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The streamflow recession analysis, always following a power law, depicts the storage-release relation in catchments. However, the understanding of hydrological recession dynamics is still insufficient. Here, a total of 80 nearly natural catchments from the reference hydrologic networks (RHNs) in the UK were selected to explore the changes and the controlling factors of recession slope curve parameters by utilizing trend analysis methods, the self-organizing map, and k-means clustering algorithms. The results demonstrated that (i) the estimation of event-scale recession parameters was sensitive to different combinations of recession extraction and fitting methods. Particularly, the combination of Brutsaert extraction and the linear regression method always obtained robust estimations of recession parameters. (ii) Changes of annual median recession parameters showed a clear spatial distribution pattern, indicating the climate-driven impact on recession processes. Up to 17 catchments in Scotland showed significant changes in recession processes, always displaying increasing trends in the recession coefficient and decreasing trends in the recession exponent. (iii) The recession exponent strongly depended on the base-flow index, rock permeability, arable area, and temporal distribution of rainfall. Additionally, the spatial patterning of recession processes further provided some insights for facilitating the understanding of the hydrological recession process.

On the Tibetan Plateau, the limited ground-based rainfall information owing to a harsh environment has brought great challenges to hydrological studies. Satellite-based rainfall products, which allow for a better coverage than both radar network and rain gauges on the Tibetan Plateau, can be suitable alternatives for studies on investigating the hydrological processes and climate change. In this study, a newly developed daily satellite-based precipitation product, termed Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks – Climate Data Record (PERSIANN-CDR), is used as input for a hydrologic model to simulate streamflow in the upper Yellow and Yangtze River basins on the Tibetan Plateau. The results show that the simulated streamflows using PERSIANN-CDR precipitation and the Global Land Data Assimilation System (GLDAS) precipitation are closer to observation than that using limited gauge-based precipitation interpolation in the upper Yangtze River basin. The simulated streamflow using gauge-based precipitation are higher than the streamflow observation during the wet season. In the upper Yellow River basin, gauge-based precipitation, GLDAS precipitation, and PERSIANN-CDR precipitation have similar good performance in simulating streamflow. The evaluation of streamflow simulation capability in this study partly indicates that the PERSIANN-CDR rainfall product has good potential to be a reliable dataset and an alternative information source of a limited gauge network for conducting long-term hydrological and climate studies on the Tibetan Plateau.

State-of-the-art global hydrological models (GHMs) exhibit large uncertainties in hydrological simulations due to the complexity, diversity, and heterogeneity of the land surface and subsurface processes, as well as the scale dependency of these processes and associated parameters. Recent progress in machine learning, fueled by relevant Earth observation data streams, may help overcome these challenges. But machine learning methods are not bound by physical laws, and their interpretability is limited by design. In this study, we exemplify a hybrid approach to global hydrological modeling that exploits the data adaptivity of neural networks for representing uncertain processes within a model structure based on physical principles (e.g., mass conservation) that form the basis of GHMs. This combination of machine learning and physical knowledge can potentially lead to data-driven, yet physically consistent and partially interpretable hybrid models. The hybrid hydrological model (H2M), extended from Kraft et al. (2020), simulates the dynamics of snow, soil moisture, and groundwater storage globally at 1∘ spatial resolution and daily time step. Water fluxes are simulated by an embedded recurrent neural network. We trained the model simultaneously against observational products of terrestrial water storage variations (TWS), grid cell runoff (Q), evapotranspiration (ET), and snow water equivalent (SWE) with a multi-task learning approach. We find that the H2M is capable of reproducing key patterns of global water cycle components, with model performances being at least on par with four state-of-the-art GHMs which provide a necessary benchmark for H2M. The neural-network-learned hydrological responses of evapotranspiration and grid cell runoff to antecedent soil moisture states are qualitatively consistent with our understanding and theory. The simulated contributions of groundwater, soil moisture, and snowpack variability to TWS variations are plausible and within the ranges of traditional GHMs. H2M identifies a somewhat stronger role of soil moisture for TWS variations in transitional and tropical regions compared to GHMs. With the findings and analysis, we conclude that H2M provides a new data-driven perspective on modeling the global hydrological cycle and physical responses with machine-learned parameters that is consistent with and complementary to existing global modeling frameworks. The hybrid modeling approaches have a large potential to better leverage ever-increasing Earth observation data streams to advance our understandings of the Earth system and capabilities to monitor and model it.

