Global warming is inducing dramatic changes in fluvial geomorphology and reshaping the hydrological connections between rivers and lakes. The water level and area of the Salt Lake have increased rapidly since the outburst of the Zonag Lake in the Hoh Xil region of the Qinghai–Tibet Plateau in 2011, threatening the downstream infrastructure. However, fewer studies have focused on its spatiotemporal variation and overflow risk over long time series. Here, we used three machine learning algorithms: Classification and Regression Trees (CART), Random Forest (RF), and Support Vector Machine (SVM) to extract the area of the Salt Lake for a long time series, analyzed its spatiotemporal variation from 1973 to 2021, and finally assessed the overflow risk. The Kappa coefficient (KAPPA) and the overall accuracy (OA) were used to evaluate the performance of the models. The results showed that Random Forest performs superior in lake extraction (KAPPA = 0.98, overall accuracy = 0.99), followed by Classification and Regression Trees and Support Vector Machine. normalized difference water index is the relatively important feature variable in both RF and CART. Before the outburst event, the area change of the Salt Lake was consistent with the variation in precipitation; after that, it showed a remarkable area increase (circa 350%) in all orientations, and the main direction was the southeast. Without the construction of the emergency drainage channel, the simulation result indicated that the earliest and latest times of the Salt Lake overflow event are predicted to occur in 2020 and 2031, respectively. The results of this paper not only demonstrate that RF is more suitable for water extraction and help understand the water system reorganization event.

In this paper, we construct a bijective mapping between a biquadratic spline space over the hierarchical T-mesh and the piecewise constant space over the corresponding crossing-vertex-relationship graph (CVR graph). We propose a novel structure, by which we offer an effective and easy operative method for constructing the basis functions of the biquadratic spline space. The mapping we construct is an isomorphism. The basis functions of the biquadratic spline space hold the properties such as linearly independent, completeness and the property of partition of unity, which are the same with the properties for the basis functions of piecewise constant space over the CVR graph. To demonstrate that the new basis functions are efficient, we apply the basis functions to fit some open surfaces.