We used the same observed runoff dataset as in , sourced from the CAMELS-CH database (Catchment Attributes and Meteorology for Large-sample Studies – Switzerland) . Runoff observations are provided at daily resolution by hydrological gauging stations installed at the outlets of Swiss catchments. Most stations are operated by the Swiss Federal Office for the Environment , with additional contributions from cantonal agencies in Aargau, Baselland, Bern, St. Gallen, and Zurich. The full dataset comprises 267 gauging stations and spans the period 1961–2024. For model training, we selected a subset of 96 catchments with minimal anthropogenic influence (e.g., hydropower, reservoirs), based on CAMELS-CH metadata and the classification of .

Daily precipitation and temperature data were derived from high-resolution, gridded observational products produced by MeteoSwiss: RhiresD for precipitation and TabsD for mean temperature . Both datasets start in 1961 and extend to 2023, providing daily coverage across Switzerland at 2 km spatial resolution.

RhiresD combines rain-gauge data from ∼ 430 Swiss stations, supplemented by stations in neighbouring countries, through a two-step interpolation procedure: first, a Parameter-elevation Regressions on Independent Slopes Model (PRISM; )-based regression generates a climatological precipitation field for the 1971–1990 baseline. Daily station anomalies are then interpolated using the SYnoptic MAPping (SYMAP) algorithm, which is based on a distance-weighted interpolation approach similar to that of , and applied to the climatology to reconstruct daily fields.

TabsD, in contrast, is based on about 90 long-term SwissMetNet stations, with additional high-elevation series to improve spatial accuracy. Its interpolation relies on a non-linear vertical profile and non-Euclidean distance weighting, enhancing performance in alpine terrain.

Both RhiresD and TabsD are widely used in hydrological and climate modelling applications . For model training in this study, daily precipitation and temperature were spatially averaged over the 96 selected catchments using all grid cells whose centre point falls within each catchment polygon. While this introduces a minor approximation along catchment boundaries, the effect is expected to remain limited given the spatial smoothness of the interpolated meteorological grids.

Static catchment descriptors were incorporated during training to improve generalization across catchments and to inform the LSTM model about physiographic differences between them . The dataset includes most of the variables used in and combines categories of static physiographic information that are also used within the PREVAH modelling framework to parameterize hydrological response units and runoff-generation processes, although the exact datasets and spatial representations differ between the two approaches.

The descriptors fall into four categories:

Topography: elevation and slope, derived from the MERIT DEM dataset .

All variables were aggregated at the catchment scale and compiled into a single feature matrix for model training, following the pre-processing workflow of .

The climate projections used in this study stem from CH2018, Switzerland’s official climate scenario initiative led by the National Centre for Climate Services (NCCS) . We employ the DAILY-GRIDDED product, which provides transient daily temperature and precipitation fields at 2 km resolution for 1981–2099. CH2018 is based on EURO-CORDEX simulations that cover a historical period forced by observed radiative drivers up to 2005, followed by the corresponding scenario run (RCPs) from 2006–2099, yielding continuous transient time series.

The underlying EURO-CORDEX simulations, based on the CMIP5 framework, combine a driving Global Climate Model (GCM) that simulates large-scale climate processes at ∼ 200 km resolution, a Regional Climate Model (RCM) that downscales GCM output to 12 or 50 km over Europe, and one of three emission scenarios (RCP2.6, RCP4.5, RCP8.5). In CH2018, these RCM outputs are subsequently downscaled and provided on a 2 km grid, consistent with the MeteoSwiss observational products, to generate the high-resolution DAILY-GRIDDED dataset used in this study .

The CH2018 DAILY-GRIDDED dataset is based on 68 such GCM–RCM–RCP model chains; in this study we use the RCP8.5 subset (N=14, see Table ), which provides the strongest forcing signal for evaluating LSTM robustness.

The raw model output is bias-corrected using quantile mapping (QM), calibrated over the reference period 1981–2010 . Correction is applied individually to each variable using Swiss gridded observations, such that during the calibration period (1981–2010) the statistical distribution of the corrected daily values approximately matches that of the observations. In the CH2018 framework, these observations correspond to the MeteoSwiss gridded products RhiresD (precipitation) and TabsD (temperature), which are also used to force the LSTM during training (Sect. 2.2). Bias adjustment is performed at the native grid resolution prior to spatial aggregation to the catchment scale. This ensures consistency between the observational reference used for bias correction and the forcing data used in the LSTM, avoiding potential inconsistencies arising from mismatched datasets. The resulting transient projections are widely used and well suited for regional to catchment-scale impact studies . Further methodological details are available in the CH2018 Technical Report .

In contrast to , who assumed static glacier coverage, we incorporate time-varying glacier fraction to better represent changing hydrological conditions under climate change. The glacier projections used in this study are based on simulations conducted by , who applied the methodology of to estimate glacier evolution across Switzerland; note that no glacier modelling was performed in this study, and we directly use the gridded outputs provided by . The same glacier projections were used in Hydro-CH2018.

Glacier evolution was simulated using the GloGEMflow model , which couples a temperature-index surface mass balance (SMB) model, driven by E-OBS observational climate data (1951–2017) and EURO-CORDEX RCM-based projections, with a flowline ice dynamics module based on the shallow-ice approximation (SIA). The model was calibrated using geodetic mass balance data from the World Glacier Monitoring Service (WGMS) and initialized in 1990 under a steady-state assumption .

Simulations were conducted for 30 CH2018 model chains, producing gridded glacier area maps at 5-year time steps from 1990–2100. This dataset was then used to compute annual glacier area fractions at the catchment level (i.e., the fraction of each catchment covered by glaciers), which served as a dynamic input for our LSTM model setup (See Sect. 3.2 for preprocessing details).

