A mixed distribution approach for low-flow frequency analysis - Part 1: Concept, performance, and effect of seasonality

In seasonal climates with a warm and a cold season, low flows are generated by different processes so that the annual extreme series will be a mixture of summer and winter low-flow events. This leads to a violation of the homogeneity assumption for all statistics derived from the annual series and gives rise to inaccurate conclusions. In this first part of a two-paper series, a mixed distribution approach to perform frequency analysis in catchments with mixed low-flow regimes is proposed. We formulate the theoretical basis of the mixed distribution approach for the lower extremes based on annual minima series. The main strength of the model is that it allows the user to estimate return periods of summer low flows, winter low flows, and annual return periods in a theoretically sound and consistent way. Using archetypal examples, we show how the model behaves for a range of low-flow regimes, from distinct winter and summer regimes to mixed regimes where seasonal occurrence in summer and winter is equally likely. The examples show in a qualitative way the loss in accuracy one has to expect with conventional extreme value statistics performed with the annual extremes series. The model is then applied to a comprehensive Austrian data set to quantify the expected gain of using the mixed distribution approach compared to conventional frequency analysis. Results indicate that the gain of using a mixed distribution approach is indeed large. On average, the relative deviation is 21 %, 39 %, and 63 % when estimating the low flow with a 20-, 50-, and 100-year return period. For the 100-year event, 75 % of stations show a performance gain of > 10 %, 41 % of stations > 50 %, and 25 % of stations > 80.6 %. This points to a broad relevance of the approach that goes beyond highly mixed seasonal regimes to include the strongly seasonal ones. We finally correlate the performance gain with seasonality indices in order to show the expected gain conditional to the strength of seasonality expressed by the ratio of average summer and winter low flow seasonality ratio (SR). For the 100-year event, the expected gain is about 70 % for SR=1.0, 20 % for SR=1.5, and 10 % for SR=2.0. The performance gain is further allocated to the spatial patterns of SR in the study area. The results suggest that the mixed estimator is relevant not only for mountain forelands but to a much wider range of catchment typologies. The mixed distribution approach provides one consistent approach for summer, winter, and annual probabilities and should be used by default in seasonal climates with a cold winter season where summer and winter low flows can occur.