Statistiscal analysis of precipitation. Part I. Area precipitation data.

Type: Report
Series: RMK 16
Author: Eriksson, B.


Precipitation data on mean values for large areas have been analysed from two points of view. In the first section of this report the data have been looked upon as time series. In the second section they have been regarded as samples from a population.

The reliability of the data is discussed. It is stated that the values are underestimated. The correction factor may be as high as 30%. Half of this correction is related to the representativity of the precipitation network and is mainly due to the fact that the proportion of stations at high levels is too low. The other half is related to measurement errors, mainly losses due to wind, turbulence and evaporation.

The time series analysis consists of three parts. In the first one a ' so-called run-test is used to investigate the stationarity of the series. There seemst o be no reason to reject the hypothesis that the series are stationary. After that the frequencies of long runs are X2 -tested against a random model and against models with very low autocorrelation lag- one coefficients. The best fit is found for the model without autocorrelation. In the third part some of the series are filtered with low-pass filters. The results are in accordance with the run-test viz that there are no detectable trends neither linear nor cyclic.

In the second section seven different distribution functions are tested. The following ones are used: Normal, log-normal (both two and three parameters), gamma (two and three parameters), Weibull and FisherTippett type I. The parameters of these functions are estimated with the maximum-likelihood method or the momentum method. The x2 -test gave no definit answer to the question which one is the mast suitable function. It was possible to reject the lagnormal distribution with three parameters, and the threeparameter r-distribution had no advantage compared with the two-parameter version.

By studying the outermost values of the distributions it was evident that neither the normal nor the lognormal distribution were able to fit the observed data satisfactory. It was not possible to say which of the two distributions, r or Weibull, is the best one. For very low and even very high values the Weibull distribution seems to be able to describe the observedvalues somewhat better than the gamma distribution can do. Arguments can be delivered both in the favour of rand of Weibull.

The percentiles, according to the gamma distribution, P01, P05, P10, P25, P50, P75, P90, P95 and P99 are presented . Even P01, P05, P95 and P99 calculated from Weibull distribution are given.

Those monthly values laying outside P01 and P99 as well as those outside P05 and P95 are listed both according to gamma and Weibull distributions.

A proposal to a climatological terminologi is presented. The range of a climatological variable is divided into 7 classes. These classes contains 1, 4, 20, 50, 20, 4 respectively 1% of the events. The values belonging to the outmost classes are called extreme values, those in the middle class should be called normal values.

At the end of the report a list is given of the 10 events, which, according to gamma distributions, have the lowest climatological probability. Some cases have extremely low probabilities.