Benjamin Renard

Etienne Leblois

M Thyer

D Kavetski

G Kuczera

Evaluation of a conditional simulation approach to quantify the uncertainty in spatial rainfall

Introduction: Spatial rainfall uncertainty

Evaluation of a conditional simulation approach to quantify the uncertainty in spatial rainfall Benjamin Renard [START_REF] Renard | Towards a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation[END_REF] , Etienne Leblois [START_REF] Renard | Towards a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation[END_REF] , Mark Thyer [START_REF] Lepioufle | Variography of rainfall accumulation in presence of advection[END_REF] , Dmitri Kavetski [START_REF] Lepioufle | Variography of rainfall accumulation in presence of advection[END_REF] , George Kuczera [START_REF] Leblois | Space-time simulation of intermittent rainfall with prescribed advection field: Adaptation of the turning band method[END_REF] Quantifying the uncertainty in spatial rainfall using a rainfall simulator and conditional simulations

2 ) 3 )••

 23 = Decomposition in two independent fields: non-zero rainfall and indicator, General principles • Some continuous distribution (e.g. gamma) for the non-zero field • Bernoulli distribution for the indicator Step 1: definition of homogeneous rainfall types Simulation Conditional or unconditional Application: the Ardèche catchment (2240 km²) of the raingauge network • Catchment areal rainfall for lumped models • Spatial rainfall for distributed models Hydrologic modeling • Quantifying data errors is a prerequisite to understand uncertainty in hydrologic models • Disentangling data and structural errors Objectives • Develop a conditional simulation (CS) approach to quantify rainfall spatial uncertainty • Evaluate its reliability in validation mode Conclusions Reliability assessment Evaluation using validation raingauges • Aggregation at a daily time step • Each line = 1 validation site Reliability of CS to quantify the uncertainty in spatial rainfall • Acceptable at a daily time step, less reliable for hourly rainfall • Rainfall types corresponding to heavy rainfall events are in general more reliable than small and scattered rainfall types Avenues for improvement (1) Irstea, UR HHLY Hydrology-Hydraulics, Lyon, France (University of Adelaide, School of Civil, Environmental and Mining, Australia (University of Newcastle, School of Engineering, Australia Simulation of 3D-fields (2D+t) R NZ I At its core, the simulator generates Gaussian fields, then transforms them using at-site distributions Specifications & Estimation At-site distributions Spatio-temporal variograms • Transformation by at-site distributions alters correlations • Corrections needed (see [1, 2, 3]) •Conditional simulation (CS): at gauged pixels, Are observations consistent with CS replicates? • At each time step, compute pval t = F t (obs t ) • If CS reliable, (pval t ) realizations from a uniform distribution • Cf. PIT diagnostic in ensemble forecasting Results •Tendency to under-prediction Evaluation using spatial statistics • At each time step, compute spatial statistics on all validation sites • Spatial mean, CV and Max • Max/Sum ('concentration') • XY of rainfall centroid • obs. vs. mean(CS rep), bars = stdev(CS rep) • Overall good consistency Going further… • In a hydrologic modeling perspective, important to evaluate the spatial structure in addition to station values • Good reliability at a daily time step • Larger discrepancies for hourly rainfall • Reliability highly variable amongst rainfall types • In general, 'heavy' rainfall types are the most reliable Cluster all hourly time steps into 10 "rainfall types" • Clustering based on three variables: • (i) mean and (ii) CV of non-zero R; (iii) fraction of rainy gauges • Kohonen self-organizing map + agglomerative hierarchical clustering Distribution of variables within each type Seasonality of rainfall types • Estimate space / time variograms + parameters of at-site distributions • Type-specific estimates

Acknowledgments. This work is supported by a FAST grant from the Department of Innovation, Industry, Science and Research (Australia), the Ministry of Higher Education and Research (France), and the Ministry of Foreign and European Affairs (France). The French Research Agency (ANR) also supports this work through the project FloodScale (http://floodscale.irstea.fr/)


Benjamin Renard

Krzysztof Kochanek

Michel Lang

Patrick Arnaud

Yoann Aubert

Thomas Cipriani

Eric Sauquet

Predictive performance of flood frequency analysis approaches: a national comparison based on an extensive French dataset

Keywords:

A data-based comparison framework [1]

Spirit of the game

General principles

The truth is known, but how realistic is the Monte-Carlo setup?

The local league: using atsite data only

Competing teams

The regional league: estimation at ungauged sites The local-regional league: at-site estimation using regional information

Results

: comparison of FFA implementations in France Importance of FFA in engineering Central in risk assessment and management: • Design of civil engineering structures • Inundation maps An abundance of approaches • Local estimation of a distribution • Regional implementations • Continuous simulation approaches Objectives Compare the predictive performance of FFA implementations • Presentation of the comparison framework • Application to an extensive dataset of French stations Conclusions The local league The regional league Main conclusions • Two winners: SHYPRE and L+R_GEV • The reliability of regional implementations is in general quite poor • Purely local estimation of a GEV distribution is dangerous

Application: FFA implementations in France

In particular, note the clear improvement for the GEV distribution, compared with both purely local and purely regional estimations Marked regional differences Mediterranean:

• GUM clearly inappropriate • SHYPRE ~ L+R_GEV • Slight over-estimation for SHYPRE?

Oceanic:

• No evidence that GUM is inappropriate • All implementations similar Using more information… • In general, purely local implementations are not sufficiently reliable • Benefit of additional information: rainfall (SHYPRE) or regional (L+R_GEV) • Perspective: combine more diverse sources of information


Dr Philippe Drobinski
email: philippe.drobinski@lmd.polytechnique.fr

V Ducrocq

P Alpert

k. bérAnger, M. borgA, i. brAuD, A. chAnzy, s. DAVolio, g. Delrieu, c. estournel, n. FilAli boubrAhMi J Anagnostou

V Font

Grubi�i�

V Gualdi

Homar

c. kottMeier, V. kotroni, k. lAgouVArDos P Ivančan-Picek

M C Lionello

W Llasat

Ludwig

A Lutoff

e. richArD, r. roMero, r. rotunno, o. roussot, i. ruin, s. soMot, i. tAuPier-letAge, J. tintore, r. uiJlenhoet, AnD h. Wernli Mariotti

A 10-Year Multidisciplinary Program on the Mediterranean Water Cycle

HyMeX strives to improve our understanding of the Mediterranean water cycle, its variability from the weather-scale events to the seasonal and interannual scales, and its characteristics over one decade , with a special focus on hydrometeorological extremes and the associated social and economic vulnerability of the Mediterranean territories.

M

OTIVATION AND MAJOR ISSUES. The countries around the Mediterranean basin face water problems, including water shortages and floods, that can impact food availability, cause epidemics, and threaten life and infrastructures. These problems are due to a combination of inadequate planning and management policies and of poor capability to predict hydrometeorological and climatic hazards (poor understanding of the processes and poor capability to model them). Indeed, the Mediterranean basin has quite a unique character that results from both physiographic and climatic conditions and historical and societal developments. Because of the latitudes it covers, the Mediterranean basin is a transition area under the influence of both midlatitudes and tropical climate variability: to the north, a large part of the atmospheric variability is linked to the North Atlantic Oscillation (NAO) and other midlatitude teleconnection patterns [START_REF] Luterbacher | Mediterranean climate variability over the last centuries: A review[END_REF], while the southern part of the region is under the influence of the descending branch of the Hadley cell materialized through the Azores high, with influence from El Niño-Southern Oscillation (ENSO) to the east [START_REF] Rodwell | Monsoons and the dynamics of deserts[END_REF].

