The value of mixed distribution approaches for low-flow frequency analysis

Extreme value statistics are well established for floods and are also receiving increasing attention in drought hydrology. They allow the user to characterize the severity of an event by a statistical probability or return period, a concept that is well understood in the scientific, policy, and public arenas. Frequency analysis is usually carried out on the basis of annual extreme event series, which  is straightforward in its application and interpretation. However, in seasonal climates with a warm and a cold season, the low-flows can be generated by different processes, which violates the basic assumptions of extreme value statistics and can lead  to inaccurate conclusions.

Here we assess the value of a mixed distribution approach for low-flows to perform frequency analysis in catchments with a mixed summer/winter regime. We first present the theoretical concept of the mixed probability estimator for low-flows. We then illustrate the characteristics of the model for archetypal low-flow regimes, from pronounced summer and winter regimes to flow mixtures with weak seasonality. We successively evaluate the gain in performance from the mixed distribution model for a range of low flow regimes, based on a comprehensive Austrian dataset. We finally scrutinize the assumption of the mixed probability estimator and review the added value of using an extended, Copula-based  framework. The results show large differences of event return periods, and suggest that the mixed estimator is relevant not only for mountain forelands, but for a much wider range of catchment typologies across Europe. These even include typical summer regimes when only single winter low-flows are mixed in. We conclude that the mixed distribution approaches outperform the conventional frequency estimator and should be used by default in seasonal climates where summer and winter low flows occur.