Abstract
Abstract. This paper is motivated by the fact that, although temperature readings made by Vaisala RS41 radiosondes at GRUAN sites (https://www.gruan.org/, last access: 30 November 2020) are given at 1 s resolution, for various reasons, missing data are spread along the atmospheric profile. Such a problem is quite common with radiosonde data and other profile data. Hence, (linear) interpolation is often used to fill the gaps in published data products. From this perspective, the present paper considers interpolation uncertainty, using a statistical approach to understand the consequences of substituting missing data with interpolated data. In particular, a general framework 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 provide similar interpolation performances using an extensive cross-validation approach based on the block-bootstrap technique. Statistical results about interpolation uncertainty at various GRUAN sites and for various missing gap lengths are provided. Since both approaches result in an underestimation of the 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 less 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. It is concluded that this approach could be implemented in a future version of the GRUAN data processing.
Highlights
The quality of climate variable profiles in the atmosphere is relevant in various scientific fields
We propose a bootstrap-corrected interpolation uncertainty estimate by merging the information of the single profile (s, l) captured by the corresponding Gaussian process (GP) and the average offset of the uncertainty given by the root MSE (RMSE): u(t|s, l)2 = standard error (SE)(t|s, l)2 + MSE(d|ALT)
This paper offers a multifaceted assessment of the interpolation uncertainty of Vaisala RS41 temperature profiles at various altitudes, using an extensive data set from seven GRUAN sites
Summary
The quality of climate variable profiles in the atmosphere is relevant in various scientific fields. Finazzi et al (2019) considered the harmonisation of low-vertical-resolution temperature and humidity radiosonde measurements and the corresponding atmospheric profiles derived from the Infrared Atmospheric Sounding Interferometer (IASI) aboard the Metop-A and Metop-B satellites These authors used spline interpolation of radiosonde profiles and indirectly assessed the related uncertainty through a comparison with GRUAN reference measurements. Considering the motivating application, which focuses on temperature readings of the Vaisala RS41 at GRUAN sites, this paper’s objective is to contribute to the understanding of interpolation uncertainty expressed as a function of missing gap length, missing frequency, altitude, and site This objective amounts to studying the feasibility of an algorithm and/or a lookup table providing interpolation uncertainty in a future version of GRUAN data processing.
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