Statistical Parameter Estimation for Observation Error Modelling: Application to Meteor Radars

Data assimilation schemes blend observational data, with limited coverage, with a short term forecast to produce an analysis, which is meant to be the best estimate of the current state of the atmosphere. Appropriately specifying observation error statistics is necessary to obtain an optimal analysis. Observation error can originate from instrument error as well as the error of representation. While representation error is most commonly associated with unresolved scales and processes, this term is often considered to include contributions from pre-processing or quality control and errors associated with the observation operator. With a focus on practical operational implementation, this chapter aims to define the components of observation error, discusses their sources and characteristics, and provides an overview of current methods for estimating observation error statistics. We highlight the implicit assumptions of these methods, as well as their shortcomings. We will detail current operational practice for diagnosing observation error and accounting for correlated observation error. Finally, we provide a practical methodology for using these diagnostics, as well as the associated innovation-based observation impact, to optimize the assimilation of meteor radar observations in the upper atmosphere.