Bivariate Flood Frequency Analysis of Krishna River using Copula Theory

Copula theory has received attention in the field of hydrology. Copula function is used to
derive the multivariate distribution of variables. Using copula have an advantage that
marginal distribution of independent variables can be of any form and the variables can be
correlated. Flood frequency analysis (FFA) help us to quantify the risk associated with flood.
In this study copula theory is used for flood frequency analysis of Krishna River in India.
Four stations (i.e., Kurundwad, Huvinhedigi, K. Agrharam, and Wadenpally) was selected on
Krishna river basin. Peak over threshold method (POT-method) was used to select the
independent events for analysis. Using methodology provided in Flood Estimation Handbook
(FEH), Volume and Duration data is extracted from the selected events. The joint
dependence structure of flood variables is derived, for frequency analysis of Peak Flow (P),
Flood Volume (V), and Flood Duration (D). Best fit marginal distributions of these flood
variables are determined using five parametric (Normal, Exponential, Extreme value,
Lognormal, and Gamma distribution) and one non-parametric (Kernel distribution)
probability distributions. Kolmogorov-Smirnov & Anderson-Darling test was performed to
find out the best fit distribution for flood variables. For modelling of the joint dependence
structure of peak flow-volume (P-V), flood volume-duration (V-D), peak flow-duration (P-
D), five Archimedean family of copulas, namely Independence, Clayton, Frank, Gumbel-
Hougaard, and Ali-Mikhail-Haq Copulas are evaluated. Goodness-of-fit (GOF) test using
Rosenblatt’s probability integral transformation was used to find out the best fitted copula for
bivariate models. Clayton copula has been identified as the best fitted copula for all the
bivariate models considered. Clayton copula function is used to obtain conditional return
periods, Conditional return periods of flood characteristics can be useful for risk based design
of water resource projects.