Learning about precipitation orographic enhancement from snow-course data improves water-balance modeling

Precipitation orographic enhancement depends on both synoptic circulation and topography. Since high-elevation headwaters are often sparsely instrumented, the magnitude and distribution of this enhancement remain poorly understood. Filling this knowledge gap would allow a significant step ahead for hydrologic-forecasting procedures and water management in general. Here, we hypothesized that spatially distributed, manual measurements of snow depth (courses) could provide new insights 5 into this process. We leveraged 11,000+ snow-course data upstream two reservoirs in the Western European Alps (Aosta Valley, Italy) to estimate precipitation orographic enhancement in the form of lapse rates and consequently improve predictions of a snow-hydrologic modeling chain (Flood-PROOFS). We found that Snow Water Equivalent (SWE) above 3000 m ASL was between 2 and 8.5 times higher than recorded cumulative seasonal precipitation below 1000 m ASL, with gradients up to 1000 mm w.e. km−1. Enhancement factors estimated by blending precipitation-gauge and snow-course data were quite consistent 10 between the two hydropower headwaters (median values above 3000 m ASL between 4.1 and 4.8). Including blended gaugecourse lapse rates in an iterative precipitation-spatialization procedure allowed Flood-PROOFS to remedy underestimations of both SWE above 3000 m ASL (up to 50%) and importantly precipitation vs. observed streamflow. Runoff coefficients based on blended lapse rates were also more consistent from year to year that those based on precipitation gauges alone (standard deviation of 0.06 and 0.19, respectively). Thus, snow courses bear a characteristic signature of orographic precipitation, which 15 opens a window of opportunity for leveraging these data sets to improve our understanding of the mountain water budget. This is all the more important due to their essential role in supporting water security and ecosystem services worldwide. 1 https://doi.org/10.5194/hess-2020-571 Preprint. Discussion started: 26 November 2020 c © Author(s) 2020. CC BY 4.0 License.

Orographic precipitation has already been subject of extensive research (Bonacina, 1945;Sarker, 1966;Alpert, 1986;Barros Mean elevation of these snow courses was much higher than the elevation captured by the precipitation-gauge and snowdepth-sensor networks (often above 3000 m ASL). The location of transects across each catchment was chosen to capture 155 a variety of physiographic characteristics, while the number of transects for each catchment-year depended on available resources. Snow depth was measured using manual probes, and location of each measurement was recorded using a portable GPS with a precision on the order of meters. Snow-course data for each area of interest were accompanied by a few measurements of bulk-snow density at representative locations, which were averaged to provide a reference estimate for each survey and hence derive SWE.

