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Precipitation Analysis over the French Alps Using a Variational Approach and Study of Potential Added Value of Ground-Based Radar Observations

CAMILLE BIRMAN CNRM, UMR 3589, Météo-France/CNRS, Toulouse, France

FATIMA KARBOU CNRM, UMR 3589, Météo-France/CNRS, Saint Martin d’Hères, France

JEAN-FRANÇOIS MAHFOUF CNRM, UMR 3589, Météo-France/CNRS, Toulouse, France

MATTHIEU LAFAYSSE,YVES DURAND,GÉRALD GIRAUD, AND LAURENT MÉRINDOL CNRM, UMR 3589, Météo-France/CNRS, Saint Martin d’Hères, France

LAURA HERMOZO CLS, Toulouse, France

(Manuscript received 24 June 2016, in ﬁnal form 20 February 2017)

ABSTRACT

A one-dimensional variational data assimilation (1DVar) method to retrieve profiles of precipitation in mountainous terrain is described. The method combines observations from the French Alpine region rain gauges and precipitation estimates from weather radars with background information from short-range numerical weather prediction forecasts in an optimal way. The performance of this technique is evaluated using measurements of precipitation and of snow depth during two years (2012/13 and 2013/14). It is shown that the 1DVar model allows an effective assimilation of measurements of different types, including rain gauge and radar-derived precipitation. The use of radar-derived precipitation rates over mountains to force the numerical snowpack model Crocus significantly reduces the bias and standard deviation with respect to independent snow depth observations. The improvement is particularly significant for large rainfall or snowfall events, which are decisive for avalanche hazard forecasting. The use of radar-derived precipitation rates at an hourly time step improves the time series of precipitation analyses and has a positive impact on simulated snow depths.

1. Introduction the snowpack and its evolution in time and for avalanche hazard forecasting. However, precipitation patterns are Reliable precipitation estimates are needed for many particularly variable in mountainous areas because of applications, including meteorology, hydrology, and the inﬂuence of altitude, orography, aspect, and the as- climate studies (Boone et al. 2004; Tapiador et al. 2012; sociated small spatial scale of convective events. Accu- Kucera et al. 2013; Kidd and Levizzani 2011; Valipour rate estimations of precipitation in mountains and of its et al. 2013; Valipour and Eslamian 2014; Valipour 2015, variability in space and time would ideally require a 2016). For instance, a good knowledge of precipitation dense rain gauge network combined with an effective in mountainous regions at appropriate spatial and tem- analysis method. Cokriging of precipitation with alti- poral scales is a prerequisite for accurate modeling of tude is one of the simplest and widely used methods, but it requires the precipitation to be strongly correlated Corresponding author e-mail: Camille Birman, camille.birman@ with altitude (Hevesi et al. 1992a,b). Such methods can meteo.fr be used for monitoring precipitation accumulation at

DOI: 10.1175/JHM-D-16-0144.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 09/28/21 01:26 AM UTC 1426 JOURNAL OF HYDROMETEOROLOGY VOLUME 18 seasonal or annual time scales. For example, Prudhomme or greater over which the meteorological variables can be andReed(1999)used topographical data to improve the assumed to be uniform. The first analysis scheme, called mapping of extreme precipitation in a mountainous re- Système d’Analyse Fournissant des Renseignements gion of Scotland, using residual kriging with a regression Atmosphériques à la Neige (SAFRAN) is used to gen- method relating topographical variables to the median of erate relevant meteorological parameters that indirectly the annual daily precipitation. Mair and Fares (2011) govern energy and mass budgets of the snowpack, at compared different geostatistical methods to estimate massif scale, on an hourly time basis. Multilayer snow- rainfall and showed that the use of topographical in- pack simulations are performed using a physical model formation improved the simulated precipitation accu- called Crocus (Brun et al. 1992; Vionnet et al. 2012), mulating on a monthly time-scale basis. Schmidli et al. which employs SAFRAN atmospheric forcing outputs, (2002) studied the long-term variability of the pre- to generate simulations of the snowpack. Avalanche cipitation over the Alps during the period 1901–90, using hazard forecasting is then performed using a system data from rain gauges to produce an analysis at a spatial called Modèle Expert d’Aide à la Prévision du Risque resolution of 25 km and a monthly time step. They d’Avalanche (MEPRA; Giraud 1992) based on expert highlighted a climatological trend with an increase of analysis of the simulated snowpack mechanical proper- winter precipitation over the northern and western Alps ties. Raleigh et al. (2015) showed that errors associated and a decrease of precipitation in autumn in the south of with the atmospheric forcing had the largest impact on the Alps. Other techniques have been used that take ac- snowpack modeling uncertainties. Precipitation being count of the aspect of slopes with respect to atmospheric one of the most important atmospheric forcing variables, flow for daily analysis, but at a low temporal resolution itsestimationrequiresasmuchcareasthemodelingof (from seasonal to yearly accumulations; Daly et al. 1994; snowpack properties. Schwab 2000). However, these methods are not suitable SAFRAN has been widely used for the analysis of for the short-term monitoring of rapidly changing phe- precipitation in mountainous areas and has been found to nomena such as floods or for avalanche hazard forecasts. provide reliable precipitation estimates (Durand et al. Long-term series of reliable estimates of precipitation are 2009b). However, the model produces precipitation an- thus necessary at spatial and temporal resolutions that alyses only at massif scale and is not suitable to provide meet hydrological and snow study requirements. analyses on smaller areas or on a regular grid. For in- Methods have been developed to derive precipitation stance, the use of SAFRAN on high-elevation glacier using a set of a priori information from climatological sites requires the use of a postprocessing method to cor- data and currently available measurements (Guan et al. rect the bias of SAFRAN estimates with respect to in situ 2005; Kyriakidis et al. 2001; Gottardi et al. 2012). Other observations (e.g., Gerbaux et al. 2005). Moreover, the long-term precipitation databases have been constructed use of indirect observations such as radar or satellite es- for mountainous areas using atmospheric reanalysis out- timates is difficult with the optimal interpolation tech- puts of numerical weather prediction (NWP) models with nique. In the framework of the European Reanalysis and appropriate downscaling techniques to account for Observations for Monitoring (Euro4M) project, another orography. Crochet (2007), Crochet et al. (2007),and precipitation analysis system called MESCAN has been Durand et al. (2009a,b), for example, used the 40-yr Eu- built, also based on an optimal interpolation technique ropean Centre for Medium-Range Weather Forecasts using conventional surface observations to produce (ECMWF) Re-Analysis over the time period 1958–2002 temperature, relative humidity, and precipitation analysis to compute precipitation estimates over mountainous (Coustau et al. 2014; Soci et al. 2016). Simulations of snow areas. Crochet (2007) and Crochet et al. (2007) have and surface fluxes using the surface model Surface Ex- produced a 1-km-resolution precipitation analysis over ternalisée (SURFEX) forced by MESCAN analysis have Iceland accounting for flow dependency and orientation given satisfactory results overall. However, limitations of slopes with respect to the predominant wind. Durand appear over mountains since the specifications of error et al. (2009a,b) have generated an analysis of all relevant statistics and correlation length scale in the MESCAN meteorological parameters for snowpack modeling, in- analysis scheme are tuned for flat areas and are not ap- cluding rainfall and snowfall rates, and studied their propriate in complex terrain. The main purpose of the evolution in time over the French Alps. present development is to build a precipitation analysis To accurately simulate the evolution of snowpack over model having a quality similar to SAFRAN (at massif mountains at massif scale together with its mechanical scale) but that can also be easily adapted to provide stability, Météo-France has developed a chain of three precipitation analyses at smaller spatial scales. The sys- models (Durand et al. 1999). For this chain of models, a tem should be able to assimilate both conventional and massif is defined as a homogeneous area of about 500 km2 remote sensing data. In the case of indirect measurements

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TABLE 1. Scores of the 1DVar precipitation analysis compared to observations not assimilated over the 23 massifs of the French Alps for the years 2012/13 and 2013/14. The values in boldface correspond to the best scores between Safran and 1DVar. The names of the massifs are indicated as well as if they are part of the northern (N) or southern (S) Alps. The scores are displayed for SAFRAN and the 1DVar analysis evaluated against rain gauges.

