2.1 Study domain and period

The study focuses on two domains covering the French Alps (Fig. 1a) and the French and Spanish Pyrenees (Fig. 1b). The French Alps domain ranges from 43.125 to 46.875^∘ N latitudes and from 4.5 to 8.5^∘ E longitudes. This domain also includes a part of the mid-altitude mountain range of Jura. The Pyrenees domain covers the latitudes from 41.6 to 43.6^∘ N and the longitudes from −2.5 to 3.5^∘ E. Hourly data, from 1 August 2010 to 31 July 2014, including in situ measurements, satellite-derived irradiance products, meteorological models and snowpack simulations, were used.

Figure 1Domains of study: (a) the French Alps and (b) the Pyrenees, with AROME topography at 2.5 km resolution. Red dots: SW↓ stations; blue dots: SW↓ and LW↓ stations; black lines: SAFRAN massifs.

2.2 Irradiance datasets

Several irradiance datasets were used in this study: forecasts from the NWP model AROME, reanalyses from the SAFRAN analysis system, LSA SAF irradiance products derived from remotely sensed observations and a hybrid LW↓ irradiance product based on a combination of LSA SAF algorithms with AROME forecasts. An in situ observation dataset was built up for validation in mountains.

2.2.5 In situ irradiance observations

To assess the distributed irradiance datasets, ground measurements of SW↓ and LW↓ were extracted from the Météo-France station network and additional automatic weather stations (AWSs). Stations with altitude higher than 1000 m were selected. As elevation influences incoming radiation (Oliphant et al., 2003), stations were not used for evaluation if the difference between the station elevation and the elevation of the four closest AROME and LSA SAF grid points was higher than 300 m. As elevation differences up to 300 m may have an influence on the comparisons, the altitudes of the grid points associated with each station are listed in Table 1 and should be kept in mind when analysing the evaluation statistics. The resulting observation database, represented in Fig. 1, includes 14 mountain SW↓ stations (8 in the French Alps, 1 in Jura and 5 in the Pyrenees) and 4 mountain LW↓ stations (3 in the French Alps and 1 in the Pyrenees). An additional station located on a plain at Carpentras (Fig. 1) has been included in the database since it is the reference station for SW↓ and LW↓ measurements in France. These stations and their characteristics are listed in Table 1.

Table 1List of ground stations, associated mountain range, altitude of the observation, altitude of the associated LSA SAF and AROME grid points, measurement uncertainties, number of hourly SW↓ observations (N), mean observation, bias and RMSE for DSSF, AROME and SAFRAN computed when the sun is not masked, from 1 August 2010 to 31 July 2014. The best metrics are given in bold. The mountain range of each station is indicated by A (Alps), J (Jura) or P (Pyrenees). Asterisks indicate official uncertainties which seem too optimistic.

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Irradiance measurements are scarce in mountainous terrain and their quality is often lower than plain measurements, due to the difficulty of maintaining these stations and the possible occurrence of frost or snow on the sensors in winter (Lapo et al., 2015a). The pyranometers from Météo-France network (Kipp & Zonen CM5, CM6B and CM11) meet the quality standards of the World Meteorological Organization (WMO, 2014) and hence an uncertainty of hourly total SW↓ irradiance of ±10 % (Leroy and Leches, 2014). Due to their altitude, the maintenance may not be systematically weekly so that uncertainties of ±10 % are probably too optimistic. The station of Carpentras, on a plain, is equipped with the pyranometer Kipp & Zonen CM21 and the pyrgeometer Kipp & Zonen CG4. This station is a reference station for radiation measurements, as it is part of the Baseline Surface Radiation Network (BSRN; Ohmura et al., 1998): the uncertainties are ±3 % for SW↓ and ±5 % for LW↓. At Col de Porte where the pyranometer Kipp & Zonen CM14 and the pyrgeometer Kipp & Zonen CG4 undergo regular maintenance, Morin et al. (2012) reported total uncertainty on the order of ±10 % (including site-dependent uncertainties). The AWSs of Bassiès (Szczypta et al., 2015), Argentière glacier and Saint-Sorlin glacier (data from GLACIOCLIM program, https://glacioclim.osug.fr, last access: 20 April 2020) have Kipp & Zonen CM3 pyranometers and CG3 pyrgeometers, classified as moderate quality after WMO's standards (WMO, 2014), for which the manufacturer reports a daily total accuracy of ±10 %. The uncertainties have not been estimated at these stations. They are possibly higher than 10 % because of the difficulty of maintaining AWSs in complex environments, particularly in winter. WMO (2014) indicates uncertainties up to ±20 % for hourly totals for this kind of instruments. The results at these stations are indicative for high altitudes but shall be considered carefully. Table 1 summarizes the measurement uncertainties at each station.

