Abstract. Soil water content (SWC) is crucial to rainfall-runoff response at the watershed scale. A model was used to decompose the spatiotemporal SWC into a time-stable pattern (i.e., temporal mean), a space-invariant temporal anomaly, and a space-variant temporal anomaly. The space-variant temporal anomaly was further decomposed using the empirical orthogonal function (EOF) for estimating spatially distributed SWC. This model was compared to a previous model that decomposes the spatiotemporal SWC into a spatial mean and a spatial anomaly, with the latter being further decomposed using the EOF. These two models are termed the temporal anomaly (TA) model and spatial anomaly (SA) model, respectively. We aimed to test the hypothesis that underlying (i.e., time-invariant) spatial patterns exist in the space-variant temporal anomaly at the small watershed scale, and to examine the advantages of the TA model over the SA model in terms of the estimation of spatially distributed SWC. For this purpose, a data set of near surface (0–0.2 m) and root zone (0–1.0 m) SWC, at a small watershed scale in the Canadian Prairies, was analyzed. Results showed that underlying spatial patterns exist in the space-variant temporal anomaly because of the permanent controls of static factors such as depth to the CaCO3 layer and organic carbon content. Combined with time stability analysis, the TA model improved the estimation of spatially distributed SWC over the SA model, especially for dry conditions. Further application of these two models demonstrated that the TA model outperformed the SA model at a hillslope in the Chinese Loess Plateau, but the performance of these two models in the GENCAI network (∼ 250 km2) in Italy was equivalent. The TA model can be used to construct a high-resolution distribution of SWC at small watershed scales from coarse-resolution remotely sensed SWC products.
Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control
