Flood as an intrinsically complex and multivariate event is of high importance, especially in these days when the world witnesses its increased natural and anthropogenic hazards and damages. Assuming the flood as a univariate event can make all the calculations done to estimate its possibly negative impacts on the upstream and/or downstream of the event imprecise and invalid to be taken into consideration for water resources planning at the future. Having the ability to be free from some fundamental assumptions for the joint probabilities such as the independence of the variables, the multivariate copula models can be so desirable to predict the probability of the extreme events to occur. In this thesis, copula functions were applied to modeling and estimating the joint probability distribution functions of the flood as an extreme event. To analyze the flood frequency in the multivariate mode, three major variables of peak discharge, volume and duration of the entering floods to Shahid Abbaspour Dam were provided as the main inputs of this study. Thereafter, five popular copula functions derived from the Archimedean copula family (Clayton, Ali-Mikhail-Haq, Gumbel-Houggard, Frank, and Joe) were chosen for the flood frequency analysis. The internal parameters of the marginal probability distribution functions and also the copula functions were tuned through two methods: Maximum Likelihood Estimation (MLE) and Optimization-Based Method (OBM). In this thesis, a newly proposed Particle Swarm Optimizer (PSO), named the Guided Adaptive Search based PSO (GuASPSO) algorithm was employed to fine tuning/optimizing the parameters of copula functions. In this algorithm, the personal best (Pbest) particles are all divided into a number of clusters. Then the best fitted particle located at each cluster is appointed as the cluster best (Cbest) particle of that cluster. In GuASPSO, each particle partly moves towards the weighted average of the Cbests of the opposite clusters to the cluster the focused particle is located in, and partly goes towards its Pbest particle. The major feature of the GuASPSO is its enhanced exploration capability that highly improves its performance while causing this algorithm to experience the least disruptions in its exploitation capability. In this study, the correlation coefficients between every couple of three major flood variables were first eva‎luated. The results showed there are strict correlations between each couple of the flood variables for the flood data recorded in the study area. The marginal probability distribution functions were assumed to be of types Gamma, Gumbel, Lognormal, Pearson type III and Extreme value type II. The Lognormal function was found to be the best marginal distribution, resulting in the best overall correlation coefficient, Akaike information, Root Mean Square Error, and Kolmogorov-Smirnov goodness-of-fit criteria. In addition, the Clayton copula function was figured out to be the best–fitting bivariate copula. For trivariate flood analysis, the three major flood variables were modeled once in a Vine structure and once again when taken together, in both of which the Clayton copula was found to be the best function. Furthermore, the Vine structure yielded the best modeling accuracy compared to the other structure. The results also revealed the higher accuracy of the predictions made by the copulas modeled through the GuASPSO algorithm as an OBM, compared to that of the copulas modeled by the classical MLE method. Finally, the flood joint probabilities were calculated by the best copula functions and applied to derive the joint and joint conditional flood return periods for the study area.

حميدرضا صفوي ، محمدحسين گل محمدي

فرشاد رضائي

رامتين معيني، مسعود طاهريون