Copula Theory as a Generalized Framework for Flow‐Duration Curve Based Streamflow Estimates in Ungaged and Partially Gaged Catchments

Flow‐duration curve (FDC) based streamflow estimation methods involve estimating an FDC at an ungaged or partially gaged location and using the time series of nonexceedance probabilities estimated from donor streamgage sites to generate estimates of streamflow. We develop a mathematical framework to illustrate the connection between copulas and prior FDC‐based approaches. The performance of copula methods is compared to several other streamflow estimation methods using a decade of daily streamflow data from 74 sites located within two river basins in the southeast United States with different climate characteristics and physiographic properties. We show that copula approaches: (1) outperform other methods in the limiting case of perfect information with regard to the rank‐based correlation structure and FDCs across the gaging network; (2) provide a hedge against poor performance when donor information becomes sparser and less informative; (3) outperform other methods when used for partially gaged sites with several years of available data; and (4) remain a competitive albeit nondominating method for ungaged sites and partially gaged sites with limited data when realistic error is introduced in the estimation of FDCs and correlations across the gaging network. Key Points Flow‐duration curve streamflow estimation methods (e.g., QPPQ) are formalized as copula models Copulas can flexibly model dependencies between streamflow at different sites Copulas approaches allow for a statistically rigorous calculation of conditional variances