The added utility of nonlinear methods compared to linear methods in rescaling soil moisture products

In this study, the added utility of nonlinear rescaling methods relative to linear methods in the framework of creating a homogenous soil moisture time series has been explored. The performances of 31 linear and nonlinear rescaling methods are evaluated by rescaling the Land Parameter Retrieval Model (LPRM) soil moisture datasets to station-based watershed average datasets obtained over four United States Department of Agriculture (USDA) Agricultural Research Service (ARS) watersheds. The linear methods include first-order linear regression, multiple linear regression, and multivariate adaptive regression splines (MARS), whereas the nonlinear methods include cumulative distribution function matching (CDF), artificial neural networks (ANN), support vector machines (SVM), Genetic Programming (GEN), and copula methods. MARS, GEN, SVM, ANN, and the copula methods are also implemented to utilize lagged observations to rescale the datasets. The results of a total of 31 different methods show that the nonlinear methods improve the correlation and error statistics of the rescaled product compared to the linear methods. In general, the method that yielded the best results using training data improved the validation correlations, on average, by 0.063, whereas ELMAN ANN and GEN, using lagged observations methods, yielded correlation improvements of 0.052 and 0.048, respectively. The lagged observations improved the correlations when they were incorporated into rescaling equations in linear and nonlinear fashions, with the nonlinear methods (particularly SVM and GEN but not ANN and copula) benefitting from these lagged observations more than the linear methods. The overall results show that a large majority of the similarities between the LPRM and watershed average datasets are due to linear relations; however, nonlinear relations clearly exist, and the use of nonlinear rescaling methods clearly improves the accuracy of the rescaled product.