the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Non-stationary low-flow frequency analysis with mixed Weibull components and Copula-based dependence framework
Abstract. Extreme low flows are a pressing challenge for water management, reducing water availability and degrading water quality. Reliable design estimates are therefore essential. Traditional low-flow frequency analysis relies on the assumption of independent and identically distributed (i.i.d.) data, which is increasingly violated under climate change and by varying low-flow generating processes. In a seasonal snow-influenced climate, annual low-flow extremes may occur in both summer and winter, potentially exhibiting seasonal dependence that challenges conventional modelling approaches. This study extends traditional low-flow frequency analysis to non-stationary conditions by jointly accounting for temporal trends, seasonal heterogeneity and inter-event dependence. Building on previously developed mixed distribution and mixed copula frameworks, we generalise these frameworks to non-stationary conditions using three-parameter Weibull distributions. Seasonal low-flow distributions and their joint mixture vary over time, with linear non-stationarity in the location parameter and in inter-event dependence. Results are presented for more than 700 catchments from the European Reference Observatory of Basins for INternational hydrological climate change detection (ROBIN) dataset. Model evaluation shows that neglecting non-stationarity when present can lead to biased assessments of low-flow severity, particularly for higher return periods. In contrast, non-stationary models provide a more realistic representation of evolving low-flow regimes by revealing temporal changes that remain hidden from traditional estimators. By preserving the conceptual consistency of the previous stationary framework, the proposed non-stationary framework improves the statistical characterisation of extreme low flows and provides an enhanced basis for low-flow frequency analysis by offering new insights into past and current low-flow processes under climate change.
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Status: final response (author comments only)
- CC1: 'Comment on egusphere-2026-1820', Chuck Kroll, 22 May 2026
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RC1: 'Comment on egusphere-2026-1820', Chuck Kroll, 28 May 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1820/egusphere-2026-1820-RC1-supplement.pdf
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AC1: 'Reply on RC1', Farhana Sweeta Fitriana, 09 Jun 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1820/egusphere-2026-1820-AC1-supplement.pdf
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AC1: 'Reply on RC1', Farhana Sweeta Fitriana, 09 Jun 2026
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RC2: 'Comment on egusphere-2026-1820', Anonymous Referee #2, 16 Sep 2026
The manuscript presents a assessment of low flow freq analysis using non-stationary extension of Weibull and copula based dependence framework. The framework is used for evaluating around 700 European catchments from the ROBIN dataset and demonstrates the implications of non-stationarity on low-flow frequency estimates, particularly for rare events. The study addresses an important topic given increasing concerns regarding climate-change induced nonstationary impacts on hydrological droughts and low-flow conditions. The manuscript is generally well structured and methodologically rigorous. However, some aspects require a bit of attention and explanation before publication. Here are some points to consider by the authors:
- The introduction provides a good overview of non-stationary frequency analysis literature, however authors should more clearly explain why existing approaches (e.g. GAMLSS-based low-flow frequency analysis) are insufficient and specifically why the proposed extension of LFAmix and LFAmixC is necessary in the set up which they have used.
- The manuscript adopts WEI3 throughout, but should the justification or advantages/disadvantages of using alternative distributions be included. Since low-flow frequency analysis often employs Lognormal, Generalized Logistic, Pearson Type III or GEV formulations, authors should discuss why WEI3 is uniquely suitable and whether results are sensitive to this choice.
- Non-stationarity is only introduced through the location parameter. While the authors justify this using parsimony arguments, climate change can influence both variability and shape of low-flow distributions. Understandable that this will make the model very more sensitive and risky….some discussion or such probabilistic sensitivity analysis is recommended.
- The framework assumes a linear temporal evolution in location and dependence parameters. However, low-flow behaviour often exhibits regime shifts, accelerations, thresholds, or oscillatory behaviour linked to climatic variability. If not nonlinear relationships related analysis is done, at least this should be discussed in detail.
- The use of PAM clustering and seasonality histograms is interesting, but the physical interpretation of the resulting clusters needs stronger discussion. For example, how sensitive are the results to the chosen clustering approach, silhouette threshold (0.2), or seasonal definitions (April–October and November–March)?
- WEI3 fitting was successful in only 76.1% of catchments. This implies nearly one-quarter of stations could not be fitted successfully. May be the characteristics of these excluded catchments should be analysed and discussed, as this may introduce regional bias into the results.
- The paper focuses heavily on one Austrian catchment. Authors should consider presenting at least one additional example, preferably from a different characteristics dominated regime, to demonstrate framework performance across contrasting hydro-climatic conditions.
- Statements such as a 100-year event becoming a 43-year event are powerful but may be misinterpreted by readers. It should be clarified that these changes are statistical diagnostics based on the fitted non-stationary model and should not be interpreted directly as future projections.
Citation: https://doi.org/10.5194/egusphere-2026-1820-RC2 -
AC2: 'Reply on RC2', Farhana Sweeta Fitriana, 27 Sep 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1820/egusphere-2026-1820-AC2-supplement.pdf
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Publisher’s note: the content of this comment was removed on 29 May 2026 since the comment was posted by mistake.