High-resolution studies of rainfall on Norfolk Island. Part IV: observations of fractional time raining

Using the same data set as in Part I of this series (obtained from a dense rain gauge network operating with 15 s sampling over the period September 1991 to December 1993), the rainfall climatology of Norfolk Island is examined in terms of the relationship between rainfall accumulations R and fractional time raining (FTR) F. In addition, linear, cubic and power-law fits to the relationship are used as estimators and compared with actual monthly mean rainfall totals at integrations of 1 h, 1 day and 1 month. Cumulative errors in estimated island mean rainfall are compared as a function of both the monthly march and as a function of increasing F. It is shown that F may be used successfully to provide estimates of rainfall accumulation even at the shortest integration time (when the R–F relationship is non-linear) by way of the cubic fit. Temporal variations in the fitting parameters are found to be similar at each gauge site and spatial differences in fitting parameters between sites are systematic. On a year-by-year basis, the mean rainfall per FTR was found to decrease at all sites. A high correlation between the two parameters of the power-law fitting method enables R and F to be related using a single-parameter, though estimates are generally inferior to the linear or cubic fit. Using integration times of 12, 24, 48 and 96 h, the data set was sampled at intervals between 15 s (the present gauge array resolution) and 1800 s (a typical remote sensing resolution) providing R–F correlation trends and mean rainfall per unit F. Outputs from the sampling could not be normalized in terms of an integration-to-sampling time ratio.