Hydro-wind system output fluctuations are the primary factors used to assess the effects of hydropower on power companies compensating for wind power intermittency. Considering that most fluctuation indices can only characterize one aspect of fluctuations, namely, the quantitative or contour variations, we present a new index that uses the standard deviation (SD) and rotation angle to detect the quantitative variations and contour changes, respectively. Herein, the new index is compared with commonly used indices, specifically, the first-order difference, SD, and Richards-Baker flashiness indices. The results of tests performed using various processes and disposals show that: (1) when dealing with the process by moving average, repeating or overlay disposal, the new index performs comparably to the other indices, while when dealing with the process by zooming disposal, it more fully describes the fluctuation characteristics by taking both quantitative and contour variations into consideration; (2) when the new index is used to characterize the hydro-wind output fluctuations with different resources and capacities, the outcomes coincide with the mechanisms of hydro-wind systems. This study presents a new way to characterize the fluctuation of hydro-wind output.

Water resources and their utilization perform a critical role in sustainable development. A full comprehension of the decoupling relationship between water consumption and economic development is a prerequisite for sustainable water resource management. This thesis developed a decoupling index analysis model based on Hodrick–Prescott filtering; analyzed the spatial aggregation characteristics of Gross Domestic Product (GDP), water consumption, and the decoupling index by the Global and Local Moran’s Index; and calculated the spatial gravity migration characteristics of GDP, water consumption, and the decoupling index. A case study in the Poyang Lake basin was selected to analyze the relationship between water and the economy. The results indicated that decoupling status was steadier after extracting trend components. The decoupling index exhibited spatial outlier characteristics. The spatial gravity center migration directions of GDP and water consumption were opposite. Furthermore, the Poyang Lake basin was in a weak decoupling status, and its water use pattern was sustainable to a certain extent.