Neural networks have been shown to be extremely effective rainfall-runoff models, where the river discharge is predicted from meteorological inputs. However, the question remains: what have these models learned? Is it possible to extract information about the learned relationships that map inputs to outputs, and do these mappings represent known hydrological concepts? Small-scale experiments have demonstrated that the internal states of long short-term memory networks (LSTMs), a particular neural network architecture predisposed to hydrological modelling, can be interpreted. By extracting the tensors which represent the learned translation from inputs (precipitation, temperature, and potential evapotranspiration) to outputs (discharge), this research seeks to understand what information the LSTM captures about the hydrological system. We assess the hypothesis that the LSTM replicates real-world processes and that we can extract information about these processes from the internal states of the LSTM. We examine the cell-state vector, which represents the memory of the LSTM, and explore the ways in which the LSTM learns to reproduce stores of water, such as soil moisture and snow cover. We use a simple regression approach to map the LSTM state vector to our target stores (soil moisture and snow). Good correlations (R2>0.8) between the probe outputs and the target variables of interest provide evidence that the LSTM contains information that reflects known hydrological processes comparable with the concept of variable-capacity soil moisture stores. The implications of this study are threefold: (1) LSTMs reproduce known hydrological processes. (2) While conceptual models have theoretical assumptions embedded in the model a priori, the LSTM derives these from the data. These learned representations are interpretable by scientists. (3) LSTMs can be used to gain an estimate of intermediate stores of water such as soil moisture. While machine learning interpretability is still a nascent field and our approach reflects a simple technique for exploring what the model has learned, the results are robust to different initial conditions and to a variety of benchmarking experiments. We therefore argue that deep learning approaches can be used to advance our scientific goals as well as our predictive goals.

Accurate river streamflow forecasts are a vital tool in the fields of water security, flood preparation and agriculture, as well as in industry more generally. Traditional physics-based models used to produce streamflow forecasts have become increasingly sophisticated, with forecasts improving accordingly. However, the development of such models is often bound by two soft limits: empiricism – many physical relationships are represented empirical formulae; and data sparsity – long time series of observational data are often required for the calibration of these models. Artificial neural networks have previously been shown to be highly effective at simulating non-linear systems where knowledge of the underlying physical relationships is incomplete. However, they also suffer from issues related to data sparsity. Recently, hybrid forecasting systems, which combine the traditional physics-based approach with statistical forecasting techniques, have been investigated for use in hydrological applications. In this study, we test the efficacy of a type of neural network, the long short-term memory (LSTM), at predicting streamflow at 10 river gauge stations across various climatic regions of the western United States. The LSTM is trained on the catchment-mean meteorological and hydrological variables from the ERA5 and Global Flood Awareness System (GloFAS)–ERA5 reanalyses as well as historical streamflow observations. The performance of these hybrid forecasts is evaluated and compared with the performance of both raw and bias-corrected output from the Copernicus Emergency Management Service (CEMS) physics-based GloFAS. Two periods are considered, a testing phase (June 2019 to June 2020), during which the models were fed with ERA5 data to investigate how well they simulated streamflow at the 10 stations, and an operational phase (September 2020 to October 2021), during which the models were fed forecast variables from the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS), to investigate how well they could predict streamflow at lead times of up to 10 d. Implications and potential improvements to this work are discussed. In summary, this is the first time an LSTM has been used in a hybrid system to create a medium-range streamflow forecast, and in beating established physics-based models, shows promise for the future of neural networks in hydrological forecasting.