Using these projections, glacier retreat is substantial across the study domain. Based on mean glacier fractions over each period, summarized by the median across the 14 RCP8.5 chains, 76 of the 307 catchments (24.8 %) exceeded 0.5 % glacier cover during the historical baseline (1991–2020). By the late 21st century (2095–2099, RCP8.5), 63 of these 76 catchments (82.9 %) had fallen below the same 0.5 % threshold, including 57 (75.0 % of the original 76) with less than 0.1 % glacier cover.

These glacier projections are applied consistently in both the LSTM and PREVAH simulations; thus, differences in projected runoff do not arise from differing glacier evolution assumptions, but from differences in model structure and process representation.

The Hydro-CH2018 dataset provides simulated daily runoff for 307 medium-sized Swiss catchments from 1981–2100 . It was generated with the semi-distributed conceptual hydrological model PREVAH, developed for mesoscale applications in mountainous regions . PREVAH simulates the water cycle through process modules for interception, evapotranspiration, soil water dynamics, snow and glacier melt, groundwater flow, runoff generation, and routing.

In Hydro-CH2018, PREVAH was implemented on a 500×500 m computational grid, providing sufficient spatial resolution to capture runoff variability across Swiss catchments.

Simulations were driven by observed meteorological inputs for the historical period (1981–2005) and by downscaled, bias-corrected CH2018 climate model chains (39 GCM–RCM combinations) for the projection period (1981–2100), including observation-driven reference runs (1981–2005) and scenario-driven projections (2006–2100). The forcing variables comprised daily precipitation, temperature, global radiation, relative humidity, and wind speed, with temperature lapse-rate correction.

Future glacier evolution was simulated externally and integrated into the hydrological modelling to represent glacier runoff contributions, using GloGEM for smaller glaciers and GloGEMflow for larger glaciers. The final dataset consists of daily runoff time series aggregated from the 500×500 m PREVAH grid to the 307 projection catchments used in this study, provided for each model chain. Hydro-CH2018 thus serves as an operational reference for Swiss-scale hydrological impact assessments .

The gridded PREVAH configuration underlying Hydro-CH2018 builds on a large-sample calibration of 140 mesoscale Swiss catchments covering different runoff regimes; this calibration framework was initially developed with particular emphasis on flood representation, while retaining water-balance consistency . The resulting parameter sets were subsequently regionalized to ungauged areas using ordinary kriging . The 307 catchments considered here are therefore represented using regionalized parameters rather than catchment-specific calibration, with this parameterization retained when PREVAH is driven by CH2018 climate-model forcing . Comparisons against observed streamflow provide additional evidence on both the performance and limitations of this framework. For six of the 307 catchments, the 500 m configuration showed satisfactory correspondence between simulated and observed hydrological drought characteristics and associated return periods . More recently, a 500 m PREVAH benchmark evaluated against observations in 98 low-impact catchments reproduced interannual runoff variability with a median correlation of r=0.91, while showing lower skill particularly in low-runoff and lake-dominated catchments . These characteristics and limitations motivate the use of PREVAH here as a spatially consistent, process-based benchmark rather than as ground truth. The underlying Hydro-CH2018 simulations for the 307 catchments, including the control run and daily simulations from the 39 climate-model chains, are publicly available through EnviDat .

Long Short-Term Memory (LSTM) networks are a class of recurrent neural networks (RNNs) specifically designed to capture long-range dependencies in sequential data . An LSTM cell comprises a memory cell and three trainable gates – input, forget, and output – that dynamically regulate information flow across time steps, allowing the model to retain or discard past information depending on its relevance .

This gating mechanism enables LSTMs to maintain internal state memory, making them particularly suitable for problems with delayed or cumulative effects such as snowmelt or soil moisture storage in hydrological systems. Moreover, LSTMs can learn nonlinear, multivariate, and nonstationary input–output relationships directly from data, without requiring explicit knowledge of underlying physical processes. As a result, they have shown particular success in rainfall–runoff modelling, often outperforming traditional conceptual models across diverse climatic regimes .

All input features, both dynamic and static, were standardized via z-transformation (zero mean, unit variance), based on the training-set statistics. Missing discharge values were masked during training so that only valid observations contributed to loss computation.

Glacier area fraction was included as a dynamic input variable, derived from gridded glacier evolution simulations provided by and aggregated to the catchment scale. Values were linearly interpolated to annual resolution to obtain annual glacier fractions for each catchment and climate chain. This represents a key deviation from , where glacier fraction was held constant in time (see Sect. 2.5 for glacier dataset description).

More specifically, the dataset was processed as follows: –

For training (1961–2024, 96 observational catchments): –

a constant glacier extent corresponding to the 1990 value was assumed for 1961–1990, supported by observations suggesting limited glacier change over this period .

We adopt the same core architecture as : an LSTM-based model that predicts daily runoff from sequential meteorological inputs and static catchment attributes. The architecture consists of a single temporal LSTM layer, followed by a fully connected output layer that maps the temporal encoding to a scalar runoff prediction for each day. Our configuration corresponds to the model setup identified by as their best-performing configuration among 24 tested alternatives (see their Sect. 3.5). In this configuration, static and dynamic inputs are first mapped to the same dimensionality, and then combined via broadcasting in time, followed by addition of their encodings. This early fusion allows catchment-specific information to directly inform the temporal encoding, thereby improving model generalization across heterogeneous hydroclimatic regimes. A full technical specification of the architecture, available hyperparameters, and optimization details is provided in the original publication. Small adaptations, e.g., taking glacier fraction as an additional dynamic input, were made here to better accommodate our study objective.

