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This brief report addresses the problem of objective analysis of fields with spatially variable mean. Conventional objective analysis is confined to fluctuations, where the larger scale is assumed to be known; this report shows how to use the method described by Davis (1985) to estimate simultaneously a large-scale component and a mesoscale component with an accurate error budget. The extension to multivariate analysis is also discussed. The method is then applied to simulated data; this illustrates its contribution in relation to conventional objective analysis.