Copula-Based Multivariate Hydrologic Frequency Analysis
Multivariate frequency distributions are being increasingly recognized for their role in hydrological design and risk management. The conventional multivariate distributions are severely limited in that all constituent marginals have to be from the same distribution family. The copula method is a newly emerging approach for deriving multivariate distributions which overcomes this limitation. Use of copula method in hydrological applications has begun only recently and ascertaining the applicability of different copulas for combinations of various hydrological variables is currently an area of active research. Since there exists a variety of copulas capable of characterizing a broad range of dependence, the selection of appropriate copulas for different hydrological applications becomes a non-trivial task. This study evaluates the relative performance of various copulas and methods of parameter estimation as well as of recently developed statistical inference procedures. Potential copulas for multivariate extreme flow and rainfall processes are then identified. Multivariate hydrological frequency analysis typically utilizes only the concurrent parts of observed data, leaving a lot of non-concurrent information unutilized. Uncertainty in distribution parameter estimates can be reduced by simultaneously including such non-concurrent data in the analysis. A new copula-based “Composite Likelihood Approach” that allows all available multivariate data of varying lengths to be combined and analyzed in an integrated manner has been developed. This approach yields additional information, enhancing the precision of parameter estimates that are otherwise obtained from either purely univariate or purely multivariate considerations. The approach can be advantageously employed in limited hydrological data situations in order to provide significant virtual augmentation of available data lengths by virtue of increased precision of parameter estimates. The effectiveness of a copula selection framework that helps in an a priori short listing of potentially viable copulas on the basis of dependence characteristics has been examined using several case studies pertaining to various extreme flow and rainfall variables. The benefits of the composite likelihood approach in terms of significant improvement in the precision of parameter estimates of commonly used distributions in hydrology, such as normal, Gumbel, gamma, and log-Pearson Type III, have been quantified.
extreme value copula, Archimedean copula, copula, dependence, statistical hydrology, multivariate frequency distributions, copula fitting, uncertainty reduction, copula inference
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