Non-stationary probabilities of dry-spell hazard in Spain

This work presents an extensive evaluation of long-term variability in dry-spell characteristics across Spain over the period 1961–2024. The analysis combines classical non-parametric approaches with an innovative non-stationary probabilistic methodology applied to exceedance series of dry-spell durations. Daily precipitation records from a dense, quality-controlled observational network were used to identify dry spells according to four precipitation thresholds (0.1, 1, 5, and 10 mm), allowing a detailed characterization of duration distributions. Generalized Pareto Distributions were estimated assuming both stationary and non-stationary formulations. Optimal exceedance thresholds were selected through a systematic percentile-based procedure, and differences between stationary and non-stationary return levels were evaluated using a bootstrap significance test. Additional analyses assessed trends in annual dry-spell frequency, average duration, and maximum dry-spell length.

The results consistently indicate that dry-spell dynamics in Spain are largely stationary. Significant non-stationary behaviour in the GPD location parameter is detected at only a very limited number of stations, while non-stationary representations of the scale, shape, or all parameters combined do not yield meaningful improvements and substantially increase uncertainty. These conclusions are reinforced by conventional trend analyses, which show that the majority of stations (more than 70–85%, depending on the precipitation threshold) display no statistically significant trends in frequency, mean duration, or maximum duration of dry spells. Spatial signals are weak and fragmented, and estimated return levels for rare events (e.g., 50-year return periods) remain remarkably stable throughout 1961–2024. Overall, the findings provide strong evidence for long-term stationarity in the hazard probabilities of extreme dry spells across Spain.