The study region comprises Austria and adjacent headwater catchments, as depicted in Fig. a. Approximately 60 % of Austria's national territory is covered by the Alps, a region that is particularly sensitive to climate change . Austria's geography and climate are therefore strongly shaped by its complex orography, with the Alps covering the west and south and the comparatively drier and flatter alpine forelands and lowlands in the north and east. Due to its central European location, the Austrian climate is influenced by both the Atlantic and the Mediterranean, while also exhibiting continental climatic influences .

In addition to modeling the whole of Austria, two high-alpine study regions were selected to validate the precipitation correction at high elevations: the reservoir catchments of Kölnbrein (50 km²; Fig. b) and Schlegeis (110 km²; Fig. c). Both are partially glaciated (11 % for Kölnbrein and 22 % for Schlegeis in 2003 ) and have similar mean elevations (2430 m for Kölnbrein and 2540 m for Schlegeis). Despite these similarities, the two regions are subject to different atmospheric conditions: Schlegeis is located north of the Alpine main ridge and is predominantly influenced by the Atlantic, whereas Kölnbrein lies south of the Alpine main ridge and is more strongly affected by Mediterranean conditions .

This study utilized 10 min measurements of temperature, wind speed, and precipitation from semi-automated weather stations, provided by GeoSphere Austria, Austria's federal institute for geology, geophysics, climatology, and meteorology . All meteorological variables required in this study are recorded automatically, while some (unused) parametrizations like cloud type, as well as downstream quality control are performed by experts. Precipitation is predominantly measured using tipping-bucket gauges, although the number of weighing gauges has increased in recent years . To ensure data quality, stations were required to provide at least ten years of measurement records for every month and to exhibit plausible average precipitation values. Stations were not required to cover a common overlapping period, which reduces the influence of decadal variability on the derived correction factors; the full period from which station data were drawn is 1995–2024. The stations are densely distributed across Austria, as shown in Fig. a. Austria's two highest stations, located at elevations of 2864 and 3109 m, were excluded from the station ensemble since they would otherwise place disproportionate weight on elevation bands with low station density. This process resulted in a final set of 261 stations, with the highest remaining station at 2327 m and the majority of stations being located below 1500 m (see Fig.  for the elevation distribution). As the catch efficiency transfer function utilized in this study was derived using 30 min measurements, the 10 min data were aggregated to 30 min temporal means for wind speed and temperature and 30 min sums for precipitation.

Temperature and precipitation data were assembled from multiple pre-existing gridded climate products, prepared by , as described in more detail below. For Austria and the Swiss Engadin, the GeoSphere Austria SPARTACUS dataset was used . SPARTACUS provides daily meteorological information intended for climatological applications. The station observations incorporated in this data set originate from long-term, homogenized weather stations in and around Austria, including totalizers in some high-alpine regions to reduce measurement errors . Consequently, the stations used in this study for undercatch correction only partly overlap with those included in the gridded data set. For the neighboring regions of the Bavarian Danube and Czech CHELSA and WorldClim 2 were used. We smoothed the transitions between the data sets using a 10 km feather-blending zone. The resulting data set consists of daily values for the period 1961–2023 with a spatial resolution of 1 km. The geographical predictors used in GAM training were derived from the same topographic data used in the SPARTACUS product. After applying the undercatch correction in this study, both the raw and corrected precipitation data were patch-interpolated to the study regions, which is an artifact-reducing, smoother, higher-order regridding method compared to bilinear interpolation. For the two study regions Kölnbrein and Schlegeis, additional meteorological variables at 250 m spatial resolution – originating from different data sets – were required to run the snowpack model Alpine3D . Global radiation data was obtained from the GeoSphere Austria APOLIS product and is crucial for accurately representing snow hydrological processes . Relative humidity was derived from downscaled SPARTACUS temperature and a station-based dew-point interpolation . Wind speed was estimated using a station-based Ridge regression . Potential evapotranspiration was calculated using the Penman-Monteith equation . Because wind directions are not realistic at 250 m resolution in complex terrain, dummy wind directions were calculated in this study. These consist of average hourly wind directions for precipitation and non-precipitation days, respectively, derived from the INCA dataset . Further, all six meteorological variables – along with the patch-interpolated precipitation – were temporally disaggregated to hourly time steps within the two high-alpine study regions. Temporal disaggregation followed methods from and statistical approaches that relate daily means to hourly patterns from the ERA5 or INCA dataset , as documented in .