Coefficient of Bias (mm) RMSE (mm) Std dev (mm) variation Safran 1DVar Safran 1DVar Safran 1DVar Safran 1DVar 1 Chablais (N) 22.47 20.34 14.28 5.63 14.07 5.62 1.48 1.70 2 Aravis (N) 24.51 20.90 16.11 6.07 15.47 6.00 1.42 1.76 3 Mont-Blanc (N) 20.036 1.08 14.64 5.50 14.64 5.39 1.51 1.63 4 Beaufortin (N) 22.65 0.54 13.90 6.06 13.64 6.03 1.51 1.59 5 Haute Tarentaise (N) 20.16 0.72 11.71 5.02 11.71 4.97 1.53 1.70 6 Vanoise (N) 20.61 0.91 10.73 4.90 10.72 4.82 1.51 1.58 7 Maurienne (N) 0.44 20.65 11.83 4.89 11.83 4.84 1.56 1.51 8 Haute-Maurienne (N) 1.08 0.03 11.55 4.68 11.50 4.68 1.57 1.80 9 Bauges (N) 22.73 20.93 16.26 7.71 16.03 7.65 1.48 1.97 10 Chartreuse (N) 24.25 20.37 14.56 6.91 13.95 6.89 1.48 1.71 11 Vercors (N) 21.78 20.90 16.24 9.59 16.15 9.55 1.57 2.26 12 Belledonne (N) 22.75 0.19 14.85 6.89 14.59 6.88 1.51 1.66 13 Grandes-Rousses (N) 20.34 1.00 11.28 5.57 11.28 5.48 1.54 1.48 14 Oisans (S) 20.90 0.13 12.62 5.18 12.59 5.18 1.59 1.70 15 Pelvoux (S) 0.32 20.32 14.20 4.48 14.19 4.46 1.56 1.73 16 Thabor (S) 21.00 20.69 10.19 5.50 10.14 5.46 1.49 1.44 17 Champsaur (S) 21.24 20.42 16.61 6.42 16.56 6.41 1.53 1.88 18 Devoluy (S) 0.06 0.009 15.12 5.69 15.12 5.69 1.57 1.74 19 Queyras (S) 20.97 20.59 12.17 5.92 12.14 5.89 1.60 1.85 20 Parpaillon (S) 20.34 20.48 11.64 5.93 11.63 5.91 1.53 1.60 21 Ubaye (S) 0.36 20.10 12.10 4.49 12.10 4.49 1.52 1.58 22 Haut Var–Haut Verdon (S) 23.20 20.55 15.29 6.28 14.95 6.26 1.54 1.74 23 Mercantour (S) 28.05 21.33 22.32 11.96 20.82 11.89 1.72 1.91 of precipitation, the analysis system should enable the use et al. 1993). SAFRAN provides hourly meteorological of a complicated, possibly nonlinear, observation opera- information at the snow–atmosphere interface over mas- tor. The aim of this study is to address the weaknesses sifs, which are assumed to be homogeneous (the 23 mas- of existing models (SAFRAN and MESCAN) by de- sifs in the French Alps are listed in Table 1). The massifs veloping a tool using a variational approach that could be are represented by discontinuous pyramids (eight expo- operated on both a large scale (scale of massifs) and sitions) for which SAFRAN analyzes vertical profiles of smaller scales. The tool should be able to produce a atmospheric variables at all elevations up to 3600 m with a vertical profile of precipitation to take better account of 300-m step. The meteorological variables are surface air the mountain specificities from various sources of pre- temperature and humidity, wind speed, cloudiness, precipitation observations. This tool is applied and evaluated cipitation rate, precipitation phase, and downward long- over two years spanning August–July for 2012/13 and wave and shortwave radiative fluxes (direct and 2013/14. Section 2 summarizes the data and systems used scattered). Observation types used in SAFRAN mainly in this study. A first evaluation of the variational method include those from conventional surface synoptic stations is given in section 3. Section 4 is dedicated to a study of (available every 6 h), automatic stations (providing hourly the potential of remote sensing observations from observations), and climatological stations (every 24 h). weather radars to provide more reliable precipitation SAFRAN can handle observations with variable time estimates in the Alps. The results are discussed in section frequencies (every hour and 6 h), which is the case with air 5,andsection 6 presents some conclusions. pressure and temperature, wind, humidity, cloudiness, etc. Other parameters, such as precipitation and minimum/ 2. Data, models, and 1DVar analysis scheme maximum temperatures, are only available on a daily basis. Over the French Alps, daily precipitation accumu- a. The SAFRAN analysis lation observations come from around 500 meteorological SAFRAN is a Météo-France operational system de- stations: either meteorological stations at lower altitude or signed to produce analyses of meteorological parameters sparser ‘‘nivo-meteo’’ stations at higher altitude. Their that influence the evolution of the snowpack (Durand altitude varies from 200 to 2500 m, and they provide daily

Unauthenticated | Downloaded 09/28/21 01:26 AM UTC 1428 JOURNAL OF HYDROMETEOROLOGY VOLUME 18 measurements of temperature, humidity, and precipitation, and potentially more parameters for some stations. It should be mentioned that the total number of precipitation observations used by SAFRAN can vary significantly in time, from more than 300 observations in winter to less than 200 in summer, with marked differences from day to day. SAFRAN uses an objective analysis method based on optimal interpolation to combine available observations with a priori information including temperature, humidity, and wind speed and direction from the French global NWP model Action de Recherche Petite Echelle Grande Echelle (ARPEGE) at 40 km resolution (Courtier et al. 1991). SAFRAN also takes account of a priori information on the vertical profile of precipitation, using climatological values computed for seven weather regimes to derive a background FIG. 1. AROME model orography over the French Alps (vertical state. For a given day, the ARPEGE geopotential height color bar) with rain gauge stations and the boundaries of 23 massifs at 500 hPa is used as a predictor to choose an appropriate defined in SAFRAN analysis. The elevation of the rain gauges climatological profile, and the optimal interpolation stations are represented with their difference of elevation with AROME relief (horizontal color bar). analysis is performed using available observations. An additional constraint preserves the gradient of the selected climatological profile. SAFRAN also uses radio- snow production (Spandre et al. 2015). SAFRAN ana- sonde and pilot balloon data when available (few stations lyses have been used as a reference to calibrate the in the Alps). Besides the ARPEGE global NWP model, downscaling methods of general circulation models or Météo-France has developed the Applications of Re- regional climate models (Boé et al. 2007; Rousselot et al. search to Operations at Mesoscale (AROME) model, 2012; Lafaysse et al. 2014). The present study used the which is a limited-area model at convective scale. SAFRAN reanalysis, which is assumed to give the AROME has been running operationally since December best estimation of precipitation, to evaluate the one- 2008 (Seity et al. 2011). This model is nonhydrostatic, dimensional variational data assimilation (1DVar) with a three-dimensional variational data assimilation model. The SAFRAN reanalysis is more accurate be- (3DVar) scheme that takes various observation types into cause it takes more observations into account than the account, including in situ measurements and remote operational real-time analysis performed when all ob- sensing observations. Its horizontal resolution for the servations may not be available yet. Precipitation outputs present study was 2.5 km and there were 60 vertical from the 1DVar were also evaluated by examining their pressure levels. Figure 1 shows the AROME model ability to provide realistic snow depth simulations using a orography with a representation of alpine massifs (drawn snow-cover model. The SURFEX/Interactions between as red polygons) and the locations of rain gauge stations. Soil, Biosphere, and Atmosphere (ISBA)/Crocus snow For more than 25 years, SAFRAN has been used for model (referred to hereinafter as Crocus; Brun et al. 1992; its initial purpose of snow modeling for avalanche Vionnet et al. 2012) is a detailed numerical snowpack forecasting. When SAFRAN forces an appropriate model having the ability to simulate water and energy surface model, the river discharges can be accurately exchanges between layers of a snowpack and at its simulated on mesoscale alpine catchments (Lafaysse boundaries. Crocus is forced by meteorological fields et al. 2011). A robust extension over France has also output by SAFRAN at hourly time steps and simulates been performed (Quintana-Seguí et al. 2008) to simulate the time evolution of several snowpack properties, in- river discharges operationally (Habets et al. 2008). cluding temperature, density, liquid water content, depth, SAFRAN also provides the atmospheric forcing for an and water equivalent, taking snow metamorphism into operational forecasting system of surface road condi- account. The Crocus snowpack model is used operations (Bouilloud et al. 2009). A number of climate tionally for avalanche forecasting over the French studies have been undertaken with SAFRAN over the mountains. For a given hour (Hr), the snow state depends last 50 years in terms of low-level meteorological pa- on the atmospheric fields at Hr as well as on the snow rameters (Durand et al. 2009b; Vidal et al. 2010b), snow state at Hr 2 1. Crocus has been used and validated in a cover (Durand et al. 2009a), soil moisture and stream- significant number of studies related to physical processes flows (Vidal et al. 2010a), and potential for artificial and internal properties of the snowpack (Carmagnola

