall	ERA Interim	163	49	273
	precipitation	ERA Interim	178	50	305
	net precipitation	ERA Interim	154	46	260
	water convergence	ERA Interim	166	60	271

.1: Long-term averaged

moisture budget terms (mm year -1 ) for the polar caps south of 60 • S, 70 • S, and the Antarctic ice sheet and plateau ; T refers to the total poleward moisture transport, P to precipitation and E to evaporation. Values in brackets are the interannual standard deviations. This table is adapted from

[START_REF] Cullather | The moisture budget of the polar atmosphere in MERRA[END_REF]

.

Table 3 .

 3 2: Climatologies of snow accumulation, snowfall, precipitation and water convergence over domains excluding the cap south of 82 • S (mm year -1 ). Apart from[START_REF] Arthern | Antarctic snow accumulation mapped using polarization of 4.3-cm wavelength microwave emission[END_REF], the climatologies start in August 2006 and end in April 2011.

Résumé : La vapeur d'eau convergeant vers les régions polaires se condense en nuages qui retiennent la chaleur terrestre. Ces nuages donnent lieu à des précipitations, qui adoucissent les océans polaires et épaississent les calottes de glace. Sans changement des vents, le transport de vapeur d'eau est appelé à augmenter dans un climat plus chaud et donc les chutes de neige sur les calottes également. Le surplus d'humidité risque cependant de rétroagir sur le réchauffement de surface. Afin de contraindre les projections futures, cette thèse se propose d'évaluer la variabilité actuelle du cycle de l'eau dans les hautes latitudes. Elle s'appuie sur sept réanalyses globales et des observations par radiosondages allant de 1979 à 2013. Leurs biais intrinsèques et les approximations de calcul n'entament pas les conclusions principales de cette étude. En Arctique, mise à part une légère surestimation, le transport d'humidité dans les réanalyses est remarquablement proche des observations, aussi bien dans le temps que dans l'espace. Dans toutes les réanalyses, les perturbations météorologiques advectent la majeure partie de la vapeur d'eau en provenance des moyennes latitudes, de 89 à 94% à 70 • N. D'après la plupart des sources, évaporation, précipitation et humidité atmosphérique augmentent en accord avec l'élévation des températures. Toutefois, les flux de vapeur d'eau ne suivent pas la loi de Clausius-Clapeyron car humidité et vents sont moins corrélés, notamment près de la surface. En Antarctique, le manque d'observations se fait sentir : la convergence de vapeur d'eau sur la calotte varie de 117 à 156 mm par an selon les réanalyses. Le transport côtier, très variable dans l'espace, résulte de l'alternance entre vents catabatiques et passages de perturbations. Sur la côte, les radiosondages signalent une augmentation significative des flux d'humidité vers le Sud. À l'échelle du continent en revanche, les réanalyses ne font état de quasiment aucune tendance. Enfin, le rôle des phénomènes météorologiques d'échelle courte est évalué de nouveau, selon plusieurs méthodes. En particulier, les cyclones extratropicaux laissent dans les flux de vapeur d'eau une empreinte caractéristique qui peut être détectée et quantifiée.

Remerciements

Conclusions

We analysed the atmospheric water budget of both polar regions in seven reanalyses for the 1979-2013 period from the perspective of moisture transport. Moisture fluxes are computed from analysed winds and humidities unlike precipitation and evaporation, which are forecasted. They are less affected by the model spin-up or by changes in the observation system.

If constrained by enough observations, reanalyses will estimate moisture transport consistently. Generally speaking, they can be computed reliably using data archived on pressure levels and without mass-correction. Small domains aside, moisture fluxes can be conflated with atmospheric water fluxes.

In the Arctic, the evaluation of the atmospheric moisture transport in the reanalyses against the radiosonde data demonstrated a qualitative agreement in terms of longitudinal, vertical and temporal patterns but also a quantitative difference, i.e., a 6-13% overestimation of the moisture fluxes by the reanalyses compared to in situ data. Net precipitation and moisture convergence are not in balance. In fact, the inter-dataset standard deviation of the net precipitation is nearly ten times that of the moisture convergence (45 mm year -1 compared to 5.1 mm year -1 ). The meridional moisture transport to the Arctic is largely dominated by transient eddies, which explain 88-94% of the total transport at 70