Norway exhibits a high heterogeneity in hydroclimatological conditions . The country spans 58 to 71° N along the west side of the Scandinavian peninsula with coastline comprising the southern, western and northern border, and with the Scandinavian mountain range running southwest to northeast. Annual precipitation amounts range from above 6000 mm in the west due to the combination of prevailing westerly winds from the Atlantic and orographic effects, to below 300 mm towards central-eastern and northeastern parts of the country. The geographical pattern of annual runoff reflects to a large degree that of annual precipitation. Annual temperatures varies from -9.5 to 9.5 °C, with the warmest areas along the southern and western coastline, and coldest in the inland high altitudes or latitudes. Although the snow season and volumes vary considerably across Norway following the heterogeneity of temperature and precipitation, most of the country has temperatures above 0 °C during summer and below 0 °C and snowfall during winter.

Floods in Norway are mainly generated by rainfall and snowmelt or a combination of the two . Whereas extreme rainfall events typically occur in summer or autumn, snowmelt typically peaks in spring or early summer. Generally, the largest floods are dominantly generated by rainfall in southern and western regions, and by snowmelt in central-eastern and northern regions.

Daily discharge data used to train the LSTM network stemmed from 200 streamflow gauging stations of the Norwegian Water Resources and Energy Directorate (NVE) hydrometric observation network in Norway (Fig. ). Of those stations, model evaluation was performed over the 103 stations used by the operational model, which serves as a benchmark (ref. Sect. ). Each day in the observed daily discharge series is divided at midnight Central European Time (CET).

The gauging stations were selected from an existing dataset that has been thoroughly quality controlled for flood analyses 530 stations;. Requirements during that selection included: The stations should not have problems with ice jams or supercritical flow during floods, they should have satisfactory rating curves and measurement conditions during floods, and they should not have homogeneity breaks for streamflow and floods that stemmed from changes in the measurements or quality control. Of the 530 stations, we selected the active stations unaffected by regulations. The original unit of m³ s⁻¹ was changed to mm d⁻¹ by normalising the streamflow values by the catchment areas. Catchment areas represented in the dataset range 0.58 up to 14 000 km². However, most areas are less than 300 km², which was expected due to the requirement of near-natural flow in a country heavily affected by hydropower.

Table  lists the catchment attributes selected for the training of the LSTM model. The 21 catchment attributes were selected to represent the variability of geometric, physiographic and climatological characteristics important for streamflow, hydrological regimes and floods. There is a large degree of overlap between our selection and attributes that have previously been selected for regional flood frequency models in Norway . Most of the catchments are influenced by seasonal snow. Of all the 200 catchments, 95 % have average winter (DJF) temperatures below 0 °C (range -13 to 3 °C), whereas average summer (JJA) temperatures are all positive, ranging 6 to 16 °C. Several of the catchments are also partly covered by glaciers. Specifically, 21 (12) of the 200 catchments have more than 3 % (10 %) of their catchment area covered by glaciers in 2019.

Daily precipitation sum (mm) and mean daily temperature (°C) from the meteorological dataset SeNorge_2018 was used to produce the dynamical forcing for LSTM (Sect. ). Flood event classification (Sect. ) was based on the same precipitation data, as well as daily snowmelt (mm) estimates simulated by the SeNorge snow model v.1.1.1 that uses SeNorge_2018 gridded daily precipitation sum and mean temperature as input. Both SeNorge_2018 and the snowmelt dataset are available from 1957 to present at a daily time step (07:00–07:00 CET). They are gridded products with a spatial resolution of 1×1 km², covering the whole of Norway as well as neighbouring regions. The SeNorge_2018 dataset is generated by statistical interpolation of in situ precipitation and temperature observations. The SeNorge snow model used for classifying flood events simulates snowmelt by a degree-day approach augmented with synthetic incoming daily solar irradiance defined as a function of latitude and time of the year.

