Jonathan Frame

Jasper A. Vrugt, Jonathan M. Frame, Ethan Bollman

Conceptual hydrologic models remain the cornerstone of rainfall-runoff modeling, yet their calibration is often slow and numerically fragile. Most gradient-based parameter estimation methods rely on finite-difference approximations or automatic differentiation frameworks (e.g., JAX, PyTorch and TensorFlow), which are computationally demanding and introduce truncation errors, solver instabilities, and substantial overhead. These limitations are particularly acute for the ODE systems of conceptual watershed models. Here we introduce a fully analytic and computationally efficient framework for differentiable hydrologic modeling based on exact parameter sensitivities. By augmenting the governing ODE system with sensitivity equations, we jointly evolve the model states and the Jacobian matrix with respect to all parameters. This Jacobian then provides fully analytic gradient vectors for any differentiable loss function. These include classical objective functions such as the sum of absolute and squared residuals, widely used hydrologic performance metrics such as the Nash-Sutcliffe and Kling-Gupta efficiencies, robust loss functions that down-weight extreme events, and hydrograph-based functionals such as flow-duration and recession curves. The analytic sensitivities eliminate the step-size dependence and noise inherent to numerical differentiation, while avoiding the instability of adjoint methods and the overhead of modern machine-learning autodiff toolchains. The resulting gradients are deterministic, physically interpretable, and straightforward to embed in gradient-based optimizers. Overall, this work enables rapid, stable, and transparent gradient-based calibration of conceptual hydrologic models, unlocking the full potential of differentiable modeling without reliance on external, opaque, or CPU-intensive automatic-differentiation libraries.

Basit A. Akinade, Amobichukwu C. Amanambu, Jonathan M. Frame et al.

AI data centres consume water for cooling, water scarcity constrains siting, and AI tools can improve water system efficiency. These dynamics are studied separately yet form a feedback loop. This review formalises the Water and AI Feedback Loop, introduces the Water Consumption Impact index to quantify community-scale utility burden, and demonstrates across ten US sites that burden spans three orders of magnitude, from 0.2% to 134% of host capacity.

Craig Pelissier, Jonathan Frame, Grey Nearing

A hybrid machine learning and process-based-modeling (PBM) approach is proposed and evaluated at a handful of AmeriFlux sites to simulate the top-layer soil moisture state. The Hybrid-PBM (HPBM) employed here uses the Noah land-surface model integrated with Gaussian Processes. It is designed to correct the model only in climatological situations similar to the training data else it reverts to the PBM. In this way, our approach avoids bad predictions in scenarios where similar training data is not available and incorporates our physical understanding of the system. Here we assume an autoregressive model and obtain out-of-sample results with upwards of a 3-fold reduction in the RMSE using a one-year leave-one-out cross-validation at each of the selected sites. A path is outlined for using hybrid modeling to build global land-surface models with the potential to significantly outperform the current state-of-the-art.