In hydrological frequency analysis, it is difficult to apply standard statistical methods to derive multivariate probability distributions of the characteristics of hydrologic or hydraulic variables except under the following restrictive assumptions: (1) variables are assumed independent, (2) variables are assumed to have the same marginal distributions, and (3) variables are assumed to follow or are transformed to normal distribution. Relaxing these assumptions when deriving multivariate distributions of the characteristics of correlated hydrologic and hydraulic variables.
The copula methodology is applied to perform multivariate frequency analysis of rainfall, flood, low-flow, water quality, and channel flow, using data from the Amite river basin in Louisiana. And finally, the risk methodology is applied to analyze flood risks.
Through the study, it was found that (1) copula method was found reasonably well to be applied to derive the multivariate hydrological frequency model compared with other conventional methods, i.e., multivariate normal approach, N-K model approach, independence transformation approach etc.; (2) nonstationarity was found more or less existed in the rainfall and streamflow time series, but according to the nonstationary test, in most cases, the stationarity assumption may be approximately valid; (3) the multivariate frequency analysis coupling nonstationarity indicated that the stationary assumption was valid for both bivariate and trivariate analysis; and (4) risk, defined by both flooding event and the damage caused by the scenario, showed the difference from that defined by T-year return period design event and the probability of total damage with the comparison indicating that only one character, i.e., T-year event or probability of total damage was not adequate to define the risk.