Interpretable Machine Learning for Reservoir Water Temperatures in the U.S. Red River Basin of the South

TL;DR

This study combines explainable machine learning with symbolic modeling to accurately predict reservoir water temperatures and uncover the physical drivers behind their dynamics, providing interpretable equations that balance simplicity and predictive power.

Contribution

It introduces a novel framework integrating ML and symbolic modeling to interpret reservoir water temperature dynamics, advancing both prediction accuracy and physical understanding.

Findings

High predictive accuracy with RMSE = 1.20°C and R^2 = 0.97.

Identified key drivers like air temperature, depth, and wind affecting RWT.

Developed interpretable equations with R^2 up to 0.92, balancing complexity and simplicity.

Abstract

Accurate prediction of Reservoir Water Temperature (RWT) is vital for sustainable water management, ecosystem health, and climate resilience. Yet, prediction alone offers limited insight into the governing physical processes. To bridge this gap, we integrated explainable machine learning (ML) with symbolic modeling to uncover the drivers of RWT dynamics across ten reservoirs in the Red River Basin, USA, using over 10,000 depth-resolved temperature profiles. We first employed ensemble and neural models, including Random Forest (RF), Extreme Gradient Boosting (XGBoost), and Multilayer Perceptron (MLP), achieving high predictive skill (best RMSE = 1.20 degree Celsius, R^2 = 0.97). Using SHAP (SHapley Additive exPlanations), we quantified the contribution of physical drivers such as air temperature, depth, wind, and lake volume, revealing consistent patterns across reservoirs. To translate these data-driven insights into compact analytical expressions, we developed Kolmogorov Arnold Networks (KANs) to symbolically approximate RWT. Ten progressively complex KAN equations were derived, improving from R^2 = 0.84 using a single predictor (7-day antecedent air temperature) to R^2 = 0.92 with ten predictors, though gains diminished beyond five, highlighting a balance between simplicity and accuracy. The resulting equations, dominated by linear and rational forms, incrementally captured nonlinear behavior while preserving interpretability. Depth consistently emerged as a secondary but critical predictor, whereas precipitation had limited effect. By coupling predictive accuracy with explanatory power, this framework demonstrates how KANs and explainable ML can transform black-box models into transparent surrogates that advance both prediction and understanding of reservoir thermal dynamics.