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  • Author or Editor: Charles A. Doswell III x
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Charles A. Doswell III and Sonia Lasher-Trapp

Abstract

Meteorological observing networks are nearly always irregularly distributed in space. This irregularity generally has an adverse impact on objective analysis and must be accounted for when designing an analysis scheme. Unfortunately, there has been no completely satisfactory measure of the degree of irregularity, which is of particular significance when designing artificial sampling networks for empirical studies of the impact of this spatial distribution irregularity. The authors propose a measure of the irregularity of sampling point distributions based on the gradient of the sums of the weights used in an objective analysis. Two alternatives that have been proposed, the fractal dimension and a “nonuniformity ratio,” are examined as candidate measures, but the new method presented here is considered superior to these because it can be used to create a spatial “map” that illustrates the spatial structure of the irregularities in a sampling network, as well as to assign a single number to the network as a whole. Testing the new measure with uniform and artificial networks shows that this parameter seems to exhibit the desired properties. When tested with the United States surface and upper-air networks, the parameter provides quantitative information showing that the surface network is much more irregular than the rawinsonde network. It is shown that artificial networks can be created that duplicate the characteristics of the surface and rawinsonde networks; in the case of the surface network, however, a declustered version of the observation site distribution is required.

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R. Jeffrey Trapp and Charles A. Doswell III

Abstract

The spherical geometry of weather radar scans results in a data distribution wherein datapoint separation in one coordinate direction and/or in one part of the analysis domain can differ widely from that in another. Objective analysis of the nonuniform radar data to a uniform Cartesian grid is desirable for many diagnostic purposes. For the benefit of the diagnostic data analyst as well as of users of these analyses, the authors evaluate properties of techniques typically used for such objective analysis. This is done partly through theoretical consideration of the properties of the schemes, but mostly by empirical testing. In terms of preservation of the phase and amplitude of the input data, predictability of the degree of smoothing and filtering, and relative insensitivity to input data unsteadiness or spatial characteristic, the isotropic Gaussian or Barnes-type weight function with constant smoothing parameter appears to be the most desirable of the schemes considered. Modification of this scheme so that the weight function varies spatially, with the datapoint spacing, results in an improved analysis, according to some commonly used measures of error. Interpretation of analyses based on such a modified scheme can be affected, however. For example, analyses of unsteady input fields suffer from a convolution of the temporal evolution of the data with spatial variations of the weight function. As a consequence, unambiguous assessment of physical evolution is precluded.

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Phillip L. Spencer, Mark A. Askelson, and Charles A. Doswell III

Abstract

Various combinations of smoothing parameters within a two-pass Barnes objective analysis scheme are applied to analytic observations obtained by regular and irregular sampling of a one-dimensional sinusoidal analytic wave to obtain gridded fields. Each of these various combinations of smoothing parameters would produce equivalent analyses if the observations were continuous and infinite (unbounded). The authors demonstrate that owing to the discreteness of the analytic observations, the actual analyses resulting from these various combinations of smoothing parameters are different. When derivatives are computed and as stations become more irregularly distributed, these differences increase. An awareness of these potentially significant analysis differences should prompt the analyst to consider carefully the choice of smoothing parameters when applying an objective analysis scheme to real observations.

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