Future Joint Probability Characteristics of Extreme Precipitation in the Yellow River Basin

The relationship between climate change and extreme precipitation is extremely complex. From a probabilistic perspective, a proper understanding of the response of extreme precipitation to climate change is of significant importance. This study was based on daily precipitation provided by CMIP6 climate models and employed copula functions to construct joint distributions of precipitation amount and precipitation intensity indices at different quantile levels. A spatial-temporal assessment of the susceptibility areas for extreme precipitation in the Yellow River Basin was conducted while considering bivariate return periods and design values. The results indicate that there were significant spatial differences in the bivariate return periods. Taking the R90P-SDII (90) index for a 20a return period as an example, the difference between the maximum and minimum joint return periods within the Yellow River Basin was 1.4 times, while the co-occurring return period was 7.0 times, and the Kendall return period was 4 times. Moreover, this difference increased with the increase in the return period. The magnitude order of the four return periods is as follows: T-And > T-Kendall > TSingle-variable > T-Or. Joint return periods (Or) and co-occurring return periods (And) could be considered as the extreme cases under single-variable return periods, serving as an estimation interval for actual return periods. Under the influence of climate change, the bivariate design values for future periods exhibited a variability increase of 6.76-28.8% compared to historical periods, and this increase grew with higher radiative forcing scenarios, ranking as SSP126 < SSP245 < SSP585. The bivariate design values showed a noticeable difference in variability compared to the single-variable design values, ranging from -0.79% to 18.67%. This difference increased with higher quantile values, with R95P-SDII (95) > R90P-SDII (90) > PRCPTOT-SDII.