Estimation of sampling errors and scale parameters using two- and three-dimensional rainfall data analyses
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This paper presents the analysis of rainfall data based on radar echoes collected in the vicinity of Darwin, Australia, during special observation periods in 1988. The study was conducted to estimate the scale parameters (such as timescale and length scale) present in the rainfall data, which are important in parameterizing many stochastic rainfall models. Another equally important issue addressed here is that of sampling errors in the rainfall observations from space. To address these issues, precipitation analyses were conducted in two and three dimensions. To perform two-dimensional analyses, precipitation fields were averaged along one dimension (i.e., x, y, or t) at a time. Three-dimensional analyses were performed on the complete time series of temporal-hourly averaged spatially distributed observations. Important results obtained from the two-dimensional analyses include isotropy of precipitation fields in space, variations in the rainfall data primarily in time, and length scales of 50 km (for Darwin I) and 52 km (for Darwin II) in both (i.e., north-south and west-east) directions. Length scales were estimated using the results from two-dimensional analyses of the data. Time-domain correlograms obtained for the time series of area-averaged precipitation were used to estimate the timescales (6 hours for Darwin I and 8 hours for Darwin II). These results could be used in simulation studies using various stochastic rainfall models. The estimates of space-time spectra obtained in three-dimensional analyses were used to evaluate the sampling errors. The sampling errors thus estimated using these data sets were quite significant (about 25% to 30% for a 12-hour sampling interval). Sampling errors were as high as 65% for Darwin I and 45% for Darwin II for a 24-hour sampling time interval, which is a possibility if the Defense Meteorology Satellite Program (DMSP) satellite is used. These results are useful in satellite mission planning activities.