A hybrid physical-machine learning approach with uncertainty propagation for quantifying the Gorgan Bay-Caspian Sea hydrodynamics

The Gorgan Bay (GB) biosphere reserve is facing endangerment due to sustained water storage and quality loss. GB is hydraulically connected to the Caspian Sea, where the bay-sea flow exchange is key for protecting GB’s ecosystems from environmental threats. Generally, quantification of bay-sea hydrological exchange is challenging due to limited measurements or estimation uncertainty. In this study, we combined physics, machine learning, and a forward uncertainty propagation approach to quantity bay-sea interaction and the associated uncertainty. Bathymetric modeling using Landsat’s visible bands within an ANN architecture achieved testing accuracy of R² = 0.84 and RMSE = 4.2 cm. Physical modeling of fluxes in GB revealed that monthly flow reverses to bay-to-sea during October-February due to low Caspian Sea/GB levels which enable river currents to reverse flow in the bay channels. Strong correlation between cumulative GB’s volume change and the Caspian Sea’s water level (r = 0.9) further confirmed sea-level fluctuations as the primary external control. Finally, results revealed that bay-sea flow exchange exhibits a statistically significant decreasing trend between October 1998- September 1999 and October 2023-September 2024. Critically, the estimation uncertainty remains high (CV = 2.7), originating from uncertainty in the storage volume estimation (i.e., ±50 cm error in water level and ±10 cm error sedimentation rate). The findings demonstrated that recession of the Caspian Sea and channel sedimentation threaten the sustainability of GB. • ANN bathymetric model achieved strong accuracy: R² = 0.84, RMSE = 4.2 cm. • High estimation uncertainty in bay-sea interaction, mainly from storage volume, sedimentation rate, and water level errors. • Caspian Sea influence on Gorgan Bay’s desiccation was pronounced. • Bay storage volume dropped 85 %, from 1443 MCM in 1998 to 220 MCM in 2024.