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Deep learning (DL) rainfall–runoff models outperform conceptual, process-based models in a range of applications. However, it remains unclear whether DL models can produce physically plausible projections of streamflow under climate change. We investigate this question through a sensitivity analysis of modeled responses to increases in temperature and potential evapotranspiration (PET), with other meteorological variables left unchanged. Previous research has shown that temperature-based PET methods overestimate evaporative water loss under warming compared with energy budget-based PET methods. We therefore assume that reliable streamflow responses to warming should exhibit less evaporative water loss when forced with smaller, energy-budget-based PET compared with temperature-based PET. We conduct this assessment using three conceptual, process-based rainfall–runoff models and three DL models, trained and tested across 212 watersheds in the Great Lakes basin. The DL models include a Long Short-Term Memory network (LSTM), a mass-conserving LSTM (MC-LSTM), and a novel variant of the MC-LSTM that also respects the relationship between PET and evaporative water loss (MC-LSTM-PET). After validating models against historical streamflow and actual evapotranspiration, we force all models with scenarios of warming, historical precipitation, and both temperature-based (Hamon) and energy-budget-based (Priestley–Taylor) PET, and compare their responses in long-term mean daily flow, low flows, high flows, and seasonal streamflow timing. We also explore similar responses using a national LSTM fit to 531 watersheds across the United States to assess how the inclusion of a larger and more diverse set of basins influences signals of hydrological response under warming. The main results of this study are as follows: The three Great Lakes DL models substantially outperform all process-based models in streamflow estimation. The MC-LSTM-PET also matches the best process-based models and outperforms the MC-LSTM in estimating actual evapotranspiration. All process-based models show a downward shift in long-term mean daily flows under warming, but median shifts are considerably larger under temperature-based PET (−17 % to −25 %) than energy-budget-based PET (−6 % to −9 %). The MC-LSTM-PET model exhibits similar differences in water loss across the different PET forcings. Conversely, the LSTM exhibits unrealistically large water losses under warming using Priestley–Taylor PET (−20 %), while the MC-LSTM is relatively insensitive to the PET method. DL models exhibit smaller changes in high flows and seasonal timing of flows as compared with the process-based models, while DL estimates of low flows are within the range estimated by the process-based models. Like the Great Lakes LSTM, the national LSTM also shows unrealistically large water losses under warming (−25 %), but it is more stable when many inputs are changed under warming and better aligns with process-based model responses for seasonal timing of flows. Ultimately, the results of this sensitivity analysis suggest that physical considerations regarding model architecture and input variables may be necessary to promote the physical realism of deep-learning-based hydrological projections under climate change.

In this study, the predictive power of three different machine learning (ML)-based approaches, namely, multi-gene genetic programming (MGGP), M5 model trees (M5Tree), and K-nearest neighbor algorithm (KNN), for long-term monthly reference evapotranspiration ( ET 0 ) prediction were investigated. The input data consist of monthly solar radiation ( R s ), maximum air temperature ( T max ), and wind speed ( W s ) derived from 163 meteorological stations in Turkey. Different input combinations were created and analyzed. The model’s performance was evaluated using criteria such as Nash–Sutcliffe efficiency, Kling-Gupta efficiency, relative root mean squared error, mean absolute percentage error, and determination coefficient. Moreover, Taylor, radar, and boxplot diagrams were created. It was determined that the MGGP model outperformed both the M5Tree and the KNN models. The equation obtained from the MGGP model, for the best-performed combination of R s - T max - W s , was presented. The best weather conditions were obtained as 0.029 to 31.814 MJ/m 2 , − 5.8 to 45.7 °C, and 0.140 to 5.086 m/s for R s , T max , and W s , respectively. It was also found that the R s was the most potent input variable for ET 0 estimation while W s was the weakest.

