Articles | Volume 10, issue 9
https://doi.org/10.5194/amt-10-3453-2017
https://doi.org/10.5194/amt-10-3453-2017
Research article
 | 
21 Sep 2017
Research article |  | 21 Sep 2017

Smoothing data series by means of cubic splines: quality of approximation and introduction of a repeating spline approach

Sabine Wüst, Verena Wendt, Ricarda Linz, and Michael Bittner

Abstract. Cubic splines with equidistant spline sampling points are a common method in atmospheric science, used for the approximation of background conditions by means of filtering superimposed fluctuations from a data series. What is defined as background or superimposed fluctuation depends on the specific research question. The latter also determines whether the spline or the residuals – the subtraction of the spline from the original time series – are further analysed.

Based on test data sets, we show that the quality of approximation of the background state does not increase continuously with an increasing number of spline sampling points and/or decreasing distance between two spline sampling points. Splines can generate considerable artificial oscillations in the background and the residuals.

We introduce a repeating spline approach which is able to significantly reduce this phenomenon. We apply it not only to the test data but also to TIMED-SABER temperature data and choose the distance between two spline sampling points in a way that is sensitive for a large spectrum of gravity waves.

Download
Short summary
Cubic splines with equidistant spline sampling points are a common method in atmospheric science for the approximation of background conditions by means of filtering superimposed fluctuations from a data series. However, splines can generate considerable artificial oscillations in the background and the residuals. We introduce a repeating spline approach which is able to significantly reduce this phenomenon and to apply it to TIMED-SABER vertical temperature profiles from 2010 to 2014.