27 Oct 2022
27 Oct 2022
Status: this preprint is currently under review for the journal HESS.

A mixed distribution approach for low-flow frequency analysis – Part 2: Modeling dependency using a copula-based estimator

Gregor Laaha Gregor Laaha
  • University of Natural Resources and Life Sciences, Vienna, Department of Landscape, Spatial and Infrastructure Sciences, Institute of Statistics, Peter Jordan-Straße 82/I, 1190 Vienna, Austria

Abstract. In climates with a warm and a cold season, low-flows are generated by different processes, which violates the homogeneity assumption of extreme value statistics. In this second part of a two-part series, we extend the mixed probability estimator of the companion paper (Laaha, G., 2022) to deal with dependency of seasonal events. We formulate a copula-based estimator for seasonal minima series and examine it in a hydrological context. The estimator is a valid generalization of the annual probability estimator and provides a consistent framework for estimating return periods of summer, winter and annual events. Using archetypal examples we show that differences to the mixed estimator are always observed in the upper part of the distribution, which is less relevant for low-flow frequency analysis. The differences decrease as the return period increases so that both models coincide for the severest events. In a quantitative evaluation, we test the performance of the copula estimator on a pan-European data set. We find a large gain of both mixed distribution approaches over the annual estimator, making these approaches highly relevant for Europe as a whole. We then examine in more detail the relative performance gain of the mixed copula versus the mixed distribution approach. The analysis shows that the gain for the 100-year event is actually minimal. However, the gain for 2-year events is considerable in some of the catchments, with a relative deviation of -15 to -23 % in the most affected regions. This points to a prediction bias of the mixed probability estimator that can be corrected using the copula approach. Using multiple regression models, we show that the performance gain can be well explained on hydrological grounds, with weak seasonality leading to a high potential for corrections and strong seasonal correlation reinforcing the need to take it into account. Accordingly, the greatest differences can be observed in mid-mountain regions in cold and temperate climates, where rivers have a strongly mixed low-flow regime. This finding is of particular relevance for event mapping, where regional severity can be misinterpreted when the seasonal correlation is neglected. We conclude that the two mixed probability estimators are quite similar, and both are more accurate as the annual minima approach. In regions with strong seasonal correlation the mixed copula estimator is most accurate and should be preferred over the mixed distribution approach.

Gregor Laaha

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2022-358', Anonymous Referee #1, 09 Nov 2022
  • RC2: 'Comment on hess-2022-358', Anonymous Referee #2, 16 Dec 2022

Gregor Laaha

Gregor Laaha


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Short summary
In seasonal climates with a warm and a cold season, low-flows are generated by different processes so that return periods will be inaccurate. We propose a novel mixed copula estimator that is shown to outperform previous calculation methods. We show that it is highly relevant for a wide range of European flow regimes and should be used by default.