The catch efficiency CE transfer function used in this study is defined as 1CE=e-aU(1-tan⁡-1(bT)+c), with the constants a=0.0623, b=0.776 and c=0.431. U denotes the 10 m-wind-speed in ms-1, capped at a maximum threshold of Uthreshold=9ms-1 and T denotes the air temperature in °C . This transfer function was developed for unshielded weighing gauges using wind speed measurements at 10 m mast height. Although tipping buckets are still the predominant gauge type in the GeoSphere Austria network, weighing gauges have been increasingly installed since the early 2000s . A similar transfer function for tipping buckets was proposed by ; however, we use the weighing-gauge formulation for our high-alpine application. This choice is motivated by the absence of an explicit temperature term in the tipping-bucket function and by its comparatively strong wind-speed correction, including corrections of around 30 % for T<2 °C and U=0ms-1, which would have been difficult to implement in high-alpine regions as wind speeds are typically considerably higher at peaks . Figure  shows the CE as a function of wind speed for different temperatures. It highlights that CE exhibits an approximately linear behavior at temperatures above the freezing point, while temperatures below freezing lead to increasingly non-linear behavior . Under pronounced cold and windy conditions, CE can drop to as low as 20 %. The corrected precipitation is calculated as 2prcorr=prCE, and subsequently aggregated to monthly values. Monthly correction factors are then obtained by relating prcorr to the uncorrected precipitation pr, resulting in one climatological correction factor per station and month. While this aggregation leads to some loss of information and may oversimplify individual events, it does not introduce a systematic bias for climatological time frames, which are the focus of this study (see Fig. S1 in the Supplement) and is easily transferable for future studies. These station-based factors subsequently served as target variables in the GAM training.

A comprehensive overview of Generalized Additive Models (GAMs) can be found in ; with the key elements briefly recited here. A GAM is a generalized linear model that predicts the response variable y as a sum of smooth functions of predictor variables xp, constructed using N splines of the form 3f(x)=Φ∑p=1Nϕp(xp), with a monotonic function Φ. Under the assumption that the response variable follows a distribution from the exponential family E (e.g. normal or Poisson), it is linked to the smooth functions with a link function g as 4g(E(y))=θ0+f1(x1)+f2(x2)+…+fm(xm), where θ0 is the intercept and fi are the smooth functions of the m predictors xi. The smooth functions are then fitted so that a measurement of error (e.g. the Akaike information criterion (AIC) or the R2 value) is minimized. To control model complexity and prevent over-fitting, an additional smoothness parameter λ is introduced, which penalizes smooth functions with high curvature (“wiggliness”). GAMs were chosen over potentially higher-performing machine learning techniques (e.g., random forests) because they allow for better and more direct physical understanding of the underlying process. Although constraining the maximum number of splines N and minimum smoothness parameter λ may reduce predictive power, the resulting smoother curves with low curvature further improved interpretability.

In this study, the response variable y – the station-based monthly undercatch factors – were approximately normally distributed after subtracting 1 and applying a logarithmic link function g=log⁡. The predictor selection was based on concurvity analysis , utilizing a HSIC-Lasso algorithm , and an untuned random forest model . The complete pool of possible geographical predictors is given in Sect. S2 in the Supplement. Both the HSIC-Lasso algorithm and the random forest model indicated high correlation between the geographical predictors, allowing the number of predictors to be significantly reduced.

The following three predictors xi were identified as the most influential:

terrain elevation, serving as a proxy for temperature, wind speed and precipitation amount,

For each month, the optimal GAM configuration was determined by performing a hyperparameter grid search over the number of splines N and the smoothing parameter λ, evaluated using a Leave-One-Out Cross-Validation (LOOCV) across the 261 stations. Model performance was assessed using the mean R2 value, with stations above and below 1200 m elevation given equal total weight to improve performance in higher elevations. The model configuration with the highest weighted R2 value was selected for each month and subsequently applied to the gridded geographical predictors. Predictor values were capped at the minimum and maximum values observed in the training data to avoid extrapolation beyond the calibrated range.

To mitigate the known uncertainties of undercatch transfer functions in complex terrain , undercatch corrected precipitation in alpine regions was evaluated iteratively using catchment-scale hydrological observations for validation. Initial iterations revealed that, even with suitable GAM training scores, undercatch was substantially overestimated in high-alpine terrain and at exposed peaks. To address this, the maximum GAM-predicted monthly undercatch factor was capped at the maximum observed monthly station factor. Further, an exposed terrain penalty of the form 5ETP=1-α⋅EX51,>0max⁡(EX51,>0), was introduced. EX51,>0 denotes the normalized, non-negative exposure derived from a 51 km smoothed topography. The penalty reduces prcorr in mountainous regions, with a lower bound equal to the uncorrected precipitation pr. The penalty strength α=2/3 was iteratively determined using hydrological modeling. The ETP aims to (1) reduce the overestimation of the undercatch magnitude in high-alpine terrain , (2) account for the use of gauge totalizators in the gridded precipitation data set , which generally exhibit lower measurement errors, and (3) accounts for potential plateauing of precipitation lapse rates near high ridges, where flow blocking and moisture depletion can reduce orographic enhancement . Figure  displays the resulting ETP, showing the strongest reductions along the Alpine main ridge and for isolated high-elevation peaks.

