Effects of sample size on estimation of rainfall extremes at high temperatures

Abstract

Abstract. High precipitation quantiles tend to rise with temperature, following the so-called Clausius-Clapeyron (CC) scaling. It is often reported that the CC-scaling relation breaks down and even reverts for very high temperatures. In our study, we investigate this reversal using observational climate data from 142 stations across Germany. One of the suggested meteorological explanations for the breakdown is limited moisture supply. Here we argue that, instead, it could simply originate from undersampling. As rainfall frequency generally decreases with higher temperatures, rainfall intensities as dictated by CC scaling are less likely to be recorded than for moderate temperatures. Empirical quantiles are conventionally estimated from order statistics via various forms of plotting position formulas. They have in common that their largest representable return period is given by the sample size. In small samples, high quantiles are underestimated accordingly. The small-sample effect is weaker, or disappears completely, when using parametric quantile estimates from a generalized Pareto distribution (GPD) fitted with L moments. For those, we obtain quantiles of rainfall intensities that continue to rise with temperature.

Observed Climatological Relationships of Extreme Daily Precipitation Events With Precipitable Water and Vertical Velocity in the Contiguous United States

“…Additionally, for very high EP amounts, the amount of PW is limiting, not −ω. Sample size of the highest PW bin (321) is below the minimum (700) recommended by Boessenkool et al (2017), suggesting that the highest bin pair comparison is less robust, although it is consistent with the adjacent bin pair.…”

“…Climate models indicate that a disproportionate increase in extreme precipitation will occur compared to the change in the annual mean total precipitation (Sillmann et al, 2013). Since Trenberth et al (2003) first proposed that in a warmer world additional latent heat release from the condensation of q could provide a positive feedback leading to super CC scaling, several studies have revealed important complexities related to scaling the changes of the mean global and large-area temperature increases to increases in q and subsequent extreme precipitation amounts (Ban et al, 2015;Bao, Sherwood, Colin et al, 2017;Boessenkool et al, 2017;Chan et al, 2016;Huang et al, 2019;Schroeer & Kirchengast, 2018;Wang et al, 2017). Additionally, changes in weather dynamics associated with new climatological weather regimes further complicate projections of extreme precipitation changes as the world warms through altered fields of vertical velocity (VV) and moisture convergence (Nie et al, 2018;O'Gorman & Schneider, 2009;Prein & Pendergrass, 2019;Sugiyama & Shiogama, 2010).…”

Subhourly rainfall in a convection-permitting model

“…For fair comparison, CCLM-02 temperatures are first aggregated to the Spain02 grid. 0.95, 0.99 and 0.999 quantiles are then computed for each temperature bin, as long as at least 20, 100, or 1000 data points are present, respectively, thus avoiding erroneous artefacts associated with inadequate sample size[55]. The resulting curves are smoothed over a width of 1.5K.…”

Mapping seasonal and annual extreme precipitation over the Peruvian Andes

“…The primary objective of this study is to develop, for the first time, probability maps of extreme precipitation for the Andes region of Peru using daily observed precipitation data and spatial interpolation techniques. In comparison to earlier studies worldwide, which focused mostly on precipitation intensity estimation (e.g., Madsen et al, ; Cooley et al, ; Boessenkool et al, ), our study extends further to different precipitation hazard metrics, including: maximum precipitation intensity, magnitude, duration and dry spell length, providing a comprehensive assessment of precipitation hazard in the study domain.…”