SW↓ and LW↓ irradiances from LSA SAF products, AROME forecasts and SAFRAN reanalyses were evaluated using these in situ measurements. The altitude of the grid points associated with each station is reported in Table 1. Biases and root mean square errors (RMSEs) were computed in absolute and relative values (with the mean of observations as reference). To account for topographic shading on irradiance in situ measurements, a topographic mask was computed with a 5^∘ interval size after a 25 m resolution digital elevation model (DEM) of IGN (French National Institute of Geographical and Forest Information) and applied to the SW↓ irradiance products at all stations except Andorre and Envalira, because the DEM of IGN was only available on the French territory. The SW↓ irradiance products were only evaluated when the sun was above the horizon, or when the observed value was higher than 20 W m⁻² at Andorre and Envalira stations (to discard periods when the sun is masked by the terrain). The LW↓ irradiance products were evaluated by day and night.

2.3 Snowpack datasets

The impact of the different irradiance datasets on distributed snowpack simulations is assessed using the snowpack model Crocus with different atmospheric forcings. These simulations are compared to in situ measurements of snow depth.

2.3.1 Snowpack model: Crocus

Snowpack simulations driven by different irradiance datasets were performed with the detailed snow cover model Crocus (Brun et al., 1992; Vionnet et al., 2012) coupled with the ISBA land surface model within the SURFEX simulation platform (Masson et al., 2013), to fully simulate the interactions between snowpack and soil. SURFEX/ISBA–Crocus (called Crocus hereafter) simulates the evolution of the snowpack physical properties along its stratigraphy, under given atmospheric forcing data (temperature and specific humidity at a given height above the surface, wind speed at a given height above the surface, SW↓ and LW↓ irradiance, solid and liquid precipitation).

The simulations were carried out over the French Alps and Pyrenees domains (Fig. 1), on the AROME regular latitude–longitude grid at 0.025^∘ resolution (Sect. 2.2.1) from 1 August 2010 to 31 July 2014. The effects of aspect and slope on incoming solar irradiance were not taken into account, because the snowpack is simulated over flat terrain, and the interactions with the vegetation and the parameterization of fractional snow cover were not activated, because the evaluation observations are located in flat and open fields. This configuration has already been used in Vionnet et al. (2016) and Quéno et al. (2016).

Figure 2Bias and RMSE of SW↓ irradiance products (DSSF in green, AROME in blue, SAFRAN in red) compared to stations organized by domain (a), range of altitude (b) and all stations (c).

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Except for incoming radiative fluxes, the atmospheric forcing of the snowpack simulations was built with AROME forecasts (Sect. 2.2.1). The radiative components of the forcings were extracted from the different irradiance datasets: (a) AROME irradiance forecasts (simulations named A-Cro hereafter), (b) SAFRAN irradiance reanalyses (simulations named AS-Cro hereafter), (c) DSSF and DSLFnew (simulations named AL-Cro hereafter), (d) DSSF and AROME LW↓ irradiance (simulations named AL_SW-Cro hereafter), and (e) DSLFnew and AROME SW↓ irradiance (simulations named AL_LW-Cro hereafter). In order to include DSSF and DSLFnew products in AROME forcing, the interpolation on the AROME grid was made to minimize the effect of elevation difference on the incoming radiative fluxes. Among the four nearest LSA SAF grid points, the grid point with the minimum altitude difference with AROME grid point was chosen. Similarly to Hinkelman et al. (2015), SW↓ irradiances were not modified, whereas a vertical gradient of −29 W m⁻² km⁻¹ (Marty et al., 2002) was applied to LW↓ irradiances to mitigate the remaining differences in altitude. The different simulations are summarized in Table 2.