The model was trained using backpropagation , which updates internal parameters to minimize the difference between predicted and observed runoff. The optimization objective was the mean squared error (MSE) between normalized simulated and observed discharge. Parameter updates were performed using the AdamW optimizer , which adapts learning rates per parameter and applies decoupled weight decay for regularization. To mitigate overfitting, early stopping was applied based on validation loss: training halted once validation performance no longer improved for a given number of epochs, and the best model (in terms of validation MSE) was retained for prediction on the test set .

Hyperparameter tuning was performed in this study using the Optuna framework during the first cross-validation iteration (see next section), following the same procedure as . The final set of parameters and search spaces are provided in Table .

We applied an 8-fold spatial cross-validation scheme to assess generalization across catchments. The 96 low-impact Swiss catchments were randomly partitioned into eight folds; in each iteration, six folds were used for training, one for validation, and one for testing. A fixed temporal split was applied within each fold: 1961–2015 for training, 2016–2018 for validation, 2019–2023 for testing. Training is restricted to minimally impacted catchments to avoid learning site-specific management effects (e.g. reservoir operations) and to isolate climate-driven runoff responses. The trained LSTM is then applied to the full set of 307 Hydro-CH2018 catchments to provide spatially continuous projections at the national scale. For catchments influenced by regulation, the resulting simulations should therefore be interpreted as naturalized runoff responses rather than managed discharge.

This two-dimensional splitting (spatial × temporal) guards against both spatial overfitting and temporal leakage. The model was retrained independently in each fold, resulting in eight sets of trained weights used for subsequent evaluation and projection. This setup therefore allows efficient use of the available data for model training.

The trained LSTM model was applied to climate projections spanning 1981–2100, using the CH2018 daily catchment-averaged meteorological forcing data, together with glacier projections and static catchment attributes. The projection inputs were combined into a single dataset. For each cross-validation fold, variables were normalized as (x-mean)/SD using the mean and standard deviation from that fold's training subset. This normalization was applied at runtime.

For the projection experiments, we used the 14 CH2018 model chains available under RCP8.5 (Table ), representing the intersection of chains for which atmospheric, hydrological (Hydro-CH2018), and glacier evolution data are jointly available. When a chain existed at both EUR11 and EUR44 resolution, the higher EUR11 resolution was selected.

For each chain, the eight LSTM models obtained from the cross-validation folds were run independently, and the daily median across these ensemble members was taken as the final prediction.

To facilitate the interpretation of differences between the data-driven LSTM model and the Hydro-CH2018 benchmark, Table  summarizes the main characteristics of both modelling frameworks. The comparison is particularly relevant for interpreting potential sources of divergence in projected runoff responses.

In this study, PREVAH is not used as a direct ground-truth for model evaluation. Instead, both PREVAH and the LSTM are considered within a regionalized, large-sample modelling context, and the comparison focuses on the consistency and divergence of their runoff responses under identical climate forcing. This framework allows differences between the models to be interpreted in light of their respective characteristics, as summarized in Table , and enables the identification of consistent and divergent runoff signals that reflect model-specific sensitivities, rather than primarily differences in performance at individual catchments.

Figure presents empirical cumulative density functions (CDFs) of test-set Nash–Sutcliffe Efficiency (NSE) for our LSTM (solid red), the CH-RUN LSTM (dotted black) and the PREVAH benchmark (dotted blue). Here, CH-RUN refers to the runoff reconstruction dataset generated with the original LSTM setup of . Vertical lines indicate each model's median NSE, facilitating a direct skill comparison. The LSTM achieved a median NSE of 0.75 across the 96 observational catchments, closely aligned with the original CH-RUN setup (0.76). This performance is also notably higher than the PREVAH benchmark, which reached 0.72 on similar catchments.

Having established baseline performance, we next assess the dynamical stability of runoff projections, asking whether the two models respond consistently across climate model chains, temporal aggregations, and future time horizons under altered climate forcing.

Visual inspection of daily runoff time series for representative catchments across contrasting hydrological regimes showed coherent temporal and seasonal streamflow dynamics, without evident non-hydrological behaviour. The analysis nevertheless focuses on aggregated temporal scales (seasonal means and interannual variability) and daily statistics, as climate-driven projections are primarily interpreted in terms of robust changes in runoff regimes and their spatial patterns, rather than the reproduction of individual discharge events or short-term hydrograph dynamics.

Figure shows the Pearson correlation coefficients between LSTM and PREVAH runoff simulations for each of the 14 RCP8.5 ensemble chains, computed separately for two time horizons (1991–2020 and 2071–2099) and two temporal aggregations (daily and annual).

Overall, correlation patterns are consistent across chains and horizons, indicating strong agreement between the runoff responses simulated by both models. Annual correlations are highest, with medians near 0.95 and narrow interquartile ranges for both horizons relative to daily correlations, showing no systematic change between past and future. Daily correlations remain strong (∼ 0.9) but decline slightly and broaden in the future period. These results provide a first indication of projection stability, before turning to spatial patterns of runoff change.

At the annual scale, both models show strong agreement in spatial patterns and magnitudes. This is demonstrated in Fig. , which maps mean seasonal runoff for 1991–2020, showing the LSTM median, the PREVAH median across all chains, and their difference. We use 1991–2020 as the historical baseline, consistent with the reference periods adopted in the most recent Swiss climate scenario assessment CH2025 . This provides a recent and coherent climatological benchmark for comparing the LSTM and PREVAH model responses.

Results are presented for three characteristic periods: Annual values integrate the full water balance and long-term trends, Winter (DJF) reflects snow accumulation and cold-season hydrological processes, and Summer (JJA) captures seasonal runoff variability driven by increased evapotranspiration, snowmelt, glacier melt, and precipitation, as well as low-flow and potential drought conditions. For spatial reference, the Swiss biogeographical regions are used (Fig. ; ).

