Intercomparison of remote sensing retrievals: An examination of prior-induced biases in averaging kernel corrections

Abstract

In remote sensing applications, Optimal Estimation (OE) retrievals are sometimes compared to independent OE retrievals of the same process. This intercomparison is often done in instrument validation, where retrievals are compared with data from a separate validation instrument, and it is sometimes done in data assimilation, where data from multiple instruments need to be adjusted to the “same footing.” In these cases, the two different retrievals are compared using an adjustment that is colloquially known as the averaging kernel correction. A general misconception in the existing literature is that this averaging kernel correction removes any bias introduced by prior misspecification by either (or both) of the two comparative OE retrievals. In this paper, we will analytically show that this is not the case and the averaging kernel correction process implicitly “shifts” both OE retrievals to a common comparison prior. We will also show that there is generally a non-zero bias that is proportional to the difference between this comparison prior mean and the true (but unobserved) mean state, which has large implications for retrieval validation and data assimilation in remote sensing. Finally, to better characterize OE retrievals and retrieval intercomparisons, we will make some recommendations for mitigating this prior-induced bias in intercomparison of OE retrievals.