Two models were used to validate the undercatch corrected precipitation data: the conceptual, semi-distributed rainfall-runoff model COSERO and the physically-based, spatially distributed snowpack model Alpine3D .

COSERO was used to validate the overall water balance in both the case study regions and across Austria. It is a HBV-style model that has been widely applied in hydrological and climate change impact studies across a range of spatial scales . All major runoff processes – including snow and glacier melt, evapotranspiration, and runoff routing – are simulated at the subcatchment scale, at an hourly resolution in the case study regions and a daily resolution for the whole of Austria. A schematic overview of the model structure is shown in Fig. . For the case-study basins, COSERO was set up with a spatial resolution of 100 m in glaciated areas and 250 m resolution in the remaining area. The Austrian-wide model was spatially discretized on a 1 km grid. The COSERO model domain includes some outlying headwater catchments, such as the Upper Inn in Switzerland (see Fig. ). Due to computational constraints, the Upper Danube, Morava, and Inn in Germany were not modeled explicitly. Instead, observed runoff at the corresponding gauging stations was added to the model to close the water balance (see Qaddinflow in Fig. ). Model calibration was performed against observed runoff using the Shuffled Complex Evolution algorithm and the logarithmic Nash-Sutcliffe Efficiency as the objective function. All basins were calibrated simultaneously to ensure seamless and spatially consistent parameter fields, with equal weighting in the objective function. Details on the initial parameter field for Austria can be found in . The case study basins used the same initial information, except for a finer digital elevation model (DEM) with a 10 m resolution . Calibration periods were 2015–2022 for the Kölnbrein catchment, 2012–2022 for the Schlegeis catchment, and 2001–2020 for the Austrian-wide model. The Austrian-wide model was independently validated for the period 1980–2000. For the two high-alpine case study regions, the full available observed runoff time series was used for calibration; therefore, no separate validation period was defined. In the Austrian-wide model, only a subset of catchments with low to medium anthropogenic influence (see , for definition) was included in the model calibration. An overview of all catchments, the calibration subset, added fluxes, gauging station information, and initial parameter fields can be found for the Austrian-wide model in . Freely available discharge data from the Austrian Federal Ministry of Agriculture and Forestry, Climate- and Environmental Protection, Regions and Water Management , as well as time series from the LamaH dataset , were used for model calibration in Austria. Reservoir inflow data for the Kölnbrein and Schlegeis catchments were provided by the Verbund Energy4Business GmbH.

Alpine3D was used to indirectly validate solid precipitation amounts in the two high-alpine case study regions by (1) comparing the modeled snow depth to satellite observations, (2) comparing the snow covered area (SCA) to satellite observations, and (3) evaluating glacier volume changes against data from . The model setup required hourly meteorological input data for precipitation, air temperature, relative air humidity, incoming solar radiation, wind speed and wind direction following the settings presented in . The same DEM and land cover information as in the COSERO setup were used. Glacier grid cells were initialized using glacier area and height maps from the Randolph Glacier Inventory (RGI) 2003 . Alpine3D was run at an hourly resolution, with a spatial resolution of 100 m for the smaller Kölnbrein catchment and 250 m for the larger Schlegeis catchment. Snowfall redistribution in Alpine3D was based on snow depth patterns derived from a WorldView-2 stereo satellite image. This map was provided by the VERBUND Energy4Business GmbH and was generated by subtracting the snow-on DEM stereo-satellite image, taken on 10 May 2021, from a snow-free airborne LiDAR DEM (taken in September 2020). The glaciated areas were omitted in the snow depth map to avoid potential offsets in snow depth due to glacier melt between autumn 2020 and spring 2021. Previous studies have shown that snow distribution patterns are generally consistent between years and can therefore be inferred from a single satellite image taken close to the timing of peak snow water equivalent . To evaluate the SCA exemplarily during the snow melt period of 2021 in the Kölnbrein catchment, Sentinel-2-derived SCA were used for all cloud-free observations (cloud cover <5 %) between May and July. Finally, modeled glacier volume changes were compared to global estimates of glacier volume change between 2000 and 2019 derived from satellite observations , providing an additional, indirect constraint on simulated solid precipitation amounts.

Figure a shows the monthly undercatch factors derived for wind, temperature, and precipitation station data as a function of station elevation, revealing a pronounced seasonal dependence of precipitation undercatch. The highest undercatch factors occur in winter, with a maximum in January, as shown spatially in Fig. b. Between May and September, all undercatch factors remain below 2.0, with minima in July and August, when factors are generally close to 1. While not all high-elevation stations show strong undercatch – indicated by the color-coding of the data points – all undercatch factors exceeding 2.5 are associated with stations with an elevation above 1300 m. These undercatch factors, along with associated station meta data, are publicly available .