For the annual panel, both models show high runoff on the northern and southern flanks of the Alps and in the western central Alps, and low values on the Plateau. A slight increase is visible in the Jura. Divergences arise where the LSTM does not reach PREVAH’s magnitude, notably in southern and central Switzerland, the eastern Alps, and parts of the west. Overall, the LSTM projects slightly lower annual runoff, and almost no catchments are hatched, indicating low inter-chain variability.

In winter, patterns remain similar but divergences increase. Both models show a northward shift of higher runoff and lower totals in the Alps and southern flank. Yet across much of Switzerland, particularly the Plateau, Jura, and western/eastern regions, LSTM values are lower, as seen in the pinkish difference maps. Both models show larger inter-chain variability in alpine and southern regions (hatched catchments), reflecting greater uncertainty in low-flow conditions.

In summer, the models again agree well, though difference maps show pronounced contrasts. This largely reflects the much higher absolute runoff magnitudes in summer compared to winter. Both capture alpine peaks and low Plateau/Jura runoff, but the LSTM tends to project higher values in the western central Alps and northern flank, while PREVAH simulates higher values in the eastern Alps and southern flank. Inter-chain variability is larger for PREVAH on the Plateau and in alpine areas, whereas the LSTM shows such variability only locally.

Across all seasons, hatching in the Δ-panels marks catchments with low inter-model robustness, where the LSTM-PREVAH median difference is small relative to inter-chain variability. It occurs only sporadically and without a clear spatial pattern, mostly coinciding with catchments showing weak inter-model differences.

With the baseline established, we next turn to projected changes towards the late 21st century.

The projections show strong consistency between models in space and magnitude: both simulate overall annual drying, wetter winters, and pronounced summer drying across nearly all catchments.

Figure maps seasonal runoff changes for 2071–2100 relative to 1991–2020 under RCP8.5, showing the ensemble-median change from the LSTM, from PREVAH, and their difference. These maps highlight agreement and divergence in projected end-century shifts. To contextualize the projected runoff responses, Fig.  compares the seasonal distributions of atmospheric forcing in the observational training data with those from late-century CH2018 projections. The comparison indicates that future forcing partly departs from the historical training domain of the LSTM, particularly for temperature.

At the annual scale, the LSTM generally predicts slightly stronger drying, especially over the Plateau, northern pre-Alps, and western central Alps. PREVAH shows the same pattern with less intensity. Notable catchment-specific differences include one glacier-rich basin where the LSTM projects positive change. While the LSTM tends to predict stronger drying overall, inter-model differences vary in sign in the central Alps.

In winter, both models consistently project wetter conditions, strongest in alpine regions. Divergences are also largest there, with PREVAH simulating slightly larger increases. Plateau changes are negligible in both models. Difference maps show LSTM increases as systematically but only slightly weaker than PREVAH's.

In summer, both models agree on strong drying, most pronounced in the Alps and southern flank, with more moderate changes on the Plateau and in the Jura. PREVAH generally simulates stronger drying, particularly in alpine regions, though a few northern Alpine catchments show the reverse, with larger LSTM declines.

Across all seasons, within-model signals are generally robust, with few catchments where ensemble spread rivals the median change (hatched catchments). Exceptions occur in winter over the Plateau, especially for LSTM, where ensemble spread is large relative to weak signals. Catchments with low inter-model robustness – as indicated by hatching in the Δ-panels – are scattered and somewhat more common in summer, especially over the Plateau and the southern flank of the Alps. A complementary comparison of seasonal atmospheric forcing distributions is provided in Fig. , showing that late-century CH2018 forcing departs from the historical training domain of the LSTM, particularly for temperature. Having established national-scale changes, we next turn to representative catchments.

Overall, PREVAH and LSTM projections align well for selected locations. Figure shows RCP8.5 runoff-change trajectories (relative to 1991–2020) for six regime-representative catchments. Thin lines denote individual ensemble chains (red = LSTM, blue = PREVAH), thick curves the chain medians, and grey lines their difference. Results are shown for Annual, Winter, and Summer. Overall, median trajectories agree well across seasons and regimes.

At the annual scale, all catchments show negative changes by 2100, though magnitudes differ. Discrepancies are largest in the highly glaciated catchment, where the difference curve departs strongly from zero: PREVAH projects stronger mid-century drying, but the LSTM becomes more negative from around mid-century onward and remains so by 2100. Together with the southern Alpine catchment, this represents the strongest decline. In contrast, slightly glaciated catchment show closer agreement with nearly overlapping median trajectories, while high-alpine snow and pre-alpine rain–snow regimes exhibit stronger LSTM drying toward the end of the century. The pre-alpine case shows a systematic median shift in the second half of the century, despite similar trends. The lowland rain regime shows smaller declines and tight agreement, whereas the southern Alpine basin displays stronger negative changes in both models, with the LSTM consistently drier. Despite variations, both models agree on the sign of change across all regimes by 2100. Individual chains show substantial scatter at annual scale, and not all agree on the sign within the same ensemble.

In winter, changes are weaker and opposite in sign, with all catchments showing positive trends by 2100. Increases emerge steadily after ∼ 2030. Differences are again largest for the highly glaciated basin, but also notable in the lowland rain catchment, where PREVAH projects stronger late-century increases. More generally, PREVAH simulates larger positive changes in snow-rich zones, while the LSTM response is more moderate.

