# Statistical Analysis of Precipitation Data Part II Frequency Analysis of Monthly Precipitation Data

Type: Report
Series: RMK 17
Author: Eriksson, B.
Published:

## Summary

The frequency distributions of monthly precipitation amounts have been investigated. Data from the period 1931-78 for 262 Swedish and 26 Norwegian stations have been used. The statistical analysis consists of determining the capacity of well-known frequency distribution functions to match the empirical distributions. The following functions were tested: gamma distributions with 2 or 3 parameters, log-normaldistributions with 2 or 3 parameters and the Weibull distribution with 3 parameters. The methods used to determine theparameters of the above-mentioned functions were either the momentum or the maximum- likelihood method. About 3500 distributions were studied. The results of the different tests gave a statistically significant answer to the question: Which of the investigated functions is superior to the other functions best in describing the observed distributions? The gamma distribution was found to have the highest score. In 86% of all case s there was no significant difference, at the 90% confidence level, between observed and computed frequencies. The log-normal distribution hasa much lower capacity to describe the empirical distributions studied.

From the gamma distribution with the obtained values of its shape and scale parameters certain percentile values were computed, namely: P01, P05, P10, P25, P50, P75, P95, and P99. The results are presented in the form of charts. The charts showing monthly isohyets for different percentile values are briefly cornrnented.

Maps of the variability of monthly precipitation amounts are also presented. The variability is expressed by means to the coefficient of variation. This variability parameter shows small differences between different regions in Sweden.

The measuring errors of precipitation observations are discussed. Corrections of measured amounts ought to be applied for the three most important errors viz, the aerodynamic, evaporation and adhesion losses. The most important losses and at the same time those which are most difficult to estimate are due to the wind effects around the orifice of the precipitation gauge. The corrections ought to be determined individually for each station and month with regard to the wind regime and the exposure of the gauge for the station concerned. With these factors in mind and knowing the proportions between snow and rain precipitation corrections have been proposed for the monthly values. On an average for all Swedish stations used in this investigation the mean annual amounts of precipitation for the period 1931-78 should be increased by 18%. In the water balance equation the values thus increased seem to agree reasonably well with generally accepted values for evaporation and run-off .