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To date, long short-term memory (LSTM) networks have been successfully applied to a key problem in hydrology: the prediction of runoff. Unlike traditional conceptual models, LSTM models are built on concepts that avoid the need for our knowledge of hydrology to be formally encoded into the model. The question, then, is how we can still make use of our domain knowledge and traditional practices, not to build the LSTM models themselves, as we do for conceptual models, but to use them more effectively. In the present paper, we adopt this approach, investigating how we can use information concerning the hydrologic characteristics of catchments for LSTM runoff models. In this first application of LSTM in a French context, we use 361 gauged catchments with very diverse hydrologic conditions from across France. The catchments have long time series of at least 30 years. Our main directions for investigation include (a) the relationship between LSTM performance and the length of the LSTM input sequence within different hydrologic regimes, (b) the importance of the hydrologic homogeneity of catchments when training LSTMs on a group of catchments, and (c) the interconnected influence of the local tuning of the two important LSTM hyperparameters, namely the length of the input sequence and the hidden unit size, on the performance of group-trained LSTMs. We present a classification built on three indices taken from the runoff, precipitation, and temperature regimes. We use this classification as our measure of homogeneity: catchments within the same regime are assumed to be hydrologically homogeneous. We train LSTMs on individual catchments (local-level training), on catchments within the same regime (regime-level training), and on the entire sample (national-level training). We benchmark local LSTMs using the GR4J conceptual model, which is able to represent the water gains/losses in a catchment. We show that LSTM performance has the highest sensitivity to the length of the input sequence in the Uniform and Nival regimes, where the dominant hydrologic process of the regime has clear long-term dynamics; thus, long input sequences should be chosen in these cases. In other regimes, this level of sensitivity is not found. Moreover, in some regimes, almost no sensitivity is observed. Therefore, the size of the input sequence in these regimes does not need to be large. Overall, our homogeneous regime-level training slightly outperforms our heterogeneous national-level training. This shows that the same level of data adequacy with respect to the complexity of representation(s) to be learned is achieved in both levels of training. We do not, however, exclude a potential role of the regime-informed property of our national LSTMs, which use previous classification variables as static attributes. Last but not least, we demonstrate that the local selection of the two important LSTM hyperparameters (the length of the input sequence and the hidden unit size) combined with national-level training can lead to the best runoff prediction performance.

Hydrological modelling of small mountainous catchments is particularly challenging because of the high spatio-temporal resolution required for the meteorological forcings. In situ measurements of precipitation are typically scarce in these remote areas, particularly at high elevations. Precipitation reanalyses propose different alternative forcings for the simulation of streamflow using hydrological models. In this paper, we evaluate the performances of two hydrological models representing some of the key processes for small mountainous catchments (< 300 km2), using different meteorological products with a fine spatial and temporal resolution. The evaluation is performed on 55 small catchments of the northern French Alps. While the simulated streamflows are adequately reproduced for most of the configurations, these evaluations emphasize the added value of radar measurements, in particular for the reproduction of flood events. However, these better performances are only obtained because the hydrological models correct the underestimations of accumulated amounts (e.g. annual) from the radar data in high-elevation areas.

To advance the discovery of scale-relevant hydrological laws while better exploiting massive multisource data, merging artificial intelligence with process-based modeling has emerged as a compelling approach, as demonstrated in recent lumped hydrological modeling studies. This research proposes a general spatially distributed hybrid modeling framework that seamlessly combines differentiable process-based models with neural networks. Specifically, we focus on hybridizing the hydrological module – built atop a differentiable kinematic wave routing over a flow direction grid – using a process-parameterization network that refines internal water fluxes, with all conceptual parameters estimated by a regionalization network trained simultaneously. We evaluate flood modeling performance and analyze the interpretability of learned conceptual parameters and corrections of internal fluxes using two high-resolution datasets (dx=1 km and dt=1 h). The first dataset involves 235 catchments in France, used for local calibration–validation and model structure comparisons between the classical Génie Rural (GR)-like model and the hybrid approach. The second dataset presents a challenging multi-catchment modeling setup in flash-flood-prone areas to demonstrate the framework's regionalization learning capabilities. The results show that the hybrid models achieve superior accuracy and robustness compared to classical approaches in both spatial and temporal validation. Analysis of the spatially distributed parameters and internal fluxes reveals the hybrid models' nuanced behavior, their adaptability to diverse hydrological responses, and their potential to uncover physical processes.

