A retrieval strategy for interactive ensemble data assimilation

As an alternative to either directly assimilating radiances or the naive use of retrieved profiles (of temperature, humidity, aerosols, and chemical species), a strategy is described that makes use of the so-called averaging kernel (AK) and other information from the retrieval process. This AK approach has the potential to improve the use of remotely sensed observations of the atmosphere. First, we show how to use the AK and the retrieval noise covariance to transform the retrieved quantities into observations that are unbiased and have uncorrelated errors, and to eliminate both the smoothing inherent in the retrieval process and the effect of the prior. Since the effect of the prior is removed, any prior, including the forecast from the data assimilation cycle can be used. Then we show how to transform this result into EOF space, when a truncated EOF series has been used in the retrieval process. This provides a degree of data compression and eliminates those transformed variables that have very small information content. In both approaches a vertical interpolation from the dynamical model coordinate to the radiative transfer coordinate is required. We define an algorithm using the EOF representation to optimize this vertical interpolation

💡 Research Summary

The paper proposes a novel data‑assimilation strategy that sits between two conventional approaches for using satellite remote‑sensing observations: (i) direct assimilation of radiances, which requires expensive radiative‑transfer modeling and complex error characterization, and (ii) naïve assimilation of retrieved atmospheric profiles, which inherits smoothing, prior bias, and correlated retrieval errors. The authors exploit two pieces of information that are by‑products of any optimal retrieval: the averaging kernel (AK) matrix and the retrieval‑noise covariance matrix.

First, they show that the AK can be used to “undo” the smoothing and prior influence embedded in the retrieved state. Starting from the linear retrieval relationship (\hat{x}=x_a+AK,(x-x_a)+\epsilon) (where (\hat{x}) is the retrieved vector, (x_a) the prior, (x) the true atmospheric state, and (\epsilon) the retrieval noise), they premultiply by (AK^{-1}) to define a transformed observation (\tilde{y}=AK^{-1}(\hat{x}-x_a)). By construction, (\mathbb{E}