Reconstruction of SMAP L3 Soil Moisture Data Using a Physical-Deep Learning Based Hybrid Approach

Soil moisture is critical for understanding hydrological processes, with applications spanning weather forecasting, agricultural management, and flood prediction. However, the fundamental requirement is not merely large data volumes, but gap-free observations with spatiotemporal continuity. Gap-free data is essential to preserve long-term time series characteristics and comprehensively understand hydrological processes. More critically, in climate modeling and extreme event forecasting under climate change, seamless observations are fundamentally required—even sporadic gaps can fundamentally alter predictions.

The SMAP L3 AM (descending) product is widely recognized as a representative remote sensing product at 36 km resolution. Even accounting for the 2-3 day orbital revisit cycle, temporal coverage is severely limited: land grids average 62% temporal gaps, rising to 71% after quality control, with numerous regions experiencing over 80% data unavailability. This extreme temporal sparsity, driven by orbital constraints, RFI, and retrieval algorithm limitations, fundamentally limits applications requiring continuous observations.

Various methods have been developed to interpolate these temporal gaps. Approaches include data fusion using ground and satellite observations, or employing data assimilation through hydrological modeling to fill gaps. Recently, methods using deep learning models—which demonstrate high predictive performance—have been extensively researched for gap-filling. However, these methods suffer from critical limitations: (i) many existing interpolation methods distort data by ignoring the inherent characteristics of the original observations; (ii) when using external data sources, uncertainties such as sensor inconsistencies, temporal misalignments, and simultaneous missing data issues are introduced; and (iii) deep learning often fails to reflect underlying physical processes, producing unexplainable black-box results.

To address these limitations, this study proposes a hybrid framework that combines a Water Balance Model (WBM) with MDN-ConvLSTM (Mixture Density Network-Convolutional Long Short-Term Memory). The framework employs residual learning, where the WBM provides physically consistent baseline predictions and the MDN-ConvLSTM learns systematic differences between model estimates and SMAP observations. The MDN captures residual characteristics inherent to SMAP, enabling reconstruction using only SMAP observations. This design maintains physical interpretability while leveraging deep learning for complex residual patterns, marking the first MDN application to satellite soil moisture reconstruction.

The study compares two learning strategies and three spatial scales (16×16, 32×32, 64×64 pixels): Closed-Loop (using actual SMAP when available) and Open-Loop (recursively using own predictions), evaluating model stability, long-term gap response, and feasibility as proxy observations. Validation against original SMAP demonstrates successful reconstruction of temporally seamless SMAP-like data (ubRMSE = 0.029 m³/m³, R = 0.726, KGE = 0.679). Notably, Open-Loop achieved comparable performance to Closed-Loop, demonstrating robustness with limited data and potential as reliable proxy observations during satellite outages. This physics-guided residual learning approach establishes a novel paradigm combining physics-based water balance modeling with data-driven residual learning using only the target satellite product.

(This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2025-23523230))