Several studies have shown that hydrological models do not perform well when applied to periods with climate conditions that differ from those during model calibration. This has important implications for the application of these models in climate change impact studies. The causes of the low transferability to changed climate conditions have, however, only been investigated in a few studies. Here we revisit a study in Austria that demonstrated the inability of a conceptual semi-distributed HBV-type model to simulate the observed discharge response to increases in precipitation and air temperature. The aim of the paper is to shed light on the reasons for these model problems. We set up hypotheses for the possible causes of the mismatch between the observed and simulated changes in discharge and evaluate these using simulations with modifications of the model. In the baseline model, trends of simulated and observed discharge over 1978–2013 differ, on average over all 156 catchments, by 95±50 mm yr−1 per 35 years. Accounting for variations in vegetation dynamics, as derived from a satellite-based vegetation index, in the calculation of reference evaporation explains 36±9 mm yr−1 per 35 years of the differences between the trends in simulated and observed discharge. Inhomogeneities in the precipitation data, caused by a variable number of stations, explain 39±26 mm yr−1 per 35 years of this difference. Extending the calibration period from 5 to 25 years, including annually aggregated discharge data or snow cover data in the objective function, or estimating evaporation with the Penman–Monteith instead of the Blaney–Criddle approach has little influence on the simulated discharge trends (5 mm yr−1 per 35 years or less). The precipitation data problem highlights the importance of using precipitation data based on a stationary input station network when studying hydrologic changes. The model structure problem with respect to vegetation dynamics is likely relevant for a wide spectrum of regions in a transient climate and has important implications for climate change impact studies.

Enhancing our understanding of the intricate interplay among hydro‐climatic processes is crucial for a comprehensive assessment of water availability and climate extremes across global land regions. Here, we propose an integrated framework to investigate networks of the global fields of multiple hydrological variables (Precipitation, Evapotranspiration, Soil Moisture). We apply a two‐layer complex network concept to formulate the independent networks of each hydrological variable and their interactions. Intra‐ (Single‐layer) and cross‐ (two‐layer) network coefficients are derived from the formulated hydrological network to quantify the linkage, spatial connection density, and scale for the independent hydrological fields (or variables) and their interactions. The joint distribution of the intra‐network coefficients reveals multiple spatial scales of connectivity for a moderately well‐connected location in case of evapotranspiration and soil moisture. With increasing global mean temperature, spatially synchronized evapotranspiration over such a large scale may lead to multi‐continental droughts and heatwaves. Furthermore, the (cross‐) network coefficients have identified regions acting as “bottlenecks” for moisture flow and the water‐dominated areas with less evaporative actions. The contrasting features of two‐layer network coefficients have provided a qualitative picture of moisture circulation and recirculation over many hydrological hotspot regions, such as the Amazonian basin, Indian subcontinents, and the Sahel region. The derived results can be employed to gain insights into the global water cycle’s multiple interacting processes (e.g., land‐atmosphere interactions). Key Points The bottleneck regions of the precipitation network act like conduits for moisture flow Drought and heatwaves can coevolve on multiple continents through spatially synchronized evapotranspiration and drying Transitional areas are important hydrologically interactive regions affirming the influence of soil moisture on distant precipitation events

Deep learning has emerged as a useful tool across geoscience disciplines; however, there remain outstanding questions regarding the suitability of unexplored model architectures and how to interpret model learning for regional-scale hydrological modelling. Here we use a convolutional long short-term memory network, a deep learning approach for learning both spatial and temporal patterns, to predict streamflow at 226 stream gauges across southwestern Canada. The model is forced by gridded climate reanalysis data and trained to predict observed daily streamflow between 1980 and 2015. To interpret the model's learning of both spatial and temporal patterns, we introduce a set of experiments with evaluation metrics to track the model's response to perturbations in the input data. The model performs well in simulating daily streamflow over the testing period, with a median Nash–Sutcliffe efficiency (NSE) of 0.68 and 35 % of stations having NSE>0.8. When predicting streamflow, the model is most sensitive to perturbations in the input data prescribed near and within the basins being predicted, demonstrating that the model is automatically learning to focus on physically realistic areas. When uniformly perturbing input temperature time series to obtain relatively warmer and colder input data, the modelled indicator of freshet timing and peak flow changes in accordance with the transition timing from below- to above-freezing temperatures. We also demonstrate that modelled August streamflow in partially glacierized basins is sensitive to perturbations in August temperature, and that this sensitivity increases with glacier cover. The results demonstrate the suitability of a convolutional long short-term memory network architecture for spatiotemporal hydrological modelling, making progress towards interpretable deep learning hydrological models.