Estimating blended gauge-course lapse rates
We derived blended precipitation-gauge-snow-course lapse rates for Beauregard (water years 2017 through 2019) and Valpelline (water years 2008 through 2013, 2015 through 2019) by first detecting the onset of the snow season for each catchment and each water year as the first hour with at least 20 cm of snow on the ground for a mid-elevation, nearby snow-depth sensor 165 (red squares in Figure 1, elevation was ∼1860 and 1970 m ASL for the snow depth sensor of Beauregard and Valpelline, respectively). We then accumulated hourly precipitation between this onset date and the snow-course date for every precipitation gauge in the same valley of each hydropower catchment -this was done separately for each water year. We finally derived orographic-precipitation enhancement factors for each valley and water year by dividing seasonally cumulative precipitation at gauges and average SWE above 3000 m ASL by seasonally cumulative precipitation at the lowest-elevation precipitation 170 gauge in the same valley; these adimensional enhancement factors measure the magnitude of orographic-precipitation elevation gradients, regardless of seasonal-precipitation totals.
Blended precipitation-gauge-snow-course lapse rates were computed as a least-square-error regression fit between elevation and these enhancement factors. Although snow-course data were also available for other three study areas ( Figure 1 and Table   1), these were too small compared to the respective valleys for deriving robust precipitation lapse rates. We therefore calibrated 175 blended precipitation-gauge-snow-course lapse rates only using data from Beauregard and Valpelline (separately, see Section 3.3 for details on the use of the additional courses in this paper).
The general assumption behind blended precipitation-gauge-snow-course lapse rates is that snow-course measurements above 3000 m ASL are representative of total precipitation fallen at those elevations from the onset of the snow season through the snow-course date. In other words, such blended lapse rates assume that the snowpack above 3000 m ASL behaves as a 180 natural precipitation gauge, with no significant mass loss throughout the accumulation season due to snowpack runoff, evaporation, or sublimation. In this framework, accumulating seasonal precipitation since the first hour with at least 20 cm of snow on the ground aimed at capturing precipitation totals for the bulk of the accumulation season, while excluding early-season snowfall events that might result in complete or partial depletion of the snowpack.
While no continuous-time measurement of SWE was available to validate the 3000m-elevation threshold above which to 185 compute average snow-course SWE, and while prescribing a constant threshold for all water years necessarily neglects inter-annual variability in weather, Hantel et al. (2012) have found snow-line elevations across the Alps on the order of ∼800 m ASL in winter and ∼3000 m ASL in summer (period 1961-2010). Thus our chosen threshold can be used to assume absence of significant snowmelt before at least May.
Because we computed blended lapse rates using seasonally cumulative precipitation and peak SWE data, these lapse rates 190 are representative of winter-precipitation gradients. Correctly capturing these seasonal gradients is vital for estimating peak snow-cover distribution and amount and thus forecast summer water supply (e.g., see Pagano et al., 2004;Harrison and Bales, 2016), although precipitation gradients for specific storms may significantly diverge from the observed seasonal lapse rates.
Likewise, these lapse rates are not necessarily representative of summer-storm elevation gradients; in this region as well as across the Alps in general, summer storms are mostly convection-driven (Giorgi et al., 2016), a process that is rare during 195 winter and therefore cannot be fully captured by peak-season SWE measurements.

Spatialization of precipitation based on blended lapse rates
Blended precipitation-gauge-snow-course lapse rates developed in Section 3.1 were used to design an iterative, two-step precipitation-spatialization procedure accounting for orographic effects above the precipitation-gauge line. The ultimate goal of designing such a spatialization procedure was twofold: on the one hand, we aimed to confirm whether annual-precipitation 200 totals obtained by blended precipitation-gauge-snow-course lapse rates agreed with annual reconstructed runoff, especially in terms of annual runoff coefficients. On the other hand, we aimed to assess whether blended precipitation lapse rates could improve hydrologic predictions (Section 3.3).
In this paper, we forced Flood-PROOFS with historical data, which corresponds a standard hydrologic simulation in reanalysis mode. The implementation of Flood-PROOFS considered in this paper runs with a spatial resolution of 120 m; the computational domain covers the entire Aosta-Valley region. More details about Flood-PROOFS's parametrizations and spatialization 210 techniques can be found in the Supporting Information, Section S1. Similar to other snow-hydrologic models, precipitation spatialization in Flood-PROOFS relies on in-situ precipitation measurements. In the current spatialization procedure, these precipitation measurements are interpolated using a modified-Kriging approach called GRISO (Random Generator of Spatial Interpolation from uncertain Observations, see Pignone et al., 2010;Puca et al., 2014). The most significant asset of GRISO is that interpolated precipitation for pixels including a precipitation 215 gauge will maintain the same value as that measured by that precipitation gauge (in other words, measurements at precipitationgauge locations are preserved during interpolation). The covariance structure for each precipitation gauge is dynamical, while precipitation-field values far from all precipitation gauges tend either towards the mean of the precipitation field observed by gauges, or towards zero. In this paper, we chose the second option, but also set an influence radius for each precipitation gauge equal to 20 km following previous validations of GRISO in Aosta Valley. No pixel of the study area was thus "far enough" from all gauges for this choice to be relevant.
This one-step precipitation-spatialization procedure assumes that measurements taken by the precipitation-gauge network are representative of the overall range of variability in precipitation across the study domain. As we outlined in the Introduction and will further show in Section 4, this assumption does not necessarily hold true in mountain regions that straddle the precipitation-gauge line, because interpolated precipitation-fields will likely underestimate precipitation totals due to oro-225 graphic effects missed by the ground-based measurement network. We overcame this issue by developing a modified, two-step GRISO approach as follows. For each time step of interest (in our case, each hour), GRISO was first run using precipitation gauges alone (GRISO1). Second, interpolated-precipitation values at select pixels above 2700 m ASL were enhanced according to their elevation and the seasonal winter enhancement-factor profile calibrated in Section 3.1. Third, GRISO was re-run using as input the measurements from the physical precipitation gauges and estimates at these select pixels (GRISO2). In this two-230 step procedure, these orographically enhanced precipitation estimates act as virtual precipitation gauges at high elevations (see location in Figure S13), with orographic enhancement being informed by snow-course measurements at peak accumulation.
High-elevation pixels were selected by first defining a regular grid with spacing equal to 5% of the longitudinal and latitudinal range of the study area, and then taking as candidate locations for these virtual gauges the nodes of this grid. Second, we filtered out any candidate virtual gauge with elevation below 2700 m ASL as well as those falling outside the study area. Figure S13 235 shows that the final location of these virtual precipitation gauges is coherent with the orography of out study region, and complements the spatial coverage of the physical precipitation-gauge network ( Figure 1).

