River runoff and sediment transport are two related random hydrologic variables. The traditional statistical analysis method usually requires those two variables to be linearly correlated, and also have an identical marginal distribution. Therefore, it is difficult to know exactly the characteristics of the runoff and sediment in reality. For this reason, copulas are applied to construct the joint probability distribution of runoff and sediment in this article. The risk of synchronous-asynchronous encounter probability of annual rich-poor runoff and sediment is also studied. At last, the characteristics of annual runoff and sediment with multi-time scales in its joint probability distribution space are simulated by empirical mode decomposition method. The results show that the copula function can simulate the joint probability distribution of runoff and sediment of Huaxia hydrological station in Weihe River well, and that such joint probability distribution has very complex change characteristics at time scales.