Spatial Upscaling of Sparse Soil Moisture Observations Based on Ridge Regression

Available ground-based observation networks for the validation of soil moisture remote sensing products are commonly sparse; thus, ground truth determinations are difficult at the validated remote sensing pixel scale. Based on the consistency of temporal trends between ground truth and in situ measurements, it is feasible to estimate ground truth by building a linear relationship between temporal sparse ground observations and truth samples. Herein, auxiliary remote sensing data with a moderate spatial resolution can be transformed into truth samples depending on the stronger representation of remote sensing data to spatial heterogeneity in the validated pixel relative to limited sites. When solving weighting coefficients for the relationship model, the underlying correlations among the in situ measurements cause the multicollinearity problem, leading to failed predictions. An upscaling algorithm called ridge regression (RR) addresses this by introducing a regularization parameter. With sparse sites, the RR method is tested in two cases employing six and nine sites, and compared with the ordinary least squares and the arithmetic mean. The upscaling results of the RR method show higher prediction accuracies compared to the other two methods. When the RR method is used, the six-site case has the same estimation accuracy as the nine-site case due to maintaining the diversity of in situ measurements through the analysis of the ridge trace and variance inflation factor (VIF). Thus, the ridge trace and VIF analysis is considered as the optimal selection method for the existing observation networks if the RR method will be used in future validation work. With a different number of sites, the RR method always displays the best estimation accuracy and is not sensitive to the number of sites, which indicates that the RR method can potentially upscale sparse sites. However, if the sites are too few, e.g., one to four, it is difficult to perform the upscaling method.