Evaluating blended precipitation-gauge-snow-course lapse rates from a water-balance perspective
We evaluated precipitation estimates informed by blended precipitation-gauge-snow-course lapse rates by comparing predictions of Flood-PROOFS using GRISO1 vs. those using GRISO2 (see Section 3.2). The evaluation period was water years 2017 240 to 2019, since these three water years saw a peak in evaluation-data availability (particularly snow-course data). Although water years 2017 to 2019 were also used to calibrate the blended precipitation-gauge-snow-course lapse rates and therefore this was not a fully independent evaluation, doing so was necessary given the lack of snow-course data before 2017 for one of the hydropower catchments (Beauregard) and the need for considering as many years as possible for lapse-rate calibration to capture interannual variability.

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Input-data maps were first used to force the snow model of Flood-PROOFS, S3M, and generate hourly equivalent-precipitation fields that were then used as an input for the hydrologic model Continuum; equivalent precipitation is the pixel-wise sum of rainfall, snowpack runoff, and glacier runoff -if any (see Section S1 for details on these models). S3M can be run in two different modes, that is, only relying on weather inputs (Open-Loop run), or assimilating SWE information from independent sources (Full-Assim run). SWE is assimilated as both weekly maps produced by ARPA VdA through interpolation of man-250 ual measurements according to physiographic features (see Section 2.2) and daily maps produced within Flood-PROOFS by training a multilinear regression across concurrent ultrasonic-snow-depth-sensor measurements (predictand) and physiographic features like elevation, slope, and aspect (predictors). In the present study, evaluation of peak-SWE predictions by S3M against snow courses was carried out with reference to both Open-Loop and Full-Assim simulations, to disentangle the impact of precipitation spatialization from that of data assimilation. Simulations of the complete Flood-PROOFS chain (S3M + Continuum) 255 were only performed in Full-Assim mode because of computational-time constraints.
As we will show in Section 4, assimilated snow maps -and in particular those derived from snow-depth sensors -suffer from a similar bias as that of precipitation at elevations above the snow-depth-sensor line (see Figure 1). This bias is likely due to the snow-depth-sensor network being skewed toward representing mid-elevation snowpack. Assimilating these biased snow maps would largely nullify the potentially positive effect of enhancing orographic effects in GRISO2, so we developed a 260 correction factor by first recalibrating the snow-depth multilinear-regression model with snow-course data in addition to snowdepth-sensor data. This recalibration was performed for each week when snow-course data were available between water years 2017 and 2019, and considering all five areas of interest were snow-course data were collected to maximize variety of data. The mean value of the ratio between recalibrated snow-depth maps and the original ones was then used as a multiplicative factor for original maps to remedy for high-elevation biases. This correction was only estimated for snow-depth-sensor-based maps both 265 because preliminary assessments showed that they are the major source of bias compared to weekly SWE maps, and because they are assimilated daily and as such play a much more important role than weekly SWE maps in driving Flood-PROOFS' accuracy.
We focused on three evaluation exercises: first, we compared basinwide estimated precipitation according to GRISO1 and GRISO2 with measured reconstructed streamflow, hence runoff coefficients; second, we ground-truthed peak-SWE predictions 270 by Flood-PROOFS's snow model (S3M) forced using GRISO1 vs. GRISO2 against snow-course data; third, we compared cumulative daily streamflow predicted by Flood-PROOFS's hydrologic model (Continuum) forced using GRISO1 vs. GRISO2 against reconstructed streamflow. The first and third evaluation exercises had a traditional water-balance perspective; they determined whether estimated precipitation with and without orographic enhancement can explain annual total runoff and its seasonal patterns (both important targets for water-supply forecasting). The second exercise assessed the impact of orographic-275 precipitation enhancement on the simulation of snow storage, an intermediate prediction target between precipitation and runoff with significant implications beyond hydrology (e.g., avalanche forecasting, glacier mass balance).