All these influences lead to a large variability at different scales, going from the multidecadal scale to the mesoscale. Indeed, the complex geography of the region, which features a nearly enclosed sea with high sea surface temperature (SST) during summer and fall, surrounded by very urbanized littorals and mountains from which numerous rivers originate (Fig. 1), plays a crucial role in steering airflow. The Mediterranean Sea acts as a moisture and heat source for the atmosphere through air-sea fluxes, so that energetic mesoscale features are present in the atmospheric circulation, which can evolve to high-impact weather systems, such as heavy precipitation and flash flooding (e.g., [START_REF] Alpert | The paradoxical increase of Mediterranean extreme daily rainfall in spite of decrease in total values[END_REF][START_REF] Tarolli | Analysis of flash flood regimes in the north-western and south-eastern Mediterranean regions[END_REF][START_REF] Reale | Synoptic climatology of winter intense precipitation events along the Mediterranean coasts[END_REF], cyclogenesis and wind storms (e.g., [START_REF] Trigo | Dense water generation on a shelf: The case of the Adriatic Sea[END_REF]Lionello et al. 2012b), or heat waves and droughts (e.g., [START_REF] Hoerling | On the increased frequency of Mediterranean drought[END_REF]Stéfanon et al. 2012a). Also on the synoptic scale, a range of phenomena contribute to the genesis of hydrometeorological extremes in the different parts of the Mediterranean. They include, for instance, cyclones in the Gulf of Genoa and in the lee of the Atlas Mountains (e.g., [START_REF] Trigo | Dense water generation on a shelf: The case of the Adriatic Sea[END_REF][START_REF] Horvath | A numerical study of the first phase of a deep Mediterranean cyclone: Cyclogenesis in the lee of the Atlas Mountains[END_REF]) over the western Mediterranean, and "tropical plumes/ cloud bands" [START_REF] Ziv | A subtropical rainstorm associated with a tropical plume over Africa and the Middle-East[END_REF], active Red Sea troughs (e.g., [START_REF] Kahana | Synoptic climatology of major floods in the Negev Desert[END_REF], and Cyprus lows (e.g., Krichak et al. 2007) over the eastern Mediterranean. Some of these phenomena also point to important tropicalextratropical interactions. In contrast to the western Mediterranean, the eastern Mediterranean is strongly affected by several tropical processes as reviewed by Alpert et al. (2005). The monsoon and Indian Ocean moisture sources (Krichak et al. 2000) as well as the Red Sea trough [START_REF] Krichak | Interaction of topography and tropospheric flow-A possible generator for the Red Sea trough? Meteor[END_REF]) play important roles. Another difference between the western and the eastern Mediterranean is the significant recent increasing 50-yr trends in daily torrential rains in some western Mediterranean regions, while in the eastern Mediterranean relatively high interannual variabilities prevent any trend from being significant [START_REF] Alpert | The paradoxical increase of Mediterranean extreme daily rainfall in spite of decrease in total values[END_REF].

Heavy precipitation and flash flooding are among the most devastating natural hazards in terms of mortality [START_REF] Jonkman | Global perspectives on loss of human life caused by f loods[END_REF][START_REF] Doocy | The human impact of floods: A historical review of events 1980-2009 and systematic literature review[END_REF]. They occur most often on the northern side of the Mediterranean Sea. Even if flash floods are usually small-scale events, their suddenness and violence account for the high proportion of human losses. According to [START_REF] Jonkman | Global perspectives on loss of human life caused by f loods[END_REF], the European and African continents display the highest mortality rate due to floods or flash floods in the world. In France, over the last two decades, more than 100 deaths and several billion euros of damage were reported [START_REF] Huet | Retour d'expérience des crues de Septembre 2002 dans les départements du Gard, de l'Hérault, du Vaucluse, des Bouches du Rhône, de l'Ardèche et de la Drome[END_REF][START_REF] Delrieu | The catastrophic flashflood event of 8-9 September 2002 in the Gard region, France: A first case study for the Cévennes-Vivarais Mediterranean Hydrometeorological Observatory[END_REF]. The mortality in Europe can reach values as high as 10% of the population affected by the hydrometeorological hazards [START_REF] Jonkman | Global perspectives on loss of human life caused by f loods[END_REF]. This is consistent with findings reported by [START_REF] Viscusi | National survey evidence on disasters and relief: Risk beliefs, self-interest, and compassion[END_REF] in a comparison between natural risks and car accident risks. These authors found that what characterizes natural risks is that a small fraction of the population accounts for a large percentage of the fatalities. Floods also occur at times on the southern side of the Mediterranean Sea, as in October 2008 over the northeastern region of Morocco, in November 1968 in Tunisia, and in Algiers, Algeria, on 10 November 2001, causing 886 victims. Regarding total costs of floods, [START_REF] Hallegatte | Future flood losses in major coastal cities[END_REF] show that the most vulnerable 20 cities, where the increase in average annual losses due to floods between 2005 and 2050 will potentially be greatest, are distributed all over the world, with a concentration in the Mediterranean basin, the Gulf of Mexico, and East Asia. Such events impact particularly the coasts. With its 46,000-km coastline with more than 146 million residents and another 100 million tourists in summer, the Mediterranean basin has one of the most crowded coasts in the world and is one of the most vulnerable regions to such hazards [START_REF] Hinrichsen | Coastal Waters of the World: Trends, Threats, and Strategies[END_REF].

Because the elements at risks are highly dispersed, the management of the flash-flood risk by means of structural measures is difficult and often unsustainable in ecological or economic terms. Therefore, there is a need for better understanding the social and natural dynamics of such events in order to improve the forecasting and warning capabilities of the exposed Mediterranean societies to increase their resilience to such extreme and frequent events. Droughts can also have very serious consequences for society with the reduction of water availability, the productivity of natural and cultivated vegetation (Ciais et al. 2005;Stéfanon et al. 2012b), and energy supply due to water shortage [START_REF] Fink | The 2003 European summer heatwaves and drought-Synoptic diagnosis and impacts[END_REF].

Finally, because it is in such a transition area, the Mediterranean basin is very sensitive to global climate change at short (decadal) and long (millennial) time scales. Continental and marine paleorecords show that the climate and the sea state have varied widely in the past, sometimes very quickly [START_REF] Combourieu Nebout | Enhanced aridity and atmospheric high-pressure stability over the western Mediterranean during the North Atlantic cold events of the past 50 k.y[END_REF]. Regarding more recent periods, several authors have reported an increase of the mean annual temperature of about 0.005°C yr -1 (Quereda-Sala et al. 2000), reaching in summer the value of 0.01°C yr -1 for 1976-2000, one of the highest rates over the entire globe, and a decrease in annual precipitation (with different seasonal trends; e.g., [START_REF] Brunetti | Europe-wide reduction in the primary productivity caused by the heat and drought in 2003[END_REF][START_REF] Frich | Observed coherent changes in climatic extremes during second half of the twentieth century[END_REF][START_REF] Klein Tank | Trends in indices of daily temperature and precipitation extremes in Europe, 1946-99[END_REF][START_REF] Klein Tank | Trends in indices of daily temperature and precipitation extremes in Europe, 1946-99[END_REF][START_REF] Bougeault | High-resolution analysis of daily precipitation trends in the central Alps over the last century[END_REF][START_REF] Barkhordarian | The expectation of future precipitation change over the Mediterranean region is different from what we observe[END_REF]). In the sea, however, the time series are too short yet to provide a reliable trend (Schroeder et al. 2013). Regarding the future projection of the Mediterranean climate in an anthropogenic scenario, [START_REF] Giorgi | Climate change hot-spots[END_REF] defines the Mediterranean area as one of the two main "hot spots" of climate change, with an increase in interannual rainfall variability in addition to a strong warming and drying for 2080-99 compared with 1980-99. The regional water cycle has therefore been affected and will continue to be affected by decadal variations in addition to long-term trends [START_REF] Mariotti | Recent changes in Mediterranean water cycle: A pathway toward long-term regional hydroclimatic change?[END_REF]Mariotti and Dell'Aquila 2012). In this context, the exposure of the Mediterranean population may increase dramatically not only because events conducive to floods and droughts may become more frequent [START_REF] Gao | Projected changes in mean and extreme precipitation over the Mediterranean region from high resolution double nested RCM simulation[END_REF]) but also because the demographic projections from the Mediterranean Action Plan suggest an increase of about 22.6% until 2025.

The ability to forecast such high-impact phenomena and predict their evolution and consequences in the present climate and in a context of global climate change is still low because of the contribution of finescale processes and their nonlinear interactions with large-scale processes as well as not wellknown interactions between oceanic, atmospheric, and hydrological processes. In detail, this is due to the large uncertainties in the quantification of the Mediterranean seawater budget at various time and spatial scales, which limit our capability to determine its feedback on the variability of the continental precipitation through air-sea interactions and to identify the processes controlling the evolution of the Mediterranean climate. The large daily/seasonal variability of precipitation impacts aquifer recharge, river discharge, soil water content, and vegetation characteristics, the feedbacks of which to the atmosphere are still not well known. Hydrological and hydrogeological transfer functions are also characteristic of the Mediterranean basin, notably because of the specificities of the peri-Mediterranean karstic and sedimentary aquifers. Progress in their understanding is of primary importance for the development of integrated management of the hydrosystems, and its adaptation to anthropogenic pressure and climate change. Indeed, a major issue is to quantify the impact of change of land use/land cover, surface states, soil degradation, and water demand on rainfall modulation and water resources with respect to climate change alone. Regarding heavy precipitation, progress has to be made on the understanding of the mechanisms that govern the location of the precipitating system as well as of those that occasionally produce uncommon amounts of precipitation. The contrasted topography, the complexity of the continental surfaces in terms of geology and land use, and the difficulty in characterizing the initial moisture state of the watersheds make the hydrological impact of such extreme rainfall events very difficult to assess and predict.