From the daily gridded variables precipitation sum and mean temperature, the following daily time series were prepared at the catchment level for LSTM modelling:

prec (mm d⁻¹): Spatially averaged daily precipitation sum

Recurrent neural networks operate on time series data by processing a d-dimensional input sequence {xt∈Rd:t=1,2,…,T} and generating a p-dimensional output sequence {yt∈Rp:t=1,2,…,T} through recursive computations. At each time step t, the network updates its internal state and produces an output according to: 1ht=f(xt,ht-1),yt=g(ht), where ht∈Rk represents the k-dimensional hidden state that encodes information from previous time steps, while f and g are parametrised functions that define the network's dynamics and output mapping, respectively.

LSTM networks implement a sophisticated version of the state update function f that allows the LSTM to selectively retain or forget information over long sequences, mitigating the vanishing gradient problem that affects traditional recurrent neural networks . In the context of streamflow prediction, this long-term memory capability enables the model to represent snowpack dynamics by retaining information about precipitation and temperature conditions during winter months, then utilizing this stored information to predict the timing and magnitude of snowmelt-driven streamflow in spring and summer . For a detailed decomposition of the LSTM state update function, see .

To predict streamflow at day t, the model requires an input sequence x(t-m):t={xτ:τ=t-m,t-m+1,…,t} of length m+1, which is processed through the LSTM to produce a corresponding output sequence y(t-m):t. The output, q^t, the streamflow at day t, is obtained by taking the final element of this output sequence, i.e., q^t=yt. To simulate streamflow for the next timestep, the input window is shifted one time step forward at each prediction.

We employed LSTM as a lumped rainfall-runoff model using the cudalstm architecture from the neuralhydrology package , a Python library containing a collection of LSTM-based models for hydrological modeling built on the PyTorch framework. The cudalstm model provides an efficient GPU-accelerated implementation of the LSTM architecture described here.

The LSTM model was trained using the 15 hydrological years 1 September 2009–31 August 2024, employing the catchment-averaged Nash-Sutcliffe efficiency (NSE) as our loss function, in line with . Details of our LSTM training and hyperparameter tuning using a 5-fold cross-validation (CV) are provided in Appendix . The model was trained using four meteorological input time series for each catchment: catchment-averaged daily precipitation sum (mm d⁻¹), catchment-averaged mean daily temperature (°C), catchment-minimum mean daily temperature (°C), and catchment-maximum mean daily temperature (°C). In addition to these dynamic inputs, the model incorporated 21 static catchment attributes as listed in Table . Following best practice , a single LSTM model was trained across all catchments, enabling the model to learn general hydrological relationships from the diverse set of catchments.

The Hydrologiska Byråns Vattenbalansavdelning (HBV) model is a widely used precipitation-runoff model, in particularly in the Nordic countries . In Norway, a version of the HBV model with a daily temporal resolution is used operationally by NVE, for national flood warning services, quality control of streamflow observations, and energy prognosis among others . For this reason, we chose the operational HBV model for benchmarking our results. Catchment-by-catchment calibration of 12 model parameters were performed using Nash-Sutcliffe efficiency (NSE) as a loss function (for calibration details, see Appendix ). The operational HBV model are currently used for 145 reference catchments with long data series of good quality and limited influence of regulations, and representative for different geographical regions in Norway . We performed all model evaluations for the 103 reference catchments that overlapped with the catchments used for training LSTM (Fig. ).

Flood events were selected from the observational time series based on a peak over threshold (POT) approach, following the methods described in . Daily streamflow values exceeding the 98th percentile calculated from the 30-year period 1 September 1994–31 August 2024 were used to identify the flood peaks. To ensure independence between flood events, only the maximum streamflow value was selected within a catchment-specific time window, using the python library pyextremes . This time window was set to twice the normal flood duration (NFD), which is defined as the sum of concentration time plus recession time of the largest flood events. The full description of the estimation of NFD is provided in . In general, a concentration time of 2–3 d was found for all catchments subject to an HBV modelling experiment inputting twice the annual rainfall over a 2 d period to a fully drained catchment. The median of two days was then chosen for all catchments. Recession times were estimated using the methods described in , which fit a recession curve to the largest flood events from the observational data series. Our 200 gauging stations have NDF spanning 2 to 45 d.

