On Measuring the Degree of Irregularity in an Observing Network

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.