Applying the Improved Set Pair Analysis Method to Flood Season Staging in Tropical Island Rivers: A Case Study of the Hainan Island Rivers in China

The seasonality of floods is a key factor affecting riparian agriculture. Flood season staging is the main means of identifying the seasonality of floods. In the process of staging the flood season, set pair analysis is a widely used method. However, the set pair analysis method (SPAM) cannot take into account the differences in and volatility of the staging indicators, and at the same time, the SPAM cannot provide corresponding staging schemes according to different scenarios. To address these problems, the improved set pair analysis method (ISPAM) is proposed. Kernel density estimation (KDE) is used to calculate the interval of the staging indicators to express their volatility. Based on the interval theory, the deviation method is improved, and the weights of the staging indicators are calculated to reflect the differences in different staging indicators. The theoretical correlation coefficient can be calculated by combining the weights and interval indicators and fitting the empirical connection coefficient corresponding to each time period. Finally, the ISPAM is established under different confidence levels to derive staging schemes under different scenarios. Based on the daily average precipitation flow data from 1961 to 2022 in the Nandujiang middle basin and surrounding areas in tropical island regions, the staging effect of the ISPAM was verified and compared using the SPAM, Fisher optimal segmentation method, and improved set pair analysis method without considering differences in the indicator weights (ISPAM-WCDIIW), and the improved set pair analysis method without considering indicator fluctuations (ISPAM-WCIF). According to the evaluation results from the silhouette coefficient method, it can be concluded that compared with the SPAM and ISPAM-WCIF, the ISPAM provided the optimal staging scheme for 100% of the years in the test set (2011–2022). Compared with the Fisher optimal segmentation method, the optimal staging scheme for more than 83% of the years (2011, 2013–2015, and 2017–2022) in the test set was provided by the ISPAM. Although the ISPAM-WCDIIW, like the ISPAM, can provide optimal staging schemes, the ISPAM-WCDIIW could not provide an exact staging scheme for more than 55% of the scenarios (the ISPAM-WCDIIW could not provide an exact staging scheme in scenarios (0.7, 0.6), (0.8, 0.6), (0.8, 0.9), (0.95, 0.6), and (0.95, 0.8)). The results show that the ISPAM model is more reasonable and credible compared with the SPAM, Fisher optimal segmentation method, ISPAM-WCDIIW, and ISPAM-WCIF. The purpose of this study is to provide a reference for flood season staging research during flood seasons.