On the Kalman Smoother Interpolation Error Distribution in Collocation Comparison of Atmospheric Profiles

The intercomparison between different atmospheric monitoring systems is key for instrument calibration and validation. Common cases involve satellites, radiosonde and atmospheric model outputs. Since instruments and/or measures are not perfectly collocated, miss-collocation uncertainty must be considered in related intercomparison uncertainty budgets. This paper is motivated by the comparison of GNSS-RO, the Global Navigation Satellite System Radio Occultation, with ERA5, the version 5 Reanalysis of the European Centre for Medium-range Weather Forecasts. We consider temperature interpolation observed at GNSS-RO pressure levels to the ERA5 levels. We assess the interpolation uncertainty using as ‘truth’ high-resolution reference data obtained by GRUAN, the Reference Upper-Air Network of the Global Climate Observing System. In this paper, we propose a mathematical representation of the interpolation problem based on the well-known State-space model and the related Kalman filter and smoother. We show that it performs the same (sometimes better) than linear interpolation and, in addition, provides an estimate of the interpolation uncertainty. Moreover, with both techniques, the interpolation error is not Gaussian distributed, and a scaled Student’s t distribution with about 4.3 degrees of freedom is an appropriate approximation for various altitudes, latitudes, seasons and times of day. With our data, interpolation uncertainty results larger at the equator, the Mean Absolute Error being MAE ∼= 0.32 K, and smaller at a high latitude, MAE ∼= 0.21 K at −80° latitude. At lower altitudes, it is close to the measurement uncertainty, with MAE < 0.2 K below the tropopause. Around 300 hPa, it starts increasing and reaches about 0.8 K above 100 hPa, except at the equator, where we observed MAE about 1 K.