Interpolation uncertainty of atmospheric temperature profiles

This paper is motivated by the fact that, although temperature readings made by Vaisala RS41 radiosondes at GRUAN sites 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 0.35K for an average gap length of 30 s and up to 0.58K for a gap of 60 s. It is concluded that this approach could be implemented in a future version of the GRUAN data processing.