1. Introduction
Reliable precipitation estimates are needed for many applications, including meteorology, hydrology, and climate studies (Boone et al. 2004; Tapiador et al. 2012; Kucera et al. 2013; Kidd and Levizzani 2011; Valipour et al. 2013; Valipour and Eslamian 2014; Valipour 2015, 2016). For instance, a good knowledge of precipitation in mountainous regions at appropriate spatial and temporal scales is a prerequisite for accurate modeling of the snowpack and its evolution in time and for avalanche hazard forecasting. However, precipitation patterns are particularly variable in mountainous areas because of the influence of altitude, orography, aspect, and the associated small spatial scale of convective events. Accurate estimations of precipitation in mountains and of its variability in space and time would ideally require a dense rain gauge network combined with an effective analysis method. Cokriging of precipitation with altitude is one of the simplest and widely used methods, but it requires the precipitation to be strongly correlated with altitude (Hevesi et al. 1992a,b). Such methods can be used for monitoring precipitation accumulation at seasonal or annual time scales. For example, Prudhomme and Reed (1999) used topographical data to improve the mapping of extreme precipitation in a mountainous region of Scotland, using residual kriging with a regression method relating topographical variables to the median of the annual daily precipitation. Mair and Fares (2011) compared different geostatistical methods to estimate rainfall and showed that the use of topographical information improved the simulated precipitation accumulating on a monthly time-scale basis. Schmidli et al. (2002) studied the long-term variability of the precipitation over the Alps during the period 1901–90, using data from rain gauges to produce an analysis at a spatial resolution of 25 km and a monthly time step. They highlighted a climatological trend with an increase of winter precipitation over the northern and western Alps and a decrease of precipitation in autumn in the south of the Alps. Other techniques have been used that take account of the aspect of slopes with respect to atmospheric flow for daily analysis, but at a low temporal resolution (from seasonal to yearly accumulations; Daly et al. 1994; Schwab 2000). However, these methods are not suitable for the short-term monitoring of rapidly changing phenomena such as floods or for avalanche hazard forecasts. Long-term series of reliable estimates of precipitation are thus necessary at spatial and temporal resolutions that meet hydrological and snow study requirements. Methods have been developed to derive precipitation using a set of a priori information from climatological data and currently available measurements (Guan et al. 2005; Kyriakidis et al. 2001; Gottardi et al. 2012). Other long-term precipitation databases have been constructed for mountainous areas using atmospheric reanalysis outputs of numerical weather prediction (NWP) models with appropriate downscaling techniques to account for orography. Crochet (2007), Crochet et al. (2007), and Durand et al. (2009a,b), for example, used the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis over the time period 1958–2002 to compute precipitation estimates over mountainous areas. Crochet (2007) and Crochet et al. (2007) have produced a 1-km-resolution precipitation analysis over Iceland accounting for flow dependency and orientation of slopes with respect to the predominant wind. Durand et al. (2009a,b) have generated an analysis of all relevant meteorological parameters for snowpack modeling, including rainfall and snowfall rates, and studied their evolution in time over the French Alps.
To accurately simulate the evolution of snowpack over mountains at massif scale together with its mechanical stability, Météo-France has developed a chain of three models (Durand et al. 1999). For this chain of models, a massif is defined as a homogeneous area of about 500 km2 or greater over which the meteorological variables can be assumed to be uniform. The first analysis scheme, called Système d’Analyse Fournissant des Renseignements Atmosphériques à la Neige (SAFRAN) is used to generate relevant meteorological parameters that indirectly govern energy and mass budgets of the snowpack, at massif scale, on an hourly time basis. Multilayer snowpack simulations are performed using a physical model called Crocus (Brun et al. 1992; Vionnet et al. 2012), which employs SAFRAN atmospheric forcing outputs, to generate simulations of the snowpack. Avalanche hazard forecasting is then performed using a system called Modèle Expert d’Aide à la Prévision du Risque d’Avalanche (MEPRA; Giraud 1992) based on expert analysis of the simulated snowpack mechanical properties. Raleigh et al. (2015) showed that errors associated with the atmospheric forcing had the largest impact on snowpack modeling uncertainties. Precipitation being one of the most important atmospheric forcing variables, its estimation requires as much care as the modeling of snowpack properties.
SAFRAN has been widely used for the analysis of precipitation in mountainous areas and has been found to provide reliable precipitation estimates (Durand et al. 2009b). However, the model produces precipitation analyses only at massif scale and is not suitable to provide analyses on smaller areas or on a regular grid. For instance, the use of SAFRAN on high-elevation glacier sites requires the use of a postprocessing method to correct the bias of SAFRAN estimates with respect to in situ observations (e.g., Gerbaux et al. 2005). Moreover, the use of indirect observations such as radar or satellite estimates is difficult with the optimal interpolation technique. In the framework of the European Reanalysis and Observations for Monitoring (Euro4M) project, another precipitation analysis system called MESCAN has been built, also based on an optimal interpolation technique using conventional surface observations to produce temperature, relative humidity, and precipitation analysis (Coustau et al. 2014; Soci et al. 2016). Simulations of snow and surface fluxes using the surface model Surface Externalisée (SURFEX) forced by MESCAN analysis have given satisfactory results overall. However, limitations appear over mountains since the specifications of error statistics and correlation length scale in the MESCAN analysis scheme are tuned for flat areas and are not appropriate in complex terrain. The main purpose of the present development is to build a precipitation analysis model having a quality similar to SAFRAN (at massif scale) but that can also be easily adapted to provide precipitation analyses at smaller spatial scales. The system should be able to assimilate both conventional and remote sensing data. In the case of indirect measurements of precipitation, the analysis system should enable the use of a complicated, possibly nonlinear, observation operator. The aim of this study is to address the weaknesses of existing models (SAFRAN and MESCAN) by developing a tool using a variational approach that could be operated on both a large scale (scale of massifs) and smaller scales. The tool should be able to produce a vertical profile of precipitation to take better account of the mountain specificities from various sources of precipitation observations. This tool is applied and evaluated over two years spanning August–July for 2012/13 and 2013/14. Section 2 summarizes the data and systems used in this study. A first evaluation of the variational method is given in section 3. Section 4 is dedicated to a study of the potential of remote sensing observations from weather radars to provide more reliable precipitation estimates in the Alps. The results are discussed in section 5, and section 6 presents some conclusions.
2. Data, models, and 1DVar analysis scheme
a. The SAFRAN analysis
SAFRAN is a Météo-France operational system designed to produce analyses of meteorological parameters that influence the evolution of the snowpack (Durand et al. 1993). SAFRAN provides hourly meteorological information at the snow–atmosphere interface over massifs, which are assumed to be homogeneous (the 23 massifs in the French Alps are listed in Table 1). The massifs are represented by discontinuous pyramids (eight expositions) for which SAFRAN analyzes vertical profiles of atmospheric variables at all elevations up to 3600 m with a 300-m step. The meteorological variables are surface air temperature and humidity, wind speed, cloudiness, precipitation rate, precipitation phase, and downward longwave and shortwave radiative fluxes (direct and scattered). Observation types used in SAFRAN mainly include those from conventional surface synoptic stations (available every 6 h), automatic stations (providing hourly observations), and climatological stations (every 24 h). SAFRAN can handle observations with variable time frequencies (every hour and 6 h), which is the case with air pressure and temperature, wind, humidity, cloudiness, etc. Other parameters, such as precipitation and minimum/maximum temperatures, are only available on a daily basis. Over the French Alps, daily precipitation accumulation observations come from around 500 meteorological stations: either meteorological stations at lower altitude or sparser “nivo-meteo” stations at higher altitude. Their altitude varies from 200 to 2500 m, and they provide daily 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 state. For a given day, the ARPEGE geopotential height at 500 hPa is used as a predictor to choose an appropriate climatological profile, and the optimal interpolation analysis is performed using available observations. An additional constraint preserves the gradient of the selected climatological profile. SAFRAN also uses radiosonde and pilot balloon data when available (few stations in the Alps). Besides the ARPEGE global NWP model, Météo-France has developed the Applications of Research to Operations at Mesoscale (AROME) model, which is a limited-area model at convective scale. AROME has been running operationally since December 2008 (Seity et al. 2011). This model is nonhydrostatic, with a three-dimensional variational data assimilation (3DVar) scheme that takes various observation types into account, including in situ measurements and remote sensing observations. Its horizontal resolution for the present study was 2.5 km and there were 60 vertical pressure levels. Figure 1 shows the AROME model orography with a representation of alpine massifs (drawn as red polygons) and the locations of rain gauge stations.
