WMOD00546 - Laserfiche WebLink

Home Browse Search

each study was calculated. These results indicate that, although the assump- tion that the "true" rainfall is represented by the highest gage dl~nsity becomes weaker as the precipitation gradient becomes increasingly steeper and the number of gages per storm decreases, the maximum gage densities in all of these studies was sufficiently high to render this assumption valid for practical purposes. The worst case resulted from the smallest area investi- gated by Light (GPR = 27.8 and G = 1.71) for which the coefficient of variation was less than 6 percent. The second issue involves the interpretation of the average absolute errors derived from the empirical relationships. In section 4 it was pointed out that the accuracy of the sample mean precipitation does not, in general, degrade with decreasing gage density or increasing precipitation gl~adient but the sample standard deviation increases under these conditions. This, of course, is the case because we have been able to simulate all possible sampl i ngs of the storm by the ga'ge networks. Thi s was not the caSE~ in the data sets used to construct the ,empirical relationships. These relationships were based on a fi nite, i nsuffi ci ent number of sampl es whi ch randomly fell on the spectrum of possibilities. Huff (1970) recognized this limitation when he stated, "Except for mean preC'ipitation, duration, and average intensity, it is difficult, if not impossible, to express these sampling error factors in quantitative terms. Thus, unless huge samples are available to permit grouping of the data according to all of these various factors, the sampling error with a given gage density "in a particular storm cannot be defined with a high degree of accuracy." He supported this point by showing the great amount of variability about the average sampling error from his empirical relationship. It is likely that the values of average sampling error are, in 16