SMPLNORM - A SIMPLE-MODEL FOR CALCULATING THE JOINT PROBABILITIES OF 2 FLOWS AND THE RELEVANT WATER-LEVEL

Most bivariate models assume the same type of marginal distribution, w ith two parameters, for two variables (gamma, type I extreme values, a nd so forth). The disadvantage of these models is that it is often dif ficult to make adjustments for observed flows. This study shows the ap plication flexibility of a program that calculates the joint probabili ty of two variables, Q1 and Q2, with marginal distributions that have three parameters. The program can also provide the probability of none xceedence of a third variable, H, mathematically related to the first two variables. Two applications are discussed, in which Q1 and Q2 are the flows of two rivers controlling the variable H, which is a level i n both cases. Theoretically, this model could also be applied to other types of variables. The proposed model is based on the hypothesis tha t a Box-Cox type of power transformation could reduce the marginal dis tributions of Q1 and Q2 to a normal distribution. One of the main conc lusions of the study addresses the importance of taking into account t he correlation between Q1 and Q2 to obtain a valid estimate of H.