Comparison of the Assimilation of Compact Phase Space Retrievals (CPSRs) with Conventional Retrieval Assimilation Methods for MOPITT CO in WRF-Chem/DART

We introduced "compact phase space retrievals" (CPSRs) for assimilating atmospheric composition observations in Mizzi et al. (2015). CPSRs address many of the challenges associated with assimilating retrievals by: (i) removing the contribution of the retrieval prior, (ii) diagonalizing the associated error covariance, and (iii) compacting the phase space retrievals. Mizzi et al. (2015) showed that the CPSRs reduced assimilation computational costs by approximately one-third while maintaining the relevant forecast skill metrics. In this paper, we examine phase space retrievals and compare CPSRs to more conventional retrieval assimilation methods. Specifically we compare the assimilation of CPSRs with that of (i) raw retrievals where the observation error is based on the diagonal of the retrieval error covariance, (ii) quasi-optimal retrievals (QORs) where the observation error is determined as (i), and (iii) QORs where the observation error is based on an SVD-based transform of the error covariance. Method (i) is the easiest to interpret because the assimilation occurs in retrieval space. Method (ii) explicitly removes the retrieval prior term's contribution but is more difficult to interpret because the assimilated observations are residuals. Finally, method (iii) is the phase space retrieval algorithm of Migliorini et al. (2008). We consider two variants: (i) withholding the inverse square scaling and (ii) using phase space filtering for optimization. We apply those methods to month-long forecast/assimilation experiments with continuous cycling.