Water-balance climatology
Average monthly precipitation across gauges in the valleys of Beauregard and Valpelline (variableP , in mm) was bimodal, 280 with peaks in November and May (Figure 2, a, reference period was water year 2009 through 2019 due to earlier gaps inP for Beauregard, Figure S14, a). Monthly precipitation was similar between the two valleys (mean difference -2.5 ±7.1 mm).
Nonetheless, precipitation in Beauregard was up to 15 mm higher than in Valpelline during fall and winter (September to March) and up to ∼6 mm lower during summer (April to August), which highlighted that Beauregard may be more exposed to winter storms coming from the Mediterranean Sea, with Valpelline being more affected by summer storms from the Atlantic

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Ocean. This tallies with the bimodal and the summer-dominated precipitation regimes of the southern and northern sides of the Alps, respectively (Frei and Schär, 1998;Isotta et al., 2014). However, we stress thatP only accounts for precipitation gauges, meaning precipitation totals above the precipitation-gauge line remained unaccounted. AnnualP in both valleys was consistent from year to year: ∼ 700 ± 84mm and ∼ 730 ± 94mm in Valpelline and Beauregard, respectively (Figure 3, a and S14, a).

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According to the reference snow-depth sensors used in Section 3.1 to accumulate winter precipitation, the average snow season started in October in both Beauregard and Valpelline (Figure 2, b, reference period is water years 2008 through 2017 due to later gaps in snow-depth data for Valpelline, see Figure 3, b). The end-of-season date generally occurred in May, with both catchments being exposed to late snowfall events even in June. In contrast with precipitation, peak snow depth showed a remarkable interannual variability (standard deviation of maximum annual snow depth was 31 and 77 cm at Beauregard and 295 Valpelline, respectively), with three of the four water years with shallow snowpacks occurring between 2014 and 2019 ( Figure   3, b and S14, b). During some of these shallow-snowpack water years, the snow cover was ephemeral at these snow-depth sensor sites (e.g., water years 2017 at Beauregard, Figure S15, b). Monthly snow depth at the reference sensor of Valpelline was significantly higher than that of Beauregard (Figure 2, b), which we explain because the former is at a higher elevation of the latter (∼ 100 m).

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Reconstructed streamflow in both catchments was highly seasonal, with minimum flow during winter and maximum flow in June, when precipitation, snow melt, and ice melt overlap (Figure 2, c, reference period is water years 2008 through 2019).
Monthly streamflow was similar between the two catchments (mean difference was -0.11 ± 18 mm), with the only exception that streamflow in Beauregard was higher (up to ∼20 mm) between November and June and lower (up to ∼45 mm) between July and October than in Valpelline. This is likely connected to average monthly precipitation in Beauregard being higher and 305 lower than in Valpelline during winter and summer, respectively (see Figure 2, a). A second argument is favor of Beauregard and Valpelline being hydrologically similar catchments was the similarity in precipitation-runoff relationship (Figure 3, d), that is, the fundamental rule relating annual precipitation to annual runoff (Saft et al., 2016;Avanzi et al., 2020b). Compared to precipitation climatology, reconstructed streamflow in both catchments showed comparatively large interannual variability ( Figure 3, c and S14, c), owing to both precipitation and climate variability.