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.
AROME model orography over the French Alps (vertical color bar) with rain gauge stations and the boundaries of 23 massifs defined in SAFRAN analysis. The elevation of the rain gauges stations are represented with their difference of elevation with AROME relief (horizontal color bar).
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
For more than 25 years, SAFRAN has been used for its initial purpose of snow modeling for avalanche forecasting. When SAFRAN forces an appropriate surface model, the river discharges can be accurately simulated on mesoscale alpine catchments (Lafaysse et al. 2011). A robust extension over France has also been performed (Quintana-Seguí et al. 2008) to simulate river discharges operationally (Habets et al. 2008). SAFRAN also provides the atmospheric forcing for an operational forecasting system of surface road conditions (Bouilloud et al. 2009). A number of climate studies have been undertaken with SAFRAN over the last 50 years in terms of low-level meteorological parameters (Durand et al. 2009b; Vidal et al. 2010b), snow cover (Durand et al. 2009a), soil moisture and streamflows (Vidal et al. 2010a), and potential for artificial snow production (Spandre et al. 2015). SAFRAN analyses have been used as a reference to calibrate the downscaling methods of general circulation models or regional climate models (Boé et al. 2007; Rousselot et al. 2012; Lafaysse et al. 2014). The present study used the SAFRAN reanalysis, which is assumed to give the best estimation of precipitation, to evaluate the one-dimensional variational data assimilation (1DVar) model. The SAFRAN reanalysis is more accurate because it takes more observations into account than the operational real-time analysis performed when all observations may not be available yet. Precipitation outputs from the 1DVar were also evaluated by examining their ability to provide realistic snow depth simulations using a snow-cover model. The SURFEX/Interactions between Soil, Biosphere, and Atmosphere (ISBA)/Crocus snow model (referred to hereinafter as Crocus; Brun et al. 1992; Vionnet et al. 2012) is a detailed numerical snowpack model having the ability to simulate water and energy exchanges between layers of a snowpack and at its boundaries. Crocus is forced by meteorological fields output by SAFRAN at hourly time steps and simulates the time evolution of several snowpack properties, including temperature, density, liquid water content, depth, and water equivalent, taking snow metamorphism into account. The Crocus snowpack model is used operationally for avalanche forecasting over the French mountains. For a given hour (Hr), the snow state depends on the atmospheric fields at Hr as well as on the snow state at Hr − 1. Crocus has been used and validated in a significant number of studies related to physical processes and internal properties of the snowpack (Carmagnola et al. 2014; Dominé et al. 2013; Morin et al. 2013), alpine (Gerbaux et al. 2005) and tropical (Lejeune et al. 2013) glacier mass balance, snow albedo of the Greenland ice sheet (Dumont et al. 2014), alpine hydrology (Etchevers and Martin 2002), wind-induced snow transport (Vionnet et al. 2014), cryosphere–climate interactions (Brun et al. 2011), and climate change impact on snow cover and avalanche hazard (Castebrunet et al. 2014). These studies have proved the reliability of the snowpack model in various applications.
b. Precipitation estimates from weather radar observations
Météo-France operates a network of C- and S-band weather radars, using wavelengths of 5 and 10 cm, respectively, to provide real-time precipitation amounts in order to anticipate high-impact events such as flash floods. These radars are mainly operated over flat areas. In mountainous areas, such as the Alps and the Pyrenees, radars cannot sample precipitating systems adequately because of a beam blockage effect. Paradoxically, it is over these areas that the spatial and temporal variability of precipitation is the highest. To overcome these limitations, the Risques Hydrométéorologiques en Territoires de Montagnes et Mediterranéens (RHYTMME) project was launched by Météo-France and the Institut National de Recherche en Sciences et Technologies pour l’Environnement et l’Agriculture (IRSTEA) in 2008 (Westrelin et al. 2013). The main goal of the project was to operate a network of meteorological X-band (wavelength of 2 cm) Doppler polarimetric radars over the southern Alps. These instruments are less sensitive to ground clutter than C- and S-band radars. They have a shorter range since the signal is more strongly attenuated by precipitation at these wavelengths. Being more compact and less costly, they can be installed in small networks to provide precipitation information over significant areas in mountainous regions. They give precipitation measurements every 5 min with a pixel size of 1 km2 like other wavelengths, over a range of 30–60 km, shorter than traditional C-band radar. The larger attenuation of the radar signal at X-band is corrected using dual-polarization capabilities.
In this work we used a mosaic of precipitation amounts produced by Météo-France using C- and S-band radars with a significant contribution from X-band radars over the southern part of the French Alps. The S-band radars of Nîmes, Bollène, and Collobrières cover the most southern and western parts of the Alps and the C-band radar of Saint-Nizier can bring useful information over the northern Alps. The X-band radars included in the mosaic were installed at Mont Vial in 2007, Mont Maurel in 2010, Mont Colombis in 2012, and Vars Mayt (noted as Risoul in Fig. 2) in 2013. We used hourly- and daily-based operational precipitation products over the period from August 2012 to August 2014. During this period, the Mont Vial radar was not included in the mosaic because of radar failure, and the precipitation estimates from the Vars Mayt radar were only available from December 2013. The mosaic of precipitation produced by Météo-France included the four X-band radars over the French Alps and the C-band radars of Collobrières, Nîmes, and Bollène covering the southern and western parts of the French Alps. Figure 2 shows the theoretical coverage of the mosaic. The areas in red correspond to a quality index greater than 84%. The static quality index shown here takes only orographic masks into account, which do not vary in time, but the dynamic quality index is also affected by the actual data availability, which is reduced when radars are out of action and by attenuation from precipitation along the scan lowering the resolution and the range of radars.
Spatial coverage of the radar observations over the southeastern part of the French Alps. The areas in red correspond to a radar background quality index greater than 84%.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
c. 1DVar analysis scheme
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 observation operator 
Under the assumption that the observation errors are uncorrelated, the observation error covariance matrix is diagonal. The errors in measurement of rain gauges located within the same massif do not influence each other as they come from distant stations situated at different altitudes. The diagnosis from Desroziers et al. (2005) was carried out and confirmed this a priori choice. Figure 3 (bottom) shows the diagnosed observation correlation matrix for the years 2012/13 and 2013/14 over the French Alps. Each column and each row corresponds to a single observation station. The value in a box is the observation error correlation between the two corresponding stations, computed over the two years. The stations present in the 23 massifs of the French Alps are gathered together in the same figure, but stations within the same massif are distant by a few kilometers to a few tens of kilometers, whereas stations in different massifs can be distant by several hundreds of kilometers. The figure shows that the correlations remain close to zero between distant stations and that the a priori choice of uncorrelated observation errors seems appropriate. The figure shows that the observation errors are weakly correlated within a massif, as nonzero values appear between neighboring points, but are close to zero between stations in different massifs.