Flood generating process (FGP) was defined for each event based on the relative contribution of rainfall and snowmelt to the flood, based on the approach in . We selected this approach from the range of available flood classification schemes because it provides a simple yet effective distinction between rainfall and snowmelt generated floods and has been successfully applied in studies conducted within our region . To account for antecedent conditions, the contribution to a specific flood was computed as the sum of rainfall and snowmelt in a catchment-specific time window prior to, and including, the flood peak day. This time window was set as the catchment-specific recession times as defined above. Figure  shows the average fractional contribution of rainfall to flood events, reflecting the dominant flood generating process (FGP) in each catchment. Using the thresholds proposed by , all flood events were classified into snowmelt generated events, rainfall generated events and mixed events depending on whether more than two thirds of the contribution stemmed from snowmelt, rainfall or neither, respectively. The distribution of all flood events' fractional rainfall contribution, along with the flood type classification thresholds, is shown in Fig. . The figure further shows two alternative pairs of classification thresholds used to assess the results' sensitivity to the chosen thresholds.

Both LSTM and our benchmark HBV model were evaluated using a period unseen during model training/calibration, i.e. 15 hydrological years comprising 1 September 1994–31 August 2009. Early 1990s is typically considered the start of thoroughly quality-controlled rating curves for a large proportion of the Norwegian streamflow gauging stations. We did not want the models to suffer from changes in the water balance from the calibration period to the evaluation period due to changes in the precipitation measuring network. To assess whether this was the case, we computed the runoff coefficient, defined as the ratio of streamflow to precipitation, for the two periods. For most catchments, the runoff coefficients were similar between the two periods (Fig. ). However, for four (13) catchments, a 30 % (20 %) change in the runoff coefficient from training to evaluation period was detected, which might have had an influence on the model performance results. Negative discharge values in the LSTM simulations were truncated to zero prior to the evaluation, and simulated series for each catchment were masked by data gaps existing in the observed series.

We evaluated model performance in terms of (i) per-catchment overall performance, (ii) descriptive statistics over all collected peaks of each flood type, and (iii) per-catchment flood peak performance of each flood type. In terms of (i), we assessed the fit between observed and simulated streamflow across the evaluation period for each catchment using Nash-Sutcliffe efficiency (NSE), the updated Kling-Gupta efficiency KGE;, and mean absolute error (MAE), all defined in Table . Additionally, we assessed the three components comprising KGE: Pearson correlation coefficient (ρ), bias ratio (β) and variability ratio (γ). The two latter are defined as: 2β=q^‾q‾ and 3γ=σq^/q^‾σq/q‾ where q^‾ is mean simulated streamflow, q‾ is mean observed streamflow, σq^ is standard deviation of simulated streamflow, and σq is standard deviation of observed streamflow.

In step (ii), we used descriptive statistics to summarise the flood peak performance in terms of timing and magnitudes over all collected flood peaks (i.e. independent of catchment) of each flood type: snowmelt generated floods, mixed floods and rainfall generated floods. Timing was evaluated by computing the percentage of peaks of a given flood type simulated at the day of observed peak (i.e. correct timing), one day too early or too late, or more than one day too early or too late. Flood peak magnitudes were evaluated by percent errors, considering both the simulated discharge magnitude at the day of observed flood peak (PEpeak,pinned) and the simulated maximum discharge within a 2 d time window of the observed flood peak (PEpeak,floating). The latter allows comparison of peak magnitudes even if the model does not match the exact day of the observed peak. The definitions of these metrics are as follows. For each catchment s∈S, let n be the number of observed floods of a specific type at catchment s. Let tj denote the timestep of the jth observed flood peak. Define qs,j:=qs,tj and q^s,j:=q^s,tj as the observed and simulated streamflow at the jth peak, respectively. Then, PEpeak,pinned for peak j at catchment s is 4PEpeak,pinneds,j=q^s,j-qs,jqs,j⋅100, for j=1,…,n and s∈S. Further, defining the window Ij={i∈Z:|i-tj|≤2}, PEpeak,floating is 5PEpeak,floatings,j=max⁡i∈Ijq^s,i-qs,jqs,j⋅100. Further, we computed the false alarm rate (FAR) and probability of detection (POD) of each flood type e.g.. FAR measures the percentage of false positives, i.e. incorrectly identified flood events by a given model, and has an optimum value at 0 %. To compute FAR, we applied the flood event selection and classification procedure described in Sect.  on the simulated streamflow series. For each detected simulated flood event, the corresponding “pinned” (i.e. exact day) and “floating” (i.e. maximum within a 2 d time window) observed streamflow value was extracted and defined as a non-flood event if the value did not exceed the 98th percentile. FARpinned and FARfloating were then defined as the percent of simulated flood events that had corresponding pinned, respectively floating, observed non-flood events. POD measures to what degree a model is able to capture the observed flood events. It has an optimum at 100 %. PODpinned and PODfloating were computed as the percent of observed flood events that had a corresponding pinned, respectively floating, simulated streamflow exceeding the 98th percentile. We compared FAR and POD results using the 98th percentile streamflow magnitudes extracted from each individual (simulated and observed) time series with results using only the observed series to define the 98th percentile streamflow magnitudes.

