Generalized extreme value shape parameter and its nature for extreme precipitation using long time series and the Bayesian approach

Abstract

Assessing the probability of extreme precipitation events is consequential in civil planning. This requires an understanding of how return values change with return periods, which is essentially described by the generalized extreme value (GEV) shape parameter. Some works in the field suggest a constant shape parameter, while our analysis indicates a non-universal value. We reanalysed an older precipitation dataset (169 stations) extended by Norwegian data (71 stations). We showed that while each set seems to have a constant shape parameter, it differs between the two datasets, indicating regional differences. For a more comprehensive analysis of spatial effects, we examined a global dataset (1495 stations). We provided shape parameter maps for two models and found clear evidence that the shape parameter depends on elevation, while the effect of latitude remains uncertain. Our results confirm an explanation in terms of dominating precipitation systems based on a proxy derived from the Köppen-Geiger climate classification. ARTICLE HISTORY

Projected Changes in the Probability Distributions, Seasonality, and Spatiotemporal Scaling of Daily and Subdaily Extreme Precipitation Simulated by a 50‐Member Ensemble Over Northeastern North America

“…The 3SP systematically displayed higher shape values than 7SP, with positive median ξ t values distributed around ξ t ≈ 0.17. This result is consistent with typical GEV shape parameter values estimated from long records (e.g., more than 100 years) and reported in the literature (e.g., Ragulina & Reitan, 2017, and references therein). For instance Koutsoyiannis (2004a) and Koutsoyiannis (2004b) reported positive ξ values lower than ≈0.23 for various locations around the world.…”

“…Third, SD shape parameter values were larger than corresponding LD values for each 3SP for more than 61% of the grid boxes, as also shown by the SD and LD ξ Ã t;r distributions (Figure 11b; note that only significant ξ Ã t;r >0 are considered in this figure). Accordingly, SD extremes displayed heavier tailed distributions than longer-duration AM, which is consistent with the hypothesis that links the shape parameter values to the characteristic precipitation systems generating AM at different temporal scales (Ragulina & Reitan, 2017).…”

Intensity-duration-frequency curves at the global scale

“…The estimation of κ is notoriously difficult due to its sensitivity to record length (Overeem et al 2008, Papalexiou and Koutsoyiannis 2013, Ragulina and Reitan 2017. Indeed, it has been demonstrated that for sample sizes less than 50, using a two parameter Gumbel distribution results in a smaller error than the three parameter GEV (Lu and Stedinger 1992).…”

Infilling Missing Data in Hydrology: Solutions Using Satellite Radar Altimetry and Multiple Imputation for Data-Sparse Regions

“…where, τ, α, and k represents location, scale and shape parameters of the distribution function. GEV like other probability distributions is affected by short hydrological time series, which results in uncertain flood estimates [85], therefore the availability of more historical data enables improved flood estimation. The 5T rule of thumb suggested by Reed [78] for the length of data required for flood frequency estimation is adopted for this study, i.e., the historical data should be at least five times the target return periods (i.e., 20 years of historical data is required for a 1-in-100-year estimation, for reasonable levels of uncertainty).…”