Correlated Versus Uncorrelated Hydrologic Samples

Spatial data are collected at various locations. Two cases are considered: (1) The observations are independent; and (2) the observations are correlated. If the data are assumed to be normally distributed with constant mean and variance, it is shown that the optimal sample sizes under the independent assumption discussed in this note provide further details correlated case (nó) are related by the expression n*=[(nó²]/(n*+2ΣΣΣS$r_{\mathrm{ij}}$), where $r_{\mathrm{ij}}$ denotes the correlation coefficient between observations at locations i and j. This note derives the preceding expression and provides further details concerning the statistical inference of correlated spatial variables. The importance of the relationship between correlated and uncorrelated sample sizes for hydrologic spatial data collection is emphasized in this work.