Unauthenticated | Downloaded 09/28/21 01:26 AM UTC MAY 2017 B I R M A N E T A L . 1429 et al. 2014; Dominé et al. 2013; Morin et al. 2013), alpine also several steps after the computation of the rain rate, (Gerbaux et al. 2005) and tropical (Lejeune et al. 2013) including correction for nonsimultaneity of radar mea- glacier mass balance, snow albedo of the Greenland ice surements with two-dimensional advection fields, sheet (Dumont et al. 2014), alpine hydrology (Etchevers weighted radar combinations, and production of 5 min and Martin 2002), wind-induced snow transport (Vionnet and 1 km 3 1 km rain accumulations (Parent-du et al. 2014), cryosphere–climate interactions (Brun et al. Chatelet^ 2003; Tabary 2007; Tabary et al. 2007). Specific 2011), and climate change impact on snow cover and processing steps are dedicated to the identification of the avalanche hazard (Castebrunet et al. 2014). These studies freezing level, including measurement of its height, have proved the reliability of the snowpack model in corrections for vertical profile of reflectivity, measure- various applications. ment of the brightband peak and thickness, and measurement of the decreasing reflectivity above the b. Precipitation estimates from weather radar freezing level. The recent network has an increasing observations number of polarimetric radars (17 polarimetric and 10 Météo-France operates a network of C- and S-band nonpolarimetric radars), which provide additional in- weather radars, using wavelengths of 5 and 10 cm, re- formation on the backscattered signal, including differ- spectively, to provide real-time precipitation amounts in ential reflectivity, correlation coefficient, and differential order to anticipate high-impact events such as flash phase, which provide information about the size and floods. These radars are mainly operated over flat areas. type of hydrometeors and the attenuation (Tabary et al. In mountainous areas, such as the Alps and the Pyrenees, 2013). For X-band radars, the reflectivities are corrected radars cannot sample precipitating systems adequately for attenuation by precipitating systems using informa- because of a beam blockage effect. Paradoxically, it is tion retrieved from the specific differential phase KDP. over these areas that the spatial and temporal variability The different variables obtained from polarimetric ra- of precipitation is the highest. To overcome these limi- dars are exploited to adapt the precipitation retrieval tations, the Risques Hydrométéorologiques en Terri- algorithms to convective or stratiform precipitation. In toires de Montagnes et Mediterranéens (RHYTMME) case of stratiform precipitation, the precipitation rate is project was launched by Météo-France and the Institut retrieved using a single Marshall–Palmer Z–R relation- National de Recherche en Sciences et Technologies pour ship for all wavelengths, where Z and R are the re- l’Environnement et l’Agriculture (IRSTEA) in 2008 flectivity and the rain rate, respectively: (Westrelin et al. 2013). The main goal of the project was 5 1:6 to operate a network of meteorological X-band (wave- Z 200R . (1) length of 2 cm) Doppler polarimetric radars over the Convective precipitation rate is computed with an southern Alps. These instruments are less sensitive to R–K relationship of the form: ground clutter than C- and S-band radars. They have a DP shorter range since the signal is more strongly attenu- 5 b R aKDP , (2) ated by precipitation at these wavelengths. Being more compact and less costly, they can be installed in small where a and b depend upon wavelength fa 5 23, 29.7, and 2 2 networks to provide precipitation information over sig- 53.4 mm [(8)m 1] 1 and b 5 0.79, 0.85, and 0.85 for X-, C-, nificant areas in mountainous regions. They give pre- and S-band radars, respectivelyg. A threshold on KDP cipitation measurements every 5 min with a pixel size of that also depends upon wavelength (KDP 5 0.58,18,and 2 1km2 like other wavelengths, over a range of 30–60 km, 18 km 1 for X-, C- and S-band radars, respectively) is shorter than traditional C-band radar. The larger atten- applied between the two algorithms (Tabary et al. 2013). uation of the radar signal at X-band is corrected using In this work we used a mosaic of precipitation amounts dual-polarization capabilities. produced by Météo-France using C- and S-band radars The radars operated at Météo-France form part of the with a significant contribution from X-band radars over Application Radar à la Météorologie Infrasynoptique the southern part of the French Alps. The S-band radars (ARAMIS) network, which consists of S-, C-, and of N^ımes, Bollène, and Collobrières cover the most X-band radars using wavelengths of 10, 5, and 2 cm, re- southern and western parts of the Alps and the C-band spectively. The processing of radar measurements at all radar of Saint-Nizier can bring useful information over the wavelengths comprises several steps before the com- northern Alps. The X-band radars included in the mosaic putation of precipitation rate, including correction for were installed at Mont Vial in 2007, Mont Maurel in 2010, ground clutter using pulse-to-pulse fluctuations of the Mont Colombis in 2012, and Vars Mayt (noted as Risoul reflectivity and correction for partial beam blockage in Fig. 2) in 2013. We used hourly- and daily-based op- and a step of reflectivity-to-rain conversion. There are erational precipitation products over the period from

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H(x) is the observation model operator; and exponents T and 21 denote the matrix transpose and inverse, respectively. Assuming H is the tangent linear of the potentially nonlinear observation operator H, the cost function is quadratic and is minimized through the gradient computation:

= 5 B21 2 1 TR21 o 2 J(x) (x xb) H [y H(x)]. (4)

The analysis state xa is such that

=J(xa) 5 0. (5)

The equations above remain valid in the case of a nonlinear observation operator, in order to assimilate observations that are indirectly related to precipitation, unlike optimal interpolation. In the present study, the

FIG. 2. Spatial coverage of the radar observations over the observation operator H is represented through a matrix southeastern part of the French Alps. The areas in red correspond with two dimensions: the number of observations in a to a radar background quality index greater than 84%. massif for a given day and the number of altitude levels. Its coefficients depend on the altitude of the available August 2012 to August 2014. During this period, the Mont observations. The background profile is defined on a Vial radar was not included in the mosaic because of radar regular grid with a 300-m vertical step and is linearly failure, and the precipitation estimates from the Vars interpolated at the altitude of the observations. Mayt radar were only available from December 2013. The Under the assumption that the observation errors are mosaic of precipitation produced by Météo-France in- uncorrelated, the observation error covariance matrix is cluded the four X-band radars over the French Alps and diagonal. The errors in measurement of rain gauges lo- the C-band radars of Collobrières, N^ımes, and Bollène cated within the same massif do not influence each other covering the southern and western parts of the French as they come from distant stations situated at different Alps. Figure 2 shows the theoretical coverage of the mo- altitudes. The diagnosis from Desroziers et al. (2005) saic. The areas in red correspond to a quality index greater was carried out and confirmed this a priori choice. than 84%. The static quality index shown here takes only Figure 3 (bottom) shows the diagnosed observation orographic masks into account, which do not vary in time, correlation matrix for the years 2012/13 and 2013/14 but the dynamic quality index is also affected by the actual over the French Alps. Each column and each row cor- data availability, which is reduced when radars are out of responds to a single observation station. The value in a action and by attenuation from precipitation along the box is the observation error correlation between the two scan lowering the resolution and the range of radars. corresponding stations, computed over the two years. c. 1DVar analysis scheme The stations present in the 23 massifs of the French Alps are gathered together in the same figure, but stations The purpose of this paper is to assess the potential of a within the same massif are distant by a few kilometers 1DVar retrieval method to be used to combine obser- to a few tens of kilometers, whereas stations in different vations of different types with background information massifs can be distant by several hundreds of kilometers. from the AROME NWP model to retrieve profiles of The figure shows that the correlations remain close to precipitation in mountainous regions. The 1DVar re- zero between distant stations and that the a priori choice trieval is performed by adjusting the precipitation state of uncorrelated observation errors seems appropriate. vector x knowing the background state xb that The figure shows that the observation errors are weakly minimizes a quadratic cost function of the following form: correlated within a massif, as nonzero values appear

1 2 between neighboring points, but are close to zero be- J(x) 5 (x 2 x )TB 1(x 2 x ) 2 b b tween stations in different massifs. In practice, the 1DVar was run for each massif by 1 2 1 [yo 2 H(x)]TR 1[yo 2 H(x)], (3) 2 optimally combining available rain gauge measurements with a priori information from a short-range forecast of where B and R are the error covariance matrices of the precipitation produced by the AROME NWP model. o background xb and the observation vector y , respectively; The minimization was performed using a quasi-Newton

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FIG. 3. (top) Schematic description of the background adjustment for 1DVar analysis over a given massif. (bottom) Diagnosed correlation matrices for observation errors using the diagnosis from Desroziers et al. (2005) over the French Alps for the years 2012/13 and 2013/14. Each line or column corresponds to a single station; the station situated inside the same massif is represented by contiguous lines or columns. algorithm that converged after one iteration with a lin- SAFRAN is used for the background (‘‘Climatological ear problem. The analysis was performed at a daily time profile from SAFRAN’’ in Fig. 3, top center) in order to step since most of the in situ observations were only ensure a consistent vertical profile. The average pre- available every 24 h. Figure 3 (top) describes the 1DVar cipitation estimate is used to translate the climatological system schematically. Twenty-four hour accumulated profile and adjust the background, keeping a consistent precipitation forecasts from the AROME model are vertical gradient (‘‘Guess adjusted with AROME’’ in used (difference between accumulated amounts at 130 Fig. 3, top right). It should be noted that obtaining a and 16 h) to calculate a mean background estimate of reliable precipitation analysis is rather difficult because precipitation over the whole massif of interest (associ- the method assumes that the massifs are homogeneous ated with a mean altitude). With this mean precipitation (with respect to their meteorological and climate con- estimate, an a priori vertical climatological profile of ditions). The area of massifs varies from 400 to 1500 km2. precipitation (also used in SAFRAN analysis; Durand The precipitation analysis also assumes that the few et al. 1993, 1999) was adjusted using the average pre- assimilated observations are sufficient to represent all cipitation computed from the AROME model. The precipitation variability within a given massif. In the best climatological profile most frequently selected from cases, 10–12 observations per day can be assimilated (in

