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.
Highlights
Remote sensing observations of emitted and reflected electromagnetic radiation provide indirect information about atmospheric quantities of interest
Optimal estimation is a state-of-the-art retrieval method in remote sensing, and it is the method of choice for a large number of remote sensing missions (e.g., Orbiting Carbon Observatory-2 (OCO-2), Spinning Enhanced Visible and Infra-Red Imager (SEVIRI), gases Observing SATellite (GOSAT), Tropospheric Emission Spectrometer (TES), etc.)
One important component of Optimal Estimation (OE) retrieval is specifying the prior mean and prior covariance of the state vector x, and it has been shown in the literature that misspecifying the prior distribution within the retrieval algorithm will result in biased retrievals
Summary
Remote sensing observations of emitted and reflected electromagnetic radiation provide indirect information about atmospheric quantities of interest. We shall call {xT, ST} the true prior because it describes the distribution that generated the hidden state x, and we shall call the parameters used within OE retrievals (i.e., {xa,i, Sa,i}) the working prior Even if both retrievals have specified the correct forward model and instrument measurement-error characteristics, if xa,1 = xa,, it is straightforward to show that the expected value of x1 is different from the expected value of x2 (i.e., E(x1) = E(x2)) [13]; or equivalently, E(x1 − x2) = 0, which implies that there is a prior-induced relative bias for OE retrievals with different priors. We will end the paper with some discussion and recommendations for mitigating this prior-induced bias in practice
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