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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-2020-161
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/amt-2020-161
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  03 Jul 2020

03 Jul 2020

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A revised version of this preprint was accepted for the journal AMT and is expected to appear here in due course.

Interpolation uncertainty of atmospheric temperature radiosoundings

Alessandro Fassò1, Michael Sommer2, and Christoph von Rohden2 Alessandro Fassò et al.
  • 1University of Bergamo, Italy
  • 2GRUAN Lead Centre, Deutscher Wetterdienst, Lindenberg, Germany

Abstract. This paper is motivated by the fact that, although temperature readings made by Vaisala RS41 radiosondes at GRUAN sites (http://www.gruan.org) are given at 1 s resolution, for various reasons, missing data are spread along the atmospheric profile. Such a problem is quite common in radiosonde data and other profile data. Hence, (linear) interpolation is often used to fill the gaps in published data products. In this perspective, the present paper considers interpolation uncertainty. To do this, a statistical approach is introduced giving some understanding of the consequences of substituting missing data by interpolated ones.

In particular, a general frame for the computation of interpolation uncertainty based on a Gaussian process (GP) set-up is developed. Using the GP characteristics, a simple formula for computing the linear interpolation standard error is given. Moreover, the GP interpolation is proposed as it provides an alternative interpolation method with its standard error.

For the Vaisala RS41, the two approaches are shown to give similar interpolation performances using an extensive cross-validation approach based on the block-bootstrap technique. Statistical results about interpolation uncertainties at various GRUAN sites and for various missing gap lengths are provided. Since both provide an underestimation of the cross-validation interpolation uncertainty, a bootstrap-based correction formula is proposed.

Using the root mean square error, it is found that, for short gaps, with an average length of 5 s, the average uncertainty is smaller than 0.10 K. For larger gaps, it increases up to 0.35 K for an average gap length of 30 s, and up to 0.58 K for a gap of 60 s.

Alessandro Fassò et al.

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Alessandro Fassò et al.

Alessandro Fassò et al.

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Latest update: 27 Oct 2020
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Short summary
Which is the uncertainty of interpolated values in atmospheric temperature profiles provided by modern radiosonde balloons, flying from ground level up to the lower stratosphere? To answer this question, we introduce a general statistical-mathematical model for the computation of interpolation uncertainty. Analysing more than 51 million measurements, we provide some understanding of the consequences of filling missing data with interpolated ones.
Which is the uncertainty of interpolated values in atmospheric temperature profiles provided by...
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