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FIG. 4. (top) RMSEs of the precipitation analysis for the years 2012/13 and 2013/14 over the 23 massifs of the French Alps obtained with various correlation heights for the background covariance matrix. The RMSEs have been normalized with respect to correlation height equal to 900 m. (bottom) RMSEs of the precipitation analysis for the years 2012/13 and 2013/14 over the 23 massifs of the French Alps obtained with various background and observation std devs. The RMSEs have been normalized with respect to background std devs equal to 8 mm and observation std devs equal to 5 mm. the northern Alps) but, for other massifs, only 3–4 ob- correlation length. The correlation is 1 along the diagonal servations are available. Moreover, for all massifs, the and decreases between distant levels. Sensitivity tests number of available observations decreases strongly were conducted with background correlation distances with increasing altitude. varying from 300 to 1500 m in order to define the most For the background covariance matrix, vertical corre- suitable correlation distance determining the influence of lations are prescribed between altitude levels, which de- an observation at a given altitude. Figure 4 (top) shows the crease with increasing distance. The correlations are RMSEs obtained over the 23 massifs of the French Alps 2 modeled through a Gaussian function, exp[2(zi 2 zj)/d ], with background correlation heights varying from 300 to where zi and zj are two level heights and d is a fixed 1500 m. The RMSEs have been normalized with respect

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FIG. 5. Scatterplots of analyzed vs observed daily precipitation accumulations over the (left) Mont-Blanc and (right) Haut Var–Haut Verdon massifs for the years 2012/13 and 2013/14. Precipitation from SAFRAN analyses is plotted in blue and from 1DVar analyses in red. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 1 s2 to a correlation distance of 900 m in each massif in order the background and a threshold equal to b o, to highlight the differences between the tuning tests. The where sb and so are the background and observation figure shows that a value of d 5 900 m minimizes the standard deviation, respectively, decreased the RMSEs. RMSEs over most of the massifs. This correlation length This threshold led to 15%–17% of observations being distributes the observation information over approxi- rejected, which decreased the RMSEs and the standard mately three levels (which have a 300-m spacing) and deviation by more than 2% on average over the French produces vertically analyzed profiles of precipitation that Alps, with values of 30%–40% in some massifs, in- are consistent with climatological profiles. cluding Vanoise and Ubaye, for example. These are The first experiments were performed with a priori among the largest massifs and were thus the most likely background and observation standard deviations similar to to have large dispersion in their daily precipitation ob- those of SAFRAN and equal to 8 and 5 mm, respectively. servations. The rejection of observations that were too Sensitivity tests were carried out to choose the most ap- far from background was particularly important over the propriate observation and background standard deviations. southern Alps, because of the large size of the massifs Small observation errors led to noisy analysis profiles, and and because of more localized precipitation events, re- small values of background errors produced analysis pro- sulting in a large dispersion within massifs. files that were very similar to the background, so little benefit could be obtained from observations. Figure 4 (bottom) shows the RMSEs of the precipitation analysis 3. Evaluation of the 1DVar in its first setup obtained with several values of background and observa- a. Daily analysis of precipitation tion standard deviations over the 23 massifs of the French Alps for the years 2012/13 and 2013/14. The RMSEs are To assess the quality of the 1DVar precipitation normalized for each massif with respect to observation and analysis, a set of assimilation experiments was per- background standard deviations equal to 5 and 8 mm, re- formed by randomly withholding one observation per spectively. We noticed that the analyzed profiles mostly day and per massif and so preventing them from being depend on the ratio between the observation and the assimilated. The set of withheld observations was then background standard deviations. Moreover, the RMSEs used as independent data to evaluate the precipitation did not vary significantly when increasing standard de- analysis. The ratio of nonassimilated to assimilated ob- viations. Sensitivity tests also showed that the RMSEs de- servations depends on the total number of observations creased when both standard deviations increased while the over each massif, which varies from 4 to 12. The total ratio between background and observation standard de- number of observations varies over the French Alps viations was kept equal to that of SAFRAN standard de- from about 150 to more than 300 in winter when ob- viations. Therefore, the standard deviations were set equal servations are available from ski resorts, which lead to 5 mm for observations and 8 mm for background, to to a ratio of nonassimilated to assimilated observa- remain consistent with the SAFRAN analysis. tions of 8% in winter to 15% in summer. Figure 5 Additional tests were undertaken to perform a quality shows scatterplots of SAFRAN and 1DVar analysis control check in order to reject observations too far from versus independent observations over two massifs: the

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Mont-Blanc massif (Fig. 5, left) in the northern Alps and detected. Therefore, the lower intensities that are mea- the Haut Var–Haut Verdon massif (Fig. 5, right) in the suredcorrespondtozerovaluesorareoverestimatedin southern Alps, for the two winter seasons 2012/13 and SAFRAN and the 1DVar analysis. This evaluation shows 2013/14. Each year begins at 0600 UTC 1 August and that the 1DVar model behaves well and is able to analyze ends at the same date of the following year. The two profiles of precipitation in rather good agreement with selected massifs are quite large (about 1500 km2 each) observations. However, these estimates, performed at with very heterogeneous topography. They are repre- massif scale, may need local corrections or adjustments to sentative of the 1DVar behavior in the northern and make them representative of the various locations within southern Alps, respectively, which are more influenced a massif. by oceanic or Mediterranean storms. The altitude range b. Impact on snowpack modeling of Mont-Blanc extends between 1200 and 3600 m, whereas in Haut Var–Haut Verdon massif, the altitude The main goal of the 1DVar precipitation analysis and ranges between 600 and 2700 m, which also explains SAFRAN meteorological analysis is to produce forcings why it receives less precipitation than Mont-Blanc on for the Crocus model in order to accurately predict the average. It can be seen that the 1DVar analysis data snowpack state. Therefore, snowpack simulations are are in good agreement with observations and that performed with a reliable snowpack model forced by the SAFRAN generates estimates associated with a much 1DVar analyzed precipitation and the results are com- larger spread than the 1DVar model does. Pre- pared to the same snowpack model forced by SAFRAN cipitation over the southern part of the French Alps is reference analysis, which represents the most accurate often affected by intense precipitation events in- snowpack simulation available. Moreover, the rain gauge sufficiently accounted for in the 1DVar; therefore, the measurements are subject to errors in mountainous areas dispersion is larger over Haut Var–Haut Verdon than and the examination of snow depth brings a comple- over Mont-Blanc. Table 1 shows statistics about the mentary evaluation of precipitation analysis. performance of SAFRAN and the 1DVar over the 23 As stated earlier, the snow model Crocus needs at- massifs of the French Alps [bias, RMSE, standard de- mospheric forcing, including precipitation, on an hourly viation, and coefficient of variation (i.e., observation minus basis to simulate the snowpack evolution. SAFRAN and analysis)]. These statistics are in favor of the 1DVar model the 1DVar scheme generate daily precipitation rates for the majority of massifs, with a systematic reduction of that need to be distributed temporally over 24 h, and the the RMSEs (from 14.6 to 5.5 mm for Mont-Blanc and from phase of the precipitation needs to be determined at 15.3 to 6.3 mm for Haut Var–Haut Verdon). The standard each time step. SAFRAN uses a temporal distribution deviation is also reduced over most massifs, from 14.6 to function that estimates a probability of precipitation 5.4 mm for the Mont-Blanc massif and from 15 to 6.3 mm given hourly interpolated values of low-level specific over the Haut Var–Haut Verdon massif. The larger values humidity. The rain–snow transition is determined ac- of the standard deviation over Haut Var–Haut Verdon cording to a temperature threshold. For the 1DVar massif than over Mont-Blanc confirm the larger dispersion model, two distribution functions are tested: the first one observed in Fig. 5, likewise the values of the coefficient of uses hourly distribution based on short-range forecasts variation, computed as the ratio between the standard of rainfall and snowfall from AROME for the hourly deviation and the mean, which are larger over Haut distribution and the determination of the phase (called Var–Haut Verdon than over Mont-Blanc (1.51 and 1.54, Distrib_AROME hereafter) and the second one uses respectively, for SAFRAN analysis and 1.63 and 1.74, re- radar precipitation estimates where they are available spectively, for the 1DVar analysis). In addition, the scat- (called Distrib_RADAR hereafter). In both cases, terplots in Fig. 5 show that low precipitation amounts of a hourly precipitation fractions of AROME forecasts or few millimeters are overestimated by both SAFRAN and radar observations are calculated (hourly precipitation/ 1DVar analysis, but the overestimation is limited to about daily precipitation) and then used to distribute the an- 10 mm for 1DVar, whereas it can reach several tens of alyzed 1DVar estimates temporally. Only the first dis- millimeters with a larger dispersion for SAFRAN analysis. tribution function is evaluated here; Distrib_RADAR is This behavior for low precipitation amounts was observed described and evaluated in section 4c. over all massifs (not shown) and is due to the difficulties in Snowpack simulations are produced using the Crocus accurately reproducing the lower precipitation intensities. model fed by precipitation analysis of the 1DVar using The rain gauges have a tendency to underestimate solid Distrib_AROME function, with other atmospheric precipitation and lower intensity can even be missed. forcing parameters coming from SAFRAN (called Moreover, precipitation analysis can hardly represent 1DVar hereafter). The reference simulations are those low accumulations that are either overestimated or not obtained using the Crocus model fed by SAFRAN for

