The Two-dimension Gumbel Model for Runoff and Rainfall Frequency Analysis and Application

The two-dimension Gumbel mixed model was proposed,the bivariate extreme value distribution model with Gumbel marginals was given to analyze the joint probability distribution of correlated rainfall and reservoir inflow.Based on the marginal distributions of these random variables,the joint distributions,the conditional probability functions,and the associated return periods were derived.The joint and conditional frequency of rainfall with different runoffs and runoff with different rainfalls were figured out with this model. It was helpful to solve the multi-variations hydrology problem.The model was tested and validated using observed data of Gangnan reservoir in the Hutuohe River Basin.Results indicated that the model was suitable for representing the joint distributions of rainfall and reservoir inflow.