Copula Approach for Reducing Uncertainty in Design Flood Estimates in Insufficient Data Situations

Sufficiently long period of data is required for making sound flood estimates corresponding to the design return periods. Such long-term and good quality flow data is often a difficult proposition, especially in developing and under-developed countries. Most watersheds in these countries that are of immediate interest and concern are either completely ungauged or are insufficiently gauged. Flood estimates in situations of inadequate length of data invariably involve large amounts of uncertainties. There is a growing interest in investigating if these uncertainties in flow estimates can be reduced by supplementing the limited flow data with that available at adjoining river gauging station(s) on the same river or that in the adjoining river basins. It is expected that additional information can be derived from the dependence among flow characteristics at these adjoining flow stations when they are considered together. The maximum likelihood procedure, with likelihood function involving univariate and joint probabilities corresponding to exclusive and concurrent periods of data availability, is employed for estimating parameters of flood frequency distributions. Copula-based bivariate distribution approach offers advantage over conventional functional forms by admitting arbitrary marginal types that are dictated by the nature of the flow regimes at these river stations under consideration. This paper presents a comparison of uncertainties in the estimated flood quantiles at a station with limited data, as obtained from the univariate consideration and that from the simultaneous consideration of additional flow data from a neighboring river gauging station. A significant reduction in uncertainty achieved by this approach indicates that substantial improvements in the accuracy of flood estimates can be made by multivariate consideration of flood frequency analysis that is facilitated by copula approach.