In summer, declines begin as early as 2020–2030, especially at medium to high elevations. Summer drying is the most consistent and severe change, exceeding winter increases. For the highly glaciated basin, the summer decline nearly matches the annual decrease. Importantly, both models agree closely on the summer trajectories, with consistent magnitude and timing across all regimes.

Because Swiss hydrological regimes are strongly tied to elevation , the next section examines results aggregated by altitude bands.

The models agree well in terms of seasonal elevation-dependent runoff change patterns, although the magnitude of changes differs. Figure displays summaries of 2071–2100 seasonal runoff changes (relative to 1991–2020), grouped into six elevation bands and contrasted between LSTM (red) and PREVAH (blue).

At the annual scale, the two models agree well on both sign and magnitude. Negative changes intensify with altitude, showing stronger drying at higher elevations. The LSTM tends to exhibit larger variability – i.e., wider distributions – especially in the highest bands, but median values remain similar, so neither model consistently projects stronger or weaker changes. When variability across catchments is considered, the LSTM leans toward slightly larger negative shifts.

In winter, the elevation signal is less regular. At low elevations (0–1000 m), the models even diverge in sign, with PREVAH showing a slight positive change and the LSTM a weak negative one, though both values are close to zero. At higher elevations, both indicate positive changes that increase to a maximum around 1500–2000 m and then decrease – while remaining positive – above 2000 m, yielding a characteristic D-shaped response. PREVAH simulates stronger increases across all bands, while the LSTM shows a more heterogeneous response.

In summer, elevation dependence is most pronounced. Both models project drying that increases almost linearly with altitude. Changes remain modest below 1500 m but intensify sharply above, reaching values comparable to annual changes. In this aggregated view, PREVAH tends to simulate slightly stronger declines, while the LSTM shows wider spreads, especially at mid to high elevations. At the level of individual catchments (Fig. 7), however, the relative signal can vary, and opposite tendencies may occur locally. Complementary catchment-scale diagnostics (Appendix A, Figs. A3–4) provide a consistent picture, showing overall agreement between the two modelling frameworks alongside increased dispersion in winter.

Having examined seasonal and elevation-dependent changes, we now turn to runoff extremes, where LSTMs are known to face limitations.

In alignment with previous studies e.g.,, our LSTM model shows a different behaviour than the reference model PREVAH for extreme runoff values. Figure summarizes national-scale patterns of annual runoff extremes under RCP8.5 for 2071–2099, displaying maxima (blue) and minima (red) from the LSTM and PREVAH, together with their differences.

Both models reproduce a similar spatial structure for annual maxima, with the largest values in the central Alps and on the southern flank. Clear magnitude differences emerge nevertheless: PREVAH systematically simulates higher peaks, particularly in the western and eastern central Alps and southern flank, with further discrepancies in parts of western Switzerland. The difference map shows a near-continuous underestimation by the LSTM, visible in widespread pink shading. Inter-chain variability is large in both models and slightly larger for PREVAH. Locations of low inter-model robustness (hatched) are rare and show no clear spatial structure.

For annual minima, spatial patterns are consistent across models, with the lowest values on the Plateau and comparatively higher minima in alpine regions. The LSTM projects less severe minima than PREVAH, especially in the western central Alps and along the northern flank, visible as green shading in the difference map. Inter-chain variability is comparatively small for the LSTM (mainly on the Plateau) but widespread for PREVAH across Switzerland. Low-robustness differences occur slightly more often than for maxima but remain spatially sporadic.

Figure further explores these divergences in catchments with the largest differences by showing how wet and dry precipitation events are translated into runoff.

For maxima, PREVAH responds much stronger to 3 d precipitation sums, with steeper runoff–precipitation slopes, especially in alpine catchments (249, 254). This is evident from the scatter plots and quadratic fits. For minima, both models show weak links to 21 d precipitation deficits, but the LSTM consistently simulates higher baseflows, evident as a systematic vertical offset between fitted curves. Here, the key difference lies in magnitude rather than sensitivity. Together, these results highlight that PREVAH exhibits stronger sensitivity to precipitation extremes, whereas the LSTM shows a regression-to-the-mean behaviour, dampening both high and low flows. This consistent response pattern informs the model limitations discussed in Sect. 5.7.

As expected, our LSTM model achieves performance closely aligned with the original CH-RUN implementation . The results confirm that our adaptations – most notably the integration of a dynamic glacier fraction and a different temporal split in the training scheme – do not compromise reconstruction skill, which remains consistent with . The absence of a measurable performance gain from the inclusion of dynamic glacier information can be attributed to the limited representation of glacierized catchments in the training dataset, which reduces their influence on aggregate performance metrics. In addition, differences in the evaluation setup likely contribute to small discrepancies: while partly assess reconstruction within the training domain using random splits, our approach emphasizes temporal extrapolation by holding out a continuous period at the end of the record, resulting in a stricter evaluation of model skill.

This strong agreement between our LSTM implementation and the original CH-RUN setup establishes a reliable baseline for subsequent projection analyses, while also emphasizing that present-day skill does not automatically guarantee robustness under future climate conditions . Nonetheless, the high reconstruction accuracy rules out calibration error as a major source of later discrepancies, strengthening confidence in the interpretability of projection results.

In addition, the two modelling frameworks do not rely on identical atmospheric forcing representations, as PREVAH explicitly incorporates additional variables related to evapotranspiration and energy-balance processes, whereas the LSTM primarily relies on precipitation and temperature as dynamic predictors. Some divergence between future runoff projections may therefore reflect differences in how the two approaches process climate information under out-of-distribution conditions.