There is strong evidence climate change will increase drought risk and severity, but these conclusions depend on the regions, seasons, and drought metrics being considered. We analyze changes in drought across the hydrologic cycle (precipitation, soil moisture, and runoff) in projections from Phase Six of the Coupled Model Intercomparison Project (CMIP6). The multi‐model ensemble shows robust drying in the mean state across many regions and metrics by the end of the 21st century, even following the more aggressive mitigation pathways (SSP1‐2.6 and SSP2‐4.5). Regional hotspots with strong drying include western North America, Central America, Europe and the Mediterranean, the Amazon, southern Africa, China, Southeast Asia, and Australia. Compared to SSP3‐7.0 and SSP5‐8.5, however, the severity of drying in the lower warming scenarios is substantially reduced and further precipitation declines in many regions are avoided. Along with drying in the mean state, the risk of the historically most extreme drought events also increases with warming, by 200–300% in some regions. Soil moisture and runoff drying in CMIP6 is more robust, spatially extensive, and severe than precipitation, indicating an important role for other temperature‐sensitive drought processes, including evapotranspiration and snow. Given the similarity in drought responses between CMIP5 and CMIP6, we speculate both generations of models are subject to similar uncertainties, including vegetation processes, model representations of precipitation, and the degree to which model responses to warming are consistent with observations. These topics should be further explored to evaluate whether CMIP6 models offer reasons to have increased confidence in drought projections.

The regionalization of hydrological model parameters is key to hydrological predictions in ungauged basins. The commonly used multiple linear regression (MLR) method may not be applicable in complex and nonlinear relationships between model parameters and watershed properties. Moreover, most regionalization methods assume lumped parameters for each catchment without considering within-catchment heterogeneity. Here we incorporated the Penman–Monteith–Leuning (PML) equation into the Distributed Time Variant Gain Model (DTVGM) to improve the mechanistic representation of the evapotranspiration (ET) process. We calibrated six key model parameters, grid by grid across China, using a multivariable calibration strategy which incorporates spatiotemporal runoff and ET datasets (0.25∘; monthly) as reference. In addition, we used the gradient boosting machine (GBM), a machine learning technique, to portray the dependence of model parameters on soil and terrain attributes in four distinct climatic zones across China. We show that the modified DTVGM could reasonably estimate the runoff and ET over China using the calibrated parameters but performed better in humid rather than arid regions for the validation period. The regionalized parameters by the GBM method exhibited better spatial coherence relative to the calibrated grid-by-grid parameters. In addition, GBM outperformed the stepwise MLR method in both parameter regionalization and gridded runoff simulations at a national scale, though the improvement pertaining to watershed streamflow validation is not significant due to most of the watersheds being located in humid regions. We also revealed that the slope, saturated soil moisture content, and elevation are the most important explanatory variables to inform model parameters based on the GBM approach. The machine-learning-based regionalization approach provides an effective alternative to deriving hydrological model parameters from watershed properties, particularly in ungauged regions.

Quantifying global terrestrial evapotranspiration (ET) relies on models with different levels of complexity. The water balance method offers a straightforward approach for benchmarking complex ET models, as evidenced by the widely-used terrestrial water-balance-based ET (ET TWB ) data. However, deriving ET TWB must rely on ground-observed runoff data, which is not feasible for ungauged or poorly-gauged regions. In this context, the atmospheric water balance (AWB) method offers an alternative for estimating ET, which can be applied to the entire global land area. Nevertheless, the accuracy of the AWB approach in estimating global ET remains poorly understood. In this study, we generated monthly atmospheric water-balance-based ET (ET AWB ) globally from 1983 to 2020 at a 0.25° resolution using multi-source data. Validations against the annual ET TWB of 56 large river basins suggest that ET AWB , estimated using the moisture convergence and atmospheric water vapor from the fifth generation of European Center for Medium-Range Weather Forecasts Reanalysis (ERA5) and the precipitation from four observation-based products, is overall accurate. Specifically, the AWB method yields Nash–Sutcliffe efficiency coefficient (NSE), root mean square error (RMSE), and relative bias (RB) of 0.88, 89.5 mm year −1 , and 2%, respectively. These statistical metrics indicate that the AWB method is generally on par with current mainstream ET models. However, the AWB approach still has certain challenges in capturing the trend in ET. The ensemble mean ET AWB , estimated using the moisture convergence and atmospheric water vapor from ERA5 and four precipitation datasets, yields a global-averaged value of 619 ± 8 mm year −1 (excluding Antarctica) and shows an increase of 2.1% from 1983 to 2020, with a trend of 0.35 mm year −1 . Tropical regions exhibit pronounced interannual variability in ET AWB due to the internal climate variability influencing precipitation and moisture convergence. The current AWB approach  can potentially improve the understanding of regional and global ET processes, as it represents an independent approach to ET estimation, distinct from current remote sensing and land surface models.

