Scale Dependence of Errors in Snow Water Equivalent Simulations Using ERA5 Reanalysis over Alpine Basins

Citation: Shrestha, S.; Zaramella, M.; Callegari, M.; Greifeneder, F.; Borga, M. Scale Dependence of Errors in Snow Water Equivalent Simulations Using ERA5 Reanalysis over Alpine Basins. Climate 2023,11, 154. https://doi.org/10.3390/cli11070154 Academic Editor: Nir Y. Krakauer Received: 9 May 2023 Revised: 17 July 2023 Accepted: 19 July 2023 Published: 21 July 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). climate Article Scale Dependence of Errors in Snow Water Equivalent Simulations Using ERA5 Reanalysis over Alpine Basins Susen Shrestha 1,* , Mattia Zaramella 2, Mattia Callegari 3, Felix Greifeneder 4and Marco Borga 2 1Center for Climate Change and Transformation (CCT), Eurac Research, 39100 Bolzano, Italy 2Department of Land, Environment, Agriculture, and Forestry, University of Padova, 35100 Padova, Italy 3Institute for Earth Observation, Eurac Research, 39100 Bolzano, Italy 4Chloris Geospatial, Boston, MA 02116, USA *Correspondence: sshr[email protected] Abstract: This study aims to evaluate the potential of ERA5 precipitation and temperature reanalysis for snow water equivalent (SWE) simulation by considering the role of catchment spatial scale in controlling the errors obtained by comparison with corresponding SWE simulations from ground stations. This is obtained by exploiting a semi-distributed snowpack model (TOPMELT) implemented over the upper Adige River basin in the Eastern Italian Alps, where 16 sub-catchments of varying sizes are considered. The comparison is carried out from 1992 to 2019. The findings show that ERA5 precipitation overestimated low-intensity rainfall (drizzle problem) and underestimated high-intensity rainfall, while ERA5 temperature underestimated observations. The overestimation of low-intensity rainfall created fictitious low-intensity snowfall events, which, when combined with colder ERA5 temperature, resulted in delayed snowmelt and increased fictitious snow-cover days over the study area. The quantile mapping (QM) technique was used to remove errors in ERA5 variables. It was shown that ERA5 could struggle to resolve the orographic enhancement in precipitation, which may be particularly important during high-SWE years. This reduces the positive precipitation bias during those years, thus reducing comparatively the ability of the quantile mapping technique to correct for bias homogeneously during all years. This study highlighted the importance of temperature correction over precipitation correction in SWE simulation, particularly for smaller basins. Keywords: TOPMELT; ERA5; seasonal snowpack simulation; snowmelt; drizzle problem; bias adjustment 1. Introduction Seasonal mountain snowpack and its melt dominate the surface hydrology of many regions, with implications for water supply, hydropower, risk assessment, and ecological processes [ 1 – 4 ]. Reliable snow-cover (SC) delineation and snow water equivalent (SWE) assessment remains crucial for snowmelt runoff prediction, operational flood control, water supply planning, and water resource management in snowmelt-dominated watersheds [ 5 ]. However, the proper assessment of SC and SWE in mountain watersheds still remains a challenge. In data-scarce basins, the use of reanalysis data, such as ERA5 [ 6 ], is of great interest to the hydrological community. Reanalysis data combine a wide array of measured and remotely sensed information within a dynamical–physical coupled numerical model. They use the analysis part of a weather forecasting model, in which data assimilation forces the model toward the closest possible current state of the atmosphere [ 7 ]. Of particular interest to the hydrological community are the largely improved (with respect to earlier reanalysis products) spatial (30 km) and temporal (1 h) resolutions of ERA5. The spatial resolution is now similar to or better than that of most observational networks in the world, with the exception of some parts of Europe and the United States. In particular, the ERA5 precipitation dataset was found to reproduce the pattern of the daily precipitation climate Climate 2023,11, 154. https://doi.org/10.3390/cli11070154 https://www.mdpi.com/journal/climate Climate 2023,11, 154 2 of 14 well in three European regions (Alps, Carpathians, Fennoscandia), with reproduction of contrasts in mean precipitation between mountains and flatland and gradients of wet-day frequency across crests [8]. In spite of the interest, the use of ERA5 data to drive snowpack models has not received large attention in the relevant literature. In two studies [ 9 , 10 ], ERA5 has been shown to provide reasonable