Area-intensity probability distributions of rainfall based on a large sample of radar data

The history of weather radar is, among other applications, a manifestation of quantitative precipitation estimation (QPE). The main objective in such activities is to develop real time meteorological and hydrological applications as well as to perform climatological studies of precipitation structures. Although in most cases an individual radar bin measurement is not as accurate as a gauge measurement at ground the time-space resolution of radar measurements is typically better than that of a conventional gauge network by a factor of 10⁶. An implication is that radar measurements provide a way to derive very large and significant samples of local precipitation climates. Probability distributions of rainfall are the basis of hydraulic and hydrological planning of construction structures needed in heavy rain and flood mitigation. In this paper we present probability distributions of rainfall in areas of 1 km², 9 km², 100 km² and 1024 km² where the length of accumulation period is 2 min, 15 min, 30 min, 60 min, 3 h, 6 h, 12 h and 24 h. The data set covers 6 summers from 7 Finnish C-band Doppler weather radars.

As "raw" radar measurements can't be used as such for quantitatively reliable precipitation statistics specific attention is paid to the quality control (QC) of radar data. Due to residual ground clutter still present after Doppler filtering, other clutter targets, partial beam overshooting and occurrance of the bright band and snow in the radar beam we have limited the basic data to the period May-September and to the range interval of 30 - 200 km. Secondly, non-meteorological bins have been removed applying fuzzy logics based target identification and thresholding of dBZ. Especially ship clutter introduces frequently large spurious dBZ-values if not removed. Hail algorithm has been applied to remove all areas indicating even a small probability of hail. Removal of hail has a significant influence on the cumulative density function (CDF) of rainfall at the high intensity end of the distribution. After all quality steps the remaining set of radar measurements consists of approximately 5•10⁹ squares of the area of 1 km² in which the average reflectivity exceeds the threshold of 10 dBZ.

Although both radar and ground level sensors in situ (e.g. optical scatterometers) introduce large random errors in individual precipitation measurements we assume that the shape of CDF of rainfall from both sensors (in quality corrected data) is not biased. Hence we have removed the statistical bias from radar measurements by applying the probability matching method (PMM). In this way we have also avoided the selection of the "optimal R(Z)" which, anyway, remains unknown. The results show an extremely good fit of the CDFs of rainfall to lognormal distribution. The results also indicate figures of the probability of very rare rainfall occasions (e.g. repeat time > 1000 years), which are practically impossible to detect with much smaller samples of ground based rainfall sensor data. Finally we compare the radar based rainfall statistics with classical, gauge based standard figures. A major conclusion is that without a proper QC radar based precipitation climatologies can easily contain significant errors.