39 Search Results

Abstract Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov‐Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN‐derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts; they demonstrate that water availability, rather than potential evapotranspiration, drives baseflow by constraining actual evapotranspiration under arid conditions. On a test set, they increase the Nash‐Sutcliffe efficiency (NSE) by 65%, decreasemore » the root mean squared error by 29%, and increase the Kling‐Gupta efficiency by 34%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water‐balance equation at the mean‐annual scale. The KAN‐derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN‐derived equations based on the original water balance. While the performance of our model and tree‐based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes. Plain Language Summary Equations used in hydrologic model are often suboptimal, resulting in reduced prediction accuracy and efficiency. We implemented Kolmogorov‐Arnold networks (KAN), a machine learning algorithm for deriving symbolic formulations, to estimate groundwater recharge and showed that it outperforms an existing state‐of‐the‐art semi‐empirical formulation. In hydrology, Nash‐Sutcliffe efficiency (NSE), root mean squared error (RMSE), and Kling‐Gupta efficiency (KGE) are commonly used to evaluate model performance. Higher NSE and KGE values indicate better performance, while lower RMSE values are preferable. Our results show that NSE increased by 71%, RMSE decreased by 32%, and KGE improved by 25%. In addition, KAN identifies an optimal functional form and can be used to derive new analytical formulas using the prior knowledge. The KAN‐inspired equation outperformed the original formulation and reduced the fitting parameters. Furthermore, we refined the water‐balance equation at the mean‐annual scale and showed that, based on the new water‐balance equation, KAN can derive new formulations that are superior to the original aridity index formulations (up to 105% increase in NSE) and KAN‐derived equations based on the original water balance. These findings highlight the significant potential of KAN to advance the scientific understanding of a wide range of hydrologic processes. Key Points Kolmogorov‐Arnold networks (KANs) enhance interpretability of machine‐learned hydrological models KAN‐derived symbolic formulations outperform state‐of‐the‐art semi‐empirical aridity indices KAN‐identified functional form yields an analytical index with fewer fitting parameters and improved performance« less

The weathering of sedimentary rocks in high-elevation catchments influences freshwater quality and the global carbon cycle. While individual biogeochemical mechanisms involved in this process are relatively well understood, quantifying their contributions to solute export and carbon fluxes under natural, transient conditions remains challenging. Here, we implement a numerical multidimensional and multiphase model to simulate coupled hydrological and biogeochemical processes in a shale-underlain, snow-dominated hillslope in the Rocky Mountains, Colorado. The model captures the dynamic interplay between soil respiration, mineral weathering, and climate-driven hydrological forcing, reproducing observed soil CO₂ dynamics, groundwater chemistry, and subsurface flow. Our results reveal that seasonal snowmeltmore » enhances carbonate weathering by promoting the infiltration of CO₂-rich water to depth, while pyrite oxidation is primarily sensitive to low water saturation that facilitates O₂ diffusion through the regolith. Topography modulates the spatial distribution of shale weathering, as steeper slopes enhance lateral drainage, favoring the delivery of reactants to greater depths. While shale weathering at our site acts as a transient carbon sink, with silicates and carbonates buffering acidity and promoting atmospheric CO₂ consumption (1% of soil-derived CO₂), the exported dissolved inorganic carbon is predominantly geogenic (∼73%). Consequently, when accounting for long-term marine carbonate precipitation. The current weathering regime represents a net source of carbon to the atmosphere. The oxidation of pyrite and petrogenic organic carbon together release approximately 0.9 mol·m⁻²·yr⁻¹ of CO₂. Our findings highlight the role of topography, hydroclimate, and the coupling between acid-base reactions in shaping the carbon balance and the solute exports in mountainous critical zones.« less

This review synthesizes methods for measuring, modeling, and managing hydrologic connectivity, offering pathways to improve practices and address environmental challenges (e.g., climate change) and sustainability. As a key driver of water movement and nutrient cycling, hydrologic connectivity influences flood mitigation, water quality regulation, and biodiversity conservation. However, traditional field-based methods (e.g., dye tracing), indirect measurements (e.g., runoff analysis), and remote sensing techniques (e.g., InSAR) often struggle to capture the complexity of catchment-scale interactions. Similarly, modeling approaches—including process-based and percolation theory-based models, graph theory, and entropy-based metrics—face limitations in fully representing these interconnected processes. Both modeling and measurement techniques are constrainedmore » by inadequate spatial and temporal coverage, high data demands, computational complexity, and difficulties in representing subsurface connectivity. Subsequently, we critique current management practices that prioritize isolated variables (e.g., streamflow, sediment transport) over system-wide strategies and emphasize the need for adaptive, connectivity-based approaches in water resource planning and restoration. Moving forward, we highlight the importance of interdisciplinary collaboration, technological innovations (e.g., AI-driven modeling, real-time monitoring), and integrated frameworks to improve connectivity measurement, modeling, and adaptive management to restore fragmented hydrologic networks. This integrated approach sets the stage for transformative water resource management, fostering proactive policy development and stakeholder engagement.« less

Information about evapotranspiration (ET) and its components, that is, evaporation and transpiration, is crucial for a wide range of water and ecosystem management applications. However, partitioning ET into its two components is often challenging because of their spatiotemporal variabilities and lack of process understanding. This study developed a machine learning (ML) framework to shed light on ET processes and assess the relative importance of different drivers by incorporating hydrometeorology and biomass productivity variables. The Shapley Additive Explanations (SHAP) approach was applied to enhance explainability and rank the importance of ET drivers and their components. A total of 62 variables coveringmore » hydrometeorological and biomass productivity dimensions were considered from the Reynolds Creek Critical Zone Observatory (CZO) station in Idaho. The variable importance assessment identified the leading drivers individually for evaporation, transpiration and ET (soil water content for evaporation, vapour pressure deficit for transpiration and soil water content for ET). The results further highlighted the value of combining hydrometeorological and biomass productivity variables to achieve better predictability of ET processes.« less

