Joint Probability Analysis of the Rich‐Poor Runoff and Sediment Discharge in Karst Watersheds

Abstract As one of the largest contiguous karst landscapes in the world, southwest China has experienced severe soil erosion because of its frequent climate extremes, special hydrogeology, shallow and discontinuous soil, steep topography, and inappropriate land use. Furthermore, the construction of dams in recent decades has rendered the relationship between runoff and sediment discharge increasingly complex. However, the joint probability distributions and joint return periods of runoff‐sediment discharge relationship are still not clear. The objective of this study was to investigate the synchronous‐asynchronous probabilities and return periods of rich‐poor combinations of annual runoff and sediment discharge using a bivariate copula function to assess the risk of soil erosion in four selected karst watersheds in southwest China. Results showed that sediment discharge has declined significantly in all watersheds except Liujiang, and annual runoff and sediment discharge were significantly positively correlated in all watersheds. The optimal marginal distribution and the best copula function of annual runoff and sediment discharge are not identical for each watershed. The synchronous and asynchronous probabilities of annual runoff and sediment discharge are close to 1:1 in the Wujiang watershed. The asynchronous probability is much higher for the combination of less runoff with more sediment discharge (r < s) than for the combination of more runoff with less sediment discharge (r > s) in Nanpanjiang. Therefore, the risk of soil erosion may be higher in the Wujiang and Nanpanjiang watersheds. The joint return periods of runoff‐sediment discharge were concentrated in less than 5 years during the historical period. These return periods can provide data references for designing the scale of water resources projects and help in better soil erosion control in the future. This study could be a technical reference for identifying the non‐stationarity of the multivariate relationship between runoff and sediment discharge in karst regions.