simulations of SWE for mountain basins. The performance of MERRA-2 and ERA-5 reanalysis meteorological forcing was compared with the distributed SnowModel in the high Atlas region [ 9 ]. Both the reanalysis products showed comparable performance for snow simulation. Nonetheless, the ERA5 simulation, due to its finer spatial resolution as compared to MERRA-2, showed better performance, whereas [ 10 ] considered ERA5 as the boundary and initial condition to force the WRF model for two mountain ranges in Lebanon. The Intermediate Complexity Atmospheric Research Model (ICAR) was nested into the WRF to develop a 1 km regional-scale snow reanalysis. The results showed a good temporal and spatial correlation of the snow variables with the MODIS fractional snow-covered area and the ground observations of SWE. In these studies, the ERA5 spatial resolution has been shown to be still too coarse to correctly represent the influence of topography on meteorological variables, which is crucial for snow modeling in mountainous regions [10–12]. Whereas a number of studies proposed downscaling techniques to approach this problem, the scale-dependent structure of errors in SWE simulations using ERA5 reanalysis over alpine basins remains largely unexplored. This is in spite of the need to better understand at which spatial scales the ERA5 spatial resolution mostly affects the SWE simulations. The scale effect is an important topic and belongs to 1 of the 23 unsolved problems in hydrology [ 13 ]. Namely, what are the hydrological laws at the catchment scale, and how do they change with scale? In this study, we attempt to answer the following questions: What is the spatial representation of ERA5 precipitation and temperature as forcing data for SWE simulation at the catchment scale? Furthermore, how do they change with scale? The aim of this work is to evaluate the quality of hourly temperature and precipitation data from ERA5 reanalysis to simulate SWE dynamics in a mountainous, snowcontrolled river system, with respect to corresponding SWE simulations obtained from a relatively high-density and quality-controlled data set obtained from ground stations, used as a reference. Therefore, this study aims (i) to isolate the impact of the input spatial aggregation on the accuracy of SWE simulations by quantifying the effects of aggregating the reference precipitation and temperature data at the ERA5 grid-scale and (ii) to evaluate the scaledependence of ERA5-based simulation errors when SWE is aggregated over a range of spatial scales. To allow these analyses, mean areal precipitation estimates and temperature will be generated at the ERA5 spatial resolution using station precipitation data. This input data is referred to as Station Input at ERA5 Resolution (SIER). Then, two sets of comparisons will be carried out: (i) SIER vs. a reference based on station data to isolate the genuine impact of the aggregation of input data at the ERA5 resolution; and (ii) ERA5 vs. SIER to evaluate the impact of ERA5-only on SWE simulation, therefore disregarding the pure effect of spatial resolution. This study was carried out in the upper Adige River basin, a 6924 km 2 wide basin located in the Eastern Italian Alps, over the 1992–2019 period. The study area was selected due to the dense network of meteorological stations used to provide input to a snowpack model and to validate the ERA-5 performance. The TOPMELT model [ 14 ] is used for seasonal snowpack dynamics and SWE simulation. TOPMELT is a semi-distributed snowpack model based on an extended temperature index approach capable of estimating the full spatial distribution of the SWE at each time step. TOPMELT exploits a statistical representation of the distribution of clear-sky potential solar radiation to drive the snowpack model, which drastically reduces the computational costs associated with the fully spatially distributed simulation of SWE over vast areas and an extended period of time while preserving simulation accuracy [ 14 ]. The good accuracy of TOPMELT SWE and SC Climate 2023,11, 154 3 of 14 simulations over the study area has been tested with respect to available in situ data and MODIS observations by [15,16]. 