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Extending Estimation Accuracy with Anisotropic Interpolation

H. Jean ThiébauxDepartment of Mathematics, Dalhousie University, Halifax, Nova Scotia

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Abstract

The possibility of improving point estimates through anisotropic interpolation is investigated. Experiments employing multivariate optimal interpolation compare rms errors for estimates based on an anisotropic geopotential correlation model with those based on three isotropic models and one using station‐specific sample correlations. Heights and winds are estimated conjointly for 87 consecutive days, using winter 500 mb data of a 48‐station North American network. By varying the array of stations in the observation set contributing to the estimates for a fixed location, measures of accuracy gains are established vis‐à‐vis observation network density and configuration.

Earlier work established the simple isotropic correlation model as a significant source of error in regions of low‐density data or irregular station configurations. With the representation of observed correlation behavior provided by a two‐dimensional correlation function modeling the well‐known anisotropy of the height field, it is shown that gains in accuracy may be substantial.

Implications for specification of the shape of optimal influence regions are discussed.

Abstract

The possibility of improving point estimates through anisotropic interpolation is investigated. Experiments employing multivariate optimal interpolation compare rms errors for estimates based on an anisotropic geopotential correlation model with those based on three isotropic models and one using station‐specific sample correlations. Heights and winds are estimated conjointly for 87 consecutive days, using winter 500 mb data of a 48‐station North American network. By varying the array of stations in the observation set contributing to the estimates for a fixed location, measures of accuracy gains are established vis‐à‐vis observation network density and configuration.

Earlier work established the simple isotropic correlation model as a significant source of error in regions of low‐density data or irregular station configurations. With the representation of observed correlation behavior provided by a two‐dimensional correlation function modeling the well‐known anisotropy of the height field, it is shown that gains in accuracy may be substantial.

Implications for specification of the shape of optimal influence regions are discussed.

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