Water Balance Regularised Modelling of Multi‐Depth Soil Moisture Dynamics in Arid Hydrological Systems

ABSTRACT Accurate and physically consistent soil moisture forecasting is essential for irrigation water supply, yet purely data‐driven models may generalise poorly and exhibit nonphysical behaviour under changing forcing and management conditions. This study develops a water balance regularised neural network for daily multi‐depth soil moisture forecasting and evaluates its performance across three agricultural monitoring stations in Kuwait (Rabyah, Sulibyah and Wafra) and three depths (10, 20 and 50 cm). The model predicts one‐day‐ahead soil moisture increments using rainfall, pan evaporation, and lagged soil moisture, while a soft water balance regularisation constrains storage changes through learnable balance and drainage coefficients. Performance is benchmarked against an unconstrained neural network using RMSE, MAE, R 2 , and Kling–Gupta efficiency metric, and further assessed through time series agreement, residual diagnostics, split‐based generalisation, paired comparisons, and bootstrap uncertainty analysis. The constrained model outperforms the unconstrained network in 6 of 9 station–depth cases for RMSE and 5 of 9 cases for MAE, with the most consistent gains observed at 50 cm depth, reflecting storage‐dominated dynamics. Bootstrap analysis indicates positive mean improvements of 4.73% in RMSE and 5.68% in MAE, although confidence intervals include zero, indicating heterogeneous benefits across regimes. A conceptual partial root zone drying application demonstrates how physically interpretable soil moisture forecasts can support threshold‐based irrigation control. Overall, the results indicate that water balance regularisation enhances the stability and interpretability of neural network based soil moisture forecasts for irrigation water supply.