Table 2Characteristics of the snowpack simulations.

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2.3.2 In situ snowpack observations

To assess the quality of Crocus simulations, an observational dataset of snow depth measurements was constituted in the French Alps and the Pyrenees, within SAFRAN massifs. Only stations with less than 150 m elevation difference to the model topography were selected, in order to use the same dataset as Quéno et al. (2016) and Vionnet et al. (2016). This dataset contains a total of 172 stations (89 in the French Alps and 83 in the Pyrenees) with daily manual measurements at ski resorts (at 06:00 UTC) and daily automatic measurements by ultra-sonic sensors at high-altitude sensors, as described in detail in Vionnet et al. (2016) for the French Alps and in Quéno et al. (2016) for the French and Spanish Pyrenees.

Figure 3Bias and RMSE of LW↓ irradiance products (DSLF in green, DSLFnew in orange, AROME in blue, SAFRAN in red) compared to each station (a) and all stations (b).

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3.1 Comparisons with in situ measurements

The SW↓ error statistics for all stations are listed in Table 1. For most stations, DSSF shows the lowest biases with an underestimation of SW↓. Biases are also mostly negative for SAFRAN, while AROME exhibits strong positive biases at most of the stations. DSSF exhibits the lowest RMSE at almost all stations. For all products, the lowest RMSE is reached at Carpentras on the plain. These metrics are summarized in Fig. 2. The distinction by domain (French Alps and Pyrenees) shows that the three products have very similar RMSE over both domains, which highlights the consistency of these error statistics. The distinction by range of altitude (1000–1500, 1500–2000, >2000 m) shows increasing RMSE with altitude for DSSF, while RMSE are higher but more constant for AROME and SAFRAN. The increasing RMSE of DSSF is mainly due to stronger negative biases at high altitudes (−39 W m⁻² above 2000 m against −8 W m⁻² between 1000 and 1500 m). SAFRAN biases are negative at all altitudes while AROME biases are positive at all altitudes. Overall, DSSF exhibits the best performance with a relative bias of −4 % and a relative RMSE of 33 %. SAFRAN has a relative bias of −7 % and a relative RMSE of 40 %. Finally, AROME exhibits the strongest relative bias (+12 %) and the highest relative RMSE (43 %).

Figure 4Mean yearly cycles of SW↓ irradiance products (DSSF in green, AROME in blue, SAFRAN in red), ground measurements (in black), bias and RMSE over the 2010–2014 period at (a) Carpentras and (b) Péone. Mean daily cycles of the same products, bias and RMSE over the 2010–2014 period at (c) Carpentras and (d) Péone.

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Figure 3 shows the biases and RMSEs of the different datasets of incoming LW↓ (DSLF, DSLFnew, AROME and SAFRAN) at the five LW↓ stations and the overall error statistics. In this figure, stations are ordered by altitude. In mountains, DSLF, DSLFnew and AROME have a negative bias, while SAFRAN bias tends to increase with altitude. At low elevation (Carpentras), the best performance is in favour of DSLFnew with a bias of +4 W m⁻² (+1 %) and a RMSE of 16 W m⁻² (5 %), which falls within the range of uncertainties of the sensor. At three mountain stations (Col de Porte, Bassiès and Argentière glacier), the lowest bias and RMSE are reached by SAFRAN, while AROME has the lowest RMSE at the Saint-Sorlin glacier. Overall, AROME exhibits the strongest negative relative bias (−6 %) and the highest relative RMSE (12 %). DSLF and DSLFnew have equivalent error statistics with a relative bias of −3 % and a relative RMSE of 11 %. Finally, SAFRAN has a relative bias of +1 % and a relative RMSE of 11 %. These global error statistics are close to the sensor uncertainties in mountains, which does not enable “best product” to be chosen. However, some trends are identified, such as an underestimation of LW↓ by DSLF, DSLFnew and AROME. The performance of LSA SAF products and models is also clearly better in terms of LW↓ than SW↓, because of lower biases and RMSE.

