Hershfield Factors For Extreme Precipitation: Variability and A Proposal For A Unified Definition

Point precipitation measured at rain gauges is widely used to estimate the quantiles of extreme rainfall, using frequency analyses, obtaining Depth (or intensity) - Duration - Frequency (DDF) values. Due to the mostly convective nature of extreme precipitation over short durations, many such events are limited to a small geographical area. This, in combination with their rarity, results in these events having small probabilities of being captured or detected by rain gauge stations, which are typically few and far between, at least in the United States. We propose that this must result in crucial effects of the density of the rain gauge network on our estimates of extreme precipitation. Moreover, the rather low 15-min time resolution at most US stations introduces a negative bias for the short durations, as the clock-time (fixed-time window) data are not able to capture the true sliding-window values when extracting the maxima.

Germany has 182 main meteorological stations and 1925 voluntary weather stations for precipitation, with long time series of observations; of these, about 900 rainfall stations provide at least 10 concurrent years of data at 1-minute resolution. The spatial density of rain gauges is thus one order of magnitude higher than in the US, where the typical time resolution of rainfall data is of only 15 minutes. In this study, we use this German data at a much higher spatial (and temporal) resolution to better understand how the density of a rain gauge network affects the estimation of extreme precipitation.

These possible effects are explored in two different ways. In a simpler framework, we will generate DDF values at every single station, independently, for durations D = 15 min, 30 min, 60 min, 90 min, 2 hr, 3 hr, 4 hr, and 6 hr, and for relatively frequent average return intervals ( ≤ 5 years), using partial duration analyses. We will use the same, short period for all stations, thus minimizing the effects of non-stationarity. The analyses will be conducted for maxima extracted both using clock data, as well as true maxima from sliding time windows. We will then subsample stations from the complete German network of rain gauges, generating possible realizations of lower-density networks. Both for the complete and lower-density networks, we will create spatial maps for the DDF values, using spatial interpolation. In a second, more complex approach, we will simulate the regionalization procedure followed in NOAA’s Atlas 14, so that the parameters of the distribution are smoothed spatially before performing frequency analyses and the subsequent spatial interpolations. Comparisons between the different outputs will allow us to explain and attribute the estimation biases due to station density, as well as those introduced by the typical regionalization techniques.