2. Materials and Methods 2.1. Study Area and In Situ Data The study area is represented by the upper Adige River basin closed at Bronzolo in the Eastern Italian Alps (Figure 1). This is an alpine catchment with a drainage area of approximately 6924 km 2 . The elevation ranges from about 200 m a.s.l. in the southern valley bottoms to around 3900 m a.s.l. in the western upper ranges, with a mean elevation of 1800 m a.s.l. The steep terrain and the high elevation gradients govern the spatial precipitation distribution [ 17 ], with the precipitation ranging from 500 mm in the northwest region to 1600 mm in the north-central region [ 18 ]. During the winter season, the precipitation is stored as snow, and the streamflow is minimum. The streamflow shows two maxima: the first due to snowmelt in the early summer and the second due to intense precipitation in autumn [ 19 ]. The main agricultural areas in the northern part of the catchment are located in the Venosta valleys, and cultivation comprises mainly fruit trees and grapes. Land use at high elevations is dominated by grass, grazing, and forest. The study area is characterized by a rather dense network of meteorological stations, with 88 rain gauges (1 per 72 km 2 ) and 124 temperature gauges (1 per 55 km 2 ) covering the study region. The Hydrographic Office of Bozen, Bolzano, has made hourly temperature, precipitation, and runoff data available from 1991 until 2019. To assess the performance of the model at varying basin sizes, sixteen sub-catchments within the study basin were selected for the analysis. The drainage areas of the study basins range from 49 km 2 to 6924 km 2 (Figure 1, Table 1). These watersheds were chosen for analysis due to the relatively minor impact of operations from artificial reservoirs, which allowed for the use of a hydrological model and ensuing comparison of simulated versus observed discharges. Climate 2023, 11, x FOR PEER REVIEW 3 of 14 model, which drastically reduces the computational costs associated with the fully spatially distributed simulation of SWE over vast areas and an extended period of time while preserving simulation accuracy [14]. The good accuracy of TOPMELT SWE and SC simulations over the study area has been tested with respect to available in situ data and MODIS observations by [15,16]. 2. Materials and Methods 2.1. Study Area and In Situ Data The study area is represented by the upper Adige River basin closed at Bronzolo in the Eastern Italian Alps (Figure 1). This is an alpine catchment with a drainage area of approximately 6924 km2. The elevation ranges from about 200 m a.s.l. in the southern valley bottoms to around 3900 m a.s.l. in the western upper ranges, with a mean elevation of 1800 m a.s.l. Figure 1. The upper Adige River basin closed at Bronzolo. The red triangles indicate the stream gauges, which are listed in Table 1. Table 1. Drainage area and elevation of the study basins. Sn Name Elevation Range (m) Mean Elevation (m) Area (km2) 1 Rio Plan at Plan 1561–3445 2387 49 2 Rio Riva at Seghe 1523–3421 2386 76 3 Rio Anterselva at Bagni 1092–3421 2026 82 4 Rio Braies at Braies 1124–3074 1911 93 5 Rio Riva at Caminata 855–3421 2278 115 6 Rio Casies at Colle 1196–2815 1961 117 7 Rio Gadera at Pedraces 1318–3111 2027 125 8 Aurino at Cadipietra 811–3111 2162 150 9 Rio Ridanna at Vipiteno 1046–3417 1933 210 10 Gadera at Mantana 944–3441 1855 397 11 Rio Passirio at Merano 336–3445 1851 414 Figure 1. The upper Adige River basin closed at Bronzolo. The red triangles indicate the stream gauges, which are listed in Table 1. Climate 2023,11, 154 4 of 14 Table 1. Drainage area and elevation of the study basins. Sn Name Elevation Range (m) Mean Elevation (m) Area (km2) 1 Rio Plan at Plan 1561–3445 2387 49 2 Rio Riva at Seghe 1523–3421 2386 76 3 Rio Anterselva at Bagni 1092–3421 2026 82 4 Rio Braies at Braies 1124–3074 1911 93 5 Rio Riva at Caminata 855–3421 2278 115 6 Rio Casies at Colle 1196–2815 1961 117 7 Rio Gadera at Pedraces 1318–3111 2027 125 8 Aurino at Cadipietra 811–3111 2162 150 9 Rio Ridanna at Vipiteno 1046–3417 1933 210 10 Gadera at Mantana 944–3441 1855 397 11 Rio Passirio at Merano 336–3445 1851 414 12 Aurino at Caminata 844–3421 2117 420 13 Aurino at S.Giorgio 817–3421 2036 608 14 Rienza at Vandoies 732–3421 1859 1919 15 Adige at Ponte Adige 236–3889 1895 2732 16 Adige at Bronzolo 236–3889 1805 6924 2.2. ERA5 Reanalysis ERA5 reanalysis is a state-of-the-art fifth-generation ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric reanalysis of the global climate [ 6 ]. It is one of the fundamental elements of the Copernicus Climate Change Service (C3S), which is funded by the European Union. ERA5 provides multiple atmospheric, land, and oceanic climate data variables with availability spanning from 1959 to the present at a spatial resolution of 0.25 degrees and a temporal resolution of 1 h at the global scale. For this research, only temperature and precipitation will be considered from ERA5. Further information about ERA5 is available on the online data documentation (https://confluence. ecmwf.int/display/CKB, accessed on 5 May 2023). It provides a detailed description of the various products and a list of all available geophysical parameters, which can be freely downloaded. Twenty-seven ERA5 grid cells that cover the upper Adige River basin at Bronzolo were considered for this study. Based on geometrical analysis, the ERA5 precipitation was partitioned over the 16 study basins. The ERA5 air temperature is scaled to the center of mass of each study basin based on the climatological monthly lapse rate valid for the region. 