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Atmospheric Measurement Techniques An interactive open-access journal of the European Geosciences Union

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Atmos. Meas. Tech., 10, 3453-3462, 2017
https://doi.org/10.5194/amt-10-3453-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
21 Sep 2017
Smoothing data series by means of cubic splines: quality of approximation and introduction of a repeating spline approach
Sabine Wüst1, Verena Wendt1,2,3, Ricarda Linz1,a, and Michael Bittner1,4 1Deutsches Fernerkundungsdatenzentrum (DFD), Deutsches Zentrum für Luft- und Raumfahrt (DLR), 82234 Oberpfaffenhofen, Germany
2Umweltforschungsstation Schneefernerhaus, Zugspitze, Germany
3Institut für industrielle Informationstechnik, Hochschule Ostwestfalen-Lippe, Ostwestfalen-Lippe, Germany
4Institut für Physik, Universität Augsburg, 86159 Augsburg, Germany
anow at: Willis Re GmbH & Co KG, München, Germany
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.


Citation: Wüst, S., Wendt, V., Linz, R., and Bittner, M.: Smoothing data series by means of cubic splines: quality of approximation and introduction of a repeating spline approach, Atmos. Meas. Tech., 10, 3453-3462, https://doi.org/10.5194/amt-10-3453-2017, 2017.
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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.
Cubic splines with equidistant spline sampling points are a common method in atmospheric science...
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