Articles | Volume 17, issue 9
Research article
25 Sep 2017
Research article |  | 25 Sep 2017

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

Berry Boessenkool, Gerd Bürger, and Maik Heistermann

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.

Short summary
Rainfall is more intense at high temperatures than in cooler weather, as can be seen in summer thunder storms. The relationship between temperature and rainfall intensity seems to invert at very high temperatures, however. There are some possible meteorological explanations, but we propose that part of the reason might be the low number of observations, due to which the actually possible values are underestimated. We propose a better way to estimate high quantiles from small datasets.
Final-revised paper