The undercatch factors in Fig. a increase with elevation as expected, reflecting the typical increase in wind speed and decrease in temperature with elevation, as well as the increased fraction of solid precipitation during winter months. As elevation is the dominant influence, temperature appears to be the main driver of undercatch. Further, as Fig. b suggests, no clear spatial structure is apparent in the undercatch factor distribution besides the tendency of increasing undercatch towards Austria's west, where highly-elevated stations are located.

Despite extensive quality control of the 261 stations, residual uncertainty is expected at high-alpine sites. This uncertainty could arise from local installation constraints, where precipitation gauges and wind sensors are not always co-located. Nevertheless, the station-based undercatch analysis yields physically plausible results, justifying the use of the derived undercatch factors as target variables for GAM training.

The results of the monthly GAM hyperparameter grid search with LOOCV, with an emphasis on interpretability over maximum predictive performance, are summarized in Table . The first column shows the month corresponding to the undercatch factors used for the GAM training. The second column shows the weighted R2 value of the LOOCV, where stations above and below 1200 m were assigned equal total weight. The average R2 value across all months is 0.826, with the lowest performance in January (0.769) and the highest in May (0.904). The third and fourth columns show the selected hyperparameters, namely the smoothing parameter λ and the number of splines N. The models tend to select either high λ combined with small N, resulting in very smooth response functions, or the opposite configuration, allowing increased curvature. This behavior is also visible in Fig. . Overall, the winter half-year tends to have smoother curves, which indicates more explainable behavior in colder conditions. A comparison of the maximum predicted factors (ypred,max; fifth column) and the true maximum station-based factors (ytrue,max; last column) indicates a tendency towards overestimation during the winter half-year and slight underestimations during summer. Since the application of GAM-derived factors on the gridded data set is capped at ytrue,max, the overestimation in winter has a limited impact on the final gridded results. Higher uncertainty at highly exposed stations can also be seen in the individual GAM plots provided in Sect. S4. Figure  presents all twelve smooth functions from the individually trained GAMs. The curves show the exponentially back-transformed relationships between the undercatch factors and the individual predictors, with the undercatch factor calculated as the product of the individual spline values. Terrain elevation (Fig. a) emerges as the dominant predictor, with contributions that can exceed those of the two exposure metrics (Fig. b, c) by up to one order of magnitude, particularly in summer at higher elevations. Although this may appear counterintuitive, the pronounced seasonal dependence of the intercept factor in Fig. d is key to understanding this behavior. The large summer values in panel (a) are multiplied with intercept factors close to zero in panel (d). Thus, the steep slopes of the elevation functions are required to accurately represent the onset of snowlines, while still predicting undercatch factors at the highest peaks. Since undercatch is generally more pronounced in winter, this behavior is not suggested by the GAMs during the winter months, when the smooth function contributions are multiplied by a larger intercept factor. The exposure predictors (Fig. b, c) tend to capture finer-scale behavior and are characterized by stronger curvature. In Fig. b, the particularly strong response in March (purple) is notable and is likely attributable to concurvity among the predictors: the simultaneous decrease of both 51 km exposure and elevation contributions in that month is compensated by a strong increase in the 5 km exposure smooth function. We therefore interpret this feature as a model artifact. In Fig. c, a clear seasonal distinction is visible: winter months show increasing undercatch with positive exposure values, whereas this response saturates or even reverses in summer, when the steep elevation smooth functions dominate the correlation at high elevations.

Figure  shows the relative monthly GAM error, averaged over all months for each station. The error generally increases with elevation (with a Pearson correlation coefficient of 0.61), following undercatch transfer-function uncertainty inferred from colder temperatures and higher wind speeds . The relative error for the 18 stations above 1500 m averages to 0.15 as compared to the average error of 0.02 for the stations below this elevation. The highest relative errors tend to occur at stations with positive exposure values, as indicated by the colorbar, which is also visible in the individual GAM smooth functions in Sect. S4.

The twelve trained GAMs show robust performance with small relative errors at low-elevation/low-exposure stations, but increasingly struggle to predict undercatch factors at highly-elevated and exposed stations. This confirms the conclusions drawn in that the applied transfer function is prone to uncertainty at highly-elevated, exposed stations with complex wind fields. While the GAMs achieve suitable weighted R2 values of approximately 0.8, they tend to overestimate undercatch at these stations (Table ), resulting in unrealistically high precipitation amounts in exposed, high-alpine terrain. Figure  and S3 further illustrate that capping the GAM-predicted undercatch factors at the observed station factors (both shown in Table ) is a crucial step to prevent excessive extrapolation at high elevations. This is particularly important given the sparse station network at high elevations where the GAMs must extrapolate beyond well-constrained training data.

