Physics-Informed Bayesian Neural Network for Groundwater Recharge in South Al-Batinah Aquifer, Oman.

Groundwater recharge in arid and semi-arid regions is very important component to quantify, however, it is highly episodic, spatially heterogeneous, and subject to substantial uncertainty. This study estimates groundwater recharge in the South Al Batinah (SAB) Basin of northern Oman using a soil-moisture mass balance framework driven by long-term remote sensing and land surface model data. Monthly water-balance components—including precipitation, evapotranspiration, runoff, and soil moisture storage change—were derived from the FLDAS Noah land surface model for the period 1990–2023 and aggregated at the basin scale. Recharge was computed as the residual of the water balance and uncertainty was quantified using Latin Hypercube Sampling (LHS) with 5,000 realizations per month. To further constrain recharge estimates and reduce physically implausible outcomes, a Physics-Informed Bayesian Neural Network (PI-BNN) was developed, integrating mass-balance constraints, non-negativity conditions, near-dry penalties, and Bayesian uncertainty quantification within a unified probabilistic framework.

Results indicate that groundwater recharge in the SAB Basin is strongly seasonal and highly variable, with negligible recharge during most dry months and irregular recharge pulses associated with intense rainfall events in winter and mid-summer. Mean monthly recharge is generally low, with the highest values occurring in December (≈5–6 mm) and moderate recharge in February–March and July. Uncertainty analysis show that precipitation variability is the dominant control on recharge uncertainty, accounting for more than 70% of total variance during wet months, followed by evapotranspiration, surface runoff, and soil storage change. The PI-BNN produces recharge estimates consistent with the water-balance approach but with a reduced uncertainty bounds, effectively ruling out implausibly large recharge values while preserving physically realistic variability.

The results show that groundwater recharge mechanism in the SAB Basin is dominated by rare, high-intensity rainfall events. The combined use of remote sensing, stochastic sampling, and physics-informed machine learning provides a good framework for recharge estimation and uncertainty reduction in data-scarce arid environments.