Quantifying the interpolation uncertainty of radiosonde humidity profiles

The global climate observing system Reference Upper Air Network (GRUAN) provides reference measurements of the essential climate variables and their measurement uncertainty. An important aspect of the measurement uncertainty is the interpolation uncertainty. This problem arises, for example, when GRUAN processes atmospheric profiles collected by Vaisala RS41 radiosondes. For various reasons, the radiosonde sensor may fail to collect some values along the vertical profile in the atmosphere. As a consequence, estimation techniques to fill the data gaps and to provide an evaluation of the related interpolation uncertainty are welcome. This paper aims to understand and quantify the interpolation uncertainty of the relative humidity (RH). In particular, we consider linear and Gaussian process interpolation either unidimensional or multidimensional. We provide results in terms of interpolation distance in seconds, which measures the distance of an interpolated data from the interpolating data. We also consider measurement altitude and launch site. Although the Gaussian interpolation results to be generally better than linear interpolation, the difference in uncertainty is relatively small. The average column uncertainty difference is in the order of 0.2% and for large data gaps around 0.4%. The interpolation uncertainty is larger in the lower atmosphere. For example at 2-4 km altitude, the uncertainty is around 2% at 10 s distance, around 5% at 40 s and 10% at 90 s. In the upper atmosphere, RH and its uncertainty decrease. For example, at 14-16 km altitude, the latter is smaller than 2% RH at all interpolation distances.