One-minute rainfall data reveal temperature dependend seasonal and diurnal variability of the power-law distribution for Germany

High resolution rainfall data are essential to quantify small scale and fast hydrological processes. The objective of the paper is to determine temporal variability and spatial patterns of precipitation statistic of one-minute resolution rainfall across Germany. The German Weather Service (DWD) started in 1993 to deploy rain gauges that achieve 1 minute temporal and 0.01 mm volumetric resolution by combining tipping buckets with weigthing (rain[e]H3 by LAMBRECHT meteo GmbH and OTT Pluvio by OTT Hydromet). 345 of those stations all over Germany have data with more than 10 years. For each station empirical cumulative distribution functions (eCDF) of precipitation intensity and dry periods were derived. Data were then aggregated to lower resolutions ranging from 2 min to 4 months. For all aggregation levels we fitted power law, log-normal and Weibull distribution functions and compared the goodness of fit. To determine spatial correlations between stations we extracted intensity and dry period duration at a given frequency from the empirical distribution function and applied a correlation analysis with station longitude, latitude, elevation and total rainfall. Annual and diurnal variations were analysed by fitting a power law to a moving window of data. A 60d segment of the yearly cycle (combining data of all years) and a 4h segment of the daily cycle (combining data of all days) were used. Similar the dependence of the power-law coefficient on temperature was analysed with a moving window of 2.5K width, shifted between -10 to 30°C.

We show that rainfall intensity measured at 1 minute resolution shows a distinct power-law distribution for all stations. The dry period durations instead are not purely power-law distributed. When aggregated, the distribution of the data transitions to lognormal distribution at 15 min aggregation level and to a Weibull distribution from 6 hours onwards. This has significant implication for estimating flood risk and deriving design storm properties as each temporal resolution requires a different statistical distribution to be fitted. We conclude that the mixing of the intensity and dry-period statistic creates this effect. While total rainfall in Germany clearly varies, with high totals in the north-west and lower values in the east, the intensity distribution does not reflect that. We find no significant correlation with longitude, latitude, elevation nor total station rainfall. But the dry-period statistic correlates well. This leads to the conclusion that rainfall intensity statistic is very similar in all of Germany and the difference in recurrence intervals and total rainfall is mostly defined by the dry periods between rain events. The power-law exponent varies annually with a sine curve from -1 to -2 in phase with the annual temperature cycle. It also shows a clear diurnal cycle. It can be expected that those cycles are driven by a strong dependence on temperature. The power-law exponent is close to -3 at 0°C and -1 at 25°C, creating higher intensities at higher temperatures.