This contribution presents a novel multi-dimensional (multi-D) hydraulic–hydrological numerical model with variational data assimilation capabilities. It allows multi-scale modeling over large domains, combining in situ observations with high-resolution hydrometeorology and satellite data. The multi-D hydraulic model relies on the 2D shallow-water equations solved with a 1D–2D adapted single finite-volume solver. One-dimensional-like reaches are built through meshing methods that cause the 2D solver to degenerate into 1D. They are connected to 2D portions that act as local zooms, for modeling complex flow zones such as floodplains and confluences, via 1D-like–2D interfaces. An existing parsimonious hydrological model, GR4H, is implemented and coupled to the hydraulic model. The forward-inverse multi-D computational model is successfully validated on virtual and real cases of increasing complexity, including using the second-order scheme version. Assimilating multiple observations of flow signatures leads to accurate inferences of multi-variate and spatially distributed parameters among bathymetry friction, upstream and lateral hydrographs and hydrological model parameters. This notably demonstrates the possibility for information feedback towards upstream hydrological catchments, that is, backward hydrology. A 1D-like model of part of the Garonne River is built and accurately reproduces flow lines and propagations of a 2D reference model. A multi-D model of the complex Adour basin network, with inflow from the semi-distributed hydrological model, is built. High-resolution flow simulations are obtained on a large domain, including fine zooms on floodplains, with a relatively low computational cost since the network contains mostly 1D-like reaches. The current work constitutes an upgrade of the DassFlow computational platform. The adjoint of the whole tool chain is obtained by automatic code differentiation.

The unprecedented hydraulic visibility of rivers surfaces deformation with SWOT satellite offers tremendous information for improving hydrological‐hydraulic models and discharge estimations for rivers worldwide. However, estimating the uncertain or unknown parameters of hydraulic models, such as inflow discharges, bathymetry, and friction parameters, poses a high‐dimensional inverse problem, which is ill‐posed if based solely on altimetry observations. To address this, we couple the hydraulic model with a semi‐distributed hydrological model, to constrain the ill‐posed inverse problem with sufficiently accurate initial estimates of inflows at the network upstreams. A robust variational data assimilation of water surface elevation (WSE) data into a 1D Saint‐Venant river network model, enables the inference of inflow hydrographs, effective bathymetry, and spatially distributed friction at network scale. The method is demonstrated on the large, complex, and poorly gauged Maroni basin in French Guiana. The pre‐processing chain enables (a) building an effective hydraulic model geometry from drifting ICESat‐2 WSE altimetry and Sentinel‐1 width; (b) filtering noisy SWOT Level 2 WSE data before assimilation. A systematic improvement is achieved in fitting the assimilated WSE (85% cost improvement), and in validating discharge at 5 gauges within the network. For assimilation of SWOT data alone, 70% of data‐model fit is in [−0.25;0.25m] $[-0.25;\\,0.25\\,\\mathrm{m}]$ and the discharge NRMSE ranges between 0.05 and 0.18 (18%–71% improvement from prior). The high density of SWOT WSE enables the inferrence of detailed spatial variability in channel bottom elevation and friction, and inflows timeseries. The approach is transferable to other rivers networks worldwide.

Estimating spatially distributed hydrological parameters in ungauged catchments poses a challenging regionalization problem and requires imposing spatial constraints given the sparsity of discharge data. A possible approach is to search for a transfer function that quantitatively relates physical descriptors to conceptual model parameters. This paper introduces a Hybrid Data Assimilation and Parameter Regionalization (HDA-PR) approach incorporating learnable regionalization mappings, based on either multi-linear regression or artificial neural networks (ANNs), into a differentiable hydrological model. This approach demonstrates how two differentiable codes can be linked and their gradients chained, enabling the exploitation of heterogeneous data sets across extensive spatio-temporal computational domains within a high-dimensional regionalization context, using accurate adjoint-based gradients. The inverse problem is tackled with a multi-gauge calibration cost function accounting for information from multiple observation sites. HDA-PR was tested on high-resolution, hourly and kilometric regional modeling of 126 flash-flood-prone catchments in the French Mediterranean region. The results highlight a strong regionalization performance of HDA-PR especially in the most challenging upstream-to-downstream extrapolation scenario with ANN, achieving median Nash-Sutcliffe efficiency (NSE) scores from 0.6 to 0.71 for spatial, temporal, spatio-temporal validations, and improving NSE by up to 30% on average compared to the baseline model calibrated with lumped parameters. Multiple evaluation metrics based on flood-oriented hydrological signatures also indicate that the use of an ANN leads to better performances than a multi-linear regression in a validation context. ANN enables to learn a non-linear descriptors-to-parameters mapping which provides better model controllability than a linear mapping for complex calibration cases.