(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.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
In practice, the 1DVar was run for each massif by optimally combining available rain gauge measurements with a priori information from a short-range forecast of precipitation produced by the AROME NWP model. The minimization was performed using a quasi-Newton algorithm that converged after one iteration with a linear problem. The analysis was performed at a daily time step since most of the in situ observations were only available every 24 h. Figure 3 (top) describes the 1DVar system schematically. Twenty-four hour accumulated precipitation forecasts from the AROME model are used (difference between accumulated amounts at +30 and +6 h) to calculate a mean background estimate of precipitation over the whole massif of interest (associated with a mean altitude). With this mean precipitation estimate, an a priori vertical climatological profile of precipitation (also used in SAFRAN analysis; Durand et al. 1993, 1999) was adjusted using the average precipitation computed from the AROME model. The climatological profile most frequently selected from SAFRAN is used for the background (“Climatological profile from SAFRAN” in Fig. 3, top center) in order to ensure a consistent vertical profile. The average precipitation estimate is used to translate the climatological profile and adjust the background, keeping a consistent vertical gradient (“Guess adjusted with AROME” in Fig. 3, top right). It should be noted that obtaining a reliable precipitation analysis is rather difficult because the method assumes that the massifs are homogeneous (with respect to their meteorological and climate conditions). The area of massifs varies from 400 to 1500 km2. The precipitation analysis also assumes that the few assimilated observations are sufficient to represent all precipitation variability within a given massif. In the best cases, 10–12 observations per day can be assimilated (in the northern Alps) but, for other massifs, only 3–4 observations are available. Moreover, for all massifs, the number of available observations decreases strongly with increasing altitude.
For the background covariance matrix, vertical correlations are prescribed between altitude levels, which decrease with increasing distance. The correlations are modeled through a Gaussian function, 
(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.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
The first experiments were performed with a priori background and observation standard deviations similar to those of SAFRAN and equal to 8 and 5 mm, respectively. Sensitivity tests were carried out to choose the most appropriate observation and background standard deviations. Small observation errors led to noisy analysis profiles, and small values of background errors produced analysis profiles 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 obtained with several values of background and observation standard deviations over the 23 massifs of the French Alps for the years 2012/13 and 2013/14. The RMSEs are normalized for each massif with respect to observation and background standard deviations equal to 5 and 8 mm, respectively. We noticed that the analyzed profiles mostly depend on the ratio between the observation and the background standard deviations. Moreover, the RMSEs did not vary significantly when increasing standard deviations. Sensitivity tests also showed that the RMSEs decreased when both standard deviations increased while the ratio between background and observation standard deviations was kept equal to that of SAFRAN standard deviations. Therefore, the standard deviations were set equal to 5 mm for observations and 8 mm for background, to remain consistent with the SAFRAN analysis.
Additional tests were undertaken to perform a quality control check in order to reject observations too far from the background and a threshold equal to 
3. Evaluation of the 1DVar in its first setup
a. Daily analysis of precipitation
To assess the quality of the 1DVar precipitation analysis, a set of assimilation experiments was performed by randomly withholding one observation per day and per massif and so preventing them from being assimilated. The set of withheld observations was then used as independent data to evaluate the precipitation analysis. The ratio of nonassimilated to assimilated observations depends on the total number of observations over each massif, which varies from 4 to 12. The total number of observations varies over the French Alps from about 150 to more than 300 in winter when observations are available from ski resorts, which lead to a ratio of nonassimilated to assimilated observations of 8% in winter to 15% in summer. Figure 5 shows scatterplots of SAFRAN and 1DVar analysis versus independent observations over two massifs: the Mont-Blanc massif (Fig. 5, left) in the northern Alps and the Haut Var–Haut Verdon massif (Fig. 5, right) in the southern Alps, for the two winter seasons 2012/13 and 2013/14. Each year begins at 0600 UTC 1 August and ends at the same date of the following year. The two selected massifs are quite large (about 1500 km2 each) with very heterogeneous topography. They are representative of the 1DVar behavior in the northern and southern Alps, respectively, which are more influenced by oceanic or Mediterranean storms. The altitude range of Mont-Blanc extends between 1200 and 3600 m, whereas in Haut Var–Haut Verdon massif, the altitude ranges between 600 and 2700 m, which also explains why it receives less precipitation than Mont-Blanc on average. It can be seen that the 1DVar analysis data are in good agreement with observations and that SAFRAN generates estimates associated with a much larger spread than the 1DVar model does. Precipitation over the southern part of the French Alps is often affected by intense precipitation events insufficiently accounted for in the 1DVar; therefore, the dispersion is larger over Haut Var–Haut Verdon than over Mont-Blanc. Table 1 shows statistics about the performance of SAFRAN and the 1DVar over the 23 massifs of the French Alps [bias, RMSE, standard deviation, and coefficient of variation (i.e., observation minus analysis)]. These statistics are in favor of the 1DVar model for the majority of massifs, with a systematic reduction of the RMSEs (from 14.6 to 5.5 mm for Mont-Blanc and from 15.3 to 6.3 mm for Haut Var–Haut Verdon). The standard deviation is also reduced over most massifs, from 14.6 to 5.4 mm for the Mont-Blanc massif and from 15 to 6.3 mm over the Haut Var–Haut Verdon massif. The larger values of the standard deviation over Haut Var–Haut Verdon massif than over Mont-Blanc confirm the larger dispersion observed in Fig. 5, likewise the values of the coefficient of variation, computed as the ratio between the standard deviation and the mean, which are larger over Haut Var–Haut Verdon than over Mont-Blanc (1.51 and 1.54, respectively, for SAFRAN analysis and 1.63 and 1.74, respectively, for the 1DVar analysis). In addition, the scatterplots in Fig. 5 show that low precipitation amounts of a few millimeters are overestimated by both SAFRAN and 1DVar analysis, but the overestimation is limited to about 10 mm for 1DVar, whereas it can reach several tens of millimeters with a larger dispersion for SAFRAN analysis. This behavior for low precipitation amounts was observed over all massifs (not shown) and is due to the difficulties in accurately reproducing the lower precipitation intensities. The rain gauges have a tendency to underestimate solid precipitation and lower intensity can even be missed. Moreover, precipitation analysis can hardly represent low accumulations that are either overestimated or not detected. Therefore, the lower intensities that are measured correspond to zero values or are overestimated in SAFRAN and the 1DVar analysis. This evaluation shows that the 1DVar model behaves well and is able to analyze profiles of precipitation in rather good agreement with observations. However, these estimates, performed at massif scale, may need local corrections or adjustments to make them representative of the various locations within a massif.
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.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
b. Impact on snowpack modeling
The main goal of the 1DVar precipitation analysis and SAFRAN meteorological analysis is to produce forcings for the Crocus model in order to accurately predict the snowpack state. Therefore, snowpack simulations are performed with a reliable snowpack model forced by the 1DVar analyzed precipitation and the results are compared to the same snowpack model forced by SAFRAN reference analysis, which represents the most accurate snowpack simulation available. Moreover, the rain gauge measurements are subject to errors in mountainous areas and the examination of snow depth brings a complementary evaluation of precipitation analysis.
As stated earlier, the snow model Crocus needs atmospheric forcing, including precipitation, on an hourly basis to simulate the snowpack evolution. SAFRAN and the 1DVar scheme generate daily precipitation rates that need to be distributed temporally over 24 h, and the phase of the precipitation needs to be determined at each time step. SAFRAN uses a temporal distribution function that estimates a probability of precipitation given hourly interpolated values of low-level specific humidity. The rain–snow transition is determined according to a temperature threshold. For the 1DVar model, two distribution functions are tested: the first one uses hourly distribution based on short-range forecasts of rainfall and snowfall from AROME for the hourly distribution and the determination of the phase (called Distrib_AROME hereafter) and the second one uses radar precipitation estimates where they are available (called Distrib_RADAR hereafter). In both cases, hourly precipitation fractions of AROME forecasts or radar observations are calculated (hourly precipitation/daily precipitation) and then used to distribute the analyzed 1DVar estimates temporally. Only the first distribution function is evaluated here; Distrib_RADAR is described and evaluated in section 4c.
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.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
(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.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
Scores of snow depth simulations relative to observations for SAFRAN reanalysis and 1DVar analysis over the whole period of 2 years.