Addressing these issues requires the production of a consistent database of all Earth compartments, allowing a deeper insight into such coupled processes and the validation of a large variety of models, from finescale research and forecasting land surface, ocean, and weather models, to regional climate system models. THE HYMEX PROGRAM. Gaps in our understanding of the Mediterranean water cycle, including the impact of a changing climate and human activity on extremes as well as on water availability, are still important. The Hydrological Cycle in Mediterranean Experiment (HyMeX; www.hymex.org) program is a concerted effort at the international level that aims to advance the scientific knowledge of the water cycle variability. It also aims to improve the processes-based models and the models of the regional climate system. Such models are needed for forecasting hydrometeorological extremes, their frequency, and severity, and for planning adaptation strategies against the impacts of climate variability and change and human activity in the Mediterranean basin. Specifically, HyMeX aims to 1) improve our understanding of the water cycle, with emphasis on hydrometeorological extremes, by monitoring and modeling the atmosphereland-ocean coupled system, its variability from the weather event to the seasonal and interannual scales, and its characteristics over one decade in the context of global change; 2) assess the social and economic vulnerability to hydrometeorological extremes and the adaptation capacity of the territories and populations; 3) provide support to policy makers to cope with water-related problems under the influence of global climate change.

HyMeX complements previous research projects like the Mesoscale Alpine Programme (MAP; [START_REF] Bougeault | High-resolution analysis of daily precipitation trends in the central Alps over the last century[END_REF], which is focused specifically on hydrological and atmospheric process studies driving orographic precipitation over the Alps; oceanographic programs in the Mediterranean Sea like Eddies and Gyres Paths Tracking (EGYPT; www.ifremer.fr /lobtln / EGYPT) and EGITTO (http://doga.ogs .trieste.it/sire/drifter/egitto_main.html); and Climate Change and Impact Research: The Mediterranean Environment (CIRCE; Navarra and Tubiana 2013), which is aimed at performing regional climate model simulations over the Mediterranean region for impact studies in a future climate. The analysis of the water cycle in HyMeX emphasizes key issues related to the water budget of the Mediterranean Sea, which is a relevant proxy to investigate the regional water cycle at the various time scales with the integration of the contribution of all Earth compartments because of the large moisture source that the Mediterranean Sea represents for the region (Mariotti et al. 2002). It requires an accurate modeling of the thermohaline circulation, including dense water formation through intense air-sea interactions. It also requires the quantification of the freshwater inputs from the continent to the sea (rivers and groundwater flows). This issue implies a better understanding and modeling of all the components of the continental water cycle, such as evapotranspiration, groundwater discharge/recharge, and streamf low, particularly when impacted by extreme flood events or during droughts, which are frequent in the region. Soil moisture is also a key variable for the continental surface-atmosphere interactions, and a key driver of the hydrological response during f lood events, which should be improved. Spring and summer droughts alternate with periods in fall favorable to extreme precipitation and floods, the impact of which on the Mediterranean societies are addressed in HyMeX by monitoring vulnerability factors and adaptation strategies to accommodate the impacts of such extreme phenomena. A schematic of the five scientific topics of the HyMeX project, which aim at addressing these open scientific issues, is shown in Fig. 2 and a comprehensive description of the HyMeX underlying science is provided in its International Science Plan (www.hymex.org).

A multiscale data modeling approach. This long-term experimental program includes a series of large field experiments for process and predictability studies over specific areas embedded in a 10-yr period of data collection over the entire Mediterranean basin that allows for capturing certain modes of variability 1066 JULY 2014 | and for getting a homogeneous observation network density as well as a good representativity of the measurements. It adopts a multidisciplinary (oceanic, atmospheric, hydrological, and social sciences) and seamless (from event scales to climate) strategy for both observation and modeling.

nesteD obserVAtions. The HyMeX observation strategy is based on three-level nested observation periods. The long-term observation period (LOP) began in September 2010 and will continue until 2020. It spans the entire Mediterranean region to collect the long-term time series required to study the variability of the Mediterranean water cycle from the seasonal to the interannual scales. The enhanced observation period (EOP) involves additional sites and/or instruments to increase the spatial and/or temporal resolution over three target areas (TA) during at least 4 years, in order to conduct both budget and process studies. The three target areas are as follows (Fig. 3):

1) The northwestern Mediterranean, where all the intense hydrometeorological phenomena of interest for HyMeX occur. Heavy precipitation systems and flash flooding occur over the Spanish [START_REF] Romero | Human exposure to flash floods-Relation between flood parameters and human vulnerability during a storm of September 2002 in southern France[END_REF], French [START_REF] Ricard | A climatology of the mesoscale environment associated with heavily precipitating events over a northwestern Mediterranean area[END_REF]Italian (Parodi et al. 2012) coasts as well as islands [START_REF] Barthlott | Sensitivity of deep convection to terrain forcing over Mediterranean islands[END_REF] during fall (see Ducrocq et al. 2014, a companion paper). The Gulf of Lions is one of the four major sites of dense water formation and deep ocean convection at the end of winter under the influence of the mistral and tramontana regional winds, and the Gulf of Genoa cyclogenesis [START_REF] Schott | Observations of deep convection in the Gulf of Lions, northern Mediterranean, during the winter of 1991/1992[END_REF].

2) The southeastern Mediterranean, which covers areas over western Greece notorious for heavy precipitation events [START_REF] Papagiannaki | A database of high-impact weather events in Greece: A descriptive impact analysis for the period 2001-2011[END_REF]); Crete Island, with a high pressure on water demand; the transboundary river basin of the Evros River (marks the Greek-Turkish border), which suffers from floods; as well as the Daliya, Besor (northern Neguev), and Qidron (Mount Scopus in Jerusalem) basins farther to the east in Israel. This target area allows for the study of intense rainstorms and flash floods in drier climatic areas of the Mediterranean [START_REF] Yakir | Hydrologic response of a semi-arid watershed to spatial and temporal characteristics of convective rain cells[END_REF]. 3) The Adriatic, which is composed of the Trentino-Alto Adige, Friuli Venezia Giulia, and Veneto regions in Italy, and the Dinaric Alps in Slovenia and Croatia, which are target areas for the study of heavy precipitation events and flash flooding [START_REF] Vrhovec | Mesoscale diagnostics of prefrontal and frontal precipitation in the southeast Alps during MAP IOP 5[END_REF]Davolio et al. 2009). Mesoscale orographic perturbation in the area of the Dinaric Alps also provides conditions for mesoscale cyclonic generation and the strengthening of local northeastern bora and southeastern jugo winds (Horvath et al. 2009;[START_REF] Jurčec | Severe Adriatic jugo wind[END_REF]. Dense water also forms to the north and south of the Adriatic subbasin (Vilibić and Supić 2005). The special observation periods (SOPs) were held in fall 2012 and winter 2013 over the northwestern Mediterranean target area to provide detailed and specific observations for studying key processes of the water cycle. In addition to the LOP and EOP observation frameworks, dedicated ground-based, shipborne, and airborne means were deployed during the SOPs. The collection of new datasets and the enhancement of observation means during HyMeX provide a unique opportunity to improve oceanic, hydrological, and weather forecasts as well as regional climate simulations over the Mediterranean region.

The long-term observation strategy. The long-term observation strategy, including LOP and EOP, is a key component of the observation strategy, since it allows one to put the events sampled during the SOPs in a climatological perspective. The strategy also allows the monitoring during a decade of variability, enhancing (combined with other observational datasets and with climate modeling) our capability to detect possible trends of the different components of the water cycle over the whole Mediterranean in the context of global change. The LOP relies either on existing international operational and research networks (oceanic and hydrometeorological observatories, radars, rain gauges, radiosoundings, surface weather stations, GPS, photometer and lightning networks, etc.) or on platforms developed specifically for HyMeX. Over land, hydrometeorological measurements are collected over 10 sites. They are the Catalan Hydrometeorological Observatory (CA), the Valencia site (VA), the Cévennes-Vivarais Mediterranean Hydrometeorological Observatory (OHM-CV; CV) (Fig. 4a), the Ligury-Tuscany site (LT), the central Italy site (CI), the northeastern Italy site (NEI, including Trentino-Alto Adige, Veneto, and Friuli Venezia Giulia), the Crete site (CR), the Israeli site (IS), and the Dinaric Alps (DA) (Fig. 3). The CV, NEI, and IS sites have been labeled by the Global Energy and Water Cycle Experiment (GEWEX) of the World Climate Research Programme (WCRP) [START_REF] Drobinski | HyMeX, a potential new CEOP RHP in the Mediterranean basin[END_REF](Drobinski et al. , 2011)). Atmospheric measurements are collected over three sites, located in Corsica (CO; Corsican Observatory for Research and Studies on Climate and Atmosphere-Ocean Environment), Lampedusa (LA) (Fig. 4c), and the Balearic Islands (BA). These sites are complemented by multiscale observations of the hydrological response over typical Mediterranean landscapes. This includes LOP localscale measurements of the surface energy balance, focusing on evapotranspiration and soil moisture | dynamics for water balance studies, such as the Crau-Camargue site (Fig. 4b).

