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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.

Abstract. High precipitation quantiles tend to rise with air temperature, following the so-called Clausius–Clapeyron scaling. This CC-scaling relation breaks down, or even reverts, for very high temperatures. In our study, we verify this reversal using a 60-year period of summer data in Germany. One of the suggested meteorological explanations is limited moisture supply, but our findings indicate that this behavior could also originate from simple undersampling. The number of observations in high temperature ranges is small, so extreme rainfall intensities following CC-scaling may not yet be recorded but logically possible. Because empirical quantile estimators using plotting positions drop with decreasing sample size, they cannot correct for this effect. By fitting distributions to the precipitation records and using their parametric quantile, we obtain estimates of rainfall intensities that continue to rise with temperature. This procedure requires far fewer values (ca. 50 for the 99.9 % quantile) to converge than classical order based empirical quantiles (ca. 700). From the evaluation of several distribution functions, the Wakeby distribution appears to capture the precipitation behavior better than the General Pareto Distribution (GPD). Despite being parametric, GPD estimators still show some underestimation in small samples.

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.