As a first step in assessing projection consistency, we examined catchment-wise correlations between LSTM and PREVAH across the RCM ensemble at daily and annual scales (see Sect. 4.2, Fig. ). Correlations remain high, particularly at the annual scale, indicating a high degree of consistency between the two models even under changing climate conditions. However, annual correlations mainly reflect agreement in the direction of change rather than its magnitude, since the LSTM may underestimate runoff in some cases (e.g., saturation effects; see ), an aspect examined later. As expected, annual correlations exceed daily ones, as temporal aggregation smooths high-frequency variability and timing mismatches, isolating the climate-driven signal. The limited spread and regularity across ensemble members at both scales further shows that the LSTM response is consistent regardless of the specific climate forcing, suggesting that variability introduced by different RCM chains is minor compared to overall model skill.

Together, these findings provide a first indication of the model's stability and its capacity to generalize from historical training to long-term projections, particularly in maintaining consistent interannual runoff dynamics across Switzerland. This dynamical consistency establishes a solid basis for examining where spatial patterns diverge, and why.

We first verify that the LSTM delivers spatially stable runoff fields under present-day forcing (Fig. ), before moving to altered climates. At the annual scale, the near-absence of hatching reflects that larger mean flows buffer chain-to-chain variability (columns one and two).

In winter, Alpine means align closely, indicating that both models are consistent in reproducing snow- and ice-controlled runoff despite the LSTM lacking an explicit cryospheric module . This robustness supports confidence in its ability to capture future cold-season dynamics. Differences over the Plateau likely reflect rain–snow partitioning, with PREVAH routing more liquid water directly to runoff. Winter hatching in columns 1 and 2 highlights greater relative uncertainty in low-flow settings, but its presence in both models reinforces signal consistency.

In summer, high alpine runoff is consistent with snow and ice melt dynamics: despite elevated evapotranspiration, meltwater sustains strong flows, while mid-elevation catchments release water earlier in spring and lower-elevation ones remain dry with little or no accumulation . Across much of the Alps, the LSTM produces slightly higher values, likely because PREVAH releases part of the melt earlier, leaving less for July–August. In the eastern central Alps, the LSTM yields lower flows, possibly reflecting different learned associations with precipitation, glacier melt, or evapotranspiration. Both models capture the very low Plateau and Jura totals, with residual biases potentially linked to LSTM-learned evapotranspiration patterns.

Overall, both models remain consistent for the historical seasonal baseline. Summer differences point to subtle variations in how snow and ice storage and melt are represented, rather than a fundamental LSTM instability. PREVAH also shows a broader spread in summer (not only where median values are low, see hatching in column two, third row), suggesting less constrained projections, while the LSTM maintains tighter consistency across chains.

Finally, the Δ-panels (Fig. , third column) add ensemble context to inter-model differences, with hatching marking catchments where the LSTM–PREVAH median difference is small or not robust relative to inter-chain variability; its scarcity indicates that most differences between the two models are spatially systematic rather than random across chains.

Having confirmed stability under present-day conditions, we now examine end-century (2071–2100, RCP8.5) change maps to test whether the LSTM extrapolates spatial signals consistently under strongly altered forcing (Fig. ).

At the annual scale, drying is broadly consistent across Switzerland, with one notable exception: a glacier-rich catchment where the LSTM projects a positive change while PREVAH shows depletion. This may reflect retained meltwater contributions in the LSTM versus earlier glacier exhaustion in PREVAH , though it could also reflect an LSTM artefact. More generally, mismatches cluster in alpine regions, where runoff volumes are highest and hydro-related processes such as rain–snow partitioning, melt rates, and storage release are most complex . Differences may stem from assumptions about the pace of glacier regime shift, with the LSTM implying a faster transition and thus steeper annual declines.

In winter, both models project wetter conditions, strongest in the Alps, consistent with reduced cryospheric storage capacity and a shift from snowfall to rainfall . PREVAH changes are systematically larger, likely because its physics convert a greater fraction of snowfall into immediate runoff. The LSTM may understate increases in catchments where rain-over-snow transitions exceed its training range . Plateau catchments remain near-zero in both models, being less sensitive to snow and glacier dynamics, and precipitation phase shift.

In summer, projections align with expectations: reduced storage and accelerated melt accentuate water deficits, especially in the Alps and southern flank (Muelchi et al., 2021; Brunner et al., 2019b). PREVAH generally produces larger declines, consistent with its wetter winters and earlier snow/ice release, while LSTM drying is weaker, possibly from preserved winter storage. Despite this amplitude shift, possibly traced to winter divergence, spatial patterns are consistent, with no indication of LSTM instability.

PREVAH’s larger winter increases likely explain its stronger summer drying. Interestingly, however, the LSTM amplifies the annual drying signal. Timing shifts alone, such as delayed snowmelt or prolonged winter storage, cannot explain this, since they would not yield a more negative annual change. A more plausible explanation is that the LSTM produces less winter runoff, offsetting weaker summer drying, or conversely that PREVAH's wetter winters balance its drier summers. The LSTM may therefore redistribute changes more evenly, producing a net annual reduction. Such behaviour may reflect its limited training exposure to extreme seasonal transitions.

The largest summer mismatches occur in the Alps (see Fig. , third row), Switzerland's key snow- and ice-fed water reservoirs, highlighting the need for close scrutiny of these basins . Still, the scarcity of hatching across change maps (columns 1–2) indicates robust within-model signals, with ensemble spread smaller than the signal itself. In the Δ-panels (Fig. , third column), hatching is sparse–mainly in summer over the Plateau and the southern Alps–indicating that, in most regions, differences between the LSTM and PREVAH median anomalies are consistent across chains. Where hatching appears, inter-model contrasts are small or not robust.

It is worth noting that EURO-CORDEX ensembles, underlying the CH2018 scenarios, tend to underestimate summer warming and drying because many RCMs neglect aerosol decline and the associated shortwave increase . Runoff changes reported here may thus be conservative relative to more recent scenarios.

