Physical Modeling and Compensation for Systematic Negative Errors in GNSS-R Snow Depth Retrieval

Previous studies have reported that signal penetration will introduce an underestimation of snow depth, referred to as the snow depth difference. So far, however, there have been few detailed investigations into the relationship between snow depth difference and signal-to-noise ratio (SNR) metrics. In this study, we briefly describe the snow depth difference and provide a physical explanation of the systematic negative error. The baseline- and short-term variations of snow depth difference and SNR metrics were identified, and their relationships during various snow periods were investigated. The results indicated that the systematic negative errors and SNR metrics during the stable and melting periods are dominated by the layered structures and liquid water content of snowfall, respectively. Meanwhile, compared with the baseline terms, the short-term variations of snow depth difference and SNR metrics were more sensitive to fresh, low-density snowfall over the old snow surface. In addition, an improved method is proposed to compensate for systematic differences using two- and five-parameter multiple linear regression (MLR) models with SNR metrics as independent variables. The results showed that the compensation values conformed with the measured values with correlation coefficients exceeding 0.85. In terms of accuracy, once the MLR models were applied, the root mean squared errors (RMSEs) decreased from 22.05 to 3.89 and 3.40 cm, respectively. Moreover, the corrected estimates agree well with the meteorological records, with regression slope deviations of less than 2% and correlation coefficients of over 0.97, suggesting no systematic errors between the estimates and reference.