Copula-Based Frequency and Coincidence Risk Analysis of Floods in Tropical-Seasonal Rivers

The conventional method of univariate flood frequency analysis based solely on peak flow ($Q$) overlooks the influence of other characteristic flood variables, such as the accumulated volume ($V$) of the flood and the duration ($D$) of flood events. A copula-based multivariate model that represents the joint behavior of these dependent flood variables could aid in computing joint return periods of flood events in tropical, seasonal rivers of India. In connection with the potential locations of high flood risk among west-flowing rivers, multivariate flood frequency analysis was performed on the Bharatapuzha, Periyar, and Chaliyar Rivers of the state of Kerala, India. A comparison of univariate return periods with multivariate return periods reveals that the intersection of flood variables corresponding to a 20-year univariate return period yields a trivariate return period of $91\mathrm{years}$ at Bharatapuzha and $144\mathrm{years}$ at Periyar and Chaliyar. The return period by the union of such flood variables is $10\mathrm{years}$. The choice of flood variables and their combination depend on the problem at hand. Additionally, basinwise confluence flood frequency models are built with the peak flow at each stream as the random variables show their spatial interdependencies using conditional probabilities and return periods. The copula-based flood coincidence risk model captures the temporal aspect of the co-occurrence of flood peaks in a basin’s streams. The co-occurrence of annual flood peaks between the stream pairs of the Bharatapuzha, Periyar, and Muvathapuzha basins is the highest toward the end of July with probabilities of approximately $2.2\times {10}^{-4}$ (at the Kumbidi and Mankara stations), $3\times {10}^{-4}$, and $1\times {10}^{-3}$, respectively. A trio of copula-based multivariate flood frequency, confluence flood frequency, and flood coincidence risk models could be used to design safe and economic hydrologic infrastructure.