Terrestrial evapotranspiration (ET) is a crucial link between Earth’s water cycle and the surface energy budget. Accurate measurement and estimation remain a major challenge in geophysical, biological, and environmental studies. Pioneering work, represented by Dalton and Penman, and the development of theories and experiments on turbulent exchange in the atmospheric boundary layer (ABL), laid the foundation for mainstream methodologies in ET estimation. Since the 1990s, eddy covariance (EC) systems and satellite remote sensing have been widely applied from cold to tropical and from arid to humid regions. They cover water surfaces, wetlands, forests, croplands, grasslands, barelands, and urban areas, offering an exceptional number of reports on diverse ET processes. Surface nocturnal ET, hysteresis between ET and environmental forces, turbulence intermittency, island effects on heterogeneous surfaces, and phase transition between underlying surfaces are examples of reported new phenomena, posing theoretical and practical challenges to mainstream ET methodologies. Additionally, based on non-conventional theories, new methods have emerged, such as maximum entropy production and nonparametric approaches. Furthermore, high-frequency on-site observation and aerospace remote sensing technology in combination form multi-scale observations across plant stomata, leaves, plants, canopies, landscapes, and basins. This promotes an insightful understanding of diverse ET processes and synthesizes the common mechanisms of the processes between and across spatial and temporal scales. All the recent achievements in conception, model, and technology serve as the basis for breaking through the known difficulties in ET estimation. We expect that they will provide a rigorous, reliable scientific basis and experimental support to address theoretical arguments of global significance, such as the water-heat-carbon cycle, and solve practical needs of national importance, including agricultural irrigation and food security, precise management of water resources and eco-environmental protection, and regulation of the urban thermal environment and climate change adaptation.

Accurate estimation of terrestrial evapotranspiration (ET) is vital for understanding global water and energy cycles. However, current global ET estimations are not well constrained. This study introduces an integrated framework combining the Maximum Entropy Production (MEP) theory with Random Forest (RF) model to improve global ET estimation. Specifically, in contrast to direct ET estimation by the RF model, the integrated framework (MEP‐RF) trains to predict error of MEP‐simulated ET. MEP‐RF outperforms RF in spatiotemporal extrapolation. Attribution analysis with in situ observations reveals that the inputs of MEP are the most critical variables for the ET process, including net radiation, vegetated area, soil moisture, and surface temperature. We further drive MEP‐RF with global reanalysis and satellite data sets of these four inputs, yielding a global mean terrestrial ET of 548 mm/year, with 77% attributed to transpiration. The global ET increased at a rate of 0.85 mm/year per year during 2003–2021, primarily due to vegetation greening rather than rising temperature, while decreasing soil moisture led to decreasing regional ET. The integrated framework provides a novel approach for the estimation of global ET without the need for hard‐to‐obtain and thus uncertain inputs, such as wind speed, surface roughness, aerodynamic and canopy stomatal resistance. Therefore, MEP‐RF offers an independent method on existing global ET products. It represents a promising physically based approach that can be incorporated into Earth System Models to enhance water and energy cycle simulations.

The evapotranspiration (ET) regime is an illustration of the water‐energy interactions at the land surface and is important for regional climate. In this study, we propose a revised framework for land aridity classification based on the ET regime and the conditional mutual information method. The proposed framework effectively captures the influences of short‐term water and energy supply on ET and highlights their potential roles in extreme events. This framework can be a supplement to the traditional classification schemes that rely on long‐term mean climate. Furthermore, we examine the sensitivity of this land aridity framework to different model physics parameterization schemes. The cumulus schemes are found to have the most important impact, followed by the radiation and microphysics schemes, while the planetary boundary layer schemes have the weakest impact. These findings provide valuable insights for the identification of land aridity and its relationship with land–atmosphere interactions. Plain Language Summary Land aridity, important for many uses, is typically measured using long‐term mean climate data (e.g., Aridity Index) and provides a static picture of how water and energy interact. In this study, we propose a new framework to classify land aridity, focusing on evapotranspiration (ET)—the process of water evaporating from the land and being released by plants. Our method looks at the changing relationship between water and energy over short periods, giving us a better understanding of how fluctuations in surface water and energy affect ET. This offers a more detailed view than indexes like the Aridity Index, and is especially helpful for studying extreme events. We also explore how different ways of modeling physical processes, such as cloud formation, sunlight and heat transfer, and air movements near the ground, impact our simulations of land aridity. Understanding these elements is key to getting a clearer picture of land aridity and how the land and atmosphere interact, which is crucial for accurate predictions and assessments in various environmental scenarios. Key Points A revised framework for land aridity classification based on the ET regime and conditional mutual information method is proposed The proposed framework effectively captures the influence of short‐term water and energy supply on ET The choice of cumulus scheme is important for model simulated land aridity while the choice of boundary layer scheme has minor impact