Unauthenticated | Downloaded 09/28/21 01:26 AM UTC MAY 2017 B I R M A N E T A L . 1435 all variables (called Safran hereafter). The two sets of account for observation representativeness within a simulations are compared with snow depth observations massif, whereas in the 1DVar analysis, the observation for two seasons (2012/13 and 2013/14). There is no as- error is defined a priori, with quality control based on similation or reinitialization in Crocus during a season, innovation (observation minus background). Figure 7 so any errors could be propagated through the whole (bottom) shows snow depth simulations at Tignes (at an season. In the following, the results of the 1DVar not altitude of 2080 m) within the Haute Tarentaise massif. using radar are mainly evaluated over the northern The station of Tignes was chosen because it is rather Alps, where radar data are not available. Figures 6 (top representative of the behavior of the 1DVar analysis and bottom) and Figure 7 (top) show scatterplots of over the northern Alps: many observations originate snow depth simulations against observations for three from ski resorts during the winter season, and the snow massifs: Chablais, Mont-Blanc, and Haute Tarentaise, depth simulations using the 1DVar analysis reproduce which are representative of snow depth simulations over rather well the observed snow depth over homogeneous the northern Alps for the two settings. Results are massifs with a relatively high number of available ob- shown according to available snow depth stations for servations (almost 10 per day). The 1DVar simulations each massif. The behavior of 1DVar is seen to be rather are closer to the observations at Tignes for the whole good when compared with independent snow depth study period. During the year 2012/13, SAFRAN anal- observations. Table 2 shows the bias, RMSE, standard ysis has a positive bias from January until May. During deviation, Nash–Sutcliffe efficiency (NSE), and corre- the year 2013/14, the two simulations are very close to lations for snow depth obtained from SAFRAN analysis each other and in good agreement with observations, and for 1DVar analysis over the Alps, the northern Alps, except during the first months (December–February), the southern Alps, and the Chablais, Mont-Blanc, and for which the 1DVar analysis is slightly better. Over the Haute Tarentaise massifs, as well as the station of whole period, the bias is 24.28 cm for 1DVar analysis Tignes. The NSE ranges from 2‘ to 1 and is defined as against 4.61 cm for Safran, the RMSE is 13.90 cm against (Nash and Sutcliffe 1970) 12.03 cm, the standard deviation is 13.11 cm against 11.24 cm, the correlation coefficient is 0.98 against 0.97, N å 2 2 and the NSE is 0.90 against 0.93 (see Table 2). (Oi Pi) 5 NSE 5 1 2 i 1 , (6) The scores over all massifs of the French Alps (in N å 2 2 Table 2) obtained from the 1DVar analyses are slightly (Oi O) i51 degraded with respect to SAFRAN analysis, but the correlations are above 0.8 in most cases. SAFRAN where Oi and Pi are the observed and predicted snow analysis performs better over the northern Alps than depths and O designates the temporal mean of the ob- over the southern Alps, and the same tendency is observations. An NSE of 1 corresponds to a perfect match served for the 1DVar analysis. SAFRAN analyses between observed and simulated snow depth, whereas show a small systematic positive bias, whereas the an efficiency of zero corresponds to a model that is as 1DVar analyses show a negative bias larger than SAFRAN accurate as the mean of observations. It is less than zero over the northern Alps, but smaller in absolute value when the model is not as good as the mean of observa- over the southern Alps. The NSE coefficients of tions. The NSE compares the square of errors to the 1DVar analysis are lower than those of SAFRAN variance of observations and represents a kind of signal- analysis, but they remain satisfactory with values above to-noise ratio that compares the variability of the model 0.5 over the southern Alps and above 0.7 over the to the variability of observations. northern Alps. Over the three massifs shown here, the correlation c. Local adjustments values (using all observations) are quite similar between Safran and 1DVar (shown in Table 2): 0.88 and 0.88 for The main goal of the 1DVar tool is to provide pre- Chablais, 0.88 and 0.89 for Mont-Blanc, and 0.81 and cipitation forcing fields to the snow model Crocus and to 0.82 for Haute Tarentaise, respectively. Results in terms adequately simulate the snowpack state during winter. of RMSEs are in favor of Safran, with 1DVar having Similarly to SAFRAN, the tool produces analyses of pre- larger values (and more specifically larger biases): the cipitation at massif scale and could not represent smaller- RMSEs for Safran and 1DVar are 38.5 and 38.4 cm over scale precipitation features. To further examine how the Chablais, 43.9 and 49.7 cm over Mont-Blanc, and 36.4 1DVar analysis is sensitive to local inhomogeneities, an and 37.8 cm over Haute Tarentaise, respectively. It additional experiment is run with a constraint on the should be noted that, in SAFRAN analysis, a posteriori maximum horizontal distance between observation and a adjustment of the weight of observations is applied to modeling point. Here the 1DVar simulations are made in

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FIG. 6. Scatterplot of observed vs simulated snow depth over the (top) Chablais and (bottom) Mont- Blanc massifs for the years 2012/13 and 2013/14, using (left) SAFRAN and (right) 1DVar precipitation analyses as input to the snow model Crocus. Colors correspond to the various snow depth observation stations.

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FIG. 7. (top) Scatterplot of observed vs simulated snow depth over the Haute Tarentaise massif for the years 2012/ 13 and 2013/14, using (left) SAFRAN and (right) 1DVar precipitation analyses as input to the snow model Crocus. Colors correspond to the various snow depth observation stations. (bottom) Snow depth simulations with Crocus model forced by precipitation analyses produced by SAFRAN (blue line) and 1DVar (red line) analyses at the Tignes station, within the Haute Tarentaise massif, for the period from August 2012 to August 2014. The observations are plotted as black plus signs. The Crocus model forced by SAFRAN analysis is plotted in blue and by the 1DVar analysis in red.

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TABLE 2. Scores of snow depth simulations relative to observations for SAFRAN reanalysis and 1DVar analysis over the whole period of 2 years.

Bias (cm) RMSE (cm) Std dev (cm) NSE Correlation Safran 1DVar Safran 1DVar Safran 1DVar Safran 1DVar Safran 1DVar Alps 5.02 28.90 35.64 40.00 35.29 39.00 0.73 0.67 0.87 0.83 Northern Alps 2.33 28.54 33.75 38.20 33.67 37.24 0.77 0.71 0.88 0.85 Southern Alps 11.01 29.78 39.68 43.78 38.12 42.68 0.63 0.55 0.84 0.77 Chablais 210.76 0.49 38.46 38.37 36.93 38.36 0.75 0.76 0.88 0.88 Mont-Blanc 219.88 226.71 43.89 49.71 39.13 41.92 0.70 0.62 0.88 0.89 Haute Tarentaise 5.41 17.14 36.41 37.80 36.00 33.68 0.61 0.59 0.81 0.82 Tignes 4.61 24.28 13.90 12.03 13.11 11.24 0.90 0.93 0.98 0.97

the vicinity of snow depth station measurement by as- to distribute daily analysis. Their potential is tested similating available rain gauge observations within a in three ways: 1) radar hourly precipitation rates are 16-km circle inside the massif of interest. The obtained used to calculate hourly precipitation fractions (hourly precipitation analysis is used to force the Crocus model to precipitation/daily precipitation) over each massif, which simulate snow depths to be compared to snow measure- were then used to distribute the analyzed 1DVar esti- ments. This new experiment is called ‘‘1DVar local.’’ The mates (function Distrib_RADAR); 2) besides using the resulting snow depth simulations are compared with ob- Distrib_RADAR function, 24-h accumulated radar- servations and some scores (RMSE and NSE) are shown derived precipitation is assimilated in the 1DVar; and in Table 3 for a selection of stations and massifs. Results 3) the 24-h radar-derived precipitation accumulations are are globally improved with the 1DVar local with respect assimilated using the Distrib_AROME function for to the 1DVar analysis. The largest improvement is ob- hourly distribution. When Distrib_RADAR is used, the tained with stations situated at midaltitudes (between phase of the precipitation at each time step is chosen 1500 and 2000 m) in massifs with a relatively high number according to SAFRAN analysis. When Distrib_AROME of observations, and the scores are improved with re- is used, the phase of the precipitation is the same as in the spect to SAFRAN analyses for several massifs (including AROME model hourly forecasts. Haute Tarentaise, Bauges, and Grandes-Rousses, shown a. Means of using radar-derived observations in Table 3). However, over a few massifs the snow depth simulations are not as good with the 1DVar local, especially Given the high temporal and spatial resolution of radar for high-altitude stations (above 2500–3000 m), when the observations and the advanced algorithms used to com- surrounding observations used in the precipitation analysis pute radar-derived precipitation rate, we examined the use have a large altitude difference with the selected station of interest, even if the horizontal distance remains small (e.g., TABLE 3. Scores of snow depth simulations relative to observa- over Vanoise and Oisans, shown in Table 3). In this case, tions for SAFRAN reanalysis, 1DVar analysis, and 1DVar analysis the closest rain gauges are not representative of pre- with station adjustments over the whole period of 2 years for the cipitation near the snow station and the nonassimilation Alps, northern Alps, southern Alps, and a selection of massifs that of distant observations situated at higher altitudes leads present contrasted conditions. The values in boldface correspond to the best scores between Safran, 1DVar, and 1DVar local. to a large underestimation of the snow depths [e.g., at Bellecote-Nivose^ (3000 m) in Vanoise massif, Les Ecrins- RMSE (cm) NSE Nivose (2978 m), and La Meije-Nivose (3100 m) in Oisans 1DVar 1DVar massif]. For massifs with few rain gauge observations, the Safran 1DVar local Safran 1DVar local 1DVar local results can hardly be better than 1DVar Alps 35.64 40.00 37.76 0.73 0.67 0.71 analysis (e.g., Mercantour, shown in Table 3). Northern Alps 33.75 38.20 36.19 0.77 0.71 0.74 Southern Alps 39.68 43.78 41.10 0.63 0.55 0.61 Haute 36.41 37.80 32.64 0.61 0.59 0.69 4. Potential of weather radar estimates Tarentaise Vanoise 18.59 26.19 39.34 0.90 0.81 0.59 Given the scarcity of rain gauge observations, addi- Bauges 30.28 30.63 24.90 0.77 0.77 0.85 tional assimilation experiments are undertaken to Grandes- 31.05 40.96 24.54 0.64 0.37 0.77 evaluate the impact of precipitation estimates derived Rousses from weather radar, both as observations to be assimi- Oisans 74.17 68.51 69.89 0.37 0.46 0.43 lated and also to compute hourly precipitation fractions Mercantour 21.11 27.93 26.62 0.93 0.88 0.89

