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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.
Two lines of research are combined in this study: first, the development of tools for the temporal disaggregation of precipitation, and second, some newer results on the exponential scaling of heavy short-term precipitation with temperature, roughly following the Clausius-Clapeyron (CC) relation. Having no extra temperature dependence, the traditional disaggregation schemes are shown to lack the crucial CC-type temperature dependence. The authors introduce a proof-of-concept adjustment of an existing disaggregation tool, the multiplicative cascade model of Olsson, and show that, in principal, it is possible to include temperature dependence in the disaggregation step, resulting in a fairly realistic temperature dependence of the CC type. They conclude by outlining the main calibration steps necessary to develop a full-fledged CC disaggregation scheme and discuss possible applications.
Our subject is a new catalogue of radar-based heavy rainfall events (CatRaRE) over Germany and how it relates to the concurrent atmospheric circulation. We classify daily ERA5 fields of convective indices according to CatRaRE, using an array of 13 statistical methods, consisting of 4 conventional (“shallow”) and 9 more recent deep machine learning (DL) algorithms; the classifiers are then applied to corresponding fields of
simulated present and future atmospheres from the Coordinated Regional Climate Downscaling Experiment (CORDEX) project. The inherent uncertainty of the DL results from the stochastic nature of their optimization is addressed by employing an ensemble approach using 20 runs for each network. The shallow random forest method performs best with an equitable threat score (ETS) around 0.52, followed by the DL networks ALL-CNN and ResNet with an ETS near 0.48. Their success can be understood as a result of conceptual simplicity and parametric parsimony, which obviously best fits the relatively simple classification task. It is found that, on summer days, CatRaRE convective atmospheres over Germany occur with a probability of about 0.5. This probability is projected to increase, regardless of method, both in ERA5-reanalyzed and CORDEX-simulated atmospheres: for the historical period we find a centennial increase of about 0.2 and for the future period one of slightly below 0.1.