A Method to Reduce the Adverse Impact that Inhomogeneous Station Distributions Have on Spatial Interpolation

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Abstract
We describe a simple and economic method for reducing the errors that can result from the irregular distribution of data points in linear interpolation schemes that use prescribed, isotropic weighting (IW) functions. The method can be applied to single-step analysis as well as to schemes consisting of more than one step. The starting point of the analysis algorithm is the generation of two datasets (with an IW scheme), one by interpolating the observed field onto the collocated observing sites, the other by interpolating the observed field onto a regular grid. These two datasets are then used independently to estimate two new gridpoint fields as outputs from the same IW analysis scheme. It is assumed that the difference between these two new gridpoint fields is a measure of the error field that results from applying the IW scheme to an inhomogeneous distribution of observing sites, and that this error field is not very different from that associated with the initial gridpoint field analysis. It is therefore used as a basis for correcting the initial gridpoint field analysis. This procedure can be applied iteratively, and is shown to converge when applied to realistic data distributions sampling both real and simulated meteorological fields. Each step of the iterative scheme is described in terms of a frequency response function in the presence of irregularly spaced data points, in order to illustrate its general convergence properties. The performance of the analysis algorithm has also been investigated in the context of the two-step Barnes analysis scheme and its application to scale separation analysis. Applications of the method to simulated and observed data show that the deviations between analyses and original fields are substantially reduced following a small number of iterations.

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