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

Abstract

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.

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).…”

The Diurnal Nature of Future Extreme Precipitation Intensification

“…The temperature scaling curves—often referred to as “binning scaling” (Zhang et al, )—for extreme convective available potential energy (CAPE) calculated for Figure b are computed as follows: for a given grid cell, all hours are assigned to overlapping temperature bins of 2 K width, with bin centers separated by 0.1 K. For each temperature bin, the empirical 99.5th percentile of CAPE is computed, producing a curve. To avoid adverse effects associated with inadequate sample size within the bins (Boessenkool et al, ), empirical percentiles are only computed when there are at least 200 data points within the temperature bin. The area mean is then computed by averaging the curves of all grid cells (as long as at least 50% of the grid cells contain sufficient data to compute empirical percentiles) and applying a 15‐point (1.5 K) smoothing.…”

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.…”