IMPROVEMENTS TO THE MODELING OF BRITISH RAINFALL USING A MODIFIED RANDOM PARAMETER BARTLETT-LEWIS RECTANGULAR PULSE MODEL

The Random Parameter Bartlett-Lewis Rectangular Pulse Model (RPBLRPM) was shown in a previous paper to provide generally good results when a pplied to a 38.5 year record of hourly rainfall from the Elmdon rainga uge, Birmingham, UK: second-order properties of the depth and the inte rvent time distributions and the proportion of dry periods for differe nt time-scales were on the whole well reproduced by the optimized para meters. However, two main problems arose, namely an overestimation of the autocorrelations for daily data in particular, and relatively poor performance in reproducing the extreme values of the depth distributi on. The first of these problems is here addressed by superposition of a jitter process on the rectangular pulse, thus providing a more reali stic representation of the continuous time process. Applying the jitte r to each rainfall cell appears more effective than applying it to the instantaneous rainfall depth and enables a more satisfactory reproduc tion of the autocorrelations. The use of a gamma variable to replace t he exponential distribution of the cell intensity provides a good repr oduction of the extreme rainfall depths at different time-scales. More over, the values of the parameters providing an optimal reproduction o f the extreme values of the depth distribution are in most cases close to those obtained by optimizing on the interevent time features, whic h provides a method for estimation and ensures that the two objectives do not conflict.