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In summary, ground-based precipitation, streamflow, and snow-depth sensor data showed that water-supply generation in both these two hydropower catchments is fundamentally cryosphere-dominated. They also showed that ground-based sensor data located across low-and mid-elevations are largely insufficient to grasp the full water balance of these cryospheredominated headwaters, as also demonstrated by (1) annualP being systematically smaller than the corresponding annual streamflow totals (Figure 3, d), and (2) peak monthly snow depth occurring in February in both catchments. While no 315 continuous-time measurement of snow-depth and SWE was available above ∼2700 m ASL (Figure 1), general consensus in the Alps as well as our experience is that peak-SWE date occurs around April 1 or later in high-elevation, Alpine catchments

Precipitation vs. SWE orographic gradients
We report in Figure 4, a and b, examples of precipitation-gauge vs. snow-course orographic gradients obtained in 2018 for Beauregard and Valpelline, respectively. At Beauregard, precipitation gauges recorded a positive, but mild precipitation lapse rate -on the order of ∼250 mm km −1 . At Valpelline, the lapse rate recorded by precipitation gauges was even smaller, ∼75 mm km −1 . The orographic trend recorded by gauges agreed with GRISO1 (see again Figure 4, a and b), which was expected given that GRISO1 used precipitation gauges as a starting point to distribute precipitation across the landscape. Snow-course data drew a substantially different picture from precipitation gauges, with SWE sharply increasing with elevation (Figure 4, a   325 and b): ∼1000 and 567 mm w.e. km −1 in Beauregard and Valpelline, respectively. Thus, peak SWE close to (or above) 3000 m ASL in 2018 was 2-3 times total winter precipitation measured by precipitation gauges below the precipitation-gauge line.
Examining all water years for which snow-course surveys were available confirmed that these surveys yield much larger orographic gradients than precipitation gauges in both hydropower catchments ( Figure 5, a and b and Figures S15 through S25, where missing panels imply that some of the information needed to perform this comparison was missing for that water year).

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In particular, precipitation gradients based on gauges hardly exceeded 200 mm w.e. km −1 , whereas snow-course gradients were often higher than 400 mm w.e. km −1 and reached values as high as 1000 mm w.e. km −1 ; snow-course-based gradients were particularly high at Beauregard compared to Valpelline. This sharp increase in snow accumulation with elevation was consistent across water years and was generally underestimated by both snow maps assimilated by Flood-PROOFS in proximity of the snow-course surveys ( Figure 5, a and b and S15 to S25); note that these independent maps do take into account physiography.

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This is another piece of evidence that ground-based sensor data located across low-and mid-elevations do not capture the complete range of variability in snow distribution at high elevations.
Snow-course-based orographic gradients increased with average snow depth above 3000 m ASL (correlation coefficient ρ = 0.67, see Figure 5, c), whereas the correlation between these gradients and snow-course survey date was much weaker (ρ = 0.2, see Figure 5, d). Moreover, the correlation of snow-course orographic gradients with average snow depth above 3000 m 340 ASL was statistically significant, while that with snow-course survey date was not (p-value of 0.02 and 0.52, respectively).
Thus, the choice of survey date had a limited impact on the quantification of snow-course orographic gradients, which suggests that these gradients may preserve themselves through time.