The measurements from the instrumented sites are completed with observations from operational or research networks measuring precipitation from radars (Fig. 5a), atmospheric water vapor from GPS/ Global Navigation Satellite System (GNSS) (Fig. 5b), and photometers and lightning from four operational lightning detection networks-that is, the two long-range networks, the Arrival Time Difference Thunderstorm Detection System Network (ATDnet; Met Office) and ZEUS (National Observatory of Athens); and the European operational network the European Cooperation for Lightning Detection (EUCLID) and the Lightning Detection Network (LINET; nowcast GmbH) (Fig. 5c). Indeed, a fundamental element that has been missing in past field experiments are nearly simultaneous measurements of the moist inf low as a function of time, height, and along-barrier distance with measurements of the precipitation over the orography. The weather radar component of HyMeX, which involves research and operational radars together with the GPS/GNSS and Aerosol Robotic Network (AERONET) photometer networks, represents the most ambitious field project to date in the endeavor to collect such basic but hardto-obtain information to advance understanding of variability and predictability of precipitation. Even though all data from these networks are still not accessible and the effort is ongoing to collect them, the available radar and GPS/GNSS data are postprocessed for climate and process studies, water budgets computations, and verification with other techniques (radiosondes and satellite for water vapor; rain gauges for rainfall). Finally, one original aspect of HyMeX is to perform multiscale and multyear intracloud and cloud-to-ground lightning detection for observational-and modeling-based multidisciplinary studies of maritime and continental Mediterranean storms and analysis of the complex relationships between precipitation (dynamics, microphysics, interaction with aerosols), electrification, and lightning occurrence. It encompasses all the HyMeX observation periods (LOP, EOP, and SOP).

Over the sea, observations are collected with a combination of platforms navigating, drifting, or fixed. At the Mediterranean Sea scale, the LOP relies on the Argo network for a permanent pool of floats (www.argo.ucsd.edu) and on the HydroChanges network of moorings (Schroeder et al. 2013). At the western Mediterranean basin scale, HyMeX made a major effort to develop autonomous systems to be used on ships of opportunity: the Sea Embedded Observing System developed by Météo-France measures and transmits the radiative fluxes, sea surface temperature, humidity, wind, and precipitation; the TRANSMED system, a network of low-cost thermosalinometers in the Mediterranean and supported by the Mediterranean Science Commission (CIESM), measures and transmits hourly the surface temperature and salinity; and GPS enables deducing the integrated water vapor content. To date the weekly ferry service from Marseille, France, to Algiers (Fig. 6c) is equipped; the ferry from Rome, Italy, to Barcelona, Spain, is next. Hydrographic cruises are also carried out yearly by an Italian companion program for a reference on the evolution of the water masses in the entire water column. At the northwestern part of the basin, observatories such as the Mediterranean Ocean Observing System on Environment (MOOSE; www .moose-network.fr/) and the Balearic Islands Coastal Observing and Forecasting System (SOCIB; www .socib.es) provide a backbone to the HyMeX LOP. The network of gliders (submarine autonomous platforms piloted remotely and equipped with multiple sensors) documents the dynamics of the water column over ~1000 m along two main transects, complemented by the dense network of CTD casts performed every 6 months by the MOOSE cruises. Off Nice, France, and in the center of the Gulf of Lions, where deep convection occurs, the equipment of the two anchored buoys from Météo-France that record measurements in the atmospheric and oceanic surface layers was enhanced with sensors measuring radiation, salinity, and precipitation at the surface, and a thermistor chain down to 250-m depth (Fig. 6b).

As part of the EOP, an effort is made at sea to deploy additional Argo floats and gliders. Regarding EOP hydrological measurements, two main catchments (Gard and Ardèche) in the CV area are instrumented in order to document the hydrological response during and between floods based on a nested subcatchments strategy. Small catchments of a few square kilometers are instrumented to follow soil moisture dynamics and runoff response (both surface and subsurface flow) during and between floods. This includes the Pradel site (Ardèche catchment), representative of lowland covered with vineyards and natural vegetation on limestone soils; and the Valescure and Tourgueille subcatchments (Gard catchment), representative of forested mountainous areas over granites and schist, respectively. At an intermediate scale (10-100 km 2 ), rain gauge networks such as the HPiconet network around the Le Pradel site (Fig. 4a) and limnimeter networks measuring the water height dynamics and, for some of them, discharge dynamics, have been installed to document the variability of the hydrological response associated with the variability of rainfall, land use, and geology. The largest scale (100-1000 km 2 ) is documented based on operational networks measuring rainfall and discharge data. In the context of the EOP, several postflood surveys have been carried out after major flash floods in the Mediterranean area, and they will continue until 2015. Indeed, flash floods have spatial and temporal scales of occurrence that are difficult to observe with the conventional measurement networks of precipitation and discharge [START_REF] Borga | Flash f loods: Observations and analysis of hydrometeorological controls[END_REF]). These postsurvey measurements will contribute to increasing our understanding of the factors affecting the basin response to heavy rainfall as well as the factors determining the consequences of Mediterranean flash floods, thus contributing to improving the risk assessment and the predictability of this hazard.

The special observation period strategy. The first SOP (SOP1) spanned 8 weeks (5 September-6 November 2012) and was dedicated to documenting the heavy precipitating events (HPE) and associated flooding, in relation with the ocean heat content. In addition to the LOP and EOP measurements, their investigation involved dedicated platforms, including aircrafts (French Falcon 20 and ATR-42 and German Do128; see Figs. 7a,b), pressurized boundary layer balloons, and the French buoy tender Le Provence. Additional radiosoundings completed those performed in the Cévennes-Vivarais, Corsica, and central Italy sites, with some launched at sea from Le Provence. During SOP1, 18 orographic or heavy precipitation events associated with floods were documented over France as well as 11 over Italy and 6 over Spain. The detailed objectives of SOP1 and specific means deployed are described in a companion article [START_REF] Ducrocq | HyMeX-SOP1, the field campaign dedicated to heavy precipitation and flash-flooding in northwestern Mediterranean[END_REF]. The second SOP (SOP2) spanned 6 weeks (1 February-15 March 2013). It was dedicated to intense air-sea interactions, mainly under strong winds in the Gulf of Lions that cause ocean convection process, resulting in dense water formation. Luckily, dense water formation occurred in winter 2013 and was intense enough to reach the sea floor (~2500 m). During the field campaign, the French research vessels Le Suroît [companion to the Marine Ecosystems Response in the Mediterranean Experiment (MerMeX)], Tethys-2, and Le Provence (Fig. 7c) contributed to sampling the water column and the air-sea fluxes, complemented by Marisonde buoys, surface velocity program (SVP) drifters, and Argo profilers specifically modified to allow deeper and more frequent profiling when drifting in the area of oceanic convection. The French aircraft ATR-42 measured boundary layer f luxes and waves over the region of oceanic convection in synergy with pressurized boundary layer balloons measuring the temperature, pressure, humidity, and wind along a quasi-Lagrangian trajectory (Fig. 7d).

MoDeling. The HyMeX modeling strategy has been designed to be consistent with the observation strategy. It aims, through an approach integrating numerical models of the atmosphere, ocean, and land surfaces, to better simulate and predict the evolution of the environment at all scales of time and space, not only as separate processes within each Earth compartment, but as coupled mechanisms with feedback loops. This requires an approach that combines a variety of models ranging from small-scale models to models of the regional climate system. Small-scale models that represent more explicitly the oceanic, hydrological, and atmospheric phenomena under scrutiny in HyMeX will be directly compared to the SOP measurements [see details in [START_REF] Ducrocq | HyMeX-SOP1, the field campaign dedicated to heavy precipitation and flash-flooding in northwestern Mediterranean[END_REF] for SOP1] and will be used in the development of parameterizations of these processes in climate system models. This also requires the coupling of the models of the atmosphere, ocean, and land surfaces at different various resolutions to analyze how the 1071 JULY 2014 AMERICAN METEOROLOGICAL SOCIETY | finescale feedbacks associated with air-sea-land interactions can substantially influence the spatial and temporal structure of the regional climate. Past European projects like CIRCE have initiated this approach with an atmosphere-ocean regional climate modeling exercise over the Mediterranean [START_REF] Gualdi | The CIRCE simulations: Regional climate change projections with realistic representation of the Mediterranean Sea[END_REF]. HyMeX aims at going one step further by increasing the horizontal resolution of the different models and by developing regional climate system models, which consist of complementing atmosphere-ocean regional climate models with tools representing other parts of the planetary makeup, for example, vegetation models and river routing schemes.

