Applications of the Barnes Objective Analysis Scheme. Part III: Tuning for Minimum Error

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Abstract
Procedures for tuning a successive corrections objective analysis scheme, described in Part I, are applied to the array of North American rawinsonde stations. Tuning is investigated for three types of Barnes schemes (two-, three-, and four-pass schemes) and for an equivalent four-pass scheme developed by Caracena. Each of the schemes uses an iteration parameter equal to 1, and each considers the influence of all observations within at least 2500 km of the interpolation point. Analysis accuracy is investigated for “errorless observations” of a simulated 300-mb height field containing a Rossby-scale wave with one of its ridges amplified to produce an asymmetric distribution of the height gradient across a circular region of locally lower heights representing a synoptic-scale low. Root-mean-square errors are evaluated at grid points for analyses of pressure height, height gradient, and the Laplacian of height over a range of values for the weight function's scale-length parameter α. Because the analyses are sensitive to errors caused by the discrete, slightly irregular sampling array, rms errors for these height analyses cannot be reduced to less than about 6 m using four-pass schemes, and to about 10 m using a two-pass scheme. In each of the schemes, it is found that the value of α that produces minimum error is different for each of the analyzed variables. The range of this difference is less for three- and four-pass schemes than for the traditional two-pass scheme, and the variation of errors across these ranges is also less in the former than the latter, thus making the three- and four-pass schemes easier to tune. Furthermore, it is demonstrated that even the two-pass results having least analysis error require application of postanalysis numerical filters to achieve reasonable derivative results, whereas error-minimizing three- and four-pass results do not. Effects of pseudorandom observation errors (maximum ±20 m) on three-pass analysis accuracy are studied in two independent tests, each having an 11-m standard deviation in the errors applied. It is found that the distribution of random errors can affect the value of error-minimizing α in unpredictable ways, and in one test the magnitude of the minimum achievable error increased by 41% over that resulting with errorless observations. Even so, the distribution of analysis errors, although distorted with respect to the distributions achieved with errorless observations, are not unreasonably different from the latter. It is concluded that three- or four-pass schemes are inherently better than the two-pass scheme, especially for analysis of derivatives, and that tuning the weight function's scale-length parameter should be accomplished on the basis of errorless observations by selecting the value of α that produces minimum error in the gradient of the variable being analyzed.

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