Subtropical regions have clay-rich, weathered soils, and long dry periods followed by intense rainfall that produces large fluctuations in soil water content (SWC) and hydrological behavior. This complicates predictions of spatio-temporal dynamics, as datasets are typically collected at too coarse resolution and observations often represent a duration that is too short to capture temporal stability. The aim of the present study was to gain further insights into the role of temporal sampling scale on the observed temporal stability features of SWC order to aid the design of optimal SWC sampling strategies. This focused on both sampling frequency and total monitoring duration, as previous analyses have not considered both of these sampling aspects simultaneously. We collected relatively high resolution data of SWC (fortnightly over 3.5 years) for various soil depths and under contrasting crops (peanuts and citrus) at the red soil region of southeast China. The dataset was split into a three-year training period and a six-month evaluation period. Altogether 13 sampling frequencies (intervals ranging from 15 to 240 days) and eight monitoring duration periods (between three and 36 months) were derived from the training period to identify temporal stability features and the most time stable location (MTSL). The prediction accuracies of these MTSLs were tested using the independent evaluation data. Results showed that vegetation type did affect the spatio-temporal patterns of SWC, whereby the citrus site exhibited a stronger temporal variation and weaker temporal stability than the peanut site. However, the effects of both sampling frequency and observation duration were more pronounced, irrespective of the role of vegetation type or soil depth. With increasing sampling interval or decreasing monitoring duration, temporal stability of SWC was generally overestimated; by less than 10% when sampling interval increased from every 15 to 240 days and by up to 40% with duration decreasing from 36 to 3 months. Our results suggest that sampling strategies and trade-offs between sampling interval and duration should focus on capturing the main variability in hydro-climatological conditions. For subtropical conditions, we found that sampling once every 45 days over 24 months to be the minimum sampling strategy to ensure errors in SWC temporal stability of less than 10%.
The Whitham-Broer-Kaup model is widely used to study the tsunami waves. The classical Whitham-Broer-Kaup equations are re-investigated in detail by the generalized projective Riccati-equation method. 20 sets of solutions are obtained of which, to the best of the authors’ knowledge, some have not been reported in literature. Bifurcation analysis of the planar dynamical systems is then used to show different phase portraits of the traveling wave solutions under various parametric conditions.
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