The feature selection highlighted terrain elevation and geographical exposure (based on a 5 and 51 km smoothed topography) as dominant predictors. Although exposure exhibits concurvity with elevation at high altitudes, it primarily captures small-scale variability, resulting in smooth functions with higher curvature (Fig. ). Terrain elevation emerges as the primary descriptor of undercatch, exhibiting a near-exponential relationship with undercatch factors (Figs.  and S3). In contrast, neither exposure predictor shows a simple monotonic relationship with undercatch. The absence of spatial predictors such as latitude, longitude, or distance to the Alpine main ridge suggests that horizontal proximity alone is insufficient for representing undercatch variability. This suggests that methodologies like ordinary Kriging are impractical to extrapolate undercatch errors.

We conclude that the GAMs produce physically plausible smooth functions that realistically capture the seasonal and elevation-dependent structure of precipitation undercatch, supporting the application of the derived factors to gridded precipitation data. While some model artifacts attributable to predictor concurvity remain, the overall form of the smooth functions, their seasonal variation, and the dominant dependence on terrain elevation are consistent with findings from previous studies . Importantly, unlike these studies – which derived elevation-dependent corrections from additional in situ or satellite snow depth observations or from rainfall–runoff modeling – our approach relies solely on correcting existing meteorological station data, yet arrives at similar conclusions. Our methodology extends previous work in two key aspects: first, by replacing stepwise linear or exponential fits with more flexible smooth functions that better capture nonlinear relationships; and second, by providing a more detailed representation of seasonal variability through monthly correction functions, rather than a simple separation into summer and winter conditions .

Figure  shows the precipitation climatologies for 1991–2020 without undercatch correction (Fig. a) and with (Fig. b) undercatch correction, their absolute difference (Fig. c), all in mm yr⁻¹, and their ratio (Fig. d). Undercatch correction leads to a domain-wide increase in precipitation, with a mean increase of 110.5 mm yr⁻¹ across the full domain. The largest absolute increases occur in the alpine regions of western Austria, where precipitation increases locally exceed 1500 mm yr⁻¹, corresponding to a correction factor of 1.9. The maximum undercatch corrected annual precipitation exceeds 4000 mm yr⁻¹, representing an increase of approximately 47 % compared to the uncorrected maximum of 2726.9 mm yr⁻¹.

Figure  shows the local precipitation lapse rates of the undercatch corrected precipitation climatology on a 9 km × 9 km basis in % per 100 m elevation gain. These lapse rates serve as a plausibility check of the corrected precipitation fields. Grid cells shown in white were masked because the local elevation range was insufficient for a meaningful calculation (less than 500 m), or because fewer than half of the 81 grid cells within the window contained valid data. At the highest elevations, lapse rates plateau and locally decrease (yellow colors), which is a direct consequence of the exposed terrain penalty. The mean precipitation increase across Austrian stations is approximately 33 mm per 100 m, corresponding to around 3 % per 100 m when normalized by the mean precipitation of our study domain (Fig. a). This is slightly lower than the mean lapse rate of 4.0 % per 100 m shown in Fig. , but remains within a plausible range when taking into account the strong corrections in the alpine regions. Since precipitation lapse rates are spatially diverse and vary across the Alpine region due to slope and shielding effects modifying the precipitation-elevation relationship , individual grid cells are difficult to verify directly. Enhanced lapse rates in regions of strong orographic lifting north of the Alpine main ridge, including the area where the maximum value occurs, appear plausible. However, the high values found in the comparatively dry deep valleys of western Austria, ranging between 7 % and 10 % per 100 m, may indicate local overestimation. This interpretation is supported by comparing these values with the lapse rates between the stations Innsbruck Flughafen and Patscherkofel (see Fig. S1), which are located in close proximity to each other at a valley floor and a mountain crest. Based on transfer-function undercatch-corrected mean annual precipitation, this station pair yields an average annual lapse rate of 4.1 % per 100 m, considerably lower than the highest local values in the gridded field.