Figure 5(a) Average of the DSLF from 1 August 2010 to 31 July 2014 in the French Alps, and relative difference with the DSLF for (b) AROME, (c) SAFRAN and (d) DSLFnew. (e) Average of the DSSF, and relative difference with the DSSF for (f) AROME and(g) SAFRAN.

The yearly cycles of SW↓ irradiances are illustrated at Carpentras for reference (Fig. 4a) and at Péone mountain station (Fig. 4b). They show higher RMSE in spring and summer for each dataset, the lowest RMSE for DSSF and the highest RMSE for AROME during the whole year, except in December and January when the three products have equivalent RMSEs. This trend was found to be similar at all stations. No specific trend was observed for the bias. The SW↓ daily cycles (Fig. 4c for Carpentras and Fig. 4d for Péone) show a lower RMSE for DSSF in the middle of the day. The SAFRAN cycle is not marked enough (positive biases in the morning and evening, negative biases in the middle of the day). AROME overestimates SW↓ all the time. DSSF represents the diurnal cycle well, with an underestimation in the afternoon. These trends were also highlighted at the other mountain stations. The study of the daily and yearly cycles of LW↓ irradiances did not indicate any particular trend for metrics following the month or the hour (not shown).

3.2 Spatial comparisons of the distributed products

Spatial comparisons of the different irradiance products were carried out over the two domains. DSSF and DSLF were taken as references. The spatial distributions of their annual mean computed using data from 1 August 2010 to 31 July 2014 and the differences with the other irradiance products are shown in Fig. 5 for the French Alps and in Fig. 6 for the Pyrenees.

The DSLF exhibits a strong correlation with the altitude, with a decreasing LW irradiance towards the highest elevations, i.e. the east of the French Alps (Fig. 5a) and the central range of the Pyrenees (Fig. 6a). AROME presents a moderate negative bias as compared to the DSLF, both in the Alps (Fig. 5b) and in the Pyrenees (Fig. 6b), while SAFRAN presents a strong positive bias, particularly in the highest areas of the Alps (Fig. 5c) and the Pyrenees (Fig. 6c). DLSFnew presents a slight positive bias over most of the domains, except over the highest peaks where the bias is slightly negative (Figs. 5d and 6d).

Figure 6(a) Average of the DSLF from 1 August 2010 to 31 July 2014 in the Pyrenees, and relative difference with the DSLF for (b) AROME, (c) SAFRAN and (d) DSLFnew. (e) Average of the DSSF, and relative difference with the DSSF for (f) AROME and (g) SAFRAN.

The DSSF exhibits a lower correlation with the topography (Figs. 5e and 6e). For given sky conditions, the SW irradiance increases with the elevation as the atmospheric transmissivity increases. But the annual mean of the DSSF follows more regional patterns of cloud cover than elevation patterns. For example, in the French Alps, Fig. 5e shows a north-west–south-east gradient of increasing DSSF: south-eastern massifs are often shielded by north-western massifs in the most frequent case of west and north-west disturbed flows. A similar gradient of precipitation was shown in Durand et al. (2009b). The heterogeneity of DSSF is even more marked in the Pyrenees (Fig. 6e) where the west–east chain acts as an orographic barrier to the prevailing northwesterlies coming from the Atlantic Ocean (Quéno et al., 2016). A clear discontinuity appears between the French Pyrenees, where the clouds are often blocked, and the Spanish Pyrenees are often affected by Foehn wind and resulting clear sky conditions. The lowest DSSF values are found in the western part of the French Pyrenees, while the eastern part is more sunny due to the abating Atlantic influence and a Mediterranean climate. AROME presents a strong positive bias (Figs. 5f and 6f), locally higher than 30 % over the highest peaks, and still higher than 15 % in many plain areas. The SAFRAN bias is very variable from one massif to another (Figs. 5g and 6g). A strong negative bias for SAFRAN can be noticed in the south-western massifs of the Spanish Pyrenees (Fig. 6g), highlighting a poor representation of the orographic blocking as already noticed in Quéno et al. (2016).

