ESTIMATES OF ROOT-MEAN-SQUARE RANDOM ERROR FOR FINITE SAMPLES OF ESTIMATED PRECIPITATION

`The random errors contained in a finite set E of precipitation estima tes result from both finite sampling and measurement-algorithm effects . The expected root-mean-square random error associated with the estim ated average precipitation in E is shown to be sigma(r) = (r) over bar [(H - p)/pN(I)](1/2), where (r) over bar is the space-time-average pre cipitation estimate over E, H is a function of the shape of the probab ility distribution of precipitation (the nondimensional second moment) , p is the frequency of nonzero precipitation in E, and N-1 is the num ber of independent samples in E. All of these quantities are variables of the space-time-average dataset. In practice H is nearly constant a nd close to the value 1.5 over most of the globe. An approximate form of sigma(r), is derived that accommodates the limitations of typical m onthly datasets, then it is applied to the microwave, infrared, and ga uge precipitation monthly datasets from the Global Precipitation Clima tology Project. As an aid to visualizing differences in sigma for vari ous datasets, a ''quality index'' is introduced. Calibration in a few locations with dense gauge networks reveals that the approximate form is a reasonable first step in estimating sigma(r).