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Hydrological parameters are used to tailor simulation models to the specific characteristics of a catchment so that models can accurately represent processes under different catchment conditions. In the case of the mesoscale Hydrological Model (mHM), its parameters are estimated via transfer functions using the Multiscale Parameter Regionalization (MPR) approach. In this study, the spatial and temporal variability in the sensitivity of transfer function parameters (TFP) and their relationships to corresponding simulated processes are investigated to understand how these TFP control simulated hydrological fluxes and state variables. Daily dominant model parameters are identified for 102 German catchments as a study domain with temperate climate using a temporally resolved parameter sensitivity analysis. This approach allows the comparison of spatial and temporal variability of TFP dominance. Three simulated hydrological fluxes and one state variable are used as target variables for the sensitivity analysis: runoff, actual evapotranspiration, soil moisture (SM), and groundwater recharge. The analysis leads to consistent and plausible patterns of parameter dominance in space. An evapotranspiration parameter dominates actual evapotranspiration and SM. Runoff and recharge are mainly controlled by soil texture, subsurface, and percolation parameters. The relevance of spatial versus temporal variability varies among model parameters and target variables. In some cases, parameter sensitivities are related to the magnitude of corresponding processes. Low spatial and temporal variability of dominant parameters is explained by MPR. In light of these results, a joint spatio‐temporal analysis is recommended to better understand how model parameters drive simulated states and fluxes in hydrological models to improve process accuracy. Hydrological models use parameters to represent the hydrologic system under varying climate and landscape conditions. The mesoscale hydrological model (mHM) uses a special regionalization approach (Multiscale Parameter Regionalization, MPR) to ensure spatial consistency in parameter patterns. In this study, we conducted a temporally resolved parameter sensitivity analysis that estimates daily parameter sensitivities for four hydrological variables (runoff, actual evapotranspiration, soil moisture (SM), recharge) across 102 gauges. In this way, we investigated how the parameter sensitivity varies across space and time. Our results indicate that an evapotranspiration parameter dominates not only simulated evapotranspiration but also SM. Runoff and recharge are mainly controlled by soil texture, subsurface and percolation parameters. The MPR approach ensures that the parameter sensitivity patterns are consistent across space. Additionally, our analysis reveals that in multiple cases the parameter sensitivity depends on the magnitude of the corresponding process. We see our analysis as a valuable contribution toward a better understanding of how parameters govern hydrological models. This study presents the first temporal parameter sensitivity analysis of a hydrologic model with multiscale parameter regionalizationSpatio‐temporal variability in dominant parameters changes with target variables (runoff, evapotranspiration, soil moisture, recharge)Daily sensitivities of some parameters are related to magnitude of corresponding process This study presents the first temporal parameter sensitivity analysis of a hydrologic model with multiscale parameter regionalization Spatio‐temporal variability in dominant parameters changes with target variables (runoff, evapotranspiration, soil moisture, recharge) Daily sensitivities of some parameters are related to magnitude of corresponding process

Accurate simulation of reservoirs has been a challenge for global hydrological models due to highly discontinuous water management and uncertainties in reservoir shape representation. In addition, at a global scale, it is crucial to consider those reservoirs that disrupt the downstream flow regime. We augment the mesoscale Hydrological Model with a newly developed lake module (LM) that incorporates an existing reservoir regulation scheme with non‐consumptive demand predictions from random forest. We also evaluate the sensitivity of reservoir shape on streamflow and evaporation for three shape approximations of varying complexities. We tested the LM across 31 non‐consumptive reservoirs covering an extensive range of hydroclimatic characteristics and demonstrate the applicability by using freely available global reservoir information. Streamflow simulations with reservoirs and model calibration show a median Kling‐Gupta Efficiency improvement of +0.94 (calibration) and +0.77 (validation) when compared against model simulations without reservoirs and default parameter set. We find reservoir evaporation highly sensitive to reservoir shape with half‐pyramid approximation consistently resulting in best fit at reservoirs with surveyed bathymetry. In contrast, the linear approximation (rectangular prism) produced a median bias of +114% relative to half‐pyramid, for estimating evaporation, across all the reservoirs. Streamflow simulations were insensitive to the reservoir shape. Our analysis shows that 30% of the non‐consumptive hydropower reservoirs of the GRanD data set are non‐disruptive and can be excluded without loss to model realism. Further work is necessary for testing the regulation approach in reservoirs with consumptive water usage. The new reservoir module of mesoscale Hydrological Model improves the median Kling‐Gupta Efficiency of streamflow simulations downstream of reservoirs by +0.94Commonly employed linear (rectangular prism) reservoir shape approximation overestimates reservoir evaporation by a factor of twoThree in ten non‐consumptive hydropower reservoirs within the GRanD data set exhibit insignificant streamflow disruption and can be omitted from simulations The new reservoir module of mesoscale Hydrological Model improves the median Kling‐Gupta Efficiency of streamflow simulations downstream of reservoirs by +0.94 Commonly employed linear (rectangular prism) reservoir shape approximation overestimates reservoir evaporation by a factor of two Three in ten non‐consumptive hydropower reservoirs within the GRanD data set exhibit insignificant streamflow disruption and can be omitted from simulations

