A linear mathematical model for accurate referencing of satellite data – atmospheric profile retrievals – to radiosonde profiles is presented. The model provides a theoretical basis and a practical tool for the assessment of the accuracy and precision of the referencing for a particular satellite system and ground site.

The satellite measurement and the profile used for reference are generally taken at a different time and space; moreover, they sample the atmosphere differently, i. e. they have different vertical sensitivity and resolution. All these factors cause apparent differences between the compared entities. To make the comparison of the satellite data accurate, the model accounts for those factors allowing one to separate them from the possible bias (accuracy) and noise (precision) of the satellite system.

To account for time and space differences the model uses statistical characteristics (mean value, covariance and correlation) of the ensembles of the true atmospheric states on which the satellite system and the system used for comparison perform the measurements. To reconcile the differences in vertical sensitivity and resolution the averaging kernel formalism is implemented.

For the case study the model has been applied to a set of radiosonde temperature profiles taken over the ARM Southern Great Plain site and simulated AIRS retrievals. It has been demonstrated how unaccounted temperature differences/errors between compared profiles depend on the time interval separating them. In this particular study, for two sets of profiles (107 profiles each) separated by less than six hours, the mean unaccounted error is within 0.3±0.2 K.

The model can be used for referencing the satellite data from instruments such as CrIMS, IASI, and AIRS to other data sets for use as Earth System or Climate Data Records (ESDRs or CDRs) as well as for assessment and interpretation of validation results when the previously mentioned sources of discrepancies are significant.