In the final evaluation step (iii), we evaluated per-catchment timing error and mean absolute percentage error of flood peaks separately for each flood type, as defined in Table . Timing error represents the percent of flood peaks that are simulated at a different day than the observed flood peaks. Corresponding to the definitions of PEpeak,pinned and PEpeak,floating above, we computed the mean absolute percentage error of flood peaks considering both pinned (MAPEpeak,pinned) and floating (MAPEpeak,floating) simulated peaks. The per-catchment flood peak performance metrics were only computed for catchments with minimum ten flood events of the given flood type in the evaluation period. A minimum of ten flood events during the evaluation period were found for 45 catchments for snowmelt generated floods, 60 catchments for rainfall generated floods (including 13 of the same catchments that had minimum ten snowmelt generated floods), and five catchments for mixed floods. Due to the low number of catchments with the required number of mixed flood events, the results for mixed floods are excluded from the per-catchment flood peak performance results.

The LSTM model performance in terms of NSE and KGE are shown for the evaluated catchments in Fig. . Importantly, all results were computed for the unseen evaluation period (ref. Sect. ). Average scores were 0.84 for NSE and 0.86 for KGE, and NSE (KGE) scores exceeded 0.7 in 100 (102) catchments. The KGE components (ρ, β and γ) and MAE results are presented in Fig . All ρ (i.e. correlation coefficient) scores exceeded 0.83, whereof 83 % of them exceeded 0.9. A total of 82 % of the catchments had a β (i.e. bias ratio) in the range 0.9–1.1 with a similar percentage of catchments below (46 %) and above (54 %) the optimum of 1. For γ (variability ratio), 70 % of the catchments had values in the range 0.9 to 1.1, and in 82 % of the catchments the coefficient of variation was underestimated (i.e. γ<1). MAE scores ranged 0.2 to 4.2 mm d⁻¹ with a average of 1.1 mm d⁻¹.

To benchmark our results, the LSTM NSE and KGE values were compared with those of the HBV model (Fig. ). A total of 99 catchments (96 %) had a higher NSE score for LSTM as compared to HBV, with the score difference exceeding 0.1 for 27 of the catchments. In terms of KGE, a higher LSTM score was found for 79 of the 103 catchments (77 %), with a KGE difference exceeding 0.1 for 12 catchments. One of the HBV KGE scores exceeded the corresponding LSTM scores by more than 0.1. The overweight of higher LSTM scores is reflected in the overweight of catchments above the diagonal line in Fig. c, d. The largest improvement in scores when comparing LSTM to HBV were found for catchments with HBV scores below 0.6. Catchments with floods predominantly generated by snowmelt (i.e. pink coloured dots) had generally higher NSE scores than catchments predominantly generated by rainfall (i.e. green coloured dots) for HBV. A similar pattern was not found for LSTM's NSE scores, nor for any of the models' KGE scores. In terms of the KGE components, LSTM had a better score for ρ in 93 %, β in 74 %, and γ in 44 % of the catchments. In all but three catchments, mean absolute errors were lower (i.e. better) for LSTM as compared to HBV.