Over the three massifs shown here, the correlation values (using all observations) are quite similar between Safran and 1DVar (shown in Table 2): 0.88 and 0.88 for Chablais, 0.88 and 0.89 for Mont-Blanc, and 0.81 and 0.82 for Haute Tarentaise, respectively. Results in terms of RMSEs are in favor of Safran, with 1DVar having larger values (and more specifically larger biases): the RMSEs for Safran and 1DVar are 38.5 and 38.4 cm over Chablais, 43.9 and 49.7 cm over Mont-Blanc, and 36.4 and 37.8 cm over Haute Tarentaise, respectively. It should be noted that, in SAFRAN analysis, a posteriori adjustment of the weight of observations is applied to account for observation representativeness within a massif, whereas in the 1DVar analysis, the observation error is defined a priori, with quality control based on innovation (observation minus background). Figure 7 (bottom) shows snow depth simulations at Tignes (at an altitude of 2080 m) within the Haute Tarentaise massif. The station of Tignes was chosen because it is rather representative of the behavior of the 1DVar analysis over the northern Alps: many observations originate from ski resorts during the winter season, and the snow depth simulations using the 1DVar analysis reproduce rather well the observed snow depth over homogeneous massifs with a relatively high number of available observations (almost 10 per day). The 1DVar simulations are closer to the observations at Tignes for the whole study period. During the year 2012/13, SAFRAN analysis has a positive bias from January until May. During the year 2013/14, the two simulations are very close to each other and in good agreement with observations, except during the first months (December–February), for which the 1DVar analysis is slightly better. Over the whole period, the bias is −4.28 cm for 1DVar analysis against 4.61 cm for Safran, the RMSE is 13.90 cm against 12.03 cm, the standard deviation is 13.11 cm against 11.24 cm, the correlation coefficient is 0.98 against 0.97, and the NSE is 0.90 against 0.93 (see Table 2).
The scores over all massifs of the French Alps (in Table 2) obtained from the 1DVar analyses are slightly degraded with respect to SAFRAN analysis, but the correlations are above 0.8 in most cases. SAFRAN analysis performs better over the northern Alps than over the southern Alps, and the same tendency is observed for the 1DVar analysis. SAFRAN analyses show a small systematic positive bias, whereas the 1DVar analyses show a negative bias larger than SAFRAN over the northern Alps, but smaller in absolute value over the southern Alps. The NSE coefficients of 1DVar analysis are lower than those of SAFRAN analysis, but they remain satisfactory with values above 0.5 over the southern Alps and above 0.7 over the northern Alps.
c. Local adjustments
The main goal of the 1DVar tool is to provide precipitation forcing fields to the snow model Crocus and to adequately simulate the snowpack state during winter. Similarly to SAFRAN, the tool produces analyses of precipitation at massif scale and could not represent smaller-scale precipitation features. To further examine how the 1DVar analysis is sensitive to local inhomogeneities, an additional experiment is run with a constraint on the maximum horizontal distance between observation and a modeling point. Here the 1DVar simulations are made in the vicinity of snow depth station measurement by assimilating available rain gauge observations within a 16-km circle inside the massif of interest. The obtained precipitation analysis is used to force the Crocus model to simulate snow depths to be compared to snow measurements. This new experiment is called “1DVar local.” The resulting snow depth simulations are compared with observations and some scores (RMSE and NSE) are shown in Table 3 for a selection of stations and massifs. Results are globally improved with the 1DVar local with respect to the 1DVar analysis. The largest improvement is obtained with stations situated at midaltitudes (between 1500 and 2000 m) in massifs with a relatively high number of observations, and the scores are improved with respect to SAFRAN analyses for several massifs (including Haute Tarentaise, Bauges, and Grandes-Rousses, shown in Table 3). However, over a few massifs the snow depth simulations are not as good with the 1DVar local, especially for high-altitude stations (above 2500–3000 m), when the surrounding observations used in the precipitation analysis have a large altitude difference with the selected station of interest, even if the horizontal distance remains small (e.g., over Vanoise and Oisans, shown in Table 3). In this case, the closest rain gauges are not representative of precipitation near the snow station and the nonassimilation of distant observations situated at higher altitudes leads to a large underestimation of the snow depths [e.g., at Bellecôte-Nivose (3000 m) in Vanoise massif, Les Ecrins-Nivose (2978 m), and La Meije-Nivose (3100 m) in Oisans massif]. For massifs with few rain gauge observations, the 1DVar local results can hardly be better than 1DVar analysis (e.g., Mercantour, shown in Table 3).
Scores of snow depth simulations relative to observations for SAFRAN reanalysis, 1DVar analysis, and 1DVar analysis with station adjustments over the whole period of 2 years for the Alps, northern Alps, southern Alps, and a selection of massifs that present contrasted conditions. The values in boldface correspond to the best scores between Safran, 1DVar, and 1DVar local.
4. Potential of weather radar estimates
Given the scarcity of rain gauge observations, additional assimilation experiments are undertaken to evaluate the impact of precipitation estimates derived from weather radar, both as observations to be assimilated and also to compute hourly precipitation fractions to distribute daily analysis. Their potential is tested in three ways: 1) radar hourly precipitation rates are used to calculate hourly precipitation fractions (hourly precipitation/daily precipitation) over each massif, which were then used to distribute the analyzed 1DVar estimates (function Distrib_RADAR); 2) besides using the Distrib_RADAR function, 24-h accumulated radar-derived precipitation is assimilated in the 1DVar; and 3) the 24-h radar-derived precipitation accumulations are assimilated using the Distrib_AROME function for hourly distribution. When Distrib_RADAR is used, the phase of the precipitation at each time step is chosen according to SAFRAN analysis. When Distrib_AROME is used, the phase of the precipitation is the same as in the AROME model hourly forecasts.
a. Means of using radar-derived observations
Given the high temporal and spatial resolution of radar observations and the advanced algorithms used to compute radar-derived precipitation rate, we examined the use of radar-derived observations of precipitation at an hourly time step directly to force the snowpack model Crocus. Figure 8 (top) shows an example of snow depth simulation over the years 2012/13 and 2013/14 at the Isola station, in the massif of Mercantour, using the Crocus model forced by SAFRAN, 1DVar analysis using only rain gauge observations, and radar observations without analysis. It shows that radar observations reproduce the variation of snow depth but largely overestimate snow depth over the two years. Some snowfall events are overestimated by 50 cm or more, producing a large discrepancy between the observed snow depths and the simulation using radar-derived observation to force the Crocus model. These overestimations are further propagated over the season as snow depth is an integrated parameter.
(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.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
For assimilation, radar-derived observations at a daily time step within a given massif are grouped by altitude range of 300 m and “superobservations” are generated by averaging radar pixels within a massif associated with each altitude level. The superobservations are computed at the same altitudes as SAFRAN ranges and are computed, for an altitude z, as an average of radar individual observations situated at altitudes between the altitudes 
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).
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
We thus end up with a set of five experiments over the southern Alps during two seasons (2012/13 and 2013/14) and the corresponding set of simulations of snow depth:
Safran: the reference experiment;
1DVar: using the Distrib_AROME function;
1DVar radar hourly: using the Distrib_RADAR function;
1DVar radar assim: 1DVar with the assimilation of radar observations; and
1DVar radar hourly+assim: 1DVar using the Distrib_RADAR function with the assimilation of radar observations.
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 hourly+assim).
