Statistical stability of cumulative distributions of rainfall rate in the UK

Rainfall rate data acquired from the UK Meteorological Office are analysed to investigate the statistical stability of cumulative distributions of rainfall rate. Information on the statistical stability of rainfall rate is useful for the design of reliable radio relay systems using frequencies above 10 GHz. By using the rainfall rate data measured at 10 typical locations which have nearly the same long-term cumulative distributions of rainfall rate, distributions of yearly and worst-month cumulative time percentages at several rainfall rate threshold levels are derived. The distributions of the yearly and the worst-month time percentages are approximated by the Gamma distribution and log-normal distribution, respectively. It is found that the parameters used in these distributions depend on the rainfall rate threshold level. By using this empirical result, a concept of a prediction risk is introduced. The dependence of the cumulative distribution on this risk is discussed.<>