The need for consistent assimilation of satellite measurements for numerical weather prediction led operational
meteorological centers to assimilate satellite radiances directly using variational data assimilation
systems. More recently there has been a renewed interest in assimilating satellite retrievals (e.g., to avoid the
use of relatively complicated radiative transfer models as observation operators for data assimilation). The
aim of this paper is to provide a rigorous and comprehensive discussion of the conditions for the equivalence
between radiance and retrieval assimilation. It is shown that two requirements need to be satisfied for the
equivalence: (i) the radiance observation operator needs to be approximately linear in a region of the state
space centered at the retrieval and with a radius of the order of the retrieval error; and (ii) any prior information
used to constrain the retrieval should not underrepresent the variability of the state, so as to retain
the information content of the measurements. Both these requirements can be tested in practice. When these
requirements are met, retrievals can be transformed so as to represent only the portion of the state that is well
constrained by the original radiance measurements and can be assimilated in a consistent and optimal way, by
means of an appropriate observation operator and a unit matrix as error covariance. Finally, specific cases
when retrieval assimilation can be more advantageous (e.g., when the estimate sought by the operational
assimilation system depends on the first guess) are discussed
