Absolute and Differential Accuracy of Analyses Achievable with Specified Observational Network Characteristics

Abstract

The dependence of the root-mean-square analysis error of an observed element, its gradient and its Laplacian upon 1) observational density, 2) observational error and 3) spatial correlation of observational error have been assessed using optimum interpolation theory. The results have been generalized by scaling the observational separation s according to a length scale parameter L, which corresponds to the Gaussian population spatial autocorrelation function ?(s)=exp(?s2L?2) of the forecast error of the observed element. The responses of different synoptic regimes (subpopulations) were discriminated according to the sub-population length-scale parameter. The number of observations considered at a grid point was limited to either 12 or 4. It has been shown that 1) an increasing spatial correlation of observational error has a different effect on the analysis errors of absolute and differential quantities, and 2) that the point of diminishing returns, below which an increasing observational density produces little improvement in analysis accuracy, is rather sensitive to the subpopulation length-scale parameter. The results highlight the necessity, for network planning, of considering the relative importance of the absolute value and differential characteristics of an observed element, and the response of defined ?extreme? synoptic regimes in addition to the gross population response. Some of the experiments were repeated with an inverse polynominal autocorrelation function instead of the Gaussian. The results suggest that if, as suggested by some climatologically based autocorrelations, the former function agrees better with observed temperature data, then the use of the Gaussian function may tend to underestimate the benefit of high-resolution remote soundings.