b. Impact of the assimilation of radar-derived observations
The results of snowpack simulations using radar-derived precipitation indicate that the assimilation of radar-derived observations generally improves snow depth simulations. Figures 10 and 11 show scatterplots of snow depth observations against simulations over the Mercantour and Haut Var–Haut Verdon massifs, with Safran, 1DVar, 1DVar radar hourly, 1DVar radar assim, and 1DVar radar hourly+assim. These massifs are associated with the best radar coverage over the period of interest. Results are split according to available snow depth stations (four stations for Mercantour and two stations for Haut Var–Haut Verdon). The rather good performance of the 1DVar is worth noting, especially for Isola station within Mercantour, for which the positive bias observed for shallow snow depths is reduced by the four 1DVar analyses with respect to Safran. This bias of 30–50 cm with Safran is reduced to 20–30 cm with the 1DVar analyses. The positive bias observed at Isola station corresponds to the underestimation of snowmelt during the months of April and May 2014 due to a wrong phase of precipitation diagnosed by Safran. Statistics are in favor of Safran for both massifs and are shown in Table 5, but 1DVar performed quite well, especially when radar-derived observations are assimilated. The assimilation of radar-derived observations was responsible for a significant reduction of bias over the two massifs with respect to 1DVar (from 7.15 cm for 1DVar to −0.72 cm for 1DVar with radar-derived observations over Mercantour massif and from 45.23 to 31.29 cm over Haut Var–Haut Verdon massif), which becomes of the same order as the bias of SAFRAN for Mercantour (3.75 cm). Another reduction of bias is obtained with 1DVar radar hourly+assim over the Haut Var–Haut Verdon (20.07 cm for 1DVar with radar-derived observations and Distrib_RADAR), for which the bias becomes of the same order as that of Safran (19.02 cm). Over Haut Var–Haut Verdon massif, the smallest bias is obtained with hourly distribution based on radar observations and rain–snow transition based on SAFRAN analysis, which is not the case for Mercantour. Over Haut Var–Haut Verdon massif, 1DVar radar hourly+assim improves the RMSE with respect to 1DVar (almost halved: 30.2 and 53.4 cm). The correlations are close to or above 0.90 with 1DVar radar hourly, 1DVar radar assim, and 1DVar radar hourly+assim (0.94, 0.89, and 0.92, respectively) and are increased with respect to 1DVar (0.86), becoming closer to Safran (0.96). The best correlations are obtained for 1DVar radar hourly and 1DVar radar hourly+assim. Over Mercantour, the correlations are unchanged with all four 1DVar experiments (0.94) and are close to Safran (0.97). Figure 12 highlights results obtained at the Isola (Fig. 12, top) and Val Casterino (Fig. 12, bottom) stations (within the Mercantour massif) by showing the time evolution of snow depth simulations. It is quite difficult to identify the best performing model at Isola given the high variability of snow depth measurements and simulations over the period. 1DVar radar hourly+assim performs better at the beginning of the two years, but 1DVar radar hourly and 1DVar radar assim are closer to the observations after February for 2012/13 and after March for 2013/14. The 1DVar radar hourly+assim seems to behave better at Val Casterino for the two years, except from March to May 2013, for which 1DVar radar assim is better. At Isola, the best scores, including RMSEs, standard deviation, correlation coefficient, and NSE, are obtained for the 1DVar radar assim simulation (24.42 cm, 23.73 cm, 0.95, and 0.89, respectively, against 29.60 cm, 29.57 cm, 0.92, and 0.84, respectively, for Safran), but the minimum bias is obtained with Safran and the 1DVar radar hourly simulations (−1.43 and 2.24 mm, respectively). At Val Casterino, the best scores are obtained with the 1DVar radar hourly+assim simulation (bias 4.87 cm, RMSE 20.02 cm, standard deviation 19.42 cm, correlation coefficient 0.95, and NSE 0.90).
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-h+assim). Colors correspond to the various snow depth observation stations.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
As in Fig. 10, but for the Haut Var–Haut Verdon massif.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
Scores of snow depth simulations with SAFRAN, 1DVar, 1DVar radar hourly, 1DVar radar assim, and 1DVar radar hourly+assim over the massifs of Mercantour and Haut Var–Haut Verdon.
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.
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
Table 6 shows the bias, RMSE, standard deviation, NSE, and correlation for Safran, 1DVar, 1DVar radar hourly, 1DVar radar assim, and 1DVar radar hourly+assim analysis above 1500 m over the southern Alps. The assimilation of radar-derived observations (1DVar radar assim) improves all scores with respect to 1DVar, but it has a limited impact on snow depth simulations. The representativeness of the radar-derived observations over a massif is affected by maskings due to orography or overshooting of steep valleys because of the radar installed on mountain tops (see Figs. 2, 9). However, 1DVar radar hourly significantly improves the scores with respect to 1DVar: it reduces the bias (−6.74 and −11.47), the RMSE (44.60 and 46.85), and the standard deviation (44.06 and 45.42) and increases the NSE (0.52 and 0.47) and the correlation (0.76 and 0.73). The use of radar-derived observations with 1DVar radar hourly, 1DVar radar assim, and 1DVar radar hourly+assim produces NSE and correlation coefficients close to or above 0.5 and 0.75, respectively.
c. Influence of the determination of the rain–snow transition
A complementary evaluation is carried out on the daily variations of snow depths. The snow depth (noted HS hereafter) variations, defined as 
Histogram of frequency of occurrence for 11 categories of snow decrease and accumulation simulated by the snow model Crocus forced by SAFRAN (blue), 1DVar (gray), 1DVar radar hourly (green), 1DVar radar assim (orange), and 1DVar radar hourly+assim (red).
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
Histogram of frequency of occurrence for 11 categories of snow decrease and accumulation simulated by the snow model Crocus forced by SAFRAN (blue), 1DVar analyses using AROME hourly forecasts for hourly distribution and rain–snow transition (gray), and 1DVar analyses using AROME hourly forecasts for hourly distribution and SAFRAN analyses for rain–snow transition (green).
Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0144.1
5. Discussion
This paper describes a tool to generate vertical profiles of precipitation in mountainous areas by using a variational approach given first guess information from a numerical weather prediction model and rain gauge and radar observations. The 1DVar tool is evaluated against in situ observations and other precipitation products in terms of analyzed vertical profiles of precipitation and in terms of snow depth simulations. The radar data used in this study come from the Météo-France system supplying a mosaic of surface precipitation amounts, which includes X-band radars from the RHYTMME project in addition to C- and S-band radars from the ARAMIS network. The use of radar for the analysis of precipitation over the French Alps has been possible since 2012. However, two years of simulations is rather short. Essery et al. (2013) showed that the performances of different snow models could vary significantly from one year to another, and thus a large number of years should be considered for a more robust evaluation. Some additional studies involving snowpack simulations with 1DVar not using radar observations were performed for the years 2010–14. The results over these four years showed that, within a massif, the performance of the 1DVar analysis could be quite variable from one year to another, depending on snow conditions and on the total amount of precipitation during the season.
The evaluation of precipitation analyses using snow depth represents an alternative evaluation when the evaluation against rain gauges is not relevant (in case of solid precipitation and/or wind), but it implies the use of a numerical snow model. However, other meteorological variables and snow model parameters can also affect the skill of simulations. This statement is supported by Fig. 5. Although the 1DVar precipitation analyses display a reduced spread with improved scores against SAFRAN, snow depth simulations using 1DVar analyses do not show systematic improvement with respect to SAFRAN. Other meteorological variables such as temperature, humidity, wind, and radiation have an impact on snowmelt, refreezing, or settlement. These variables should also be analyzed in a 1DVar framework in order to produce consistent meteorological forcing for snowpack simulations. In particular, the altitude of the rain–snow transition of precipitation impacts the snow depth simulations, and a small error can lead to large differences in snow depth simulations. The 1DVar simulations using Distrib_AROME and Distrib_RADAR illustrate the importance to adequately diagnose rain–snow transition since the differences between these simulations are due not only to different hourly precipitation distributions but also to a different rain–snow transition at each time step. Nevertheless, the dominant parameters for snowpack evolution are the precipitation amounts and the temperature, which governs the altitude of the melting layer within clouds or the precipitation layer in the atmosphere and thus the phase of precipitation when it reaches the ground. Moreover, snow depth modeling could also be improved through optimal calibration of the Crocus parameters.
The snowpack is simulated at the massif scale, whereas evaluations are performed at observation points. The massifs are assumed to be homogeneous areas, but some differences inevitably occur between distant points within the same massif because of the orientation of slopes with respect to the dominant wind and because of small-scale convective events situated in areas of the massifs that are not covered by precipitation observations. Heterogeneity within a massif, which is not taken into account in the meteorological forcing, spreads into snowpack simulations. This issue has been addressed with the experiment called 1DVar local, in which a maximum distance is set between the observations and the snow depth simulation sites. The results on snow depth simulations show an improvement with respect to the 1DVar analysis and also with respect to SAFRAN for several massifs. However, a more robust investigation would be necessary to take more effects into account. Moreover, local heterogeneity in the snowpack is also influenced by wind-induced snow transport, which is not taken into account in the operational Crocus snow model. Therefore, the performance of the model can vary significantly between stations, as shown by Lafaysse et al. (2013). A more robust evaluation should ideally involve comparisons against gridded variables from satellite products. For example, Moderate Resolution Imaging Spectroradiometer (MODIS) radiances were used by Mary et al. (2013) to retrieve the specific surface area of snow that was compared to field measurements and SAFRAN-Crocus outputs. Gascoin et al. (2015) also used MODIS products to monitor the effects of climate on snow dynamics in the Pyrenees. Sirguey et al. (2009) produced regional maps of seasonal snow cover over the Southern Alps of New Zealand using MODIS reflectance data. MODIS data were also used by Rahimi et al. (2015) to estimate evapotranspiration.
