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.