Leveraging Neural Operator and Sliding Window Technique for Enhanced Subsurface Soil Moisture Imputation Under Diverse Precipitation Scenarios

Environmental monitoring and decision-making are sometimes hampered by missing sensor data, particularly in soil moisture (SM) records that underpin hydrological modeling, agricultural management, and climate studies. We present a novel imputation framework based on Fourier neural operators (FNO) that robustly reconstructs missing SM values by learning global spatiotemporal dependencies directly in the frequency domain. Our approach segments high-frequency hydro-meteorological time series into overlapping windows, incorporating rainfall, soil temperature, and normalized time coordinates and leverages spectral convolution layers with a sliding window strategy to capture both short- and long-term dynamics. Through extensive experiments using multidepth SM measurements (10, 20, 30, and 40 cm), we systematically assess the impact of varying missing data ratios (from 5% to 50%) and temporal lag configurations. The FNO model demonstrates statistically better performance as compared to the traditional statistical and machine learning imputation methods. The FNO shows high correlation coefficients and low root mean square errors even under challenging rain and no-rain conditions. Although the imputation accuracy of all models decreases during rain events, we observed that incorporating a temporal delay marginally improves performance by reducing the imputation error by up to 15%. These results establish the FNO framework as a paradigm shift in environmental data imputation, demonstrating unparalleled accuracy by harnessing global spatiotemporal dependencies to effectively overcome data sparsity even under the most challenging conditions.