A multivariate index-flood approach for flood frequency analysis of ungauged watersheds: a case study on state of Kerala in India

Abstract

The multivariate index-flood method (MIF) advances flood risk evaluation at ungauged watersheds by utilizing information from gauged sites within a uniform region to forecast flood attributes where direct data is absent. It aims to enhance flood frequency analysis at ungauged watersheds by considering the interdependence between multiple flood variables using copulas and multivariate quantile curves. The proposed methodology involves screening data for anomalies, delineating homogeneous regions based on physiographic and hydrological descriptors, and selecting appropriate regional marginal distributions and copulas. Regional Flood Frequency Analysis and the index-flood method, MIF, can produce dependable multivariate quantile approximations, enhancing the precision of flood projections and risk evaluations at ungauged watersheds. Nine watersheds in the Indian state of Kerala situated along rivers flowing westward have been subjected to the suggested multivariate technique, which focuses on the bivariate case. This implementation involves recorded data series on flood volume and peak flow. The dataset includes daily maximum discharge data from India-WRIS, gridded precipitation and temperature data from IMD, and a 30 × 30 m DEM from USGS SRTM. The data record span 31–39 years. Subsequently, given a specific return period, a set of occurrences where volume and peak fall within a bivariate quantile curve is established at a designated watershed. The quantile curves derived from the regional methodology are juxtaposed with those obtained through the local method to assess the efficacy of the MIF technique. The model performed well for Arangali, Kalampur, Pattazhy, Pudur, and Mankara stations, as the quantile curves generated by the regional and local approaches matched well at these watersheds. In contrast, the regional and local quantile curves differ considerably at Perumannu, Ramamangalam, Kidangoor, and Erinjipuzha watersheds, indicating the effect of small sample size, higher sensitivity to local factors, modeling approach, and uncertainty involved. This investigation significantly enhances flood risk assessment in river areas using the MIF method to generate regional quantile curves, identify homogeneous regions, and compare regional and local quantile estimates, improving predictive accuracy at ungauged watersheds. The study confirmed data homogeneity across nine Kerala watersheds, with multivariate discordancy measures ?Di?<2.6, and a homogeneity test H value of -0.76. The BB8 copula best modeled the joint distribution of mean flood volume (V) and peak flow (Q), achieving a Kendall’s tau of 0.711 at Arangali. Regional quantile curves aligned well with standardized data, with the Gaussian copula (?)=0.4427, p<(1.75E-27) selected for multivariate regional analysis. © The Author(s) under exclusive licence to Institute of Geophysics, Polish Academy of Sciences 2025.