Parameter sensitivity analysis plays a critical role in efficiently determining main parameters, enhancing the effectiveness of the estimation of parameters and uncertainty quantification in hydrologic modeling. In this paper, we demonstrate an uncertainty and sensitivity analysis technique for the holistic Soil and Water Assessment Tool (SWAT+) model coupled with new gwflow module, spatially distributed, physically based groundwater flow modeling. The main calculated groundwater inflows and outflows include boundary exchange, pumping, saturation excess flow, groundwater–surface water exchange, recharge, groundwater–lake exchange and tile drainage outflow. We present the method for four watersheds located in different areas of the United States for 16 years (2000–2015), emphasizing regions of extensive tile drainage (Winnebago River, Minnesota, Iowa), intensive surface–groundwater interactions (Nanticoke River, Delaware, Maryland), groundwater pumping for irrigation (Cache River, Missouri, Arkansas) and mountain snowmelt (Arkansas Headwaters, Colorado). The main parameters of the coupled SWAT+gwflow model are estimated utilizing the parameter estimation software PEST. The monthly streamflow of holistic SWAT+gwflow is evaluated based on the Nash–Sutcliffe efficiency index (NSE), percentage bias (PBIAS), determination coefficient (R2) and Kling–Gupta efficiency coefficient (KGE), whereas groundwater head is evaluated using mean absolute error (MAE). The Morris method is employed to identify the key parameters influencing hydrological fluxes. Furthermore, the iterative ensemble smoother (iES) is utilized as a technique for uncertainty quantification (UQ) and parameter estimation (PE) and to decrease the computational cost owing to the large number of parameters. Depending on the watershed, key identified selected parameters include aquifer specific yield, aquifer hydraulic conductivity, recharge delay, streambed thickness, streambed hydraulic conductivity, area of groundwater inflow to tile, depth of tiles below ground surface, hydraulic conductivity of the drain perimeter, river depth (for groundwater flow processes), runoff curve number (for surface runoff processes), plant uptake compensation factor, soil evaporation compensation factor (for potential and actual evapotranspiration processes), soil available water capacity and percolation coefficient (for soil water processes). The presence of gwflow parameters permits the recognition of all key parameters in the surface and/or subsurface flow processes, with results substantially differing if the base SWAT+ models are utilized.

Analyzing process interactions in hydrological systems typically requires catchment‐scale hydrological models, where greater model complexity enhances the representation of physical process behavior but also poses challenges related to parameter equifinality. To investigate process interactions in a snow dominated alpine headwater catchment, we have analyzed spatial and temporal parameter sensitivities of the fully distributed, physically based Water Balance Simulation Model WaSiM. We focused on the role of model structural parameters and the interaction between a variety of processes including evapotranspiration (ET), snowmelt, and soil moisture on sub‐daily (1 hr) as well as seasonal scales. Utilizing process specific performance metrics, we evaluated parameter equifinality, process affiliation and ‐interaction. Parameters of the pre‐known dominant processes (snow and energy‐balance) show the highest sensitivities across processes, but their magnitude varies across scales, seasons and elevations. Parameters of less dominant processes (ET, soil water dynamics) showed generally lower sensitivities and higher temporal and spatial variations. However, the results show a pronounced shift in parameter dominance on ET during dry‐down events. While under moist conditions, energy and temperature related parameters are dominant, structural soil parameters gain importance as dry‐day sequences lengthen. Similar patterns emerge along elevation gradients at the seasonal scale, where soil parameters gain importance in high elevation areas that frequently dry out. The analysis of parameter sensitivities thus allows the spatial and temporal investigation and validation of interactions between catchment processes with limited influence on the overall water balance and is therefore an important step in the development of future‐proof models.