Land surface models (LSMs) are widely used to study the continental part of the water cycle. However, even though their accuracy is increasing, inherent model uncertainties can not be avoided. In the meantime, remotely sensed observations of the continental water cycle variables such as soil moisture, lakes and river elevations are more frequent and accurate. Therefore, those two different types of information can be combined, using data assimilation techniques to reduce a model's uncertainties in its state variables or/and in its input parameters. The objective of this study is to present a data assimilation platform that assimilates into the large-scale ISBA-CTRIP LSM a punctual river discharge product, derived from ENVISAT nadir altimeter water elevation measurements and rating curves, over the whole Amazon basin. To deal with the scale difference between the model and the observation, the study also presents an initial development for a localization treatment that allows one to limit the impact of observations to areas close to the observation and in the same hydrological network. This assimilation platform is based on the ensemble Kalman filter and can correct either the CTRIP river water storage or the discharge. Root mean square error (RMSE) compared to gauge discharges is globally reduced until 21 % and at Óbidos, near the outlet, RMSE is reduced by up to 52 % compared to ENVISAT-based discharge. Finally, it is shown that localization improves results along the main tributaries.

A method of multiple working hypotheses was applied to a range of catchments in the Mediterranean area to analyse different types of possible flow dynamics in soils during flash flood events. The distributed, process-oriented model, MARINE, was used to test several representations of subsurface flows, including flows at depth in fractured bedrock and flows through preferential pathways in macropores. Results showed the contrasting performances of the submitted models, revealing different hydrological behaviours among the catchment set. The benchmark study offered a characterisation of the catchments' reactivity through the description of the hydrograph formation. The quantification of the different flow processes (surface and intra-soil flows) was consistent with the scarce in situ observations, but it remains uncertain as a result of an equifinality issue. The spatial description of the simulated flows over the catchments, made available by the model, enabled the identification of counterbalancing effects between internal flow processes, including the compensation for the water transit time in the hillslopes and in the drainage network. New insights are finally proposed in the form of setting up strategic monitoring and calibration constraints.

The absence of validation or comparison data for verifying flood mapping methods poses a significant challenge in developing operational hydraulic approaches. This article aims to address this gap by presenting a benchmark dataset for flash flood mapping in the French Mediterranean region. The dataset described in this paper (https://doi.org/10.57745/IXXNAY, Nicolle et al., 2024) includes flood hazard maps and simulation results of three actual flash flood events, all computed in a steady regime at a 5 m resolution using a 2D SWE (shallow water equation) model (neglecting inertia) named Floodos (Davy et al., 2017). Additionally, it includes the input data necessary (digital terrain models, inflow discharges, hydrographic network) for conducting similar simulations with other hydrodynamic modelling approaches in both steady and unsteady regimes. A comprehensive validation dataset, comprising observed flood extents, high water marks, and rating curves, is also provided, enabling a detailed evaluation of 2D hydraulic simulation results. The simulation results from Floodos, compared against stage–discharge rating curves available at gauging stations, yielded highly encouraging outcomes. The median error (sim.–obs.) was −0.04 m for the 2-year return period and −0.14 m across all simulated return periods, ranging from 2 to 1000 years.

The smash software is a differentiable and regionalizable framework enabling modular high-resolution hydrological modeling and data assimilation, from catchment to regional and country scales, for water research and operational applications. smash combines various process-based conceptual operators for vertical and lateral flows, which can be hybridized with a descriptor-to-parameter neural network for regionalization. smash features an efficient, differentiable Fortran solver using Tapenade to automatically derive the adjoint model that supports CPU forward–inverse parallel computing and spatially distributed optimization of large parameter vectors thanks to an accurate cost gradient, interfaced in Python using f90wrap. This article presents smash algorithms and their open-source code, documentation, and tutorials. It highlights foundational research, benchmarking on state-of-the-art datasets, and readiness for scientific and operational use. To ensure reproducibility, open-source datasets are used to demonstrate the main functionalities of smash, including parallel computation performances and the application of multiple spatially distributed conceptual model structures over a large catchment sample. These functionalities include uniform or spatially distributed calibration and regionalization by learning the relation between descriptors and parameters. The provided Python tool allows application to any other catchment from globally available datasets. Using CAMELS, as per recent articles, a median Kling–Gupta efficiency (KGE)>0.8 is obtained in local spatially distributed calibration for daily Génie Rural (GR)-like and variable infiltration capacity (VIC)-like model structures at dx=1′30′′ (∼3km) and KGE>0.6 in spatiotemporal validation in a regionalization context. The regionalization of a high-resolution hourly GR-like model structure at dx=500m over a difficult Mediterranean flash-flood-prone case results in a Nash–Sutcliffe efficiency (NSE)>0.6 in spatiotemporal validation. The proposed differentiable and regionalizable spatially distributed modeling framework is designed for gradient-based variational data assimilation, applicable to initial state (not shown) and parameter estimation at multiple timescales, and is intended for collaborative research and operational applications. Additionally, smash supports the implementation of other differentiable hydrological and hydraulic models, as well as hybrid physics–AI models, further enhancing its versatility and applicability.