The monthly climatologies, averaged for the full domain and the study regions (see Fig. ), are shown in Fig. a. Undercatch corrected precipitation is displayed as solid lines, while uncorrected data is shown as dashed lines. Figure b shows the fraction of corrected and uncorrected monthly precipitation. The strongest relative increase occurs during the winter months. Both high-alpine study regions exhibit a similar annual precipitation increase of approximately 29 %, reflecting their comparable elevation distributions, while the domain-wide mean increase amounts to 10.6 %. A pronounced peak is visible in November in the case study climatology, even though the correction factor of approximately 1.6 is similar to the December value. This peak is caused by individual strong months in the precipitation climatology, especially November 2019 with values of 520 mm per month (280 mm per month) in Kölnbrein (Schlegeis), compared to the climatological average of 139 mm per month (106 mm per month). The summer months are only marginally corrected in all cases. Most notably, the correction substantially alters the seasonal structure of precipitation in the two high-alpine study regions. While the uncorrected data exhibits a clear summer precipitation peak in both regions, which is generally in line with findings in alpine regions , the corrected data shows a comparable or higher precipitation peak in winter, with spring and autumn receiving the least precipitation. Analogous seasonality shifts driven by severe undercatch have been reported at wind-prone sites in the Rocky Mountains , and high-alpine hydrological studies in the Alps have reached similar conclusions . However, a reversal of the dominant summer precipitation peak in Alpine catchments represents a novel finding of this study, making the plausibility of the corrected winter precipitation a central focus of the hydrological validation in the following section.

After initial hydrological validations showed an overestimation of runoff and snow depth likely caused by a too high precipitation correction, an exposed terrain penalty (ETP) is introduced to reduce the precipitation in exposed orography (Fig. ). The application of the GAM-derived factors and the ETP produces the undercatch corrected precipitation climatologies in Fig. . The ETP addresses multiple uncertainties at once: it reduces the potential over-correction of the undercatch transfer function and mitigates the influence of totalizers in the base precipitation data, which dominate interpolation results in high-alpine terrain but generally exhibit lower precipitation measurement errors . The precipitation lapse rates (Fig. ) consequently show the steepest increase starting at slopes close to valley floors and plateau at the highest peaks, mimicking potential flow blocking and moisture depletion . However, this indicates that some processes in high-alpine, wind-exposed terrain are not fully captured by the transfer function, either because the proposed relationship for the change in catch efficiency is modified by the complex, turbulence-inducing terrain, or the wind speed measurement is not representative of the conditions at the gauge orifice. We therefore conclude that the undercatch correction carries the greatest uncertainty at the highest peaks and that further research specifically targeting precipitation undercatch processes in complex terrain is needed.

In the following section, the hydrological validation of the undercatch corrected precipitation across different processes and spatial scales is presented. We first evaluate the high-alpine case study regions, where the undercatch errors are expected to be more pronounced and the discrepancies between observed and simulated water balance components (reservoir inflow, snow pack accumulation, glacier mass changes) are especially high. Then the Austrian wide COSERO results will be examined with a focus on runoff quantities.

Figure  shows the COSERO simulation results for the two high-alpine reservoir basins Kölnbrein (Fig. a, period 2015–2022) and Schlegeis (Fig. b, period 2012–2022) as long-term cumulative water balances. The individual components are displayed for simulations using uncorrected (dashed) and undercatch corrected (solid) precipitation input and compared against the observed reservoir inflow (black solid line). Both study regions show substantial improvements in closing the water balance when using the undercatch corrected precipitation. The runoff deficits of 24 % in Kölnbrein (2082 mm yr⁻¹ observed runoff) and 20 % in Schlegeis (1926 mm yr⁻¹ observed runoff) are reduced to less than 1 % for both study regions (2102 mm yr⁻¹ simulated for Kölnbrein and 1988 mm yr⁻¹ simulated for Schlegeis), while glacier melt and evapotranspiration are not altered considerably and remain within realistic magnitudes. Runoff is only displayed for days with valid runoff records, since the observed timeseries contain missing values. The total simulated runoff is slightly higher (2121 mm yr⁻¹ for Kölnbrein and 2189 mm yr⁻¹ for Schlegeis). The average monthly water balance components are provided in Sect. S5 and highlight the improved runoff simulation in the summer months.

Next, we present the validation of snowpack and glacier mass balance modeling with Alpine3D in the two high-alpine case study areas. Figure  compares snow depth on 10 May 2021 derived from the WorldView-2 stereo satellite (Fig. c) with the simulated snow depth by Alpine3D using uncorrected (Fig. a) and undercatch corrected (Fig. b) input data. Figure d displays the snow depth distribution of individual grid cells as boxplots. The modeled snow depth on 10 May 2021 is severely underestimated when using uncorrected precipitation data, with a median (mean) bias of -0.87 m (-0.78 m). The use of corrected precipitation data leads to a lower, positive bias of 0.15 m (0.30 m). While the median (mean) simulated and observed snow depths are similar, the range of simulated values (Fig. d) shows a larger spread and includes higher values. However, the overall pattern is captured well with a clear elevation-dependent distribution of snow depths, particularly for the undercatch corrected variant.

