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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%, decrease 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. 

ABSTRACT Controls of hydrology, landscape and soil characteristics on redox potentials, particularly at fine spatial and temporal scales, are poorly quantified and understood. Using high‐frequency sensors (30 min), the variability of redox potentials (Eh) in riparian soils was investigated for multiple depths and across diel, event and seasonal time scales over a period of 2 years. Sampling was performed for two riparian sites upstream of dams with contrasting soil textures. Incremental changes in soil moisture triggered abrupt and disproportionately large shifts in soil Eh values, a threshold‐like behaviour that has not been reported before. Contrary to expectations, Eh values initially decreased as the soil dried and then abruptly increased with further drying and oxidation of soil. Diel Eh patterns differed between sites, with the sand‐rich site oxidising by day and reducing at night, while the clay‐ and silt‐rich site showed the opposite pattern. These differences were attributed to differential oxygen diffusion and consumption by processes such as photosynthesis, evapotranspiration and microbial respiration. Sharp Eh shifts also occurred at soil depths with textural discontinuities. These redox hot spots and hot moments were attributed to differences in site topography, hydrology and soil characteristics such as texture, moisture, organic matter content and microbial biomass. Identifying and understanding these fine‐scale spatial and temporal patterns of Eh is critical for improved characterisation and quantification of biogeochemical processes in redox‐sensitive environments. This study underscores the value of high‐frequency redox sensors in making such assessments. 

Abstract Understanding the balance between denitrification and dissimilatory nitrate reduction to ammonium (DNRA) in riparian systems is essential for managing watershed nitrogen (N) budgets and evaluating restoration practices. This balance is influenced by several factors including concentrations and ratio of various organic and inorganic electron donors (dissolved organic carbon [DOC], Fe²⁺) to acceptor (NO₃⁻). In riparian sediments, these factors can change rapidly over space and time, complicating measurement and quantification. We used a PFLOTRAN batch reactor model calibrated to laboratory microcosm experiments where the denitrification and DNRA rates in riparian sediments were measured using¹⁵N stable isotopes. Although DOC/NO₃⁻ratios influenced the relative proportions of denitrification and DNRA, the processes were also affected by elemental concentrations. For a starting DOC concentration of 0.12 mgL⁻¹, DNRA exceeded denitrification at DOC/NO₃⁻ = 6; however, this shift was not observed within a range of DOC/NO₃⁻ = 30 at higher DOC concentration of 12 mgL⁻¹. Heterotrophic pathways dominated NO₃‐N reduction with smaller contribution from autotrophic pathways. These findings suggest that although heterotrophic pathways are important in carbon‐rich sediments, autotrophic pathways can be significant in carbon‐depleted conditions in the presence of inorganic electron donors such as Fe²⁺. Our simulations also highlighted key challenges with constraining model rate constants and parameters and the need for site specific calibrations. This work highlights the value of process‐based modeling in quantifying denitrification‐DNRA partitioning and the variable controls of electron donors and acceptors. Such simulations could be extended to riparian buffers to determine if they are effective management sinks for N mitigation. 

IntroductionDissolved organic matter (DOM) composition varies over space and time, with a multitude of factors driving the presence or absence of each compound found in the complex DOM mixture. Compounds ubiquitously present across a wide range of river systems (hereafter termed core compounds) may differ in chemical composition and reactivity from compounds present in only a few settings (hereafter termed satellite compounds). Here, we investigated the spatial patterns in DOM molecular formulae presence (occupancy) in surface water and sediments across 97 river corridors at a continental scale using the “Worldwide Hydrobiogeochemical Observation Network for Dynamic River Systems—WHONDRS” research consortium. MethodsWe used a novel data-driven approach to identify core and satellite compounds and compared their molecular properties identified with Fourier-transform ion cyclotron resonance mass spectrometry (FT-ICR MS). ResultsWe found that core compounds clustered around intermediate hydrogen/carbon and oxygen/carbon ratios across both sediment and surface water samples, whereas the satellite compounds varied widely in their elemental composition. Within surface water samples, core compounds were dominated by lignin-like formulae, whereas protein-like formulae dominated the core pool in sediment samples. In contrast, satellite molecular formulae were more evenly distributed between compound classes in both sediment and water molecules. Core compounds found in both sediment and water exhibited lower molecular mass, lower oxidation state, and a higher degree of aromaticity, and were inferred to be more persistent than global satellite compounds. Higher putative biochemical transformations were found in core than satellite compounds, suggesting that the core pool was more processed. DiscussionThe observed differences in chemical properties of core and satellite compounds point to potential differences in their sources and contribution to DOM processing in river corridors. Overall, our work points to the potential of data-driven approaches separating rare and common compounds to reduce some of the complexity inherent in studying riverine DOM. 

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs.