Bridging spatio-temporal discontinuities in global soil moisture mapping by coupling physics in deep learning

The launch of Soil Moisture Active Passive (SMAP) satellite in 2015 has resulted in significant achievements in global soil moisture mapping. Nonetheless, spatiotemporal discontinuities in the soil moisture products have arisen due to the limitations of its orbit scanning gap and retrieval algorithms. To address these issues, this paper presents a physics-constrained gap-filling method, PhyFill for short. The PhyFill method employs a partial convolutional neural network technique to explore spatial domain features of the original SMAP soil moisture data. Then, it incorporates variations in soil moisture induced by precipitation events and dry-down events as penalty terms in the loss function, thereby accounting for monotonicity and boundary constraints in the physical processes governing the dynamic fluctuations of soil moisture. The PhyFill model was applied to SMAP soil moisture data, resulting in continuous spatially daily soil moisture data on a global scale. Three validation strategies are employed: visual inspection through global pattern, simulated missing-region validation, and soil moisture validation with in situ measurements. The results indicated that the reconstructed soil moisture achieved a higher spatial coverage with satisfactory spatial continuity with neighbouring pixels. The simulated validation of the missing regions revealed that the averaged unbiased root mean square difference (ubRMSD) and correlation coefficient (R) were 0.01 m3/m3 3 /m 3 and 0.99, respectively versus the gap filled SMAP product. The core validation sites demonstrated that the reconstructed soil moisture data has a consistent ubRMSD compared with the original SMAP soil moisture data (0.04 m3/m3 3 /m 3 vs. 0.04 m3/m3). 3 /m 3 ). The PhyFill method can generate globally continuous, high accurate soil moisture estimates, providing remarkable support for advanced hydrological applications, e.g., , global soil moisture dry-down events and patterns.