This effort to improve the representation of processes in models is essential to better predict extreme hydrometeorological events but also the variability of the water cycle at intraseasonal to interannual scales and its evolution in the context of global climate change. The modeling strategy therefore includes the setup, validation, and improvements of multicomponents' regional climate models dedicated to the Mediterranean area: ocean, atmosphere, land surface, and hydrology in order to study interannual variability, past trends, and future climate change. Basin-scale regional climate modeling, a large part of the HyMeX activities, is common with the Mediterranean region of the Coordinated Downscaling Experiment (Giorgi et al. 2009). The joint HyMeX-MED-CORDEX activity consists of the downscaling of the Interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim; hindcast simulations including the HyMeX period between 2010 to present and until 2020) and simulations from phase 5 of the Coupled Model Intercomparison Project (CMIP5) at a horizontal resolution of 50 km or less (the resolution of the atmospheric model can be as low as 12 km and the ocean components have much higher resolutions, which can be as low as 6-7 km) for improving our knowledge of the variability of the hydrometeorological processes in the Mediterranean (e.g., [START_REF] Dubois | Future projections of the surface heat and water budgets of the Mediterranean sea in an ensemble of coupled atmosphere-ocean regional climate models[END_REF][START_REF] Gualdi | The CIRCE simulations: Regional climate change projections with realistic representation of the Mediterranean Sea[END_REF]Flaounas et al. 2013;Stéphanon et al. 2014). About 14 modeling groups contribute to the HyMeX-MED-CORDEX regional climate modeling activity, including groups in Italy, Spain, France, Israel, Turkey, Germany, Tunisia, and Serbia. Among them, 11 use regional climate system models coupling at least land surface/ ocean/atmosphere models and some also include river runoff [START_REF] Artale | An atmosphere-ocean regional climate model for the Mediterranean area: Assessment of a present climate simulation[END_REF][START_REF] Herrmann | Representation of daily wind speed spatial and temporal variability and intense wind events over the Mediterranean Sea using dynamical downscaling: Impact of the regional climate model configuration[END_REF][START_REF] Kržič | Changes in climate indices for Serbia according to the SRES-A1B and SRES-A2 scenarios[END_REF][START_REF] Drobinski | Effects of interactive vegetation phenology on the 2003 summer heat waves[END_REF][START_REF] L'hévéder | Interannual variability of deep convection in the northwestern Mediterranean simulated with a coupled AORCM[END_REF]. At present, seven groups have already performed the simulations and four plan to do so. In addition, stand-alone atmosphere, ocean, and land surface models have been run or are planned to run in forced mode at various horizontal resolution for process studies. They also serve as reanalysis tools for land surface and ocean properties and help in delineating error propagation in atmosphere/land/ocean regional coupled models. HyMeX being a processedbased project, the analysis of the hindcast simulations together with HyMeX observations will also help in the improvement and uncertainty reduction of MED-CORDEX downscaling of CMIP5 simulations. As an example, Fig. 8 shows Taylor diagrams comparing rainfall from ERA-Interim, the European Climate Assessment and Dataset (ECA&D) gridded dataset, and HyMeX/MED-CORDEX simulations performed with the Weather Research and Forecasting Model (WRF) to the rainfall measured at three station observations, at the Cévennes-Vivarais observatory in France, in northeastern Italy, and in Israel for the period 2003-08 (GEWEX-labeled HyMeX stations).

Finally, regarding forecasting, the modeling strategy includes the refinement of convective-scale deterministic forecast systems to improve the prediction capabilities of Mediterranean high-impact weather events. The SOP data provide a unique highresolution database to validate these new numerical hydrometeorological prediction systems. It also aims to design high-resolution ensemble modeling approaches coupled with hydrological models to issue probabilistic forecasts of the impact in terms of hydrological response, and to develop new parameterizations and novel data assimilation systems for the different Earth components. EOP and LOP data are also used to develop and improve models of the hydrological response at various scales and to propose a regional modeling strategy that will contribute to Basin-scale monitoring of water cycle: From satellite to data assimilation. Satellite data for Earth observation are an essential means of access to observations at time scales ranging from one day to several years throughout the Mediterranean basin, particularly over the Mediterranean Sea, where few in situ data are available. They allow for integrating in situ measurements and evaluating models used in HyMeX at various spatial and temporal scales (e.g., [START_REF] Claud | A high resolution climatology of precipitation and deep convection over the Mediterranean region from operational satellite microwave data: Development and application to the evaluation of model uncertainties[END_REF]. For the atmosphere, ocean, and land surfaces, many satellite products are already available at various data centers (cloud classifications, air temperature and humidity, wind speed deduced from cloud motions, precipitation, temperature and wind at the sea surface, radiative fluxes, aerosols, soil water content, etc.). However, some of these products are difficult to use over the coasts, which limits significantly the use of these data in complex terrain regions. Initiation of precipitating systems often occurs over the Mediterranean Sea, but the systems are not well documented by ground observations (e.g., due to the limited quantitative range, 150 km, of coastal radars). Access to new satellite rainfall measurements by the National Aeronautics and Space Administration (NASA)-Japan Aerospace Exploration Agency (JAXA) Global Precipitation Measurement (GPM; [START_REF] Hou | Global precipitation measurement[END_REF]) and improvements through ground validation over complex coastal and mountainous regions supported by HyMeX observations constitute major progress toward the quantification of the Mediterranean water cycle. Indeed, GPM aims to provide global precipitation data at a quality and scale that can facilitate flood modeling and water management applications in the mountainous terrain of the Mediterranean region. The primary contribution from GPM over the currently available satellite rainfall observations is the core satellite (dualfrequency radar and radiometer), which is expected to advance the detection and quantification of snow and light precipitation from space, which are in fact not trivial issues in the Mediterranean. In addition to the core observations, GPM will facilitate advancements in the high-resolution merged products due to the availability of more frequent observations.

To overcome the lack of reliable data or the existence of sparse data in space and time, satellite and in situ data merging or assimilation is an essential action in the HyMeX project. It includes, for instance, improved assimilation of satellite radiance from Infrared Atmospheric Sounding Interferometer (IASI) [START_REF] Vincensini | IASI retrievals over Concordia within the framework of the Concordiasi program in Antarctica[END_REF] or ozone data from the Global Ozone Monitoring Experiment-2 (GOME-2) [START_REF] Sbii | Exploring the potential application of MetOp/GOME2 ozone data to weather analysis[END_REF] as well as background error modeling. Over the ocean, one objective is to build a high-resolution reanalysis of the Mediterranean Sea circulation. T he HyMeX database (www.hymex.org/database/) implemented by Observatoire Midi Pyrénées (OMP) and L'Institut Pierre-Simon Laplace (IPSL) includes a metacatalogue that gathers information about historical, LOP, EOP, SOP, satellite, and model data; a field data relational database; a database portal website including user registration and management; and access to the data catalogue with dataset ordering thanks to a multicriteria data request interface. It is ruled by the HyMeX data policy, which gives open access to the data for research activities once the 2-yr period of exclusive access is over. For the LOP, the provision of data is sometimes performed by interoperability with data centers collecting observations or by the provision of metadata. The storage of the regional climate model simulations is performed at the Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA) in the frame of MED-CORDEX (www.medcordex.eu) with interoperability with the HyMeX database. The HyMeX database should foster collaboration between the scientists of the different disciplines (meteorology and climate, oceanography, hydrology, human sciences) and cross-cutting activities. Its general objectives are to provide the easiest possible access to all of the datasets and their associated documentation, which will facilitate their use for scientific studies beyond the HyMeX project.

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JULY 2014 | into land surface models [e.g., Organizing Carbon and Hydrology in Dynamic Ecosystems (ORCHIDEE) model; Interactions between Soil, Biosphere, and Atmosphere (ISBA)-Ags model] is a way to assess the modeling uncertainties and to consolidate monitoring systems able to describe land climate variables. The characterization of droughts requires the elaboration of a climatology of the land variables affected by droughts, such as surface soil moisture, leaf area index, the fraction of absorbed photosynthetically active radiation. Satellite-derived variables have been measured since the end of the 1980s and are available through the HyMeX database (see the sidebar for additional information). A whole land data assimilation system over the Europe-Mediterranean area and coupled to river discharge model will permit the characterization of meteorological, hydrological, and agricultural droughts [START_REF] Wilhite | Drought as a natural hazard: Concepts and definitions[END_REF]. Comparison with observations of river discharges and of soil moisture will allow the assessment of the added value of the inclusion of the satellite products and of various versions of the land surface model, and will contribute to the verification of long-term hindcast simulations. Finally, specific reanalyses will be conducted for the SOPs using the collected data.

