On the use of smoothing splines to filter CO2data

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Abstract
The use of smoothing splines in the analysis of CO2data is reviewed in the light of recent mathematical studies of spline fitting considered as a filtering operation. The digital filtering interpretation is particularly appropriate because many recent analyses of CO2data can be regarded as signal extraction studies. It is suggested that the most appropriate formulation of smoothing splines for analyzing CO2and similar data is the form in which the trade‐off between smoothness and data fitting is expressed by fixing the relative scaling factor, λ. This form has a direct interpretation as a digital filter with a specific transfer function and so spline fits for different stations can be standardized for comparisons. The scaling factor should be chosen according to the spectral characteristics of the signal that is to be estimated. Smoothing splines are particularly suitable for interpolating irregularly spaced data, since the filtering properties are only weakly dependent on the data density. However, for signal estimation problems involving uniformly spaced data, special‐purpose digital filters will frequently give performance superior to smoothing splines. The discussion is illustrated by an analysis of CO2data from Cape Grim, Tasmania.

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