Figure  shows the overall ability of LSTM and HBV to simulate the correct timing of the flood peaks, shown separately for snowmelt generated events, mixed events and rainfall generated events. Both models had a notably higher percentage of correctly simulated peak day for rainfall generated events as compared to mixed events, and mixed events as compared to snowmelt generated events. LSTM simulated the correct peak day for 50 % of the snowmelt generated events, 67 % of the mixed events and 77 % of the rainfall generated event. The corresponding correct peak day percentages for HBV were 14–16 pp smaller. For all flood types, a higher percentage of peak events were simulated too early by HBV than by LSTM. For example, 40 % of the snowmelt generated events are simulated too early by HBV, as compared to 21 % for LSTM. For rainfall generated events, the corresponding numbers are 27 % for HBV and 9 % for LSTM. The corresponding results using two alternative pairs of flood type classification thresholds were very similar (Figs. –).

The distributions of percent error of simulated flood peak magnitudes are relatively similar for snowmelt, mixed and rainfall generated events (Fig. ). Hence, the two alternative pairs of flood type classification thresholds tested produced very similar results (Figs. –). Slightly better results were found for PEpeak,floating as compared to PEpeak,pinned, as expected since the former allows for extracting the simulated flood peak despite the model missing the peak day by 1 or 2 d (ref. Fig. ). For LSTM, close to half of the snowmelt (46 %) and rainfall generated events (49 %) are within ±20 % of PEpeak,floating values, compared to 36 %, respectively 38 %, of the events for HBV. Regardless of model and flood type, most (77 % to 91 %) of the observed peak magnitudes were underestimated. More events had relatively large underestimations (-40 % to -100 %) for HBV as compared to LSTM.

FAR and POD results for the different flood types and models are shown in Fig. . For FAR, a lower value is desirable, whereas a higher value is desirable for POD. As expected, all results allowing for a two day shift in the flood peak timing (“floating”) are better than corresponding results requiring exact day match (“pinned”). Further, using time series specific flood thresholds generally resulted in higher percentages than corresponding results using only observed flood thresholds. LSTM results ranged 21 %–39 % for FAR and 52 %–70 % for POD. LSTM's FAR and POD results for rainfall and snowmelt generated flood events were generally similar, and 6–11 pp better than those of mixed flood events. HBV had slightly higher FAR values (except FARfloating for mixed and rainfall generated events) and lower POD values than LSTM.

The resulting per-catchment flood peak performance scores for LSTM and HBV are shown in Fig. , and maps showing the differences in scores between the two models are presented in Fig. . Across all peak metrics and flood types, LSTM had better scores than HBV for the majority of the catchments. LSTM had the lowest percentage of timing error in 84 % of the catchments for snowmelt generated flood events, and 78 % of the catchments in terms of rainfall generated flood events. Median improvement by LSTM across catchments was 14 pp for snowmelt and 11 pp for rainfall generated floods, but improvements exceeding 30 pp were found for several catchments. Both models had a markedly lower timing error when considering rainfall generated events (catchment averages of 24 % for LSTM and 38 % for HBV) as compared to snowmelt generated events (catchment averages of 49 % for LSTM and 66 % for HBV).

Most MAPEpeak,pinned scores were in the range 10 % to 40 %, with catchment average of 25 % to 26 % for LSTM and 32 % for HBV. MAPEpeak,pinned for snowmelt generated floods had the largest median model difference of 6.5 pp, in the favour of LSTM. For both error metrics considering peak magnitude (MAPEpeak,pinned and MAPEpeak,floating), LSTM had smaller errors than HBV for a larger proportion of the catchments when considering snowmelt generated floods as compared to rainfall generated floods. On the other hand, more catchments had a relatively larger difference between the models when considering rainfall generated floods, in particular for catchments where HBV had a relatively high (>40 %) error score.