Social vulnerability and resilience. The Mediterranean region is characterized by an increasing demography, leading to urban sprawl especially on coastal areas. In a context of climate change, the population is confronted with challenging environmental changes, such as short-time extreme events (heavy precipitation, flash floods, etc.) and long-term modifications (change in access to water resources, droughts, etc.). Potential security problems and migrations produced as a consequence of floods, water scarcity, and droughts are on the agendas of national and international administrations (i.e., European Commission 2008, 2009). Studies on adaptation capacity from an economical and societal perspective are in progress at the international level [START_REF] Adger | Vulnerability[END_REF][START_REF] Bazerman | Climate change as a predictable surprise[END_REF][START_REF] Berkhout | Learning to adapt: Organizational adaptation to climate change impacts[END_REF]), but systematic observation of social vulnerability and resilience has still to be organized at a more local scale (e.g., [START_REF] Llasat | Flash-floods in Catalonia: The social perception in a context of changing vulnerability[END_REF]e.g., Ruin et al. 2008). The HyMeX program is in part dedicated to this aspect, focusing on the development of methods to integrate environmental and social dynamics across scales. The results of the HyMeX project will provide new achievements on the dynamics of the water cycle and its impact in population and economic activities, ecosystems, and water resources, including the improvement of seasonal forecasting and future scenarios. On the other hand, the last Intergovernmental Panel on Climate Change (IPCC) report on extremes [START_REF] Allen | Summary for policymakers[END_REF][START_REF] Hallegatte | Future flood losses in major coastal cities[END_REF]) has insisted on the important roles played by changes in vulnerability and exposure in the increasing flood impact detected in the last years. The HyMeX project deals with such issues and is expected to produce different kinds of products that will have social benefit. Indeed, the improvement of the knowledge on Mediterranean storms and floods and their potential increase and synergies in future climate and the creation of databases and postevent surveys will add to analyzing the societal impact as well as the perception and resilience of populations. Besides our own outreach activity of the project, this new knowledge and information can be integrated into local and national strategies like climate change adaptation plans and laws, updating the European water directive and associated directives on floods and droughts, and civil protection strategies, including warning channel improvement.

The HyMeX approach consists of studying all factors that can influence the impact of such floods and droughts. To monitor social vulnerability to such extreme events and to learn from continuously evolving adaptive capacity and resilience processes at various space and time scales, social sciences techniques (interviews, surveys, impact reports, etc.) are used to collect behavioral, perceptual, and disaster impact data. The aim is to build a database suitable for analyzing social processes in connection with natural dynamics ranging from short-fuse and small-scale weather events (e.g., flash floods) to longer and largerscale events (e.g., water scarcity and drought). A flood database is also developed with special consideration to the societal impact (Llasat et al. 2013a,b). Starting from the work developed in the Mediterranean Experiment (MEDEX) program [START_REF] Amaro | Preliminary results of the Social Impact Research group of MEDEX: The request database (2000-2002) of two meteorological services[END_REF][START_REF] Amaro | Preliminary results of the Social Impact Research group of MEDEX: The request database (2000-2002) of two meteorological services[END_REF], the database focuses on four regions representative of the northwestern Mediterranean region (Catalonia and the Balearic Islands in Spain; Calabria in Italy; and Languedoc-Roussillon, Midi-Pyrénées, and Provence-Alpes-Côte d'Azur in France). Besides the catastrophic impact of some flash floods, this database highlights the importance of minor but frequent events that produce casualties and damages, which increase as a consequence of land-use changes and enhanced vulnerability and exposure. Figure 9 shows an example of behavioral analysis for the 15 June 2010 flash-flood event at the beginning of the HyMeX LOP, which occurred in the Var region in southern France (Ruin et al. 2014). It shows that space-time sequences of actions, classified into five categories (usual, information, organization, protec-

Fig. 1 .

 1 Fig. 1. Mediterranean basin (also HyMeX/MED-CORDEX simulation domain; more details in the text).

Fig. 2 .

 2 Fig. 2. Schematic of the main scientific topics of the HyMeX project.

Fig. 4 .

 4 Fig. 4. Examples of HyMeX LOP and EOP sites: (a) CV, (b) flux tower deployed at the Crau-Camargue hydrological site, and (c) LA. [Source: (a) B. Boudevillain; (b) S. Garrigues; (c) A.G. Di Sarra.]

Fig

  Fig. 5. (a) Ground-based network of operational radar systems in the Mediterranean (dual-polarimetric systems are shaded). (b) Permanent G P S / G N S S n e t w o r k s i n North Africa and Europe as of Nov 2011 [orange triangles indicate the International GPS Service (IGS) network; yellow triangles indicate the European Permanent Network (EPN); green diamonds indicate the University Navigation Satellite Timing and Ranging (NAVSTAR) Consortium (UNAVCO) network; red, green, and blue dots indicate the European Meteorological Network (EUMETNET) GNSS Water Vapour Programme/ Instituto Geografico Nacional de España ( EGVAP / IGE ) , EGVAP/Service de Géodésie et N ivelleme nt ( EGVAP / SGN), and EGVAP/Agenzia Spaziale Italiana (EGVAP/ ASI) networks, respectively; and gray crisscrosses indicate North African stations]. (c) ZEUS network observations collected on 26 Oct 2012 over the Mediterranean Sea. It must be noted that all the data from these networks are still not accessible and effort is ongoing to collect them (especially in some southern and eastern Mediterranean countries) . [Source: (a) O. Bousquet; (b) O. Bock; (c) V. Kotroni.]

Fig. 6 .

 6 Fig. 6. (a) Gliders and (b) instrumented buoy deployed in the Gulf of Lions in the frame of the HyMeX EOP and LOP. (c) Instrumented commercial ship Marfret Niolon carrying the weekly service from Marseille to Algiers in the frame of the HyMeX LOP. [Source: (a) P. Testor; (b) C. Dubois; (c) I. Taupier-Letage.]

Fig. 7 .

 7 Fig. 7. (a) French and (b) German aircrafts deployed during SOP1, (c) Le Provence operated during SOP2, and (d) pressurized boundary layer balloons launched from Candillargues during SOP2. The French ATR42 (foreground) and Falcon 20 (background) in (a) were based at Montpellier airport and the German Do128 in (b) was based in Corsica at Solenzara airport. [Source: (a),(d): P. Drobinski; (b) C. Kottmeier; (c) I. Taupier-Letage.]

Fig. 8 .

 8 Fig. 8. Taylor diagrams for (left) winter and (right) summer rainfall showing standard deviation (dotted black lines), centered root-mean-square difference (dashed gray lines), and correlation (diagram angle) of ERA-Interim, ECA&D, and WRF outputs with respect to three station observations at (top) the Cévennes-Vivarais observatory in France, (middle) in northeastern Italy, (bottom) Israël for the period 2003-08 (GEWEX-labeled HyMeX stations; Drobinski et al. 2009, 2011; Flaounas et al. 2012, 2013). Black dot = ECA&D; red symbols = WRF and ERA-Interim, where red dot = station observations, × = ERA-Interim, star (*) and circle (o) = two configurations of WRF at 50-km resolution; cross (+) and diamond (◊) = two configurations of WRF at 20 km. (Source: E. Flaounas.)

JULY 2014 AMERICAN METEOROLOGICAL SOCIETY

JULY 2014 |

| tion, recovery) based on respondents' narratives, mostly follow the pace of change of environmental conditions. During this event, most of the people avoided dangerous situations based on their own perception of environmental cues or thanks to unofficial warnings and emerging solidarity that took place locally and spontaneously.

INTERNATIONAL ORGANIZATION.

More than 400 scientists from over 20 countries from both sides of the Mediterranean Sea, Europe, and the United States participate in HyMeX in atmospheric sciences, hydrology, oceanography, and human and social sciences. They contributed to the working groups (WG) addressing the five topics of the HyMeX International Science Plan (ISP), which describes the scientific questions to be tackled and defines the general program strategy (Fig. 2). To implement the ISP, task teams (TT) have been set up to plan and put into operation specific types of instruments and modeling tools. Transversal task teams called task support (TS) coordinated the activities carried out by the TT. The TT and TS elaborated the International Implementation Plan (IIP). Such organization has therefore been set up at an international level as shown in Fig. 10 and is composed of the following:

• An International Scientific Steering Committee (ISSC) that is responsible for the formulation of well-defined and coherent scientific objectives and ensures the fulfillment of HyMeX objectives. The international HyMeX program benefits from several national and pan-national projects (e.g., HyMeX-France, HyMeX-Spain) or coordination at the national level (e.g., Italy). HyMex has an inclusive approach, aiming at enlarging the contribution and participation to the southeastern Mediterranean institutions. HyMeX fits into the large interdisciplinary international program the Mediterranean Integrated Studies at Regional and Local Scales (MISTRALS), which is dedicated to the understanding of the Mediterranean basin's environmental process under the planet's global change (www.mistrals-home.org). It aims to coordinate, across the Mediterranean basin, interdisciplinary research on the atmosphere, hydrosphere, lithosphere, and paleoclimate, including environmental ecology and social sciences. The objectives are i) to achieve a better understanding of the mechanisms shaping and influencing the landscape, environment, and human impact of this ecoregion; ii) to predict the evolution of habitable conditions in this large ecosystem; iii) to meet the public policies concerning resources and environment; iv) to anticipate the evolution of local societies; and v) to propose policies and adaptation measures that would optimize them.

HyMeX Such a project would not have been possible without very many people, from administrative staff to the directions of national agencies, universities, and European and international programs. We thank them all for their contribution to HyMeX and especially the EC-ISC, TT, TS, and PO members. We also acknowledge the help from the staff and the crews of the maritime companies MARFRET (www.marfret.fr) and Linea Messina (www.messinaline.it), for the installation of instruments on board their ships; and of the research aircraft service unit SAFIRE.