Additionally, the SCA in the Kölnbrein catchment is analyzed during the melting period at different timestamps in 2021. The percentage of SCA based on Sentinel-2 images is compared to the Alpine3D simulations with corrected and uncorrected precipitation input data, as visible in Fig. . The SCA of the uncorrected (red) simulation consistently underestimates the SCA observed by Sentinel-2 (black), indicating a too early melt out, i.e. an underestimation of snow amounts. While the undercatch corrected (blue) simulation is closer to the observation throughout all dates, it slightly overestimated the satellite SCA, indicating a too late melt-out in some grid cells, i.e. an overestimation of snow amounts. However, this temporal SCA analysis shows that applying the undercatch corrected precipitation data for the snowpack simulation overall leads to more realistic snow accumulation and melting behavior in 2021. A spatial representation of snow-cover at all four dates, as well as detailed performance metrics, are given in Sect. S6.

These validations show that the uncorrected precipitation product leads to insufficient snow amounts in the Kölnbrein catchment, as shown exemplarily for 2021 by the underestimation of snow height on 10 May and underestimated SCAs during the melting period. Hence, by undercatch correcting the precipitation (especially in winter months), the simulation of snow melt timing is improved, which in turn leads to an improved fit between simulated and observed runoff (see Sect. S5). The amount of snow and the timing of snow melt subsequently affect the glacier mass balance by determining the date when bare ice first appears and starts to melt. Figure  shows the glacier volume change of all glaciers with a surface area greater than 1 km² located in the more heavily glaciated Schlegeis study region for the period 2000–2023 (for details on the selected glaciers see Sect. S7). The Alpine3D simulations are compared to the average volume change (black line) of the same glaciers between 2000 and 2019 derived by , which amounts to a loss of -0.21 km³ (or -0.011 km³ yr⁻¹). The undercatch corrected data (blue line) shows good agreement with the reference data, while the uncorrected precipitation data (red line) leads to too high volume loss. This indicates that an insufficient amount of solid precipitation is covering the glaciers, resulting in a too early onset of ice melt.

After examining the effects of using the undercatch corrected precipitation data in the case study regions, the product is examined across Austria. Figure  shows the calibration results of the COSERO simulations across Austria. Displayed is the bias 6β=Q‾simQ‾obs, which is the fraction of the long-term simulated and observed mean runoff in the calibration period. The two upper panels display β for simulations using uncorrected (Fig. a) and undercatch corrected (Fig. b) precipitation input. The uncorrected simulation shows distinct spatial heterogeneities, with the expected runoff underestimation in catchments along the Alpine main ridge. An overestimation can be seen in low-lying catchments in the south, east and north-east. After applying the undercatch correction (Fig. b), especially the catchments along the Alpine main ridge are improved, indicated by β≈1, while catchments that already show values of β>1 for uncorrected precipitation naturally show similar biases when applying the undercatch correction. The water balance in these catchments is characterized by high evapotranspiration rates and low precipitation amounts, leading to low annual runoff sums of only a few 100 mm per year or even less. This means that already slight deviations from the observed values lead to poor goodness-of-fit measures, and in this case an overestimation in β. This can also be seen in Fig. c, where β is displayed across different elevation bands. The catchments in elevations below 1000 m show median β values above 1 both before and after the correction, and show the overall highest β outliers with values above 4. On the other hand, a significant improvement can be seen for the 39 catchments above 2000 m, where β values are notably below 1 before the correction. Median β values in catchments between 1500 and 2000 m increase from slightly below 1 to slightly above 1. For the entire modeling domain, the median β improves from 1.13 to 1.09 when using the undercatch corrected precipitation input. At first glance, this may appear counterintuitive, as increasing precipitation inputs would be expected to increase simulated runoff and thus β. This behavior stems from the simultaneous calibration approach: when optimizing a single objective function (runoff) across the spatially heterogeneous domain with uncorrected inputs, the algorithm compensates for precipitation deficits in alpine catchments by reducing evapotranspiration rates. While this compensation improves fit in alpine regions, it also exacerbates runoff overestimation in low-lying basins where precipitation deficits are less pronounced. The undercatch correction eliminates this artificial compensation mechanism, yielding more physically consistent water balance estimates and parameter sets across the elevation bands.

Similar figures for two other measures of goodness-of-fit, the Kling–Gupta Efficiency and the Nash–Sutcliffe Efficiency , can be found in Sect. S8. Both metrics show not only improved median performance (NSE: from 0.50 to 0.54, KGE: from 0.55 to 0.62), but also substantial reduction in the lower tail of the performance distribution, indicating fewer poorly performing catchments. Precipitation and evapotranspiration per elevation band for both model runs are provided in Sect. S9. The undercatch correction increases precipitation inputs in all elevation bands above 1000 m, while precipitation below 1000 m remains largely unchanged. Correspondingly, actual evapotranspiration increases across all elevation zones when using corrected precipitation, reflecting the elimination of artificial ET suppression that previously compensated for input deficits during calibration.