Figure  combines the model comparisons of overall performance (KGE) and flood peak performance (MAPEpeak,pinned). Catchments in quadrant IV (lower right square in each plot) have a better metric score for LSTM as compared to HBV in terms of both KGE and MAPEpeak,pinned. The majority of catchments (76 % and 75 %) are found in quadrant IV. A few catchments show notably better results for LSTM, with a >0.1 larger KGE and a smaller MAPEpeak,pinned of more than 5 pp. The minority (2 % and 8 %) of the catchments are found in quadrant II that represents better HBV scores for both metrics. Figures  and show model difference in NSE, respectively KGE, versus model difference in all three flood peak metrics. In the corresponding plots using NSE instead of KGE, nearly all catchments are located in quadrants I and IV, as LSTM had the highest NSE scores for 96 % of the catchments.

A per-catchment summary of the best-performing model in terms of all evaluated metrics is presented in Fig. . LSTM had the best scores for the majority of the catchments for all evaluated metrics except (the KGE component) γ. For MAE, NSE and ρ, 93 % to 97 % of the catchments had a better score for LSTM. To indicate the catchment specific best model across metrics, the percentage of metrics where LSTM had a better score is given at the top of each catchment column. For eight of the 103 catchments, HBV had better scores for minimum two thirds of the metrics. LSTM on the other hand, had better scores for minimum two thirds of the metrics for 90 of the catchments.

LSTM NSE scores were generally high, exceeding 0.7 for 100 catchments, and with an average NSE of 0.84 as compared to 0.76 for HBV. For one catchment in particular (catchment ID 2.439), the models were unable represent the time series well, with NSE<0.6 and KGE<0.7 for both LSTM and HBV. This catchment had calibration NSE of 0.90 (LSTM) and 0.79 (HBV), and a 30 % drop in runoff coefficient from training to evaluation period, indicating problems with the observed meteorological or streamflow data during the evaluation period rather than an inability of the models to represent the catchment's streamflow behaviour. Many of the snowmelt dominated catchments were among the catchments with the highest NSE scores for HBV, in line with previous studies demonstrating that models typically achieve higher NSE and KGE values in catchments with strong seasonality . However, for LSTM in terms of NSE, and for both models in terms of KGE, there were no distinct relation between catchment dominant FGP and model performance score.

A higher percentage of catchments were improved by LSTM in terms of NSE (96 %) as compared to KGE (77 %). Of the three components constituting KGE, the one reflecting the variability (γ) of the model was the only evaluated metric with a better HBV score for the majority of the catchments (Fig. ). LSTM generally underestimated γ for more catchments and to a larger degree than HBV (Fig. ). The underestimated variability may partly relate to the applied loss function (NSE) which normalises the prediction errors by the variability of the time series. has previously shown how the variability has to be underestimated to maximise NSE. In terms of the bias ratio (β), the majority of catchments exhibited better scores for LSTM than HBV. Due to precipitation undercatch, the HBV model includes catchment specific correction factors for rain and snow precipitation that were calibrated to support conservation of the water balance. The LSTM model, on the other hand, has no water balance constraints and has therefore no need for precipitation correction factors. We suggest that the improved bias ratios obtained by LSTM result from the absence of water balance constraints, allowing for a more accurate representation of average streamflow. Further, LSTM outperformed HBV in all but three catchments in terms of mean absolute error, implying a systematically higher accuracy in the LSTM predictions.

The results revealed notable differences in the ability of LSTM to simulate the correct peak timing of snowmelt versus rainfall generated floods. Whereas 77 % of rainfall generated flood peaks were simulated at the correct day, the corresponding percentage for snowmelt generated flood peaks was only 50 % (Fig. ). This finding was robust across the three different pairs of classification thresholds tested (Figs. –). As snowmelt generated floods react to snowmelt typically spanning days to weeks, the floods often last multiple days and may not have a very distinct peak as compared to rainfall generated floods e.g. Fig. 2 in. Relatively small differences between peak discharge and discharge magnitudes in adjacent days may explain the lower percentage of correctly simulated peak days for snowmelt generated floods. This reasoning is supported by the similar mean absolute percentage errors at the day of observed peak (MAPEpeak,pinned) and FAR and POD results for snowmelt and rainfall generated floods (Fig. ). The same reasoning may explain the intermediate position of the timing results for mixed flood (better than snowmelt generated floods and worse than rainfall generated floods).