D Alpay

M Mboup

A characterization of Schur multipliers between character-automorphic Hardy spaces

Keywords: Character-automorphiuc functions, Hardy spaces, de Branges Rovnyak spaces, Schur multipliers Mathematics Subject Classification (2000). Primary: 30F35, 46E22. Secondary: 30B40

We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for matrix-valued analytic functions due to Leech.

Introduction

Let Γ be a Fuchsian group of Möbius transformations of the unit disk D = {z ∈ C ; |z| < 1} onto itself. For 1 p ∞ and for any character α of Γ, we consider the spaces

H α p = {f ∈ H p | f • γ = α(γ)f, ∀ γ ∈ Γ} .
These spaces are called character-automorphic Hardy spaces. A characterization of such spaces in terms of Poincaré theta series may be found in [START_REF] Ch | On the Green's function of Fuchsian groups[END_REF], [START_REF] Samokhin | Some classical problems in the theory of analytic functions in domains of Parreau-Widom type[END_REF], [START_REF] Metzger | Approximation of Fuchsian groups and automorphic forms of dimension -2[END_REF], [START_REF] Earle | On Poincaré series with application to H p spaces on bordered Riemann surfaces[END_REF]. In particular, Pommerenke showed in [START_REF] Ch | On the Green's function of Fuchsian groups[END_REF] that the series

f (z) = b 0 (z) b ′ 0 (z) γ∈Γ α(γ)θ(γ(z))h(γ(z)) γ ′ (z) γ(z) (1.1)
1 defines a bounded linear operator from the classical Hardy space H p (D) into the subspace H α p (D).

In the present paper we restrict ourselves to the case p = 2. We first give a characterization of the character-automorphic Hardy space H α 2 (D) in terms of an associated de Branges Rovnyak space of functions analytic in the open unit disk; see Theorem 3.2. We also characterize the contractive multipliers between H βα 2 (D) and H α 2 (D), where α and β two given characters; see Theorem 4.2. Our method is mainly based on analytic extension of positive kernels and factorization results from Nevanlinna-Pick interpolation theory.

A review on character-automorphic Hardy spaces 2.1 Fuchsian groups and automorphic functions

Let G be a group of linear transformations, T (z) = az+b cz+d , ad -bc = 1, in the complex plane and let ι denotes the identity transformation. Two points z and z ′ in C are said to be congruent with respect to G, if z ′ = T (z) for some T ∈ G and T = ι. Two regions R, R ′ ⊂ C are said to be G-congruent or G-equivalent if there exists a transformation T = ι which sends R to R ′ . A region R which does not contain any two G-congruent points and such that the neighborhood of any point on the boundary contains G-congruent points of R is called a fundamental region for G. A properly discontinuous group is a group G having a fundamental region [START_REF] Ford | Automorphic functions[END_REF]. This amounts to saying that the identity transformation is isolated. Definition 2.1 A Fuchsian group is a properly discontinuous group each of whose transformation maps D, T and C\D onto themselves.

A Fuchsian group Γ is said to be of convergence type (see e.g. [START_REF] Ch | On the Green's function of Fuchsian groups[END_REF]) if

γ∈Γ 1 -|γ(z)| 2 = 1 -|z| 2 γ∈Γ |γ ′ (z)| < ∞ z ∈ D.
Then, the Green's function [START_REF] Ch | On the Green's function of Fuchsian groups[END_REF] of Γ with respect to a point ξ ∈ D is defined as the Blaschke product

b ξ (z) = γ∈Γ γ(ξ) -z 1 -γ(ξ)z |γ(ξ)| γ(ξ) . (2.2) It satisfies b ξ (ϕ(z)) = µ ξ (ϕ)b ξ (z), ∀ϕ ∈ Γ, (2.3)
where µ ξ is the character of Γ associated with b ξ (z). A function satisfying the relation (2.3) is said to be character-automorphic with respect to Γ while a Γ-periodic function, as for example |b ξ (z)| = |b ξ (ϕ(z))|, is called automorphic with respect to Γ.

Spaces of character-automorphic functions

We now briefly mention the main properties pertaining to spaces of characterautomorphic functions. The materials presented here are essentially borrowed from [START_REF] Ch | On the Green's function of Fuchsian groups[END_REF] and [START_REF] Sodin | Almost periodic Jacobi matrices with homogeneous spectrum, infinite-dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions[END_REF] (see also [START_REF] Hasumi | Hardy classes on infinitely connected Riemann surfaces[END_REF][START_REF] Samokhin | Some classical problems in the theory of analytic functions in domains of Parreau-Widom type[END_REF]). Let Γ be the dual group of Γ, i.e. the group of (unimodular) characters. For an arbitrary character α ∈ Γ, associate the subspaces of the classical space L 2 (T)

L α 2 = {f ∈ L 2 | f • γ = α(γ)f, ∀γ ∈ Γ} H α 2 (D) = L α 2 H 2 (D)
Let Γ be a Fuchsian group without elliptic and parabolic element. We say that Γ is of Widom type if, and only if, the derivative of b 0 (z) is of bounded characteristic. In this case, Widom [START_REF] Widom | H p sections of vector bundles over Riemann surfaces[END_REF] has shown that the space H α ∞ is not trivial for any character α ∈ Γ and we have Theorem 2.2 (Pommerenke [START_REF] Ch | On the Green's function of Fuchsian groups[END_REF]) Let Γ be of Widom type and let θ(z) be the inner factor of b ′ 0 (z). If α is any character of Γ and if h(z) is in H p (D), 1 p ∞, then the function defined by (1.1) is in H α p (D) and

f p h p , f (0) = θ(0)h(0).
The Poincaré series [START_REF] Poincaré | Sur l'uniformisation des fonctions analytiques[END_REF] in (1.1) thus defines, in particular, a projection:

P α : θH 2 (D) → H α 2 (D)
. An important property of the space H α 2 (D) that we will need is that, point evaluation f → f (ξ), ξ ∈ D is a bounded linear functional. The space therefore admits a reproducing kernel k α :

f (z), k α (z, ξ) H α 2 (D) = f (ξ), ξ ∈ D for all f ∈ H α 2 (D) with k α (z, ξ) ∈ H α 2 (D), ∀ ξ ∈ D Since H α 2 (D) = {const}, we have k α (ξ, ξ) = k α (•, ξ) 2 H α
Let Γ be a group of Widom type and let E be associated 1 to it in such a way that C\E be equivalent to the Riemann surface D/Γ, obtained by identifying Γ-congruent points. Then, there exists a universal covering map z :

D → C\E ≃ D/Γ such that • z maps D conformally onto C\E,
• z is automorphic with respect to Γ:

z • γ = z, ∀ γ ∈ Γ • and z(z 1 ) = z(z 2 ) ⇒ ∃γ ∈ Γ | z 1 = γ(z 2 )
In particular, z maps one-to-one the normal fundamental domain of Γ with respect to the origin,

F = {z ∈ D : |γ ′ (z)| < 1 for all γ ∈ Γ, γ = ι} (2.4)
conformally onto some sub-domain of C\E. We assume that z is normalized so that (zb)(0) is real and positive. In all the sequel, the character associated to the Green's function b(z) will be denoted by µ. The starting point of the next section is the following result:

Lemma 2.3 ([12])
The reproducing kernel for the space H α 2 (D) has the form

k α (z, ω) = c(α) k αµ (z,0) b(z) k α (ω, 0) * -k αµ (ω,0) b(ω) * k α (z, 0) z(z) -z(ω) * (2.5)
where

c(α) = z(0)b(0) k αµ (0, 0) > 0. (2.6)
3 An associated de Branges-Rovnyak space

In this section we give a characterization of the space H α 2 (D) in terms of an associated de Branges Rovnyak space. To begin, let

Ω + = {z ∈ D ; Im z(z) > 0} . Setting A α (z) = c(α) 2
k αµ (z, 0) b(z) + ik α (z, 0) B α (z) = c(α) 2
k αµ (z, 0) b(z) -ik α (z, 0)
we can rewrite the reproducing kernel k α as

k α (z, ω) = 2A α (z) 1 -iz(z) 1 -S α (z)S α (w) * 1 -σ(z)σ(w) * 2A α (w) * 1 + iz(w) * (3.1)
where S α (z) = B α (z)/A α (z) and σ(z) = 1+iz(z) 1-iz(z) . We note that the functions A α (z) and B α (z) are character-automorphic with the same character α while S α and σ are automorphic functions. From now on, the notation f ν (z) will means that the function f ν (z) is character-automorphic with the superscript ν ∈ Γ being the associated character, and the notation f ν (z) will stand for a function depending on the character ν (automorphic or not). Proposition 3.1 There exists a Schur function S α such that S α (z) = S α (σ(z)).