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FIG. 8. (top) Snow depth simulations with Crocus model forced by precipitation analyses produced by SAFRAN (blue line), 1DVar (gray line) analyses, and radar-derived observations (green line) at the Isola station, within the Mercantour massif for the period from August 2012 to August 2014. The observations are plotted as black plus signs. (bottom) Individual radar-derived precipitation accumulations vs altitude over the Haut Var–Haut Verdon massif on 5 Mar 2013. of radar-derived observations of precipitation at an hourly 50 cm or more, producing a large discrepancy between the time step directly to force the snowpack model Crocus. observed snow depths and the simulation using radar- Figure 8 (top) shows an example of snow depth simulation derived observation to force the Crocus model. These over the years 2012/13 and 2013/14 at the Isola station, in overestimations are further propagated over the season as the massif of Mercantour, using the Crocus model forced snow depth is an integrated parameter. by SAFRAN, 1DVar analysis using only rain gauge ob- For assimilation, radar-derived observations at a daily servations, and radar observations without analysis. It time step within a given massif are grouped by altitude shows that radar observations reproduce the variation of range of 300 m and ‘‘superobservations’’ are generated by snow depth but largely overestimate snow depth over the averaging radar pixels within a massif associated with each two years. Some snowfall events are overestimated by altitude level. The superobservations are computed at the

Unauthenticated | Downloaded 09/28/21 01:26 AM UTC 1440 JOURNAL OF HYDROMETEOROLOGY VOLUME 18 same altitudes as SAFRAN ranges and are computed, for from SAFRAN and from 1DVar using Distrib_RADAR an altitude z, as an average of radar individual observa- and using Distrib_AROME. Table 1 provides the names tions situated at altitudes between the altitudes z 2 dz/2 of the massifs corresponding to the numbers shown in and z 1 dz/2, where dz 5 300 m. Figure 8 (bottom) shows Fig. 9. As stated earlier, Fig. 9 shows that only the the daily radar individual precipitation observations ver- southern Alps have good radar coverage with a quality sus altitude over the Haut Var–Haut Verdon massif on index greater than 70%. Regarding precipitation distri- 5 March 2013. The observations are averaged at the same bution, SAFRAN tends to apply a sawtooth distribution, altitudes as the SAFRAN range between altitudes which is quite different from that provided by the z 2 dz/2 and z 1 dz/2, where z are SAFRAN altitude AROME forecast or by radar observations. This feature levels and dz 5 300 m, to compute superobservations, was also noticed by Mérindol et al. (2013) and results which are then assimilated in the 1DVar. Sensitivity tests from the threshold that is applied on near-surface specific on radar superobservation errors show that a value of humidity to discriminate the precipitating time steps from 5 mm gave the radar-derived precipitation sufficient the nonprecipitating ones. weight to bring useful information into the analysis. Al- We thus end up with a set of five experiments over the though the superobservations are supposed to represent a southern Alps during two seasons (2012/13 and 2013/14) large area of the massif, and thus to be more reliable than and the corresponding set of simulations of snow depth: point observations, they are subject to errors related to the d Safran: the reference experiment; incomplete radar coverage of each massif and to the d 1DVar: using the Distrib_AROME function; presence of solid precipitation, among other effects. d 1DVar radar hourly: using the Distrib_RADAR Sensitivity tests are performed to examine the impact of function; varying the standard deviation of radar-derived observa- d 1DVar radar assim: 1DVar with the assimilation of tions with respect to rain gauge observations, thus varying radar observations; and their weight in the analysis process. A rather small sensi- d 1DVar radar hourly1assim: 1DVar using the Distrib_ tivity to radar standard deviation is observed. When the RADAR function with the assimilation of radar standard deviation of radar-derived observations is de- observations. creased, the weight of the radar-derived observations is increased in the analysis and the RMSEs of the analysis The experimental setup is summarized in Table 4. profile of precipitation decrease over small massifs with b. Impact of the assimilation of radar-derived rather homogeneous radar coverage (e.g., Chartreuse), observations but they are not as good over large massifs with heterogeneous precipitation (e.g., Haut Var–Haut Verdon). The results of snowpack simulations using radar- Radar observations are subject to different sources of derived precipitation indicate that the assimilation of errors related to the averaging of pixel observations and to radar-derived observations generally improves snow the reflectivity–rain-rate conversion. Setting the standard depth simulations. Figures 10 and 11 show scatterplots deviation of the radar observations equal to that of rain of snow depth observations against simulations over the gauge observations, all observations (rain gauge or radar) Mercantour and Haut Var–Haut Verdon massifs, with have the same weight in the analysis, despite their quite Safran, 1DVar, 1DVar radar hourly, 1DVar radar assim, different sources of error. The use of radar-derived ob- and 1DVar radar hourly1assim. These massifs are as- servations is limited to the southern Alps, for which the sociated with the best radar coverage over the period of quality index of radar-derived precipitation is greater than interest. Results are split according to available snow 70%. The threshold is applied to the dynamic quality in- depth stations (four stations for Mercantour and two dex, which takes into account not only static orographic stations for Haut Var–Haut Verdon). The rather good masks but also the actual data availability for radars in performance of the 1DVar is worth noting, especially for operation and the attenuation from precipitating systems Isola station within Mercantour, for which the positive along the scan, which reduces the range of radars. Al- bias observed for shallow snow depths is reduced by the though the use of KDP for polarimetric radars alleviates four 1DVar analyses with respect to Safran. This bias of the problem of attenuation from precipitating systems, the 30–50 cm with Safran is reduced to 20–30 cm with the attenuation is only partially corrected and a potential bias 1DVar analyses. The positive bias observed at Isola against heavy rain or snow remains. Figure 9 illustrates the station corresponds to the underestimation of snowmelt precipitation estimates on 5 March 2012. It shows the ra- during the months of April and May 2014 due to a wrong dar coverage and precipitation estimates, the quality in- phase of precipitation diagnosed by Safran. Statistics are dex of radar observations, the 24-h forecast from in favor of Safran for both massifs and are shown in AROME, and the resulting precipitation distribution Table 5, but 1DVar performed quite well, especially

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FIG. 9. Daily precipitation (mm) on 5 Mar 2013 derived from (a) radar measurements; (b) quality index of radar- derived precipitation; (c) 24-h forecast from the AROME convective scale model; and (d) precipitation fractions over the Haut Var–Haut Verdon massif from SAFRAN analysis (Safran; blue line), from 1DVar analysis using Distrib_RADAR (1D-Var radar-h; red line), and from 1DVar analysis using Distrib_AROME (1D-Var Arome; orange line). when radar-derived observations are assimilated. The and Distrib_RADAR), for which the bias becomes of assimilation of radar-derived observations was re- the same order as that of Safran (19.02 cm). Over sponsible for a signiﬁcant reduction of bias over the two Haut Var–Haut Verdon massif, the smallest bias is massifs with respect to 1DVar (from 7.15 cm for 1DVar obtained with hourly distribution based on radar ob- to 20.72 cm for 1DVar with radar-derived observations servations and rain–snow transition based on SAFRAN over Mercantour massif and from 45.23 to 31.29 cm over analysis, which is not the case for Mercantour. Over Haut Var–Haut Verdon massif), which becomes of the Haut Var–Haut Verdon massif, 1DVar radar hourly1assim same order as the bias of SAFRAN for Mercantour improves the RMSE with respect to 1DVar (almost (3.75 cm). Another reduction of bias is obtained with 1DVar halved: 30.2 and 53.4 cm). The correlations are close to radar hourly1assim over the Haut Var–Haut Verdon or above 0.90 with 1DVar radar hourly, 1DVar radar (20.07 cm for 1DVar with radar-derived observations assim, and 1DVar radar hourly1assim (0.94, 0.89,

TABLE 4. Experimental setup and use of various observations for SAFRAN, 1DVar, 1DVar with hourly distribution based on radars (1DVar radar hourly), 1DVar with assimilation of radar observations (1DVar radar assim), and 1DVar with assimilation of radar observations and use of radar for hourly distribution (1DVar radar hourly1assim).

