Journal cover Journal topic
Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union
doi:10.5194/nhess-2016-183
© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
27 Jun 2016
Review status
This discussion paper is under review for the journal Natural Hazards and Earth System Sciences (NHESS).
Effects of sample size on estimation of rainfall extremes at high temperatures
Berry Boessenkool, Gerd Bürger, and Maik Heistermann Potsdam University, Institute for Earth and Environmental Sciences, Karl-Liebknecht-str. 24, Haus 1, 14476 Potsdam Golm, Germany
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.


Citation: Boessenkool, B., Bürger, G., and Heistermann, M.: Effects of sample size on estimation of rainfall extremes at high temperatures, Nat. Hazards Earth Syst. Sci. Discuss., doi:10.5194/nhess-2016-183, in review, 2016.
Berry Boessenkool et al.
Berry Boessenkool et al.
Berry Boessenkool et al.

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Short summary
Rainfall is more intense at high temperatures than in cooler weather, as you can notice in summer thunder storms. The relationship between temperature and rainfall intensity seems to inverse 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.
Rainfall is more intense at high temperatures than in cooler weather, as you can notice in...
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