Overall, across both the 1991–2020 baseline and the RCP8.5 end-century change maps, the LSTM is consistent with PREVAH in reproducing Switzerland-wide change patterns, confirming that a data-driven model can generalize its learned hydroclimate relationships to out-of-distribution forcing, despite a few mismatches discussed below .

With chain-by-chain and then large-scale stability established, we next zoom from national maps to six representative catchments that typify Switzerland's runoff regimes (Fig. ). The aim is to test whether LSTM–PREVAH agreement holds at the catchment level and whether skill diverges in specific regime types. For this, ensemble-median trajectories from both models were compared for annual, winter, and summer runoff.

On an annual scale, drying intensifies after 2040 in slightly and highly glaciated catchments, reflecting the expected post-“peak water” decline . PREVAH appears more buffered in glacier-fed regimes, while the LSTM projects stronger drying by 2100, consistent with national maps.

In winter, both models simulate increasing runoff driven by the shift from snowfall to rainfall, again consistent with national projections . PREVAH produces larger changes, likely due to its representation of snow-to-rain transitions at lower elevations and immediate routing at higher, snow- and glacier-dominated catchments. LSTM shows a dampened rise, possibly reflecting delayed release of precipitation inputs.

During summer, both models project strong declines in glaciated and alpine catchments, clearly consistent with meltwater exhaustion . These declines nearly match the annual changes, underscoring summer's dominant role in driving long-term reductions . Increasing winter runoff does not offset these losses but instead accelerates summer depletion, as seen in Sect. 5.4. In lowland, southern Alpine, and pre-Alpine catchments, summer declines are likely driven by increased evapotranspiration and reduced soil moisture recharge, though magnitudes remain moderate and may be buffered by enhanced convective precipitation .

Overall, the LSTM remains consistent with PREVAH across all regimes, with the clearest mismatches confined to glacier-rich and snow-transition catchments. Prior studies show that LSTMs trained on large, diverse datasets can generalize runoff predictions to unseen basins, often outperforming traditional regionalization approaches . By leveraging cross-catchment patterns and static descriptors, LSTMs can internalize regime-specific processes and translate climate-forcing changes into realistic runoff responses, even in ungauged basins .

Our catchment-scale results support this ability, as the LSTM reproduced regime-dependent responses across Swiss catchments (see Fig. ). Given the strong link between hydrological regimes and elevation, examining results across elevation bands provides a complementary perspective on whether these strengths and weaknesses persist at a Switzerland-wide scale .

Elevation is a primary control on hydrological regimes in Switzerland, and the previously identified LSTM–PREVAH mismatches in glacier-fed and snow-transition catchments suggest a systematic altitudinal component (Fig. ). Aggregating results by elevation bands therefore helps to evaluate how these discrepancies manifest across Switzerland’s vertical gradient, which is particularly relevant for climate adaptation given the role of high-altitude reservoirs .

On an annual basis, both models agree that drying intensifies with elevation. Historically, alpine flows depend strongly on snow and glacier melt, but under RCP8.5 these sources are depleted by reduced snow accumulation, earlier melt, and long-term glacier loss . Since winter gains no longer compensate summer losses, annual changes become increasingly negative at higher altitudes.

In winter, runoff increases across all elevations, strongest at mid-elevations where small temperature shifts cause large rain–snow transitions, producing the observed “D-shaped” profile with peak increases at 1500–2000 m and weaker signals above and below. This reflects the present-day zero-degree line . At low elevations, warming adds little to already rain-dominated regimes, while at high elevations, temperatures may remain cold enough for much winter precipitation to persist as snow even under RCP8.5, limiting change. PREVAH systematically projects stronger increases than the LSTM, particularly at mid- to high elevations, likely because it routes rain and snowmelt more immediately to runoff, whereas the LSTM delays release into spring. These differences mirror the cryospheric process divergences noted at the catchment scale, now generalized across elevation bands. This is consistent with catchment-scale scatter plots (Appendix A, Figs. A3–4), which show strong overall agreement but increased dispersion in winter, reflecting the greater sensitivity to snow-related processes in that season.

In summer, the strongest drying occur in high-elevation catchments (>2000 m), underscoring the vulnerability of snow- and glacier-fed regimes . Drying intensifies with altitude as these flows have historically been sustained by snow and glacier melt . The LSTM projects slightly weaker declines than PREVAH and shows a wider spread at the highest bands, likely reflecting both the uncertainty of extrapolating to rarely observed glacier-fed conditions and its lack of explicit glacier dynamics. Still, both models capture the same spatial trend and seasonal timing, confirming the LSTM’s capacity to reproduce elevation-dependent responses to climate change.

These elevation-based results extend the catchment-level analysis, confirming that the agreement between LSTM and PREVAH holds beyond individual catchments and can be generalized to groups of catchments sharing similar altitude-dependent hydrological regimes. Both consistently capture the direction of change, though magnitude differences increase at high elevations, particularly in winter and summer. As also seen in Fig. and discussed in Sect. 5.4, the LSTM dampens seasonal contrasts, projecting smaller winter increases and weaker summer decreases, while amplifying drying on an annual basis.

This pattern suggests that simple timing shifts cannot explain the divergence: either the LSTM produces less winter runoff while PREVAH offsets drier summers with wetter winters, or the LSTM redistributes changes more evenly across seasons.