1DVar radar Safran 1DVar 1DVar radar hourly 1DVar radar assim hourly1assim Assimilation of surface observations Yes Yes Yes Yes Yes Use of radars for hourly distribution of No No Yes No Yes daily precipitation accumulations Assimilation of radar-derived observations No No No Yes Yes

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FIG. 10. Scatterplots of simulated vs observed snow depth over the Mercantour massif for the years 2012/13 and 2013/14. Simulations were performed with the snow model Crocus forced with SAFRAN analysis (Safran), 1DVar analysis using Distrib_AROME (1D-Var), 1DVar analysis using Distrib_RADAR (1D-Var Radar-h), 1DVar analysis with assimilation of radar-derived precipitation and using Distrib_AROME (1D-Var Radar-assim), and 1DVar analysis assimilating radar-derived precipitation and using Distrib_RADAR (1D-Var Radar-h1assim). Colors correspond to the various snow depth observation stations.

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FIG. 11. As in Fig. 10, but for the Haut Var–Haut Verdon massif.

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TABLE 5. Scores of snow depth simulations with SAFRAN, 1DVar, 1DVar radar hourly, 1DVar radar assim, and 1DVar radar hourly1assim over the massifs of Mercantour and Haut Var–Haut Verdon.

Bias (cm) RMSE (cm) Std dev (cm) NSE Correlation Mercantour Safran 3.75 21.11 20.77 0.93 0.97 1DVar 7.15 27.93 27.00 0.88 0.94 1DVar radar hourly 212.40 32.26 29.78 0.84 0.94 1DVar radar assim 20.72 27.60 27.59 0.88 0.94 1DVar radar hourly1assim 223.18 39.36 31.81 0.76 0.94 Haut Var–Haut Verdon Safran 19.02 24.46 15.38 0.79 0.96 1DVar 45.23 53.40 28.37 0.41 0.86 1DVar radar hourly 32.78 38.64 20.45 0.48 0.94 1DVar radar assim 31.29 41.01 26.51 0.41 0.89 1DVar radar hourly1assim 20.07 30.50 22.97 0.67 0.92

and 0.92, respectively) and are increased with respect to representativeness of the radar-derived observations 1DVar (0.86), becoming closer to Safran (0.96). The best over a massif is affected by maskings due to orography or correlations are obtained for 1DVar radar hourly and overshooting of steep valleys because of the radar installed 1DVar radar hourly1assim. Over Mercantour, the cor- on mountain tops (see Figs. 2, 9). However, 1DVar radar relations are unchanged with all four 1DVar experiments hourly significantly improves the scores with respect to (0.94) and are close to Safran (0.97). Figure 12 highlights 1DVar: it reduces the bias (26.74 and 211.47), the RMSE results obtained at the Isola (Fig. 12, top) and Val Casterino (44.60 and 46.85), and the standard deviation (44.06 and (Fig. 12, bottom) stations (within the Mercantour 45.42) and increases the NSE (0.52 and 0.47) and the cor- massif) by showing the time evolution of snow depth relation (0.76 and 0.73). The use of radar-derived obser- simulations. It is quite difficult to identify the best vations with 1DVar radar hourly, 1DVar radar assim, and performing model at Isola given the high variability of 1DVar radar hourly1assim produces NSE and correlation snow depth measurements and simulations over the coefficients close to or above 0.5 and 0.75, respectively. period. 1DVar radar hourly1assim performs better at the c. Influence of the determination of the rain–snow beginning of the two years, but 1DVar radar hourly and transition 1DVar radar assim are closer to the observations after February for 2012/13 and after March for 2013/14. The A complementary evaluation is carried out on the daily 1DVar radar hourly1assim seems to behave better at Val variations of snow depths. The snow depth (noted HS

Casterino for the two years, except from March to May hereafter) variations, defined as dHSj 5 HSj 2 HSj21,are 2013, for which 1DVar radar assim is better. At Isola, the used to avoid cumulative errors in the snowpack occurring best scores, including RMSEs, standard deviation, cor- during the winter season, as used by Schirmer and relation coefficient, and NSE, are obtained for the 1DVar Jamieson (2015) and Quéno et al. (2016). Figure 13 shows radar assim simulation (24.42 cm, 23.73 cm, 0.95, and 0.89, the histogram of frequency of occurrence for 11 categories respectively, against 29.60 cm, 29.57 cm, 0.92, and 0.84, of snow depth variations from one day to the next day respectively, for Safran), but the minimum bias is ob- (accumulation or decrease) during the period 2012–14, tained with Safran and the 1DVar radar hourly simula- with SAFRAN and the four 1DVar simulations. The daily tions (21.43 and 2.24 mm, respectively). At Val snow depth variations account for precipitation and ab- Casterino, the best scores are obtained with the 1DVar lation and settlement processes, but are not influenced by radar hourly1assim simulation (bias 4.87 cm, RMSE earlier errors in snow depth simulations. The results with 20.02 cm, standard deviation 19.42 cm, correlation co- 1DVar radar assim are systematically better than those of efficient 0.95, and NSE 0.90). 1DVar and 1DVar radar hourly for strong decrease (more Table 6 shows the bias, RMSE, standard deviation, than 10-cm category), accumulations between 5 and 20 cm NSE, and correlation for Safran, 1DVar, 1DVar radar and above 60 cm, but the results for intermediate cate- hourly, 1DVar radar assim, and 1DVar radar hourly1assim gories are slightly degraded with respect to SAFRAN and analysis above 1500 m over the southern Alps. The as- 1DVar for accumulations between 20 and 40 cm. The re- similation of radar-derived observations (1DVar radar sults for the larger accumulations are probably due to assim) improves all scores with respect to 1DVar, but some intense, localized convective events that can be it has a limited impact on snow depth simulations. The captured by radars but are missed by rain gauges. The use

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FIG. 12. Snow depth simulations from the snow model Crocus forced by various precipitation analyses over two years from August 2012 to August 2014 at (top) Isola and (bottom) Val Casterino. The observations are plotted as black plus signs. The Crocus model forced by SAFRAN analyses is plotted in blue, by the 1DVar analysis with Distrib_AROME is in gray, by the 1DVar analysis with Distrib_RADAR is in green with dashed line, by the 1DVar analysis with radar-derived observations and Distrib_AROME is in orange with dashed line, and by the 1DVar analysis with radar observations and Distrib_RADAR is in red. of radar observations with 1DVar radar hourly, 1DVar variations between 20.2 and 0.2 cm. The impact of using radar assim, or 1DVar radar hourly1assim signiﬁcantly Distrib_RADAR (1DVar radar hourly and 1DVar ra- improves the frequencies of occurrence for strong de- dar hourly1assim) is particularly marked for decreases creases (more than 10 cm) and accumulations above 5 cm. larger than 10 cm and accumulations larger than 20 cm. The results are not as good for small accumula- These differences are partly due to the hourly distribution tions between 0.2 and 5 cm and are almost unchanged of daily precipitation and to the rain–snow transition at for moderate decreases between 0.2 and 10 cm and each time step, which is based on the SAFRAN rain–snow

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TABLE 6. As in Table 5, but for over the southern Alps above 1500 m altitude.

Bias RMSE Std dev (cm) (cm) (cm) NSE Correlation Safran 11.73 42.56 40.91 0.55 0.81 1DVar 211.47 46.85 45.42 0.47 0.73 1DVar radar 26.94 44.60 44.06 0.52 0.76 hourly 1DVar radar assim 29.63 46.02 45.00 0.49 0.74 1DVar radar 24.52 45.14 44.91 0.51 0.76 hourly1assim transition for 1DVar radar hourly and 1DVar radar hourly1assim, and on the AROME rain–snow transition for 1DVar and 1DVar radar assim. Figure 14 shows the histogram of frequency of occurrence for 11 categories of daily variations of snow depth for observed snow depths FIG. 13. Histogram of frequency of occurrence for 11 categories and those simulated using the Crocus model. The dif- of snow decrease and accumulation simulated by the snow model ferent simulations correspond to forcing from SAFRAN, Crocus forced by SAFRAN (blue), 1DVar (gray), 1DVar radar from the 1DVar model using AROME hourly forecasts hourly (green), 1DVar radar assim (orange), and 1DVar radar hourly1assim (red). for the hourly distribution of daily precipitation and for the rain–snow transition at each time step, and forcing forecasting, since they play a major role in avalanche from the 1DVar model using AROME hourly forecasts triggering. for hourly distribution but SAFRAN for the phase of precipitation. The only difference between the two 1DVar simulations was the methodology to determine 5. Discussion the phase of precipitation. The figure shows that, for large This paper describes a tool to generate vertical profiles snow depth variations (from 30 to 60 cm), using the of precipitation in mountainous areas by using a varia- SAFRAN rain–snow transition produces better results, tional approach given first guess information from a whereas the use of the AROME rain–snow transition underestimates the frequency of occurrence of snow increments between 30 and 60 cm. The same behavior of the SAFRAN rain–snow transition is observed for large snow decreases. However, for larger snow accumulations (above 60 cm), the behaviors of the two 1DVar simulations are similar and are rather close to the observations whereas SAFRAN does not diagnose any events in this category. Therefore, the underestimation of categories between 20 and 60 cm for the 1DVar and the 1DVar radar assim with respect to SAFRAN, 1DVar radar hourly, and 1DVar radar hourly1assim is mainly due to the difference in rain–snow transition between SAFRAN and AROME. However, some significant differences between simulations and observations remain for decreases larger than 10 cm, which probably result not simply from precipitation biases but rather from biases in other meteorological variables or from systematic errors in the Crocus model. These results highlight the contri- FIG. 14. Histogram of frequency of occurrence for 11 categories bution of radar-derived observations for intense small- of snow decrease and accumulation simulated by the snow model scale events that are infrequent but produce large Crocus forced by SAFRAN (blue), 1DVar analyses using AROME hourly forecasts for hourly distribution and rain–snow transition amounts of precipitation, either rainfall or snowfall, and (gray), and 1DVar analyses using AROME hourly forecasts for thus have a large impact on snow depth modeling. These hourly distribution and SAFRAN analyses for rain–snow transition events are particularly important for avalanche hazard (green).

