Dependence of Satellite Sampling Error on Monthly Averaged Rain Rates:Comparison of Simple Models and Recent Studies

Abstract

Considerable progress has been made in recent years with using satellite data to generate maps of rain rate with grid resolutions of 1°–5° square. In parallel with these efforts, much work has been devoted to the problem of attaching error estimates to these products. There are two main sources of error, the intrinsic errors in the remote sensing measurements themselves (retrieval errors) and the lack of continuity in the coverage by low earth-orbiting satellites (sampling error). Perhaps a dozen or so studies have attempted to estimate the sampling-error component. These studies have been based on rain gauge and radar-derived data, and the estimates vary so much that it is clear that the sampling error cannot be represented satisfactorily by a single value. These studies are reviewed. Some of the results reported in these studies are based on a method referred to in this paper as “resampling by shifts.” The authors find that the method unfortunately tends to produce estimates that are subject to too much uncertainty to be used quantitatively. After setting these results aside, the authors find that the variability in the remaining sampling-error estimates can be explained to a considerable extent using assumptions common to many statistical models of rain. All such models predict that sampling error relative to the average rain rate R is proportional to R^−1/2. Although the sampling error at any given site seems (to the extent that data have been examined) to change with R in the way predicted by the model, the proportionality constant in this relationship seen in the various studies appears to change from site to site. This constant can be obtained from the satellite estimates themselves if retrieval errors are not correlated over scales of the order of the grid-box size.