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Assimilation of transformed retrievals obtained from clear‐sky IASI measurements

A recent study, which provided theoretical justifications to show that the assimilation of radiances and retrievals can be equivalent when some key requirements are met – namely when remote‐sounding data are related to model variable perturbations in an approximately linear way and when the same prior constraints are used to solve the inverse problem – has brought new insight into the problem of how to assimilate satellite measurements in numerical weather prediction. In this article, we explore this new theoretical framework in practical terms and investigate the viability of assimilating transformed retrievals from hyperspectral infrared sounders such as the Infrared Atmospheric Sounding Interferometer (IASI) in an optimal way. First, the dependence of a measure of information content of temperature‐ and humidity‐sensitive observations from IASI in clear‐sky conditions on the forecast (or ‘background’) uncertainty used to constrain the retrievals is assessed. Subsequently, numerical comparisons between profiles obtained from direct radiance assimilation and those obtained from assimilating appropriately transformed retrievals are performed, for different atmospheric conditions. By making use of the new concept of degrees‐of‐freedom (DFS) weighting function, it is shown that the background error covariance matrix plays a crucial role in determining the conditions for equivalence between assimilation of radiances and transformed retrievals. The numerical comparisons confirm the theoretical results stating that the temperature and humidity profiles obtained from both the direct assimilation of radiances and the assimilation of transformed retrievals are equal within the analysis error as long as the same prior constraints are used. Finally, when the prior differs, it is shown how the characteristics of background error matrices are crucial to guarantee the numerical equivalence between the two methods; the best is when the background matrix utilised to calculate the transformed retrievals is characterised by larger variances than the one utilised in the assimilation.