Climate influences near-surface biogeochemical processes and thereby determines the partitioning of carbon dioxide (CO₂) in shale, and yet the controls on carbon (C) weathering fluxes remain poorly constrained. Using a dataset that characterizes biogeochemical responses to climate forcing in shale regolith, we implement a numerical model that describes the effects of water infiltration events, gas exchange, and temperature fluctuations on soil respiration and mineral weathering at a seasonal timescale. Our modeling approach allows us to quantitatively disentangle the controls of transient climate forcing and biogeochemical mechanisms on C partitioning. We find that ~3% of soil CO₂ (1.02 mol C/m²/y) ismore » exported to the subsurface during large infiltration events. Here, net atmospheric CO₂ drawdown primarily occurs during spring snowmelt, governs the aqueous C exports (61%), and exceeds the CO₂ flux generated by pyrite and petrogenic organic matter oxidation (~0.2 mol C/m²/y). We show that shale CO₂ consumption results from the temporal coupling between soil microbial respiration and carbonate weathering. This coupling is driven by the impacts of hydrologic fluctuations on fresh organic matter availability and CO₂ transport to the weathering front. Diffusion-limited transport of gases under transient hydrological conditions exerts an important control on CO₂(g) egress patterns and thus must be considered when inferring soil CO₂ drawdown from the gas phase composition. Our findings emphasize the importance of seasonal climate forcing in shaping the net contribution of shale weathering to terrestrial C fluxes and suggest that warmer conditions could reduce the potential for shale weathering to act as a CO₂ sink.« less

Terrestrial-aquatic interfaces (TAI) play important roles in mediating the exchange of water and chemicals between land, surface and subsurface water systems, which is tightly coupled with biogeochemical transformations that influence water quality and ecosystem health (Harvey and Gooseff, 2015; Harvey et al., 2019). Understanding and predicting the interactions between the hydrologic, ecologic, and biogeochemical processes at those interfaces is crucial for the sustainable management of water resources and promotion of healthy ecosystems under different environmental stresses and disturbances, including climate change, human activities, and more frequent occurrence of extreme events. Both process-based and data-driven approaches have emerged to address criticalmore » challenges at TAIs as integral parts of the Earth system (e.g., Ward and Packman, 2019; Chen et al., 2021; Dwivedi et al., 2022). In this Research Topic, we sought research that advances the understanding of coupled hydrologic, ecologic, and biogeochemical processes along various TAIs from the summit to sea, e.g., river corridors and coastal TAI systems. We invited observational, experimental, theoretical, analytical, numerical, and data-driven research that aims to understand hydro-biogeochemical processes such as the redox dynamics and biogeochemical transformations of carbon, nutrients, and metals occurring at the TAIs and address their heterogeneity and scaling challenges.« less

Abstract We computationally explore the relationship between surface–subsurface exchange and hydrological response in a headwater-dominated high elevation, mountainous catchment in East River Watershed, Colorado, USA. In order to isolate the effect of surface–subsurface exchange on the hydrological response, we compare three model variations that differ only in soil permeability. Traditional methods of hydrograph analysis that have been developed for headwater catchments may fail to properly characterize catchments, where catchment response is tightly coupled to headwater inflow. Analyzing the spatially distributed hydrological response of such catchments gives additional information on the catchment functioning. Thus, we compute hydrographs, hydrological indices, and spatio-temporalmore » distributions of hydrological variables. The indices and distributions are then linked to the hydrograph at the outlet of the catchment. Our results show that changes in the surface–subsurface exchange fluxes trigger different flow regimes, connectivity dynamics, and runoff generation mechanisms inside the catchment, and hence, affect the distributed hydrological response. Further, changes in surface–subsurface exchange rates lead to a nonlinear change in the degree of connectivity—quantified through the number of disconnected clusters of ponding water—in the catchment. Although the runoff formation in the catchment changes significantly, these changes do not significantly alter the aggregated streamflow hydrograph. This hints at a crucial gap in our ability to infer catchment function from aggregated signatures. We show that while these changes in distributed hydrological response may not always be observable through aggregated hydrological signatures, they can be quantified through the use of indices of connectivity.« less

Abstract. High-resolution gridded datasets of meteorological variables are needed in order to resolve fine-scale hydrological gradients in complex mountainous terrain. Across the United States, the highest available spatial resolution of gridded datasets of daily meteorological records is approximately 800 m. This work presents gridded datasets of daily precipitation and mean temperature for the East–Taylor subbasin (in the western United States) covering a 12-year period (2008–2019) at a high spatial resolution (400 m). The datasets are generated using a downscaling framework that uses data-driven models to learn relationships between climate variables and topography. We observe that downscaled datasets of precipitation and mean temperaturemore » exhibit smoother spatial gradients (while preserving the spatial variability) when compared to their coarser counterparts. Additionally, we also observe that when downscaled datasets are upscaled to the original resolution (800 m), the mean residual error is almost zero, ensuring no bias when compared with the original data. Furthermore, the downscaled datasets are observed to be linearly related to elevation, which is consistent with the methodology underlying the original 800 m product. Finally, we validate the spatial patterns exhibited by downscaled datasets via an example use case that models lidar-derived estimates of snowpack. The presented dataset constitutes a valuable resource to resolve fine-scale hydrological gradients in the mountainous terrain of the East–Taylor subbasin, which is an important study area in the context of water security for the southwestern United States and Mexico. The dataset is publicly available at https://doi.org/10.15485/1822259 (Mital et al., 2021).« less