Land surface hydrologic models adeptly capture crucial terrestrial processes with a high level of spatial detail. Typically, these models incorporate numerous uncertain, spatially varying parameters, the specification of which can profoundly impact the simulation capabilities. There is a longstanding tradition wherein parameter calibration has served as the conventional procedure to enhance model performance. However, calibrating distributed land surface hydrologic models presents a great challenge, often resulting in uneven spatial performance due to the compression of information inherent in model outputs and observations into a single‐value objective function. To address this problem, we propose a novel Generative Adversarial Network‐based Parameter Optimization (GAN‐PO) method. By leveraging a deep neural network to discern model spatial biases, we train a generative network to produce spatially coherent parameter fields, minimizing distinctions between simulations and observations. By leveraging neural network‐based surrogate models to make the physical model differentiable, we employ GAN‐PO to calibrate the Variable Infiltration Capacity (VIC) model against evapotranspiration (ET) over China's Huaihe basin. The results show that GAN‐PO can diminish errors in simulated ET derived from default parameters across nearly all grid cells within the study region, surpassing the conventional calibration approach based on the parameter regionalization technique. Ablation analysis indicates that relying solely on the traditional loss could lead to deteriorated model performance, underscoring the crucial role of the discriminator. Notably, due to the discriminator's explicit identification of model spatial biases, GAN‐PO excels in maintaining spatial consistency, outperforming the state‐of‐the‐art differentiable parameter learning (dPL) method in terms of model spatial performance. Key Points A novel generative adversarial network‐based parameter estimation method is proposed to calibrate distributed land surface hydrologic models By employing a discriminator to identify model spatial biases, this method contributes to effective and spatially coherent parameter estimation This method can substantially reduce model simulated errors at grid scale and achieve consistent spatial performance

Recurrent Neural Networks (RNNs) such as Long Short-Term Memory (LSTM) have achieved significant success in hydrological modeling. However, the recent breakthroughs of foundation models like ChatGPT and the Segment Anything Model (SAM) in natural language processing and computer vision have raised interest in the potential of attention mechanism-based models for hydrologic predictions. In this study, we propose a deep learning framework that seamlessly integrates multi-source, multi-scale data and multi-model modules, creating an automated platform for multi-dataset benchmarking and attention-based model comparisons beyond LSTM-centered tasks. The proposed framework enables evaluation of deep learning models across diverse hydrologic prediction tasks, including regression (daily runoff, soil moisture, snow water equivalent, and dissolved oxygen prediction), forecasting (using lagged hydrologic observations combined with meteorological inputs), autoregression (forecasting based solely on historical observations), spatial cross-validation (assessing model generalization to ungauged regions), and zero-shot forecasting (prediction without task-specific training data). Specifically, we benchmarked 11 Transformer-based architectures against a baseline Long Short-Term Memory (LSTM) model and further evaluated pretrained Large Language Models (LLMs) and Time Series Attention Models (TSAMs) regarding their capabilities for zero-shot hydrologic forecasting. Results show that LSTM models perform best in regression tasks, especially on the global streamflow dataset (median KGE = 0.75), surpassing the best-performing Transformer-based model's KGE value by 0.11. However, as tasks become more complex (from regression and forecasting to autoregression and zero-shot prediction), attention-based models gradually surpass LSTM models. This study provides a robust framework for comparing and developing different model structures in the era of large-scale models, providing a valuable benchmark for water resource modeling, forecasting, and management.