The dependence of the different irradiance products on the altitude was further explored with the study of altitudinal gradients. Figure 7 represents the vertical evolution of the LW↓ and SW↓ averaged over the SAFRAN massifs of the French Alps and the Pyrenees by steps of 100 m of elevation over the whole study period, together with the associated standard deviations.

Figure 7Vertical evolution by steps of 100 m: LW↓ products (a) in the French Alps and (b) in the Pyrenees, and SW↓ products (c) in the Alps and (d) in the Pyrenees, averaged over SAFRAN massifs from 1 August 2010 to 31 July 2014, with LSA SAF in green, AROME in blue, SAFRAN in red, DSLFnew in orange. The envelopes represent the mean ± the standard deviation. The dashed black line represents the climatological LW↓ vertical gradient of −29 W m⁻² km⁻¹ from Marty et al. (2002).

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Table 3Mean altitudinal LW↓ gradient for AROME, SAFRAN, DSLF and DSLFnew in the French Alps and the Pyrenees.

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The strong dependency of LW↓ irradiance on altitude is confirmed in Fig. 7a for the French Alps and Fig. 7b for the Pyrenees. As a reference, the altitudinal gradient for annual LW↓ means of −29 W m⁻² km⁻¹ found by Marty et al. (2002) in the Swiss Alps is plotted in dashed lines, while Table 3 lists the mean altitudinal gradient for each dataset in both domains. All datasets present a steady decrease in LW↓ with altitude and are close to each other below approximately 1200 m. For higher elevations, SAFRAN annual mean value is significantly stronger than AROME, DSLF and DSLFnew, due to a lower vertical gradient (Table 3). We showed in Sect. 3.1 that AROME, DSLF and DSLFnew had a negative bias at the four mountain stations. This effect may come from a vertical gradient that is too strong (Table 3). DSLFnew is larger than AROME and DSLF at all altitudes below approximately 2900 m in the French Alps (Fig. 7a) and 2200 m in the Pyrenees (Fig. 7b). It gets lower at the highest altitudes due to a stronger vertical gradient. The stronger vertical gradient of DSLFnew compared to DSLF is the confirmation that the use of forecasts of higher resolution for the algorithm takes the topography into account more. The excessive vertical gradient may originate from the cold bias of AROME near-surface temperatures, enhanced with the altitude (Vionnet et al., 2016), leading to a strong underestimation of the fluxes by DSLFnew at the highest altitudes.

In terms of SW↓ irradiance, Fig. 7c and d highlight that AROME fluxes are significantly stronger than SAFRAN and DSSF at all altitudes. SAFRAN is marked by an increase in incoming SW↓ fluxes with altitude, while AROME and DSSF present a more variable evolution, and particularly a decrease in the fluxes at the highest altitudes in the Alps (Fig. 7c). This decrease may reflect the more frequent presence of clouds blocked by the highest peaks. Furthermore, these figures underline a weaker dependency of SW↓ irradiance with altitude than LW↓ irradiance. Indeed, the standard deviation of LW↓ at a given altitude is small compared to the total variation of the mean LW↓ with altitude for all products (Fig. 7a and b), whereas they can reach similar values for SW↓ (Fig. 7c and d). This spatial variability at a given altitude is particularly marked at low- and mid-altitudes (<1800 m) in the Pyrenees for AROME and DSSF, reflecting a good representation of the strong climate heterogeneity between French and Spanish foothills. SAFRAN, which gives homogeneous analyses for each massif, does not account for the spatial variability within the massif as is the case for AROME and DSSF.

Table 4Bias and root mean square error (RMSE) of snow depth at 172 stations of the French Alps and the Pyrenees over the period 2010–2014 for simulations A-Cro, AL-Cro and AS-Cro. The best metrics are given in bold.

