Application of ergodicity in regional rainfall frequency analysis

Accurate estimation of rainfall quantiles at ungauged locations is critical for designing hydraulic infrastructure that can withstand extreme rainfall events over a broad range of timescales. However, short rainfall series often fail to capture the full variability and distribution of rainfall, leading to sampling bias. Geographical and climatological factors further complicate the estimation of rainfall frequencies in ungauged locations. To address these challenges, the concept of ergodicity in spatio-temporal patterns of rainfall extremes has been revisited. Ergodicity, in the context of stochastic processes, ensures that long-term time averages converge to the ensemble mean. This principle enables the pooling of rainfall data from multiple rain gauges within homogeneous regions to construct "regional" intensity-duration-frequency (IDF) curves. This mathematical framework has been investigated using normalized data from 100 rain gauges in Slovakia, with rainfall aggregated over time intervals ranging from 5 to 240 minutes. The analysis focused on low-probability rainfall events (p = 10^-2 – 10^-3) corresponding to recurrence intervals far exceeding the length of available records (approx. 15 years). Homogeneous regions were identified using fuzzy C-means clustering, revealing two homogenous clusters of rain gauges. Each cluster was assessed for ergodic behavior. To estimate the rainfall quantile for each cluster, the GEV distribution was applied to annual maximum series with parameters inferred using a Bayesian approach. Unique IDF curves were generated for each cluster, satisfying the criteria of ergodicity. These findings demonstrate the potential of the ergodicity-based approach to improve regional rainfall frequency estimates.

 

Acknowledgment: This work was supported by the Slovak Research and Development Agency under Contract No. APVV-23-0332.