The identified differences in model performance for different flood types were not unique to LSTM. Similar differences were found for HBV. In terms of MAPEpeak,pinned, HBV exhibited the highest errors (exceeding 40 %) for rainfall generated floods in several catchments. Similarly high errors were only found in three catchments for LSTM. Flood-type dependent performance has also previously been demonstrated by , who identified differences in a model's flood peak performances in catchments of different regimes across four different process-based hydrological models.

The value of a hydrological model for specific applications depends on the model performance with regards to relevant characteristics. Thus, model evaluations beyond the metrics considering the entire streamflow time series (e.g. NSE and KGE) are often necessary. Figure  shows that the model preferred for simulating the full streamflow time series (KGE) does not always match the one preferred for reproducing peak magnitudes (MAPEpeak,pinned). Whereas the majority of the catchments had better LSTM scores for both overall and flood peak metrics (quadrant IV), the preferred model depended on the metric for approx. one fifth of the catchments (quadrants I and III). Notably, some catchments had a slightly (<0.025) lower KGE for LSTM than HBV, whereas the peak magnitude errors were reduced by 5 to 10 pp. In such cases, LSTM may be the preferred model for flood-specific applications despite the somewhat lower overall score.

We included three different flood peak specific evaluation metrics in this study to account for different aspects relevant for flood applications. Specifically, MAPEpeak was evaluated both for simulated discharge at the day of observed peak (“pinned”), and for simulated maximum discharge within 2 d of the observed peak (“floating”). For HBV, which generally had higher timing errors, the differences between the two MAPEpeak metrics were larger than for LSTM. However, the overweight of catchments with a better LSTM MAPEpeak,floating score make evident that peak magnitudes were better represented by LSTM regardless of the timing errors by HBV. Generally, our flood peak evaluation results demonstrated that LSTM does a better job than HBV for most catchments. At the local (i.e. catchment) scale, however, the conclusion on the preferred model depends in some cases on the desired characteristic, and the desired characteristics depend on the application. For issuing flood warning, for example, the timing may be crucial, whereas inundation mapping depend more on magnitudes being correctly simulated.

A related interesting model evaluation step, outside of scope of this study, is to evaluate to what degree flood event classification using data from the hydrological models correspond to the applied classification. However, such an evaluation has to be done differently for the two models. For HBV, flood classification using model simulated snowmelt and derived rainfall can be compared with the classification performed using SeNorge derived rainfall and snowmelt. LSTM, on the other hand, does not simulate snowmelt, and an evaluation of its ability to classify flood events into dominant FGP, would rely on explainable machine learning techniques. One such technique proposed by uses integrated gradients to trace back contributions of each input sequence (precipitation and temperature) to individual flood events, and applies cluster analysis to identify dominant flooding mechanisms. They identified three main FGPs across Europe, two of them dominating in Norway and strongly reflecting snowmelt and rainfall generated flood events, respectively. A primary aim of a comparison of such a classification approach with the one used here, could be to assess the robustness of classification technique and subjective choices regarding FGP definitions. The relatively simple classification technique and related subjective choices used in this study is subject to uncertainties, and a comparison with other techniques would be an interesting further study. That said, we expect limited effect of chosen technique on our main results and conclusions, as indicated by the very similar results produced using alternative classification thresholds.

In this study, we constrained the dynamical forcing data and training period for LSTM to match that of our benchmark model in order to have a reasonably fair comparison. By doing so, we ensured that differences in model performances could not be attributed to differences in how informed the models were about local hydrometeorological conditions in each catchment. However, given the fundamentally different nature of the two models, the premises for training the best model are different. Accordingly, premade choices suitable of the benchmark model is not the best suitable choices for deep learning models, and there is a further potential to improve the LSTM simulations. Low-hanging fruit to achieve an LSTM model with even higher performance include expanding the training period considerably where possible and forcing the model with a wider range of atmospheric variables and datasets . Another possibility is finetuning of the LSTM model for individual catchments to explore the potential to improve the model further for local conditions . Such potential avenues should be explored in case an LSTM model is considered for operational use to unleash the best potential based on the premises of deep learning models.