Nonstationary Extreme Value Analysis in Hydrological Systems

Nonstationary extreme value analysis addresses the reality that the statistical properties of hydrological extremes evolve over time under the influence of climate change, land-use alterations and anthropogenic drivers. Traditional approaches assume stationarity, treating the frequency and magnitude of floods, droughts and intense precipitation as unchanging. By contrast, nonstationary frameworks allow distribution parameters to vary with covariates such as time, climate indices or catchment characteristics. These methods typically use extensions of the generalized extreme value or generalised Pareto distributions, with parameters modelled as functions of external variables via regression, splines or Bayesian hierarchical models. The result is a dynamic characterisation of return periods, quantiles and risk profiles that better reflects observed trends in hydroclimatic indicators. This approach has seen applications in flood design, infrastructure resilience, water resource planning and coastal management, revealing that ignoring temporal changes can lead to substantial underestimation of risk. Key challenges include limited record lengths, detecting genuine change points, selecting appropriate covariates and quantifying uncertainty arising from model complexity and sampling variability. Advances in change-point detection, wavelet methods and process-based covariate selection are improving the robustness of nonstationary analyses, while emerging data sources and high-resolution climate projections offer new opportunities for regional and global applications.

Research from Nature Portfolio

Recent studies have demonstrated the inadequacy of stationary design curves for precipitation extremes under a changing climate. A seminal work introduced a Bayesian framework to estimate nonstationary intensity-duration-frequency (IDF) relationships, quantifying how extreme rainfall intensities evolve with time. The approach integrates prior information on climatic trends and explicitly propagates uncertainty in parameter estimates, yielding time-varying IDF curves. This methodology revealed that design rainfalls based on stationary assumptions may underestimate extremes by up to 60 %, highlighting the need for updated guidelines in infrastructure design and flood protection standards.

Nonstationary Extreme Value Analysis in Hydrological Systems publication trend

The graph below shows the total number of articles in nonstationary extreme value analysis in hydrological systems across all publications each year (not limited to Nature Index journals).

Technical terms

Nonstationarity: Temporal variation in the statistical properties of a process, such as mean or variance, often induced by external drivers.

Generalized extreme value distribution: A family of probability distributions modelling block maxima, with parameters for location, scale and shape.

Intensity-duration-frequency curves: Graphical representations of the relationship between rainfall intensity, event duration and return period under specified conditions.

Covariate: An external variable incorporated into a statistical model to explain changes in distribution parameters over time.

Return period: The inverse of annual exceedance probability, representing the average recurrence interval of a given extreme event magnitude.

References

1. Nonstationary weather and water extremes: a review of methods for their detection, attribution, and management. Hydrology and Earth System Sciences (2021).
2. Nonstationary Precipitation Intensity-Duration-Frequency Curves for Infrastructure Design in a Changing Climate. Scientific Reports (2014).
3. Application of nonstationary extreme value analysis in the coastal environment – A systematic literature review. Weather and Climate Extremes (2023).
4. Study on a mother wavelet optimization framework based on change-point detection of hydrological time series. Hydrology and Earth System Sciences (2023).
5. Nonstationary quantity-duration-frequency (QDF) relationships of lowflow in the source area of the Yellow River basin, China. Journal of Hydrology Regional Studies (2023).