Orographic-enhancement factors
Snow-course measurements of peak SWE above 3000 m ASL were between ∼2 and ∼8.5 times and between ∼4 and ∼5.5 345 times winter cumulative precipitation at the lowest-precipitation gauge of Valpelline and Beauregard valleys, respectively ( Figure 6). Interannual variability was significant and partially driven by snowpack amount, with the four highest enhancement factors being associated with water years with low or medium snowpack (see again Figure 6). However, this was not systematic, since the five lowest enhancement factors were recorded during years with mixed characteristics (two with low snowpack, one with medium snowpack, and two with high snowpack). This tallies with Figure 5, c, where only some dependency between confirmed that Flood-PROOFS simulations forced by GRISO1 generally underestimated water supply in these catchments.
Yet, Kling-Gupta Efficiencies (KGE, see Gupta et al., 2009;Kling et al., 2012) for Q v1 were consistently higher than 0.65 and 420 thus well above the benchmark represented by mean flow (-0.41, see Knoben et al., 2019), which has been often regarded as an arguable threshold between "bad" and "good" model performance (Schaefli and Gupta, 2007;Knoben et al., 2019). Contrary to RMSE and biases, KGE is the composition of bias, variability, shape, and timing error terms (Santos et al., 2018), meaning the issue with GRISO1-based simulations was really with total volume rather than with seasonal patterns.
Simulations using GRISO2 improved Q v2 /Q obs compared to Q v1 /Q obs for four out of six catchment-water years (Table 2 425 and Figure 8). Predictions of Q v2 also yielded smaller biases and RMSEs (as absolute values) for all water years and catchments ( Table 2). The improvement of Q v2 over Q v1 was particularly evident during the late-melt period (that is, from May on), when the highest elevations in these catchments start contributing runoff (Figure 8). Improvements during the accumulation period were much more modest, likely because streamflow generation during that period of the year is governed by processes that we did not focus on here (e.g., groundwater flow, year-round glacier runoff due to basal melt). KGE coefficients also improved in 430 five out of six catchment-water years, reaching values as high as 0.93.
Focusing on SWE, simulations of S3M using GRISO1 underestimated snow-course measurements both whether an Open-Loop and whether a Full-Assim mode was used (Figure 9). This underestimation was particularly significant for Open-Loop simulations, which agreed with results for precipitation vs. equivalent precipitation above (Table 2), whereas it showed no consistent trend with elevation, which is instead consistent with results in Section 4.3 and Figure 7 regarding snowpack elevation 435 gradients being particularly elusive to capture. Biases using GRISO2 were smaller than those using GRISO1 in five out of six catchment-water years (Full Assim mode), but again elevation trends were inconsistent (Figure 9). Using an Open-Loop simulations with GRISO2 would actually overestimate at the highest elevations in two out of six cases (2017 and 2018, Valpelline, We derived two main results from this final focus on SWE: the first is an expected, net improvement in predicting high-440 elevation SWE when snow-course measurements are used in model development (especially at Beauregard). The second is that precipitation orographic gradients are highly seasonal as well as spatially variable, and remain challenging to fully capture with a one-fits-all approach as the one we used here (e.g., Equation 1 and Figure 7, d and h).

