Estimates of Root-Mean-Square Random Error for Finite Samples of Estimated Precipitation

The random errors contained in a finite set E of precipitation estimates result from both finite sampling and measurement–algorithm effects. The expected root-mean-square random error associated with the estimated average precipitation in E is shown to be σr = r̄(H − p)/pNI1/2, where r̄ is the space–time-average precipitation estimate over E, H is a function of the shape of the probability distribution of precipitation (the nondimensional second moment), p is the frequency of nonzero precipitation in E, and NI is the number of independent samples in E. All of these quantities are variables of the space–time-average dataset. In practice H is nearly constant and close to the value 1.5 over most of the globe. An approximate form of σr is derived that accommodates the limitations of typical monthly datasets, then it is applied to the microwave, infrared, and gauge precipitation monthly datasets from the Global Precipitation Climatology Project. As an aid to visualizing differences in σr for various 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 σr.