6. Conclusions
This study presents an original 1DVar assimilation scheme to retrieve hourly precipitation profiles in mountainous areas by combining observations from rain gauges and weather radars with background information from short-range forecasts of the convective-scale NWP model AROME. The method was evaluated using independent observations made over the French Alps during the 2-yr period from August 2012 to August 2014. The 1DVar precipitation analyses were found to be in very good agreement with independent observations (not used in the assimilation process). The 1DVar precipitation analysis has been compared against the well-validated SAFRAN model, and the results of the 1DVar precipitation analyses are better than SAFRAN analyses in terms of RMSEs and standard deviation. The performance of the 1DVar was also evaluated by examining the quality of simulation of snow depth using the snowpack model Crocus (forced by the 1DVar precipitation analyses). Snow depth simulations were found to agree rather well with independent observations and are comparable to SAFRAN reference model. It appears that snow depth simulations using SAFRAN results are better than the 1DVar ones in terms of correlation and RMSE. Such behavior can be understood by recalling that SAFRAN takes the representativeness of observations within a massif into account and adjusts their weight accordingly in the analysis. The fact that more observations are used also forms part of the explanation. Several other experiments were performed using weather-radar-derived precipitation to improve the 1DVar analyses. We have shown that the assimilation of radar-derived observations brings a systematic improvement in areas where such observations are available, especially for events producing large precipitation accumulations, as the latter are of particular interest for avalanche hazard forecasting. In addition, we have also shown that weather radar observations can be used on an hourly basis to improve the time series of precipitation analyses and that this has a positive impact on simulated snow depths.
Although snow depth simulations are generally improved using 1DVar analysis without radar-derived observations over the massifs covered by radars, the results using radar observations at some stations can remain unchanged with respect to the simple 1DVar configuration. The full complexity of the meteorological parameters is not taken into account within a given massif, as they are assumed to be horizontally homogeneous. The latter assumption does not hold when the atmospheric flow produces large differences within a massif. Depending on the orientation of their slopes with respect to the dominant flow, different stations situated at the same altitude can receive very different amounts of precipitation, whereas the 1DVar analysis assimilating radar observations produces an amount that depends only on the position of the radar with respect to surrounding mountains and the direction of the precipitating system. To support this assumption of representativeness issues, an experiment conducted with an additional constraint on the maximum distance between the observations and the simulation point improved the results over most of the massifs with respect to the 1DVar analysis and also to SAFRAN. When radar observations are considered for hourly distributions, a similar limitation appears, increased by the aggregation of altitudes for hourly fraction computations. At lower elevation, radar overshoot causes the derived hourly fractions to be poorly representative of the location where they are applied. In this case, the additional information contributed by radar-derived observations is not relevant for the hourly precipitation distribution.
Further studies will include the analyses of other relevant meteorological variables in order to produce consistent meteorological analysis for Crocus snowpack model forcing. The period of evaluation should also be extended as more radar observations become available in the future. The current 1DVar analysis system allows great flexibility in adapting precipitation analysis to various spatial scales and including different types of observations. With an appropriate, possibly nonlinear, observation operator, observations that are related to precipitation in a complex manner could be assimilated. For example, the vertical profile of reflectivity could be exploited to retrieve information about the three-dimensional characteristics of precipitation. Future work will involve a complex approach combining a vertical analysis depending on altitude with high-resolution spatial analyses in order to account for spatial variability within massifs. Such an analysis would make better use of high-resolution radar data by using gridpoint observations combined with a high-resolution NWP model like AROME.
This method has been developed over the French Alps but could be applied to other mountainous regions. Over the French mountainous areas, including the Pyrenees and Corsica, where SAFRAN analyses are available, the method can be applied using descriptions of massif limits and climatological precipitation profiles from SAFRAN. To run 1DVar over other mountainous areas, it is necessary to define small homogeneous areas and a vertical climatological profile of precipitation (using a historical observation database, reanalyses, etc.). Within the selected homogeneous areas, a sufficient number of observations should be available for assimilation. Daily precipitation forecasts from an NWP model are also necessary to adjust the background profile to the meteorological conditions of each day, and daily precipitation observations are needed to compute an analyzed profile.
Acknowledgments
The authors sincerely thank Charles Fierz and two anonymous reviewers for their relevant and very constructive suggestions and comments. We are grateful to Vincent Vionnet, Marie Dumont, and Cécile Coléou for useful discussions about the use of AROME forecasts to feed the 1DVar and about ways to evaluate the 1DVar performances. We also wish to thank Louis Quéno for his assistance in producing some plots. We are also grateful to Samuel Morin, Marc Bocquet, Frédéric Gottardi, and Sid Boukabara for useful discussions and advice during the study. We also thank Susan Becker for her suggestions to improve English language.
REFERENCES
Boé, J., L. Terray, F. Habets, and E. Martin, 2007: Statistical and dynamical downscaling of the Seine basin climate for hydro-meteorological studies. Int. J. Climatol., 27, 1643–1656, doi:10.1002/joc.1602.
Boone, A., and Coauthors, 2004: The Rhône-Aggregation Land Surface Scheme intercomparison project: An overview. J. Climate, 17, 187–208, doi:10.1175/1520-0442(2004)017<0187:TRLSSI>2.0.CO;2.
Bouilloud, L., and Coauthors, 2009: Road surface condition forecasting in France. J. Appl. Meteor. Climatol., 48, 2513–2527, doi:10.1175/2009JAMC1900.1.
Brun, E., P. David, M. Sudul, and G. Brunot, 1992: A numerical model to simulate snowcover stratigraphy for operational avalanche forecasting. J. Glaciol., 38, 13–22, doi:10.1017/S0022143000009552.
Brun, E., and Coauthors, 2011: Snow/atmosphere coupled simulation at Dome C, Antarctica. J. Glaciol., 57, 721–736, doi:10.3189/002214311797409794.
Carmagnola, C., S. Morin, M. Lafaysse, F. Dominé, B. Lesaffre, Y. Lejeune, G. Picard, and L. Arnaud, 2014: Implementation and evaluation of prognostic representations of the optical diameter of snow in the SURFEX/ISBA–Crocus detailed snowpack model. Cryosphere, 8, 417–437, doi:10.5194/tc-8-417-2014.
Castebrunet, H., N. Eckert, G. Giraud, Y. Durand, and S. Morin, 2014: Projected changes of snow conditions and avalanche activity in a warming climate: A case study in the French Alps over the 2020–2050 and 2070–2100 periods. Cryosphere, 8, 1673–1697, doi:10.5194/tc-8-1673-2014.
Courtier, P., C. Freydier, J. Geleyn, F. Rabier, and M. Rochas, 1991: The Arpege project at Météo-France. Proc. Seminar on Numerical Methods in Atmospheric Models, Vol. 2, Reading, United Kingdom, ECMWF, 193–231. [Available online at http://www.ecmwf.int/sites/default/files/elibrary/1991/8798-arpege-project-meteo-france.pdf.]
Coustau, M., E. Martin, C. Soci, E. Bazile, and F. Besson, 2014: Evaluation of the MESCAN system in particular for snow (using the SURFEX off-line simulation driven by MESCAN). EURO4M Project Rep., 28 pp. [Available online at http://www.euro4m.eu/downloads/D2.11_Evaluation%20of%20the%20newly%20developed%20MESAN-SAFRAN%20system%20in%20particular%20for%20snow.pdf.]