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5.1 Quality of irradiance datasets in mountainous terrain

We presented an overview of the quality of several irradiance datasets through an in-depth assessment of the irradiance fields in mountainous terrain. In terms of SW↓ irradiances, DSSF exhibits the best metrics in mountains, particularly below 2000 m. Above 2000 m, its RMSE is similar to SAFRAN and AROME, due to a strong negative bias. AROME presents systematic and large overestimations of SW↓ irradiances, contrarily to SAFRAN's tendency to underestimate them. The spatial variations of SW↓ irradiances are better represented in DSSF and AROME than in SAFRAN. In terms of LW↓ irradiances, the obtained errors are comparable and it is difficult to identify the best product. The use of forecasts at higher spatial resolution to compute DSLFnew enhances the topographic dependence, which limits the underestimation of LW↓ irradiance at low and mid-altitudes found with DSLF but strengthens the negative bias at high altitude. The resulting altitudinal gradient is probably too strong. It may originate from the cold bias of AROME near-surface temperatures, enhanced with the altitude (Vionnet et al., 2016), which leads to a strong underestimation of the fluxes by DSLFnew at the highest altitudes.

Several studies evaluated LSA SAF irradiance products at hourly time steps (when the sun is above the horizon for SW↓) at plain stations. For DSSF, we showed in this study a bias of −14 W m⁻² and a RMSE of 117 W m⁻² (Fig. 2), while for plains, Geiger et al. (2008b), Ineichen et al. (2009) and Cristóbal and Anderson (2013) reported biases of +2, +5 and −5 W m⁻² respectively, and RMSE of 87, 103 and 65 W m⁻² respectively. The higher RMSE in mountains may partly be explained by higher mean values. For DSLF, we showed in this study a bias of −8 W m⁻² and a RMSE of 32 W m⁻² (Fig. 3), while for plains, Trigo et al. (2010) and Ineichen et al. (2009) reported biases of +3 and −11 W m⁻² respectively, and RMSE of 25 and 29 W m⁻² respectively. The error statistics for mountains are close to those for plains and lie within the range of uncertainty of LW↓ sensors in mountains (Table 1). Thus, the performance of LSA SAF irradiance products remains satisfactory compared to previous evaluations of these products on plains, even though they generally do not reach the target accuracy (Sect. 2.2.3), derived from reference plain stations.

Hinkelman et al. (2015) similarly evaluated the CERES SYN products at mountain stations for 3 h averages. In terms of SW↓ irradiance, they showed biases between −13 and +51 W m⁻² and RMSE between 93 and 162 W m⁻². In terms of LW↓ irradiance, they showed biases between −17 and +31 W m⁻² and RMSE between 24 and 40 W m⁻². Despite a coarser spatial resolution, the obtained irradiance errors are similar to those of LSA SAF products, but they are reduced by the 3 h average. Reaching a similar performance at hourly time steps can then be considered as an improvement. The shorter time step of LSA SAF products also enables a finer representation of the SW↓ diurnal cycle.

These results suggest that LSA SAF satellite-derived estimates of SW↓ and LW↓ irradiances are suitable to drive distributed snowpack simulations in mountainous terrain. DSLF can be replaced by DSLFnew up to mid-altitudes (2200 m approximately), where the performance is improved. These products constitute beneficial alternatives to NWP and analysis systems in complex terrain.

5.2 Limitations due to the topographical influence on radiation

Limitations to the use of kilometric-resolution irradiance products in complex terrain arise from the high topographical influence on incoming radiation. These limitations are tackled here following three axes: (i) limitations of satellite-derived irradiance products in mountainous terrain, (ii) local topographical effects on radiation in the radiative forcing of snowpack simulations, and (iii) influence of local topography on the evaluation of the irradiance products and snowpack simulations.

First, satellite data sometimes require corrections when applied over mountains. For instance, the HelioMont solar irradiance product (Stöckli, 2013; Castelli et al., 2014) is calculated using the MSG SEVIRI High Resolution Visible (HRV; 0.45–1.1 µm) channel and five other near-infrared and infrared channels (0.6, 0.8, 1.6, 10.8, 12.0 µm). In this method, the satellite data depending on the HRV channel (at 1 km resolution) require an orthorectification to avoid artificial geometric shifts in terrain due to its high resolution compared to the terrain elevation (Stöckli, 2013), while the satellite data from the other channels (at MSG pixel resolution, i.e. more than 3 km) are not orthorectified. The DSSF and the DSLF only use data from the 0.6, 0.8 and 1.6 µm channels, which do not require orthorectification, similarly to the HelioMont method. Corrections may also be applied to the meteorological inputs. The DSSF does not rely as much as the DSLF on meteorological forecasts but it still uses the total column water vapour content (TCWV) forecast from ECMWF IFS at 16 km resolution. Since the TCWV is dependent on the elevation, the DSSF could be improved with AROME forecasts of TCWV at kilometric resolution, similarly to DSLFnew. Despite that, the DSSF still exhibits a better performance than AROME and SAFRAN in mountains.

