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The Interpolation of Data Series Using a Constrained Iterating Technique

Ali HarzallahLaboratoire de Météorologie Dynamique du CNRS, Ecole Normale Supérieure, Paris, France

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Abstract

A consistent interpolation technique, applicable to data series, is presented. Demonstrative examples are given where consistency is defined as conservation of mean or of second-order moment; the interpolants are linear or spline functions. The choice of interpolants can be extended to other desired definitions. The method is based on an iterating technique that forces the interpolant to satisfy the consistency constraint. The method works for an evenly spaced series and does not suppose periodicity. The method is applied to interpolate monthly series of sea surface temperature from yearly sampled values; it is shown that the method provides satisfactory results.

Abstract

A consistent interpolation technique, applicable to data series, is presented. Demonstrative examples are given where consistency is defined as conservation of mean or of second-order moment; the interpolants are linear or spline functions. The choice of interpolants can be extended to other desired definitions. The method is based on an iterating technique that forces the interpolant to satisfy the consistency constraint. The method works for an evenly spaced series and does not suppose periodicity. The method is applied to interpolate monthly series of sea surface temperature from yearly sampled values; it is shown that the method provides satisfactory results.

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