Unauthenticated | Downloaded 09/28/21 01:26 AM UTC MAY 2017 B I R M A N E T A L . 1447 numerical weather prediction model and rain gauge the atmosphere and thus the phase of precipitation when and radar observations. The 1DVar tool is evaluated it reaches the ground. Moreover, snow depth modeling against in situ observations and other precipitation could also be improved through optimal calibration of the products in terms of analyzed vertical profiles of pre- Crocus parameters. cipitation and in terms of snow depth simulations. The The snowpack is simulated at the massif scale, radar data used in this study come from the Météo- whereas evaluations are performed at observation France system supplying a mosaic of surface pre- points. The massifs are assumed to be homogeneous cipitation amounts, which includes X-band radars from areas, but some differences inevitably occur between the RHYTMME project in addition to C- and S-band distant points within the same massif because of the radars from the ARAMIS network. The use of radar orientation of slopes with respect to the dominant wind for the analysis of precipitation over the French Alps and because of small-scale convective events situated in has been possible since 2012. However, two years of areas of the massifs that are not covered by precipitation simulations is rather short. Essery et al. (2013) showed observations. Heterogeneity within a massif, which is that the performances of different snow models could not taken into account in the meteorological forcing, vary significantly from one year to another, and thus a spreads into snowpack simulations. This issue has been large number of years should be considered for a more addressed with the experiment called 1DVar local, in robust evaluation. Some additional studies involving which a maximum distance is set between the observa- snowpack simulations with 1DVar not using radar ob- tions and the snow depth simulation sites. The results on servations were performed for the years 2010–14. The snow depth simulations show an improvement with re- results over these four years showed that, within a spect to the 1DVar analysis and also with respect to massif, the performance of the 1DVar analysis could be SAFRAN for several massifs. However, a more robust quite variable from one year to another, depending on investigation would be necessary to take more effects snow conditions and on the total amount of pre- into account. Moreover, local heterogeneity in the cipitation during the season. snowpack is also influenced by wind-induced snow The evaluation of precipitation analyses using snow transport, which is not taken into account in the opera- depth represents an alternative evaluation when the tional Crocus snow model. Therefore, the performance evaluation against rain gauges is not relevant (in case of of the model can vary significantly between stations, as solid precipitation and/or wind), but it implies the use shown by Lafaysse et al. (2013). A more robust evalu- of a numerical snow model. However, other meteoro- ation should ideally involve comparisons against grid- logical variables and snow model parameters can also ded variables from satellite products. For example, affect the skill of simulations. This statement is sup- Moderate Resolution Imaging Spectroradiometer ported by Fig. 5. Although the 1DVar precipitation (MODIS) radiances were used by Mary et al. (2013) to analyses display a reduced spread with improved scores retrieve the specific surface area of snow that was against SAFRAN, snow depth simulations using 1DVar compared to field measurements and SAFRAN-Crocus analyses do not show systematic improvement with re- outputs. Gascoin et al. (2015) also used MODIS prod- spect to SAFRAN. Other meteorological variables such ucts to monitor the effects of climate on snow dynamics as temperature, humidity, wind, and radiation have an in the Pyrenees. Sirguey et al. (2009) produced regional impact on snowmelt, refreezing, or settlement. These maps of seasonal snow cover over the Southern Alps of variables should also be analyzed in a 1DVar framework New Zealand using MODIS reflectance data. MODIS in order to produce consistent meteorological forcing for data were also used by Rahimi et al. (2015) to estimate snowpack simulations. In particular, the altitude of the evapotranspiration. rain–snow transition of precipitation impacts the snow depth simulations, and a small error can lead to large 6. Conclusions differences in snow depth simulations. The 1DVar simulations using Distrib_AROME and Distrib_RADAR This study presents an original 1DVar assimilation illustrate the importance to adequately diagnose rain– scheme to retrieve hourly precipitation profiles in snow transition since the differences between these sim- mountainous areas by combining observations from rain ulations are due not only to different hourly precipitation gauges and weather radars with background information distributions but also to a different rain–snow transition from short-range forecasts of the convective-scale NWP at each time step. Nevertheless, the dominant parameters model AROME. The method was evaluated using in- for snowpack evolution are the precipitation amounts dependent observations made over the French Alps and the temperature, which governs the altitude of the during the 2-yr period from August 2012 to August 2014. melting layer within clouds or the precipitation layer in The 1DVar precipitation analyses were found to be in

Unauthenticated | Downloaded 09/28/21 01:26 AM UTC 1448 JOURNAL OF HYDROMETEOROLOGY VOLUME 18 very good agreement with independent observations to the 1DVar analysis and also to SAFRAN. When radar (not used in the assimilation process). The 1DVar pre- observations are considered for hourly distributions, a cipitation analysis has been compared against the well- similar limitation appears, increased by the aggregation validated SAFRAN model, and the results of the 1DVar of altitudes for hourly fraction computations. At lower precipitation analyses are better than SAFRAN ana- elevation, radar overshoot causes the derived hourly lyses in terms of RMSEs and standard deviation. The fractions to be poorly representative of the location performance of the 1DVar was also evaluated by ex- where they are applied. In this case, the additional in- amining the quality of simulation of snow depth using formation contributed by radar-derived observations is the snowpack model Crocus (forced by the 1DVar pre- not relevant for the hourly precipitation distribution. cipitation analyses). Snow depth simulations were found Further studies will include the analyses of other rel- to agree rather well with independent observations and evant meteorological variables in order to produce are comparable to SAFRAN reference model. It ap- consistent meteorological analysis for Crocus snowpack pears that snow depth simulations using SAFRAN re- model forcing. The period of evaluation should also be sults are better than the 1DVar ones in terms of extended as more radar observations become available correlation and RMSE. Such behavior can be un- in the future. The current 1DVar analysis system allows derstood by recalling that SAFRAN takes the repre- great flexibility in adapting precipitation analysis to sentativeness of observations within a massif into various spatial scales and including different types of account and adjusts their weight accordingly in the observations. With an appropriate, possibly nonlinear, analysis. The fact that more observations are used also observation operator, observations that are related to forms part of the explanation. Several other experiments precipitation in a complex manner could be assimilated. were performed using weather-radar-derived pre- For example, the vertical profile of reflectivity could be cipitation to improve the 1DVar analyses. We have exploited to retrieve information about the three- shown that the assimilation of radar-derived observa- dimensional characteristics of precipitation. Future tions brings a systematic improvement in areas where work will involve a complex approach combining a such observations are available, especially for events vertical analysis depending on altitude with high- producing large precipitation accumulations, as the lat- resolution spatial analyses in order to account for spa- ter are of particular interest for avalanche hazard fore- tial variability within massifs. Such an analysis would casting. In addition, we have also shown that weather make better use of high-resolution radar data by using radar observations can be used on an hourly basis to gridpoint observations combined with a high-resolution improve the time series of precipitation analyses and NWP model like AROME. that this has a positive impact on simulated snow depths. This method has been developed over the French Although snow depth simulations are generally im- Alps but could be applied to other mountainous regions. proved using 1DVar analysis without radar-derived Over the French mountainous areas, including the Pyr- observations over the massifs covered by radars, the enees and Corsica, where SAFRAN analyses are avail- results using radar observations at some stations can able, the method can be applied using descriptions of remain unchanged with respect to the simple 1DVar massif limits and climatological precipitation profiles configuration. The full complexity of the meteorological from SAFRAN. To run 1DVar over other mountainous parameters is not taken into account within a given areas, it is necessary to define small homogeneous areas massif, as they are assumed to be horizontally homo- and a vertical climatological profile of precipitation geneous. The latter assumption does not hold when the (using a historical observation database, reanalyses, atmospheric flow produces large differences within a etc.). Within the selected homogeneous areas, a suffi- massif. Depending on the orientation of their slopes cient number of observations should be available for with respect to the dominant flow, different stations assimilation. Daily precipitation forecasts from an NWP situated at the same altitude can receive very different model are also necessary to adjust the background amounts of precipitation, whereas the 1DVar analysis profile to the meteorological conditions of each day, and assimilating radar observations produces an amount daily precipitation observations are needed to compute that depends only on the position of the radar with re- an analyzed profile. spect to surrounding mountains and the direction of the precipitating system. To support this assumption of Acknowledgments. The authors sincerely thank representativeness issues, an experiment conducted Charles Fierz and two anonymous reviewers for their with an additional constraint on the maximum distance relevant and very constructive suggestions and com- between the observations and the simulation point im- ments. We are grateful to Vincent Vionnet, Marie proved the results over most of the massifs with respect Dumont, and Cécile Coléou for useful discussions about

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