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

Reducing uncertainty in estimates of frequency distribution parameters using composite likelihood approach and copula‐based bivariate distributions

Conventional multivariate hydrological frequency analysis utilizes only the concurrent parts of data sets, leaving a lot of nonconcurrent data unutilized. Simultaneous inclusion of such nonconcurrent data can significantly reduce uncertainty in hydrologic design estimates. The methodology proposed in this paper allows varied length multivariate data to be combined and analyzed in an integrated framework through a “Composite Likelihood Approach.” The method employs copula‐based multivariate distributions in order to provide necessary flexibility of admitting arbitrary marginals. The paper presents the theoretical basis of the approach and highlights its advantages through two applications. A significant reduction in uncertainty in design flood quantiles of a relatively shorter flood series is achieved by utilizing an associated downstream flood data. The advantage of the methodology is further demonstrated by establishing significant information gain for six different combinations of Gaussian and non‐Gaussian marginals. The proposed approach marks a paradigm shift in hydrologic design procedures, particularly for partially gauged basins, wherein a higher precision in hydrologic designs is achieved by leveraging associated information that has hitherto remained unutilized. It is opined that the approach will enable offsetting the impact of dwindling hydrological observation networks around the world by enhancing information that is derivable from existing networks