Proof: Since the kernel k α (z, ω) is positive in D, and hence in Ω + , it is clear that 1-Sα(z)Sα(w) * 1-σ(z)σ(w) * is also positive in Ω + . Now, observe that the function σ maps Ω + ∩ F into some subset ∆ ⊂ D and this mapping is one-to-one. Let ς be given by: (ς • σ)(z) = z, ∀z ∈ Ω + ∩ F (in particular this will also hold for any region congruent to Ω + ∩ F ) and let the function S α be defined on ∆ by:

S α (λ) = (S α • ς)(λ), ∀λ ∈ ∆.
Then it comes that the kernel

1 -S α (λ) S α (µ) * 1 -λµ *
is positive on ∆. Now, this implies (see for instance [1, Theorem 2.6.5]) the existence of a unique extension of S α (λ), analytic and contractive in all D. We subsequently call S α (λ) this extension, and denote by H(S α ) the reproducing kernel Hilbert space with reproducing kernel

K Sα (λ, µ) = 1 -S α (λ)S α (µ) * 1 -λµ *
By construction, the equality

S α (z) = S α (σ(z))
holds for all z ∈ Ω + ∩ F . Since S α (z) is analytic in D, it must also hold for all D. 2

In connection with the previous proposition and the next theorem, we recall that reproducing kernel Hilbert spaces H(S ) of functions analytic in the open unit disk and with a reproducing kernel of the form

1 -S (λ)S (µ) * 1 -λµ *
were introduced and studied by de Branges and Rovnyak; see [START_REF] De Branges | Canonical models in quantum scattering theory[END_REF]Appendix], [START_REF] De Branges | Square summable power series[END_REF]. We also refer the reader to [START_REF] Dym | J-contractive matrix functions, reproducing kernel Hilbert spaces and interpolation[END_REF] and [START_REF] Alpay | Algorithme de Schur, espaces à noyau reproduisant et théorie des systèmes, volume 6 of Panoramas et Synthèses[END_REF] for more information on these and on related spaces.

Theorem 3.2

The character-automorphic Hardy space H α 2 (D) can be described as

H α 2 (D) = F (z) = √ 2A α (z) 1 -iz(z) f (σ(z)) ; f ∈ H(S α ) (3.2)
with the norm

F H α 2 (D) = f H(Sα)
. Proof: Recall that the map which to F ∈ H α 2 (D) associates its restriction F | Ω + to Ω + is an isometry from H α 2 (D) onto the reproducing kernel Hilbert space with reproducing k α (z, ω) defined by (2.5), where z, ω are now restricted to Ω + . We denote this last space by H α 2 (D) Ω + . By Proposition 3.1 and using (3.1) we see that the operator of multiplication by 2A α (z) 1-iz(z) is an isometry from the reproducing kernel Hilbert space H with reproducing kernel 1

-S α (σ(z))S α (σ(w) * 1 -σ(z)σ(w) * onto H α 2 (D) Ω + .
Furthermore, the composition map by σ is an isometry from the de Branges Rovnyak space H(S α ) onto H. We have that

H = {f • σ ; f ∈ H(S α )} , with norm f • σ H = f H(Sα) , as follows from the equalities f (σ(ω)) = f (•), K Sα (•, σ(ω)) H(Sα) = f • σ(•), K Sα (σ(•), σ(ω)) H
Thus the restrictions of the elements of H α 2 (D) to Ω + are of the form as in (3.2) for z restricted to Ω + . By analytic extension, the elements of H α 2 (D) have the same form in the whole of D.

β (z) is a contraction from H βα 2 (D) into H α 2 (D).
Equivalently, the character-automorphic function s β (z) is a Schur multiplier if and only if the kernel

K α s β (z, w) = k α (z, w) -s β (z)s β (w) * k βα (z, w) (4.1)
is positive in D. The kernel K s β (z, w) is in particular positive in Ω + , and we will consider it in Ω + . We note that in view of [

s β (z) = A α (z) A βα (z) Σ 12 (σ(z)) 1 -S βα (z)Σ 22 (σ(z)) (4.2) S α (z) = Σ 11 (σ(z)) + Σ 12 (σ(z))S βα (z)Σ 21 (σ(z)) 1 -S βα (z)Σ 22 (σ(z)) (4.3)
Proof: The positivity of the kernel (4.1) in Ω + is equivalent to the positivity in Ω + of the kernel

K Sα (σ(z), σ(ω)) -T (z)T (ω) * K S βα (σ(z), σ(ω)),
where

T (z) = A βα (z) A α (z) s β (z).
As in the proof of Proposition 3.1, we note that the function σ maps Ω + ∩ F into some subset ∆ ⊂ D and this mapping is one-to-one, and consider again the function ς defined by: (ς • σ)(z) = z, ∀z ∈ Ω + ∩ F . The kernel

K Sα (λ, µ) -T (ς(λ))T (ς(µ)) * K S βα (λ, µ), (4.4)
is positive in ∆. We now show that T • ς admits an analytic extension to D.

To that purpose we consider the linear relation in H(S α ) × H(S βα ) spanned by the elements of the form

(K Sα (•, ω), T (ς(ω)) * K S βα (•, ω)), ω ∈ ∆.
It is densely defined and it is contractive because of the positivity of the kernel (4.4) in ∆. It is therefore the graph of a densely defined contraction X. We note its extension to H(S α ) by X. For ω ∈ ∆ and f ∈ H(S α ) we have

(X * f )(ω) = X * f, K Sα (•, ω) H(Sα) = f, T (ς(ω)) * K S βα (•, ω) H(Sα) = T (ς(ω))f (ω).
Let f 0 (λ) = K S βα (λ, ω 0 ) where ω 0 ∈ D. We have

T (ς(λ)) = (X * f 0 )(λ) f 0 (λ) , λ ∈ ∆.
It follows that T • ς has an analytic extension to D, which we will denote by R. Thus the kernel This unpublished result of R.B. Leech has been proved using the commutant lifting theorem by M. Rosenblum; see [START_REF] Rosenblum | A corona theorem for countably many functions[END_REF]Theorem 2,p. 134] and [17, Example 1, p. 107]. Further discussions and applications can also be found in [START_REF] Alpay | On the existence and construction of solutions to the partial lossless inverse scattering problem with applications to estimation theory[END_REF]. It can also be proved using tangential Nevanlinna-Pick interpolation and Montel's theorem.

K Sα (λ, µ) -R(λ)R(µ) * K S βα (λ, µ), ( 4
Finally we replace in (4.6) λ by σ(z) where z ∈ Ω + ∩ F . We obtain the formulas in the statement of the theorem for z ∈ Ω + ∩ F , and hence for z ∈ D by analytic extension.

2

2 4

 2 Schur multipliers A Schur function is a function analytic and contractive in the open unit disk. Equivalently, it is a function s such that the operator of multiplication by s is a contraction from the classical Hardy of the open unit disk into itself. This last definition is our starting point to define character-automorphic Schur multipliers. Definition 4.1 A character-automorphic function s β (z), with character β, will be called a Schur multiplier if the operator of multiplication by s

. 5 )

 5 is analytic in λ and µ * in D. Therefore it is still positive in D; see [7, Lemma 2, p. 142],[START_REF] Alpay | Schur functions, operator colligations, and reproducing kernel Pontryagin spaces[END_REF] Theorem 1.1.4, p. 10]. By [2, Theorem 11.1, p. 61], a necessary and sufficient condition for the kernel (4.5) to be positive is that there exists a C 2×2 -matrix valued Schur function Σ(λ) such thatR(λ) = Σ 12 (λ) 1 -S βα (λ)Σ 22 (λ) (4.6) S α (λ) = Σ 11 (λ) + Σ 12 (λ)S βα (λ)Σ 21 (λ) 1 -S βα (λ)Σ 22 (λ) .(4.7)The above mentioned result from[START_REF] Alpay | On tangential interpolation in reproducing kernel Hilbert space modules and applications[END_REF] stems from rewriting the positive kernel (4.5) asA(λ)A(µ) * -B(λ)B(µ) * 1 -λµ * where A(λ) = 1 R(λ)S βα (λ) B(λ) = S α (λ) R(λ) ,and using a factorization result known as Leech's theorem, which insures the existence of a C 2×2 -valued Schur function Σ such that B(z) = A(z)Σ(z), from which (4.6) follows.

  7, Lemma 2, p. 142], [4, Theorem 1.1.4, p. 10], the positivity of the analytic kernel K s β on Ω + implies its positivity on D. Theorem 4.2 A character-automorphic function s β is a Schur multiplier if and only if there exists a C 2×2 -matrix valued Schur function Σ(z) such that

(D) > 0 for every ξ ∈ D. In the sequel, the Green's function b 0 (z) with respect to 0, will be denoted by b(z) for short.

See[START_REF] Yuditskii | Two remarks on Fuchsian groups of Widom type. In Operator theory, system theory and related topics[END_REF] for an example of a construction of a group Γ associated with a finite union of disjoint arcs of the unit circle.

Acknowledgments. The first author thanks the Earl Katz family for endowing the chair which supports his research. This work was done while the second author was visiting the department of mathematics of Ben-Gurion University. The second author thanks the Center for Advanced Studies in Mathematics (CASM) of the department of mathematics of Ben-Gurion University which supported his stay.