Across elevation bands, the spread varies systematically with altitude: LSTM projections are wider at mid- to high elevations, likely reflecting the under-representation of glacier- and snow-fed basins in training (Fig. ) and the absence of explicit physical constraints, which together inflate variability when extrapolating beyond its core domain . Stronger climate signals at higher elevations may amplify this sensitivity. By contrast, in lowland rainfall-driven catchments, well represented in training, LSTM spreads are narrower and sometimes smaller than those of PREVAH.

Overall, vertical stratification of climate impacts is reproduced by both models and aligns with established hydrological understanding in Switzerland . Conclusively, both regime-specific and country-wide tests demonstrate that the LSTM mirrors PREVAH's mean-flow responses in space and time under altered climate, with remaining challenge at the distribution tails, where LSTMs risk peak-flow saturation .

Runoff extremes are critical for applications such as energy production, infrastructure management, and ecosystem protection , but they remain a recognized challenge for LSTM models due to:

saturation of the network state, which limits responsiveness to very large inputs (mechanical limitation; );

This domain-shift concern is supported by a complementary forcing diagnostic (Appendix, Fig. ), which compares seasonal precipitation and temperature distributions in the observational training data with those from late-century CH2018 forcing under RCP8.5. The figure shows that future forcing departs substantially from the historical training domain, particularly for temperature, while precipitation distributions also shift seasonally. Although this does not by itself explain the LSTM–PREVAH differences, it indicates that the LSTM is applied under conditions that partly exceed its training domain, which may contribute to the projected divergence. Comparing LSTM and PREVAH therefore provides valuable insights.

Figure corroborates the maps in Fig. : the LSTM shows clear signs of peak-flow saturation. PREVAH responds more strongly to heavy precipitation, with a steeper runoff–precipitation slope (Fig. ), while the LSTM's dampened slope supports the interpretation of saturation (even though it does not display the flat saturation plateau sometimes reported in the literature).

From the ensemble perspective (Fig. ), widespread hatching in columns 1–2 indicates strong chain-to-chain sensitivity of peak-flows, and likely nonlinear hydrologic responses during high-flow events. In contrast, hatching in the the Δpanel is scarce, showing that the negative LSTM–PREVAH differences in annual maxima are spatially consistent across ensemble members rather than random. Hence, despite large internal variability, the relative bias between the two models is robust–model formulation matters more than forcing-chain choice.

In contrast, PREVAH tends to simulate deeper lows (Figs. , ), with differences that concern magnitude more than sensitivity to precipitation deficits (see Fig. , bottom row). However, literature suggests that PREVAH may over-dry under high evaporative demand, implying the LSTM could provide a more moderate – and possibly more realistic – baseline representation of future low-flow conditions . Still, this interpretation requires caution.

Ensemble patterns also diverge: PREVAH shows extensive hatching, reflecting greater chain-to-chain variability, while the LSTM exhibits sparser hatching, likely due to stronger observational regularization and less ability to generate divergent trajectories. Importantly, a broader spread for PREVAH should not be conflated with lower realism, given the challenges of simulating low flows under strong warming. In the Δ-panel (Fig. ), hatching appears slightly more often for minima but remains spatially sporadic. This pattern indicates that low-flow differences between LSTM and PREVAH are smaller in magnitude and less robust across chains, reflecting greater sensitivity to chain-specific conditions than for maxima.

Extremes therefore expose the main boundary of LSTM projections: systematic peak-flow saturation leading to muted maxima relative to a process model. This behavior is consistent with prior findings and unlikely to result from PREVAH overestimating wet extremes .

LSTM-based models offer several advantages over traditional hydrological models. Their computational efficiency enables rapid ensemble simulations, facilitating large-scale scenario testing that can support a broad range of applications, as those highlighted in the Introduction . They also learn complex temporal dependencies directly from data and capture cross-basin patterns for built-in regionalization . Unlike process-based models, they also avoid potentially biased parameterizations .

A key limitation, however, lies in their strong dependence on large and high-quality training datasets . Evidence shows that LSTMs perform best when trained on diverse, multi-basin records , which are not always available. However, ongoing advances in data acquisition, such as remote sensing and expanding global hydrological databases may gradually alleviate this constraint . Another challenge is interpretability: pure LSTMs provide little insight into the mechanisms they learn .

As a result and without further complementary experiments, divergences from process-based projections can often only be hypothesized rather than explained. Part of the divergence between LSTM and PREVAH can, however, be interpreted in light of their contrasting structural assumptions. PREVAH explicitly represents key hydrological processes such as snow accumulation and melt, evapotranspiration, and glacier evolution within a mass-conserving framework , whereas the LSTM infers runoff from data without imposing such explicit physical constraints. These conceptual differences, summarized in Table , provide an important context for interpreting the model differences discussed in Sect. 5.4–5.7.

Agreement between LSTM and PREVAH projections should therefore not be interpreted as proof of correctness, nor should divergence alone identify which modelling framework is more realistic. Rather, consistent responses across two structurally different approaches increase confidence in the robustness of the corresponding runoff signal, whereas systematic divergences highlight components of projection uncertainty that require cautious interpretation. This also highlights the need for improved interpretability and physically informed modelling strategies. Encouragingly, new interpretability tools reveal internal LSTM representations consistent with hydrological knowledge , offering a path toward greater transparency.

One promising avenue to improve both interpretability and robustness include hybrid approaches that combine data-driven efficiency with physical knowledge . These retain the self-learning capacity of LSTMs while enforcing realism through physical constraints, making them at least partially interpretable . Other promising directions include transfer learning, which improves transferability to unseen climates ; physics-guided architectures, which use soft constraints to enhance realism ; and the use of improved input features and higher-quality training data, which provide more reliable signals for capturing hydrological processes . Collectively, these developments may address current limitations in extreme-event representation, strengthen confidence in projections, and enable more systematic attribution of hydrological responses to specific model components.