2.3. The Snowpack Model: TOPMELT The snowpack model used in this work is TOPMELT [ 14 ]. TOPMELT is a semidistributed snowpack model which takes advantage of the extended temperature index approach to simulate SWE at full spatial distribution for each hourly time step [ 10 , 12 ]. Clear-sky shortwave solar radiation is computed at each element of the digital terrain model (DTM) by taking into account shadow and complex topography, calculating the apparent sun motion, and the intersection of radiation with topography. Diffuse radiation is computed by accounting for self-shading (by slope and aspect) and occlusions produced by the visible horizon. For model simulation, each basin is divided into n b elevation bands, and the full spatial distribution of clear-sky potential solar radiation is discretized into a number of radiation classes for each elevation band. This is achieved by dividing each elevation band into n c equally distributed radiation classes, where the i th class contains the band Climate 2023,11, 154 5 of 14 sub-area corresponding to the i th percentile of the incident radiation energy. TOPMELT accounts separately for snow and glacier melt; to account for the presence of a glacier area associated with an energy class, each one of the n b× n c model cells is characterized by the corresponding fraction of glacier area. Snowpack simulation is carried out for each radiation class rather than for each DTM pixel, which significantly improves computational efficiency. The analysis by [ 14 ] showed that the division of the elevation bands into ten radiation classes provides results comparable to a full spatially distributed model. Therefore, in this work, the elevation bands are subdivided into ten radiation classes based on the spatial distribution of the clear-sky solar radiation of the pixels included in each elevation band. The model uses the Thiessen polygon method to estimate the mean precipitation over the basin, while the air temperature data is used to calculate the hourly temperature lapse rate for the basin. The precipitation data are corrected with the snow correction factor (SCF) to account for gauge catch deficiencies during snowfall. The SCF is a multiplier applied to precipitation data when the station temperature goes below the threshold temperature T c , which identifies solid precipitation. Lastly, the basin precipitation, p basin , is obtained by applying a precipitation correction factor (PCF),which is a non-dimensional constant used to take into account the poor spatial coverage of the rain gauge stations. For a given i th elevation band, the model computes the precipitation p i (t) (mm h −1 ) at time tby applying a vertical precipitation gradient G(km −1 ), which considers increased precipitation over elevation as given in Equation (1): Pi(t) = Pbasin(t)1+Ghi−hre f 1000 (1) where hi , hre f (m a.s.l) are the mean altitude of the i th elevation band and of the basin, respectively. For the temperature, T i ( ◦ C) is provided as input for each time step and elevation band. The use of a vertical temperature lapse rate helps to obtain the mean air temperature over the i th elevation. The estimation of the precipitation phase (solid or liquid) is performed using the threshold temperature T c , thus obtaining the snow water equivalent of the precipitation at time t,snowi(t). The snowmelt algorithm is applied to each radiation class of a given elevation band. For a given i th elevation band and j th radiation class, the snowmelt rate Fi,j(t)hmmh−1i at time tis calculated as in Equation (2): Fi,j(t)=CMF·RIi,j(t)·(1−albi(t))·max{0; Ti(t)−Tb}(2) Here, CMF is the combined melting factor considering both thermal and radiative effects, RIi,j(t) is the cell radiation index, albi(t) is the snow albedo [-] at time t, Ti (t) is the air temperature at the i th elevation band at time t, while Tb = 0 ◦ C is the temperature threshold above which snowmelt is assumed to occur, both in [ ◦ C]. The snow albedo at each elevation band is computed using the method described by [20] as given in Equation (3): alb(t)=ALBS −β2·[log10∑ k Ti(tk)](3) where ALBS is the albedo of fresh snow, β2 is a dimensionless parameter, and ∑kTi(tk)(◦C) is the summation of the positive hourly temperatures that are above the threshold base temperature (T b ) from