Main findings 445
Snow courses have been a frequent option for conducting snow surveys since the seminal 1910 campaign by Church (1914Church ( , 1933 at Mount Rose, Nevada (US). Compared to stand-alone devices like snow pillows (Cox et al., 1978), courses allow operators to capture spatial variability of snow cover and so derive a more representative estimate of SWE across the landscape (Malek et al., 2017). This is why courses are now a cornerstone of water-supply forecasting in the western US (Pagano et al., 2004;Harrison and Bales, 2016) and elsewhere (Metsämäki et al., 2005). In addition to their century-old role as indicator of 450 snow water resources, in this paper we hypothesized that snow courses could be rethought as natural precipitation gauges, in the hope that they could provide new information about precipitation totals and their orographic trends at elevations that are usually ungauged. This hypothesis follows intuitions by other authors, such as Lundquist et al. (2015) or Zhang et al. (2017), who used pillow SWE and snow depth as a surrogate of precipitation, respectively. Others, such as Immerzeel et al. (2015), addressed this problem by inferring precipitation from glacier mass balances and runoff. Our novelty was to mine new 455 information from snow courses, which provide spatial snapshots in lieu of point values.
The main findings of this paper in this regard are two. First, peak-season snow-course SWE above 3000 m ASL can be 2 to 8.5 times higher than measured winter cumulative precipitation at elevations below 2000 m ASL (Figure 6), with orographic trends that are up to five times those captured by the precipitation-gauge network (Figure 2). While orographic precipitation has been a target of extensive research so far (see the Introduction), extrapolating precipitation-gauge signal above the precipitation-460 gauge line still lacks solid guidelines (Ruelland, 2020). In this paper, we contributed highly-needed, multi-year estimates of orographic trends across sharp altitudinal gradients.
Second, leveraging snow courses to refine the precipitation-and snow-depth-spatialization algorithms of an operational flood-forecasting chain (Flood-PROOFS) allowed for improvements in modeling accuracy not only for SWE (Figure 9), but importantly for the whole water balance (Figure 8). This result is encouraging given that no model recalibration was performed, 465 and as such we did not mix the effect of precipitation correction with other confounding factors that may lead to equifinality issues (Beven and Freer, 2001;Lundquist et al., 2015). Although the bulk of mountain river basins in the European Alps lies below 2000 m ASL (Elsen et al., 2020), areas above the precipitation-gauge line are a fundamental hydropower resource and represent a significant portion of higher-elevation mountain ranges such as the Himalayas. This paper outlined opportunities to obtain more robust hydrologic predictions without necessarily investing into long recalibration efforts.

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Despite these promising findings, the question remains whether our blending approach (Section 3.1) reconstructed the true precipitation lapse rate, or whether it captured other drivers of snowpack distribution at high elevations (e.g., wind drift). While both scenarios would be an argument in favor of using snow courses for informing hydrologic predictions, only the first would imply that we achieved the right answer for the right reason (Kirchner, 2006). In essence, this question points to determining whether snow-course data are primarily a reflection of orographic precipitation or, e.g., of wind drift or solar radiation.

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Several hints point to our reconstruction method capturing actual orographic trends in precipitation, rather than other snowdistribution processes. First, previous studies in the Alps already showed that annual mean precipitation at 1000-2000 m ASL is generally up to 2 times precipitation below 1000 m ASL, (Frei and Schär, 1998;Napoli et al., 2019), a mechanism that the precipitation network at Beauregard and Valpelline did not fully capture but that is consistent with our estimates of blended orographic-enhancement factors ( Figure 6 and Equation 1). Second, several previous attempts to improve estimates of 480 hydrologic models in mountain regions through snow-data assimilation alone reported inconclusive results (Tang and Lettenmaier, 2010), whereas the clear improvements in this study suggest that we did capture at last some components of orographic precipitation in addition to snow patterns. Third, we computed orographic-enhancement factors by averaging snow-course measurements above 3000 m ASL rather than considering each of them individually, in an effort to reduce the effects of smallscale spatial variability. Fourth, values of snow-course SWE at elevations close to the local precipitation-gauge line (∼2000 m Only a subset of the five areas was surveyed every year, due to budgetary and logistical constraints. The spatial distribution of these samples is showed in Figures   S2-S12, Supporting Information. Note that 2641 out of 5349 measurements collected at Goillet in 2017 were performed on 10/04. Snow courses for this area and water year were part of a large intercomparison workshop, hence the much larger sample size than other years and areas.   https://doi.org/10.5194/hess-2020-571 Preprint. Discussion started: 26 November 2020 c Author(s) 2020. CC BY 4.0 License. Table 2. Evaluation metrics of Flood-PROOFS simulations driven by GRISO1 vs. those driven by GRISO2. The first distributed precipitation only using precipitation gauges, whereas the second included an orographic correction developed in the present study based on snow courses.
Q, P and R are annual streamflow, precipitation, and equivalent precipitation, respectively (with equivalent precipitation being the sum of rainfall, snowpack runoff, and glacier runoff). obs, v1 and v2 refers to observed data and simulated data according to GRISO1 and GRISO2,