While deep learning (DL) models exhibit superior simulation accuracy over traditional distributed hydrological models (DHMs), their main limitations lie in opacity and the absence of underlying physical mechanisms. The pursuit of synergies between DL and DHMs is an engaging research domain, yet a definitive roadmap remains elusive. In this study, a novel framework that seamlessly integrates a process‐based hydrological model encoded as a neural network (NN), an additional NN for mapping spatially distributed and physically meaningful parameters from watershed attributes, and NN‐based replacement models representing inadequately understood processes is developed. Multi‐source observations are used as training data, and the framework is fully differentiable, enabling fast parameter tuning by backpropagation. A hybrid DL model of the Amazon Basin (∼6 × 106km2) was established based on the framework, and HydroPy, a global‐scale DHM, was encoded as its physical backbone. Trained simultaneously with streamflow observations and Gravity Recovery and Climate Experiment satellite data, the hybrid model yielded median Nash‐Sutcliffe efficiencies of 0.83 and 0.77 for dynamic and distributed simulations of streamflow and total water storage, respectively, 41% and 35% higher than those of the original HydroPy model. Replacing the original Penman‒Monteith formulation in HydroPy with a replacement NN produces more plausible potential evapotranspiration (PET) estimates, and unravels the spatial pattern of PET in this giant basin. The NN used for parameterization was interpreted to identify the factors controlling the spatial variability in key parameters. Overall, this study lays out a feasible technical roadmap for distributed hydrological modeling in the big data era. A fully differentiable framework that seamlessly integrates physics and deep learning was developed for distributed hydrological modelingThe framework flexibly fuses multi‐source observations and improves the efficiency and accuracy of large‐scale hydrological modelingThe hybrid model for the Amazon Basin exhibits excellent fidelity and physical plausibility and provides insights into the ET process A fully differentiable framework that seamlessly integrates physics and deep learning was developed for distributed hydrological modeling The framework flexibly fuses multi‐source observations and improves the efficiency and accuracy of large‐scale hydrological modeling The hybrid model for the Amazon Basin exhibits excellent fidelity and physical plausibility and provides insights into the ET process

This study presents diagnostic evaluation of two large‐domain hydrologic models: the mesoscale Hydrologic Model (mHM) and the Variable Infiltration Capacity (VIC) over the contiguous United States (CONUS). These models have been calibrated using the Multiscale Parameter Regionalization scheme in a joint, multibasin approach using 492 medium‐sized basins across the CONUS yielding spatially distributed model parameter sets. The mHM simulations are used as a performance benchmark to examine performance deficiencies in the VIC model. We find that after calibration to streamflow, VIC generally overestimates the magnitude and temporal variability of evapotranspiration (ET) as compared to mHM as well as the FLUXNET observation‐based ET product, resulting in underestimation of the mean and variability of runoff. We perform a controlled calibration experiment to investigate the effect of varying number of transfer function parameters in mHM and to enable a fair comparison between both models (14 and 48 for mHM vs. 14 for VIC). Results of this experiment show similar behavior of mHM with 14 and 48 parameters. Furthermore, we diagnose the internal functioning of the VIC model by looking at the relationship of the evaporative fraction versus the degree of soil saturation and compare it with that of the mHM model, which has a different model structure, a prescribed nonlinear relationship between these variables and exhibits better model skill than VIC. Despite these limitations, the VIC‐based CONUS‐wide calibration constrained against streamflow exhibits better ET skill as compared to two preexisting independent VIC studies. Continental domain fluxes and states derived by two calibrated hydrologic models (mHM and VIC) are evaluated to diagnose model functional deficienciesThe more skillful (benchmark) model can help to identify the other model's functional deficienciesThe new VIC parameters based on streamflow calibration exhibit better ET skill compared to two preexisting VIC configurations

We present a 250‐year (1766–2015) inventory of European meteorological, hydrological, and agricultural droughts derived from ensemble simulations of the mesoscale Hydrological Model (mHM). The inventory of droughts takes into account an ensemble of 100 simulations from the hydrological model, allowing for assessment of how different meteorological forcing and model parameterizations affect a drought ranking. For the most extreme droughts, the variability in the ranking of drought events is low, while for the years with moderate precipitation deficits, the variability increases. Despite the underlying uncertainties, our drought inventory shows increased recurrence of soil moisture droughts in the Mediterranean and declining spatial extent of hydrological drought in Central Europe over the last three decades. Drought is one of the most costly natural hazards. Complete understanding of this phenomenon evades us because drought needs a long period of time to evolve and when it does, it might propagate through different components of the hydrological cycle. For example, meteorological drought, which is a lack of rainfall, might result in hydrological drought (low discharge/lake levels), agricultural drought (low soil moisture), or both. This is why it is important to record past occurrences of individual droughts to better understand under what conditions they propagated. To address this, herein we produce a 250‐year long European drought inventory based on hydrological modeling that presents the interaction of the three types of drought, namely, meteorological, hydrological, and agricultural, as well as their properties in a single, comprehensive framework. A 250‐year inventory depicts the major meteorological, hydrological, and agricultural droughts across EuropeVisualization of ensemble allows for an effective comparison among major drought years (severity and spatial extent)Increased recurrence of soil moisture droughts across the Mediterranean in the recent decades