The Austrian-wide COSERO model was independently validated for the period 1980–2000. Using undercatch-corrected precipitation results in slightly improved median performance, with β values of 1.08 (uncorrected) and 1.07 (corrected), NSE values of 0.52 and 0.54, and KGE values of 0.60 and 0.65, respectively. Elevation-dependent validation metrics are provided in Sect. S10. Consistent with the calibration results, improvements are most pronounced in high-elevation catchments, where NSE and KGE distributions shift towards higher values and fewer poorly performing basins are observed.

Overall, the hydrological validation across Austria (Fig. ) shows an improvement in model biases in alpine catchments when using the undercatch corrected precipitation input. This is demonstrated in the two case study regions by (1) closing the long-term water balance (Fig. ), (2) improving severe negative mean and median biases in snow depth modeling (Fig. ), (3) improved representation of snow melt out behavior (Fig. ), and (4) more realistic glacier volume changes (Fig. ). The Austrian-wide COSERO simulations show the same elevation-dependent results, with the undercatch correction leading to improved simulation in catchments above 2000 m (Fig. ). Poor model performance is evident in both the uncorrected and corrected runs for lower-elevation catchments in the south, east, and north-east. This issue could be attributed to: (1) inaccurate precipitation in the base data set , (2) shortcomings in the hydrological model and/or its calibration, or (3) shortcomings in the observed runoff data. We assume that the uncertainties related to (3) are on average low, since the data is quality controlled. Therefore, the observed runoff data likely provides reliable information on catchment processes and can be used to diagnose the remaining potential sources of error, namely the model structure/calibration (2) or the precipitation input (1). Runoff overestimation occurs in two distinct regions. First, in southern Austria along the Gail and Drau (Drava) rivers and their tributaries, which exhibit pluvial-nival regimes with spring maxima (April) and secondary winter peaks (November). This spatial bias cannot be attributed to regime type alone, as the model performs well for catchments with similar regimes in the northern Alpine foothills (e.g., Danube tributaries Ybbs, Erlauf, and Pielach). The overestimation in the south likely reflects either regional biases in the base gridded precipitation dataset , unresolved spatial processes during GAM training, or distinct weather regimes affecting northern versus southern Austria . Signed distance to the Alpine main ridge was not selected as a predictor during model development, which suggests that the north-south differences may stem from atmospheric processes that cannot be adequately represented by topographic variables alone. The second region with systematic runoff overestimation covers the eastern and northeastern catchments along the Raab and Thaya rivers and their tributaries. These lowland areas exhibit pluvial regimes with a single runoff peak in early spring (March), low annual runoff totals, high air temperatures, and consequently high evapotranspiration rates. The poor model performance in these catchments likely stems from multiple compounding factors: (i) the simultaneous domain-wide calibration strategy inadequately captures the distinct hydrological behavior of these low-gradient systems, particularly their flashy response characteristics and actual evapotranspiration; and (ii) observational uncertainty is highest in these catchments due to measurement challenges at low flow volumes, potentially providing unreliable calibration targets. Runoff underestimation is evident in basins located in the central regions of Austria, north of the Alpine main ridge. This is plausible given that these are karstic regions where orographic catchment boundaries do not necessarily coincide with hydrological catchment boundaries, and underground flow paths may be neglected in the model. Additionally, natural or anthropogenic diversions may not be adequately represented in the model structure despite careful consideration, potentially causing discrepancies between observed and modeled runoff.

Two further sources of overall uncertainty merit discussion. First, actual evapotranspiration (ETA) is difficult to validate due to the scarcity of measurements, particularly at the regional scale. COSERO estimates potential evapotranspiration (ETP) using the Thornthwaite method and calculates actual evapotranspiration from interception and soil storage, as well as snow sublimation. In the calibration process, ETA is not constrained, meaning it may be adjusted to close the water balance and improve the objective function, potentially resulting in implausible values. While we verified that spatial patterns and approximate quantities fall within a plausible range, uncertainties remain. Future research could address this by constraining ETA using satellite-derived products such as the Global Land Evaporation Amsterdam Model (GLEAM, ,). Second, the strong topographic and hydrological heterogeneities across Austria likely prevent a simultaneous, all-in-one calibration routine from identifying optimal parameters for every region, potentially leading to poor performance in some catchments. Using an optimization routine that relates model parameters to landscape properties, thereby retaining physical process realism (e.g. ), could be a topic for further research.

Overall, the proposed methodology for generating undercatch-corrected gridded precipitation performs well across Austria. Nevertheless, several limitations remain and should be considered when interpreting the results:

The undercatch transfer function from showed reduced accuracy in precipitation measurement at the only high-alpine calibration station in their study. This indicates limited applicability of the catch efficiency function in Austria's high-alpine complex orography. This necessitated the introduction of the exposed terrain penalty in our study and highlights the need for further research to better understand processes influencing precipitation undercatch in high-alpine terrain.