Crochet, P., 2007: A study of regional precipitation trends in Iceland using a high-quality gauge network and ERA-40. J. Climate, 20, 4659–4677, doi:10.1175/JCLI4255.1.
Crochet, P., T. Jóhannesson, T. Jónsson, O. Sigurosson, H. Björnsson, F. Pálsson, and I. Barstad, 2007: Estimating the spatial distribution of precipitation in Iceland using a linear model of orographic precipitation. J. Hydrometeor., 8, 1285–1306, doi:10.1175/2007JHM795.1.
Daly, C., R. P. Neilson, and D. L. Phillips, 1994: A statistical-topographic model for mapping climatological precipitation over mountainous terrain. J. Appl. Meteor., 33, 140–158, doi:10.1175/1520-0450(1994)033<0140:ASTMFM>2.0.CO;2.
Desroziers, G., L. Berre, B. Chapnik, and P. Poli, 2005: Diagnosis of observation, background and analysis-error statistics in observation space. Quart. J. Roy. Meteor. Soc., 131, 3385–3396, doi:10.1256/qj.05.108.
Dominé, F., S. Morin, E. Brun, M. Lafaysse, and C. Carmagnola, 2013: Seasonal evolution of snow permeability under equi-temperature and temperature-gradient conditions. Cryosphere, 7, 1915–1929, doi:10.5194/tc-7-1915-2013.
Dumont, M., and Coauthors, 2014: Contribution of light-absorbing impurities in snow to Greenland’s darkening since 2009. Nat. Geosci., 7, 509–512, doi:10.1038/ngeo2180.
Durand, Y., E. Brun, L. Mrindol, G. Guyomarch, B. Lesaffre, and E. Martin, 1993: A meteorological estimation of relevant parameters for snow models. Ann. Glaciol., 18, 65–71, doi:10.1017/S0260305500011277.
Durand, Y., G. Giraud, E. Brun, L. Mérindol, and E. Martin, 1999: A computer-based system simulating snowpack structures as a tool for regional avalanche forecasting. J. Glaciol., 45, 469–484, doi:10.1017/S0022143000001337.
Durand, Y., G. Giraud, M. Laternser, P. Etchevers, L. Mérindol, and B. Lesaffre, 2009a: Reanalysis of 47 years of climate in the French Alps (1958–2005): Climatology and trends for snow cover. J. Appl. Meteor. Climatol., 48, 2487–2512, doi:10.1175/2009JAMC1810.1.
Durand, Y., M. Laternser, G. Giraud, P. Etchevers, B. Lesaffre, and L. Mérindol, 2009b: Reanalysis of 44 yr of climate in the French Alps (1958–2002): Methodology, model validation, climatology, and trends for air temperature and precipitation. J. Appl. Meteor. Climatol., 48, 429–449, doi:10.1175/2008JAMC1808.1.
Essery, R., S. Morin, Y. Lejeune, and C. B. Ménard, 2013: A comparison of 1701 snow models using observations from an alpine site. Adv. Water Resour., 55, 131–148, doi:10.1016/j.advwatres.2012.07.013.
Etchevers, P., and E. Martin, 2002: Impact d’un changement climatique sur le manteau neigeux et l’hydrologie des bassins versants de montagne. Colloque Int. L’eau en montagne, Megève, France, Réseau International des Organismes de Bassin, 8 pp. [Available online at http://www.riob.org/IMG/pdf/Etchevers-2.pdf.]
Gascoin, S., O. Hagolle, M. Huc, L. Jarlan, J.-F. Dejoux, C. Szczypta, R. Marti, and R. Sánchez, 2015: A snow cover climatology for the Pyrenees from MODIS snow products. Hydrol. Earth Syst. Sci., 19, 2337–2351, doi:10.5194/hess-19-2337-2015.
Gerbaux, M., C. Genthon, P. Etchevers, C. Vincent, and J. Dedieu, 2005: Surface mass balance of glaciers in the French Alps: Distributed modeling and sensitivity to climate change. J. Glaciol., 51, 561–572, doi:10.3189/172756505781829133.
Giraud, G., 1992: MEPRA: An expert system for avalanche risk forecasting. Proc. Int. Snow Science Workshop, Breckenridge, CO, ISSW, 97–106. [Available online at http://arc.lib.montana.edu/snow-science/objects/issw-1992-097-104.pdf.]
Gottardi, F., C. Obled, J. Gailhard, and E. Paquet, 2012: Statistical reanalysis of precipitation fields based on ground network data and weather patterns: Application over French mountains. J. Hydrol., 432–433, 154–167, doi:10.1016/j.jhydrol.2012.02.014.
Guan, H., J. L. Wilson, and O. Makhnin, 2005: Geostatistical mapping of mountain precipitation incorporating autosearched effects of terrain and climatic characteristics. J. Hydrometeor., 6, 1018–1031, doi:10.1175/JHM448.1.
Habets, F., and Coauthors, 2008: The SAFRAN–ISBA–MODCOU hydrometeorological model applied over France. J. Geophys. Res., 113, D06113, doi:10.1029/2007JD008548.
Hevesi, J. A., A. L. Flint, and J. D. Istok, 1992a: Precipitation estimation in mountainous terrain using multivariate geostatistics. Part II: Isohyetal maps. J. Appl. Meteor., 31, 677–688, doi:10.1175/1520-0450(1992)031<0677:PEIMTU>2.0.CO;2.
Hevesi, J. A., J. D. Istok, and A. L. Flint, 1992b: Precipitation estimation in mountainous terrain using multivariate geostatistics. Part I: Structural analysis. J. Appl. Meteor., 31, 661–676, doi:10.1175/1520-0450(1992)031<0661:PEIMTU>2.0.CO;2.
Kidd, C., and V. Levizzani, 2011: Status of satellite precipitation retrievals. Hydrol. Earth Syst. Sci., 15, 1109–1116, doi:10.5194/hess-15-1109-2011.
Kucera, P. A., E. E. Ebert, F. J. Turk, V. Levizzani, D. Kirschbaum, F. J. Tapiador, A. Loew, and M. Borsche, 2013: Precipitation from space: Advancing Earth system science. Bull. Amer. Meteor. Soc., 94, 365–375, doi:10.1175/BAMS-D-11-00171.1.
Kyriakidis, P. C., J. Kim, and N. L. Miller, 2001: Geostatistical mapping of precipitation from rain gauge data using atmospheric and terrain characteristics. J. Appl. Meteor., 40, 1855–1877, doi:10.1175/1520-0450(2001)040<1855:GMOPFR>2.0.CO;2.
Lafaysse, M., B. Hingray, P. Etchevers, E. Martin, and C. Obled, 2011: Influence of spatial discretization, underground water storage and glacier melt on a physically-based hydrological model of the Upper Durance River basin. J. Hydrol., 403, 116–129, doi:10.1016/j.jhydrol.2011.03.046.
Lafaysse, M., and Coauthors, 2013: Towards a new chain of models for avalanche hazard forecasting in French mountain ranges, including low altitude mountains. Proc. Int. Snow Science Workshop, Grenoble–Chamonix Mont-Blanc, France, ISSW, 4 pp. [Available online at http://arc.lib.montana.edu/snow-science/objects/ISSW13_paper_O1-02.pdf.]
Lafaysse, M., B. Hingray, A. Mezghani, J. Gailhard, and L. Terray, 2014: Internal variability and model uncertainty components in future hydrometeorological projections: The Alpine Durance basin. Water Resour. Res., 50, 3317–3341, doi:10.1002/2013WR014897.
Lejeune, Y., J.-M. Bertrand, P. Wagnon, and S. Morin, 2013: A physically based model of the year-round surface energy and mass balance of debris-covered glaciers. J. Glaciol., 59, 327–344, doi:10.3189/2013JoG12J149.
Mair, A., and A. Fares, 2011: Comparison of rainfall interpolation methods in a mountainous region of a tropical island. J. Hydrol. Eng., 16, 371–383, doi:10.1061/(ASCE)HE.1943-5584.0000330.
Mary, A., and Coauthors, 2013: Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snowpack model. Cryosphere, 7, 741–761, doi:10.5194/tc-7-741-2013.