the last snowfall until the current time t. The model accounts for rainon-snow and melting during the night employing a temperature index approach through two additional parameters: the rain melt factor (RMF) and the night melt factor (NMF). The SWE (we i,j , mm) for each model cell is updated considering the snow water equivalent of the precipitation and melt, as given in Equation (4): wei,j(t) = wei,j(t−1) + snowi(t)−Fi,j(t) (4) Climate 2023,11, 154 6 of 14 The model also computes ice melt. When we i,j is less than a threshold (WETH), ice melt begins. The glacier melt is computed as given in Equation (2), but the snow albedo is replaced with a constant glacier albedo (ALBG). TOPMELT can simulate the full spatial distribution of the SWE; hence, the output from the TOPMELT can be compared against the point ground observations and also with snow-cover products like MODIS. The snow-cover area (SCA) is calculated here by considering a pixel as snow-covered when the simulated SWE exceeds a threshold of 5 mm, based on [16]. 2.4. The Hydrological Model: ICHYMOD The ICHYMOD hydrological model, developed by [ 21 ], combines the TOPMELT snowpack model from [ 14 ] with a conceptual rainfall–runoff hydrological model at the basin scale. This model converts snowmelt and excess precipitation into runoff at the basin outlet and includes a snow routine, soil moisture routine, and flow routine. The soil moisture routine uses the probability-distributed model (PDM) developed by [ 22 ] to describe the spatial distribution of water storage capacity across the basin. The cubic law storage model is used to route base discharge from groundwater to the catchment outlet. The Hargreaves method [ 23 ] is used to compute losses due to evapotranspiration, taking into account the status of soil moisture stored in the PDM. The model represents fast and slow response pathways using storage-based representations and calculates the total basin flow by summing the spatially lumped representations of fast and slow response at the outlet. Drainage to the slow flow path is a function of basin moisture storage, and the slow or base flow component of the total runoff is routed through an exponential store. Direct runoff from areas where storage capacity is exceeded is routed through a geomorphologybased distributed unit hydrograph, using a geomorphologic filter based on a threshold drainage area to distinguish hillslopes and channel networks. The routing time for each site in the basin is evaluated by assigning different typical velocity values to each pixel and classifying them as either hillslope or channel flow, with two velocities used to describe the flow routing. As the TOPMELT model operates in conjunction with the ICHYMOD model, the model parameters for TOPMELT were calibrated based on runoff simulations at 16 river gauge stations, each corresponding to a sub-catchment outlet as given in Table 1and MODIS snow-cover data as in [16]. 2.5. ERA5 Bias Adjustment Method To simulate the regional snow dynamics realistically, it is necessary to correct the ERA5 precipitation and temperature for biases. For this, a quantile-quantile mapping (QM) transformation [ 24 ] is used here for precipitation and temperature. The implemented QM scheme was based on the R package qmap [ 25 ]. For a given variable, the cumulative density function (CDF) of ERA5 is first matched with the CDF of the references, generating a correction function depending on the quantile. Then, this correction function is used to unbias the ERA5 variable quantile by quantile. QM was applied separately for each month. To avoid overfitting due to the small sample size of monthly values included in the calibration, the quantile adjustment was computed by considering deciles instead of centiles and applied by linearly interpolating the empirical distribution. For precipitation, a wet-day correction equalizing the fraction of days with precipitation between the observed and the modeled data was applied. The correction was applied to each cell separately. For precipitation, the procedure was calibrated over a calibration period (1992–2005). A validation period (2005–2019) was used to examine the quality of the correction scheme. Examination of the temperature data showed a step change in 2005, confirmed by using the Pettitt test [ 26 ]. Based on this evidence, the QM procedure was applied separately for the two periods, namely, before and after 2005. In the following, three QM-corrected ERA5 inputs are considered: one where only precipitation is corrected (termed precipitation-corrected ERA5, PC-ERA5), another one Climate 2023,11, 154 7 of 14 with only the temperature correction (termed temperature-corrected ERA5, TC-ERA5), and lastly, where both precipitation and temperature are corrected (termed precipitation– temperature-corrected ERA5, PTC-ERA5). Additionally, for the case of temperature, a blind test to evaluate the effectiveness of using bias correction from the calibration period over the whole period is reported. This is termed PTC-cali-ERA5. The results of these comparisons are limited to SWE error calculations for the validation period. 