A nonstationary copula-based framework for analyzing hydrological drought concurrence and propagation in river networks

Hydrological drought is among the most impactful hydro-climatic extremes, with effects that often propagate along river networks and affect extensive downstream regions. Although drought processes differ fundamentally from floods in terms of their underlying mechanisms, both types of extremes exhibit pronounced nonstationarity under the combined influence of climate change and human activities, and both require advanced statistical tools to characterize their evolving risks. In particular, the dependence structures among hydrological extremes at different spatial locations remain insufficiently understood, especially from the perspective of river-network connectivity and propagation processes.

In this study, we focus on the nonstationary dependence of hydrological droughts along upstream–downstream river systems and the associated concurrence risk. Using a series of hydrological gauging stations distributed along tributaries and the main stem of the Yangtze River basin, we develop a drought concurrence analysis framework based on extreme value theory and nonstationary copulas to characterize the spatio-temporal evolution of multi-site drought dependence. The framework first identifies and matches drought events at the event scale across multiple stations, ensuring that copula modelling is built upon genuinely concurrent extreme drought processes. This event-based treatment avoids the potential mixing of asynchronous drought events that may arise when copulas are directly constructed from time series at fixed time steps. Subsequently, extreme drought characteristics, such as drought duration, are modelled using extreme value theory for the marginal distributions, while time-varying parameters are introduced in a nonstationary copula to describe the evolution of inter-site drought dependence.

Compared with existing studies, the proposed framework addresses two key limitations in current copula-based drought concurrence analyses: the insufficient representation of true event concurrence and the lack of explicit modelling of nonstationary dependence structures. This integrated approach enables a direct comparison of drought dependence between adjacent (local-scale) and non-adjacent (long-range) upstream–downstream station pairs, providing a unified, probabilistic, and transferable statistical tool for quantifying multi-site extreme drought concurrence risk and its temporal evolution.

The results reveal pronounced nonstationarity in upstream–downstream drought dependence, with clear strengthening or weakening trends over recent decades. Notably, dependence structures inferred from non-adjacent station pairs differ substantially from those estimated using only adjacent stations. This finding highlights the importance of accounting for multi-station propagation effects in drought analysis, rather than relying solely on local relationships. The evolution of dependence structures further leads to significant changes in concurrent drought risk, with particularly strong implications for downstream regions, where streamflow dynamics integrate hydrological signals from multiple upstream sub-basins.

By explicitly linking drought nonstationarity, spatial dependence, and concurrence risk, this study contributes to a more comprehensive understanding of hydrological extremes at the river-network scale. The proposed framework is flexible and can be extended to other drought definitions, different river basins, and even to the joint analysis of droughts and floods. The findings provide valuable scientific insights for drought risk assessment and adaptive water resources management under a changing climate.