Mérindol, L., Y. Durand, B. Fradon, R. Tzanos, and S. Samuel, 2013: Use of RHYTMME radar images including X band data, to improve hourly disaggregation of SAFRAN daily precipitation analyse. Application on Mercantour and Haut-Var/Haut-Verdon. Proc. Int. Snow Science Workshop, Grenoble–Chamonix Mont-Blanc, France, ISSW, 8 pp. [Available online at http://arc.lib.montana.edu/snow-science/objects/ISSW13_paper_P2-08.pdf.]
Morin, S., F. Dominé, A. Dufour, Y. Lejeune, B. Lesaffre, J.-M. Willemet, C. Carmagnola, and H.-W. Jacobi, 2013: Measurements and modeling of the vertical profile of specific surface area of an alpine snowpack. Adv. Water Resour., 55, 111–120, doi:10.1016/j.advwatres.2012.01.010.
Nash, J. E., and J. V. Sutcliffe, 1970: River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol., 10, 282–290, doi:10.1016/0022-1694(70)90255-6.
Parent-du Châtelet, J., 2003: Aramis, le réseau français de radars pour la surveillance des précipitations. Meteorologie, 40, 44–52, doi:10.4267/2042/36263.
Prudhomme, C., and D. W. Reed, 1999: Mapping extreme rainfall in a mountainous region using geostatistical techniques: A case study in Scotland. Int. J. Climatol., 19, 1337–1356, doi:10.1002/(SICI)1097-0088(199910)19:12<1337::AID-JOC421>3.0.CO;2-G.
Quéno, L., V. Vionnet, I. Dombrowski-Etchevers, M. Lafaysse, M. Dumont, and F. Karbou, 2016: Snowpack modelling in the Pyrenees driven by kilometric resolution meteorological forecasts. Cryosphere, 10, 1571–1589, doi:10.5194/tc-10-1571-2016.
Quintana-Seguí, P., and Coauthors, 2008: Analysis of near-surface atmospheric variables: Validation of the SAFRAN analysis over France. J. Appl. Meteor. Climatol., 47, 92–107, doi:10.1175/2007JAMC1636.1.
Rahimi, S., M. A. Gholami Sefidkouhi, M. Raeini-Sarjaz, and M. Valipour, 2015: Estimation of actual evapotranspiration by using MODIS images (a case study: Tajan catchment). Arch. Agron. Soil Sci., 61, 695–709, doi:10.1080/03650340.2014.944904.
Raleigh, M., J. Lundquist, and M. Clark, 2015: Exploring the impact of forcing error characteristics on physically based snow simulations within a global sensitivity analysis framework. Hydrol. Earth Syst. Sci., 19, 3153–3179, doi:10.5194/hess-19-3153-2015.
Rousselot, M., Y. Durand, G. Giraud, L. Mérindol, I. Dombrowski-Etchevers, and M. Déqué, 2012: Statistical adaptation of ALADIN RCM outputs over the French Alps—Application to future climate and snow cover. Cryosphere, 6, 785–805, doi:10.5194/tc-6-785-2012.
Schirmer, M., and B. Jamieson, 2015: Verification of analysed and forecasted winter precipitation in complex terrain. Cryosphere, 9, 587–601, doi:10.5194/tc-9-587-2015.
Schmidli, J., C. Schmutz, C. Frei, H. Wanner, and C. Schär, 2002: Mesoscale precipitation variability in the region of the European Alps during the 20th century. Int. J. Climatol., 22, 1049–1074, doi:10.1002/joc.769.
Schwab, M., 2000: The Alpine precipitation climate: Evaluation of high-resolution analysis scheme using comprehensive rain-gauge data. Ph.D. thesis, Swiss Federal Institute of Technology of Zurich, doi:10.3929/ethz-a-004121274.
Seity, Y., P. Brousseau, S. Malardel, G. Hello, P. Bénard, F. Bouttier, C. Lac, and V. Masson, 2011: The AROME-France convective-scale operational model. Mon. Wea. Rev., 139, 976–991, doi:10.1175/2010MWR3425.1.
Sirguey, P., R. Mathieu, and Y. Arnaud, 2009: Subpixel monitoring of the seasonal snow cover with MODIS at 250 m spatial resolution in the Southern Alps of New Zealand: Methodology and accuracy assessment. Remote Sens. Environ., 113, 160–181, doi:10.1016/j.rse.2008.09.008.
Soci, C., E. Bazile, F. Besson, and T. Landelius, 2016: High-resolution precipitation re-analysis system for climatological purposes. Tellus, 68A, 29879, doi:10.3402/tellusa.v68.29879.
Spandre, P., H. François, S. Morin, and E. George-Marcelpoil, 2015: Dynamique de la neige de culture dans les Alpes Françaises. Contexte climatique et état des lieux. Rev. Geogr. Alp., 103 (2), doi:10.4000/rga.2840.
Tabary, P., 2007: The new French operational radar rainfall product. Part I: Methodology. Wea. Forecasting, 22, 393–408, doi:10.1175/WAF1004.1.
Tabary, P., J. Desplats, K. Do Khac, F. Eideliman, C. Gueguen, and J. Heinrich, 2007: The new French operational radar rainfall product. Part II: Validation. Wea. Forecasting, 22, 409–427, doi:10.1175/WAF1005.1.
Tabary, P., B. Fradon, and A.-A. Boumahmoud, 2013: La polarimétrie radar à Météo-France. Meteorologie, 83, 59–67, doi:10.4267/2042/52055.
Tapiador, F. J., and Coauthors, 2012: Global precipitation measurement: Methods, datasets and applications. Atmos. Res., 104–105, 70–97, doi:10.1016/j.atmosres.2011.10.021.
Valipour, M., 2015: Long-term runoff study using SARIMA and ARIMA models in the United States. Meteor. Appl., 22, 592–598, doi:10.1002/met.1491.
Valipour, M., 2016: Optimization of neural networks for precipitation analysis in a humid region to detect drought and wet year alarms. Meteor. Appl., 23, 91–100, doi:10.1002/met.1533.
Valipour, M., and S. Eslamian, 2014: Analysis of potential evapotranspiration using 11 modified temperature-based models. Int. J. Hydrol. Sci. Technol., 4, 192–207, doi:10.1504/IJHST.2014.067733.
Valipour, M., M. E. Banihabib, and S. M. R. Behbahani, 2013: Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir. J. Hydrol., 476, 433–441, doi:10.1016/j.jhydrol.2012.11.017.
Vidal, J., E. Martin, L. Franchistéguy, F. Habets, J.-M. Soubeyroux, M. Blanchard, and M. Baillon, 2010a: Multilevel and multiscale drought reanalysis over France with the SAFRAN–ISBA–MODCOU hydrometeorological suite. Hydrol. Earth Syst. Sci., 14, 459–478, doi:10.5194/hess-14-459-2010.
Vidal, J., E. Martin, L. Franchistéguy, M. Baillon, and J.-M. Soubeyroux, 2010b: A 50-year high-resolution atmospheric reanalysis over France with the SAFRAN system. Int. J. Climatol., 30, 1627–1644, doi:10.1002/joc.2003.
Vionnet, V., E. Brun, S. Morin, A. Boone, S. Faroux, P. L. Moigne, E. Martin, and J.-M. Willemet, 2012: The detailed snowpack scheme Crocus and its implementation in SURFEX v7.2. Geosci. Model Dev., 5, 773–791, doi:10.5194/gmd-5-773-2012.
Vionnet, V., E. Martin, V. Masson, G. Guyomarc’h, F. N. Bouvet, A. Prokop, Y. Durand, and C. Lac, 2014: Simulation of wind-induced snow transport and sublimation in alpine terrain using a fully coupled snowpack/atmosphere model. Cryosphere, 8, 395–415, doi:10.5194/tc-8-395-2014.
Westrelin, S., P. Mériaux, S. Dalle, B. Fradon, and G. Jamet, 2013: Déploiement d’un réseau de radars pour anticiper les risques hydrométéorologiques. Meteorologie, 83, 59–67, doi:10.4267/2042/52056.