2.6. Reference Precipitation at ERA5 Spatial Resolution To investigate the scale-dependence character of ERA5 errors, mean areal precipitation estimates were generated at the ERA5 spatial resolution using station precipitation data. This input data was referred to as Station Input at ERA5 Resolution (SIER). The Thiessen polygon method was used to redistribute the observed hourly station precipitation data over each ERA5 grid footprint. For temperature, the observed dataset was used without any modifications. The availability of SIER estimates permitted to obtain two sets of comparisons: (i) SIER vs. the reference based on station data to isolate the genuine impact of the aggregation of input data at the ERA5 resolution; and (ii) ERA5 vs. SIER to evaluate the impact of ERA5-only on SWE simulation, therefore disregarding the pure effect of spatial resolution. 2.7. Comparison Statistics The comparison is carried out using the Kling–Gupta efficiency (KGE) [ 27 ] as calculated using Equation (5): KGE =1−q(γ−1)2+(β−1)2+(α−1)2(5) and the mean bias ratio (MBR) as given in Equation (6). β=Estimated Re f erence (6) Here, γ represents the correlation component, represented by Pearson’s correlation coefficient; β is the mean bias ratio, represented by the ratio of estimated and reference means, respectively indicated as Estimated and Re f erence in Equation (6); and α is the variability component, represented by the ratio of the estimated and reference coefficients of variation. KGE ranges from negative infinity to one, where a value of one indicates a perfect match between the two series. The Kling–Gupta efficiency (KGE) is calculated based on all data points except intervals where both data sources are zero. 3. Results Figure 2a,b report the time series of annual mean values of temperature and precipitation, respectively, for the Adige River basin closed at Bronzolo, reporting both the reference and ERA5 values. An overall bias of 1.36 affects the annual ERA5 precipitation totals, resulting from over-prediction of smaller precipitation and under-prediction of larger precipitation events. In contrast, ERA5 temperature data exhibits a non-stationary behavior, with two different cold biases observed for the first and second half of the data. Applying the Pettitt test to detect changes in ERA5 temperature, it showed a change point in 2005, with a bias of − 0.91 ◦ C for the 1991–2005 period and a bias of − 0.29 ◦ C for the 2005–2019 period. Figure 3a,b shows a comparison of uncorrected and QM-corrected ERA5 precipitation for the calibration period. Hourly mean areal precipitation data of the 16 study basins are considered. Figure 3c,d show the same comparison for the validation period. The KGE values of ERA5 precipitation for both periods indicate similar performances, which highlights the robustness of the QM procedure employed in this study. Climate 2023,11, 154 8 of 14 Climate 2023, 11, x FOR PEER REVIEW 8 of 14 (a) (b) Figure 2. Adige at Bronzolo: mean annual (a) temperature and (b) precipitation. Figure 3a,b shows a comparison of uncorrected and QM-corrected ERA5 precipitation for the calibration period. Hourly mean areal precipitation data of the 16 study basins are considered. Figure 3c, d show the same comparison for the validation period. The KGE values of ERA5 precipitation for both periods indicate similar performances, which highlights the robustness of the QM procedure employed in this study. (a) (b) (c) (d) Figure 3. KGE of precipitation: (a) ERA5-calibration, (b) PC-ERA5-calibration, (c) ERA5-validation, (d) PC-ERA5-validation. Figure 2. Adige at Bronzolo: mean annual (a) temperature and (b) precipitation. Climate 2023, 11, x FOR PEER REVIEW 8 of 14 (a) (b) Figure 2. Adige at Bronzolo: mean annual (a) temperature and (b) precipitation. Figure 3a,b shows a comparison of uncorrected and QM-corrected ERA5 precipitation for the calibration period. Hourly mean areal precipitation data of the 16 study basins are considered. Figure 3c, d show the same comparison for the validation period. The KGE values of ERA5 precipitation for both periods indicate similar performances, which highlights the robustness of the QM procedure employed in this study. (a) (b) (c) (d) Figure 3. KGE of precipitation: (a) ERA5-calibration, (b) PC-ERA5-calibration, (c) ERA5-validation, (d) PC-ERA5-validation. Figure 3. KGE of precipitation: ( a ) ERA5-calibration, ( b ) PC-ERA5-calibration, ( c ) ERA5-validation, (d) PC-ERA5-validation. Climate 2023,11, 154 9 of 14 The KGE shows a clear increasing trend with the basin size in all cases, with the smallest basin (Rio Plan at Plan) exhibiting a KGE of less than 0.2 and the largest basin (Adige at Bronzolo) showing a KGE of just over 0.5. The QM technique applied to ERA5 precipitation reduces the bias of the ERA5 precipitation while maintaining the correlation intact. However, the overestimation of the variability of the observations only results in a marginal improvement in the KGE of PC-ERA5. Figure 4a,b report the KGE for SIER precipitation for the calibration and validation period, respectively, as compared with the observation. As expected, the figure shows a clear scale dependence in the errors generated by aggregating the reference precipitation at the ERA5 resolution. For basins larger than 1000 km 2 , the KGE is close to one, whereas it decreases markedly for basins smaller than 1000 km 2 and even more remarkably for basins less than 100 km2, with values around 0.6 for the smallest basin. Climate 2023, 11, x FOR PEER REVIEW 9 of 14 The KGE shows a clear increasing trend with the basin size in all cases, with the smallest basin (Rio Plan at Plan) exhibiting a KGE of less than 0.2 and the largest basin (Adige at Bronzolo) showing a KGE of just over 0.5. The QM technique applied to ERA5 precipitation reduces the bias of the ERA5 precipitation while maintaining the correlation intact. However, the overestimation of the variability of the observations only results in a marginal improvement in the KGE of PC-ERA5. Figure 4a,b report the KGE for SIER precipitation for the calibration and validation period, respectively, as compared with the observation. As expected, the figure shows a clear scale dependence in the errors generated by aggregating the reference precipitation at the ERA5 resolution. For basins larger than 1000 km2, the KGE is close to one, whereas it decreases markedly for basins smaller than 1000 km2 and even more remarkably for basins less than 100 km2, with values around 0.6 for the smallest basin. (a) (b) Figure 4. KGE of SIER precipitation with station: (a) calibration and (b) validation. Figure 5a,b show the SWE simulations for the whole period for Braies and Adige at Bronzolo, respectively, using three different inputs: reference, ERA5, and PTC-ERA5. Braies is selected because it shows the worst performance (KGE = −0.351) for the ERA5 SWE simulation over the entire study period. The Adige at Bronzolo is selected as it represents the whole study basin. (a) Figure 4. KGE of SIER precipitation with station: (a) calibration and (b) validation. Figure 5a,b show the SWE simulations for the whole period for Braies and Adige at Bronzolo, respectively, using three different inputs: reference, ERA5, and PTC-ERA5. Braies is selected because it shows the worst performance (KGE = − 0.351) for the ERA5 SWE simulation over the entire study period. The Adige at Bronzolo is selected as it represents the whole study basin. Climate 2023, 11, x FOR PEER REVIEW 9 of 14 The KGE shows a clear increasing trend with the basin size in all cases, with the smallest basin (Rio Plan at Plan) exhibiting a KGE of less than 0.2 and the largest basin (Adige at Bronzolo) showing a KGE of just over 0.5. The QM technique applied to ERA5 precipitation reduces the bias of the ERA5 precipitation while maintaining the correlation intact. However, the overestimation of the variability of the observations only results in a marginal improvement in the KGE of PC-ERA5. Figure 4a,b report the KGE for SIER precipitation for the calibration and validation period, respectively, as compared with the observation. As expected, the figure shows a clear scale dependence in the errors generated by aggregating the reference precipitation at the ERA5 resolution. For basins larger than 1000 km2, the KGE is close to one, whereas it decreases markedly for basins smaller than 1000 km2 and even more remarkably for basins less than 100 km2, with values around 0.6 for the smallest basin. (a) (b) Figure 4. KGE of SIER precipitation with station: (a) calibration and (b) validation. Figure 5a,b show the SWE simulations for the whole period for Braies and Adige at Bronzolo, respectively, using three different inputs: reference, ERA5, and PTC-ERA5. Braies is selected because it shows the worst performance (KGE = −0.351) for the ERA5 SWE simulation over the entire study period. The Adige at Bronzolo is selected as it represents the whole study basin. (a) Figure 5. Cont.