Issues of spatial correlation arising from the use of TRMM rainfall estimates in the Brazilian Amazon

This paper discusses issues arising when Tropical Rainfall Measuring Mission (TRMM) estimates of rainfall characteristics are calculated for the sparsely gauged Brazilian Amazon. The particular issue considered is the calculation of statistical uncertainty in (1) comparisons between TRMM estimates of rainfall characteristics and their corresponding rain gauge estimates and (2) interpolated estimates of rainfall characteristics, which are conditional on local TRMM estimates near ungauged sites. Three characteristics selected for particular comparison are (1) mean annual rainfall, 1998-2005, (2) mean value, over these years, of the 95% quantile of within-year daily rainfall, and (3) mean number of days in the year with rainfall of 2 mm or more. The paper demonstrates how positive spatial correlation leads to underestimation of the uncertainty in the comparisons (i.e., the standard errors of differences), so that the significance of differences, when observed, is likely to be overestimated if spatial correlation is ignored. For the three characteristics mentioned, the Matern spatial correlation function with shape parameter kappa = 1/2, giving an exponential correlation function, was found to be adequate for modeling spatial correlation. It is also argued that the statistic 1 - b, where b is the slope of the regression of a rain gauge estimate of a rainfall characteristic on its counterpart derived from satellite instrumentation, is a measure of the errors in the satellite (spatially averaged) estimates. Finally, although issues of spatial correlation are discussed with particular reference to rainfall, it is argued that the same issues arise whenever satellite-derived estimates of a component of the water cycle must be combined with ground-based measurements.