At sub-kilometric scale, the local topography strongly influences the solar and longwave irradiance variability. Oliphant et al. (2003) identified the following surface characteristics as causes of radiative flux variability, by order of importance: slope aspect, slope angle, elevation, albedo, shading, sky view factor (SVF) and leaf area index. These local factors are not taken into account in AROME, SAFRAN and LSA SAF irradiance products. This study aims at assessing the practical benefits of different irradiance datasets to be used as radiative forcing for distributed snowpack simulations at 2.5 km resolution in mountains. In the context of representing the mean state of the snowpack over a considered flat pixel, at a given altitude and a given location in the mountain range, the terrain influence on the radiation does not need to be taken into account in the radiative forcing. However, to capture the sub-kilometric variability of the snowpack, it will be necessary to consider sub-grid effects of the surrounding terrain on the radiation, and thus a topographical correction of irradiance products (e.g. Helbig and Löwe, 2012) such as that applied to MSG satellite-derived solar fluxes by the HelioMont method (Stöckli, 2013; Castelli et al., 2014).

The main limitation implied by local topography effects regards the evaluation of the irradiance products and the snowpack simulations through in situ comparisons. Indeed, in situ irradiance and snow depth measurements are affected by these effects. The location of stations in flat and open fields reduces the impacts of slope, aspect and vegetation. The evaluation of solar irradiances at periods when the sun is not masked by the surrounding topography enables the terrain shadowing effect on direct solar radiation to be discarded. However, this effect is not considered for snow depth comparisons. Additionally, the limited sky view and the reflection effects on diffuse solar radiation are not taken into account, and neither are the limited sky view and terrain thermal radiation effects on longwave irradiance. According to the incoming radiation budget accounting for topography effects on a flat surface (e.g. Müller and Scherer, 2005), the bias for not taking into account the SVF in the shortwave irradiance is ($\mathrm{1}-\mathrm{SVF})\cdot ({\mathrm{SW}}_{\mathrm{dif}}-{\mathrm{SW}}_{\mathrm{ref}})$), where SW_dif is the diffuse shortwave irradiance and SW_ref is the terrain-reflected shortwave radiation. This bias is small in clear-sky conditions, because the SVF contribution is then significantly lower than topographic shading (e.g. Olson et al., 2019), but it increases in cloudy conditions with a stronger relative contribution of SW_dif. The bias for not taking into account the SVF in the longwave irradiance is ($\mathrm{1}-\mathrm{SVF})\cdot ({\mathrm{LW}}_{\mathrm{atm}}-{\mathrm{LW}}_{\mathrm{ter}}$), where LW_atm is the atmospheric longwave irradiance and LW_ter is the terrain thermal radiation. This bias is more significant when LW_atm is low (Sicart et al., 2006) but is usually small compared to LW_atm on horizontal surfaces (Plüss and Ohmura, 1997), which is the case of the measurement locations.

5.3 Sensitivity of snowpack simulations to the radiative forcing

DSSF and DSLFnew irradiance datasets were used to replace AROME irradiance forecasts as radiative forcing of Crocus simulations. The rest of the atmospheric forcing was taken from AROME forecasts. A similar experiment was done with SAFRAN irradiances. The performance of the snowpack simulations was degraded when using DSSF and DSLFnew products, with an increased positive snow depth bias. On the contrary, the use of SAFRAN irradiances was found to decrease the positive bias obtained with AROME-Crocus. Vionnet et al. (2016) and Quéno et al. (2016) already showed an overestimation of snow depth by AROME-Crocus in the French Alps and the Pyrenees respectively. In addition, Quéno et al. (2016) partly attributed this overestimation to an underestimation of strong melting. Thus, replacing AROME irradiance forecasts by lower or equivalent values (DSSF and DSLFnew) logically enhances the overestimation, despite the better quality of the new irradiance products. In this case, improving the radiative forcing leads to degraded snowpack simulations, which is consistent with the strong interaction effect in snowpack simulations highlighted by Günther et al. (2019). This effect may be attributed to error compensations within the atmospheric forcing and/or within the snowpack model:

• Quéno et al. (2016) showed that the positive snow depth bias is not due to an overestimation of daily snowfall by AROME-Crocus. The strong overestimation of SW↓ by AROME shown in this study would also tend to increase the melting and reduce the snow depth bias. We showed here it is not counterbalanced by the underestimation of LW↓. However, the underestimated melting may be linked to an underestimation of the turbulent fluxes. It may have several causes that need to be further explored, e.g. a possible influence of the T_2 m cold bias, particularly marked at the highest altitudes (−2.8 K above 2500 m; Vionnet et al., 2016).

• Within the snowpack model Crocus, Quéno et al. (2016) showed an underestimation of snow settling, with a direct effect on snow depth bias. The snow compaction scheme used in Crocus depends on the weight of overlying snow, temperature and density of snow, liquid water content, and snow grain size (Vionnet et al., 2012). The parameterization of the albedo evolution also needs to be questioned: Lafaysse et al. (2017) underlined a positive bias of Crocus-simulated albedo at Col de Porte (Fig. 1a), which they partly attributed to the parameterization of albedo decrease in the visible range as a function of the age of the snow layer and the altitude of the site. An overestimation of the albedo indeed decreases the absorption of solar energy, hence enhancing the positive snow depth bias.

These results endorse the idea that snowpack ensemble simulations are necessary to mitigate error compensations, as recently developed for Crocus with the multiphysical ensemble system ESCROC (Ensemble System Crocus; Lafaysse et al., 2017).

The sensitivity of Crocus snowpack simulations to the radiative forcing can be interpreted in the light of several works quantifying the impact of atmospheric forcing errors on snowpack simulations (Raleigh et al., 2015; Lapo et al., 2015b; Sauter and Obleitner, 2015). First, Sauter and Obleitner (2015) studied the influence of uncertainties on atmospheric forcing variables on simulations of glacier mass-balance using Crocus in the Svalbard islands (European Arctic). They identified LW↓ uncertainty as the main source of variance (50 %) of the surface energy balance throughout the year. However, the prevailing effect of LW↓ compared to SW↓ is more marked at high latitudes, because of the lack of solar insolation in winter. In our study, we showed that the new LW↓ forcing from DSLFnew (with a positive bias compared to AROME) had a significant impact on the mass budget during the whole winter at low altitudes (Fig. 10), while the impact was more limited at high altitudes (Fig. 11). It can be explained by decreasing LW↓ irradiances with altitude together with increasing SW↓ irradiances, leading to a more significant impact of SW↓ at high altitudes. It is also due to the earlier snowmelt at low altitudes, which limits the crucial role played by SW↓ in spring.

Furthermore, the differences between the different radiative forcing datasets mainly consist of biases rather than random errors: a typical example is the difference between AROME and DSSF in SW↓ at high altitudes, shown in Fig. 11. Their effect is then cumulated during the whole season, rather than counterbalanced, which increases their impact. It is consistent with the outcomes of Raleigh et al. (2015) who showed that snowpack models are more sensitive to biases than random errors in the forcings. It was particularly highlighted for incoming radiative fluxes by Lapo et al. (2015b). Finally, although the SWE is not impacted by the differences in incoming radiative fluxes at high altitude during the accumulation period (Fig. 11), impacts are to be expected in terms of snow surface temperatures, with possible consequences on the snow metamorphism processes. Lapo et al. (2015b) indeed showed more sensitivity of the snowpack simulations to irradiance errors at the coldest sites when evaluated in terms of snow surface temperature rather than SWE. Future works could thus focus on the impact of the different incoming radiative flux datasets on the surface energy budget and the resulting effects on the snowpack stratigraphy.