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

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https://doi.org/10.5194/amt-2016-399
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
08 Feb 2017
Review status
This discussion paper is a preprint. A revision of this manuscript was accepted for the journal Atmospheric Measurement Techniques (AMT) and is expected to appear here in due course.
Smoothing data series by means of cubic splines: quality of approximation and introduction of an iterative spline approach
Sabine Wüst1, Verena Wendt1,2,a, Ricarda Linz1, and Michael Bittner1,3 1Deutsches Fernerkundungsdatenzentrum, Deutsches Zentrum für Luft- und Raumfahrt, 82234 Oberpfaffenhofen, Germany
2Umweltforschungsstation Schneefernerhaus, Zugspitze, Germany
3Institut für Physik, Universität Augsburg, 86159 Augsburg, Germany
anow at: Institut für industrielle Informationstechnik, Hochschule Ostwestfalen-Lippe, Ostwestfalen-Lippe, Germany
Abstract. Cubic splines with equidistant spline sampling points are a common method in atmospheric science for the approximation of undisturbed background conditions by means of filtering superimposed fluctuations from a data series. Often, not only the background conditions are of scientific interest but also the residuals – the subtraction of the spline from the original time series.

Based on test data sets, we show that the quality of approximation is not increasing continuously with increasing number of spline sampling points/decreasing distance between two spline sampling points. Splines can generate considerable artificial oscillations in the data.

We introduce an iterative 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 we are 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 an iterative spline approach, Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2016-399, in review, 2017.
Sabine Wüst et al.
Interactive discussionStatus: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
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RC1: 'Referee Comment', Anonymous Referee #2, 07 Mar 2017 Printer-friendly Version Supplement 
AC1: 'Answer to comments of anonymous referee #2', Sabine Wüst, 28 Apr 2017 Printer-friendly Version Supplement 
 
RC2: 'Reviewer Comment', Anonymous Referee #1, 21 Mar 2017 Printer-friendly Version 
AC2: 'Answer to comments of anonymous referee #1', Sabine Wüst, 28 Apr 2017 Printer-friendly Version Supplement 
Sabine Wüst et al.
Sabine Wüst et al.

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Short summary
Cubic splines are a common method in atmospheric science for filtering superimposed fluctuations from a data series. However, splines can generate considerable artificial oscillations. We introduce an iterative spline approach which is able to significantly reduce this phenomenon and apply it to TIMED-SABER vertical temperature profiles from 2010 to 2014.
Cubic splines are a common method in atmospheric science for filtering superimposed fluctuations...
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