On statistical approaches to generate Level 3 products from remote sensing retrievals
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Remote sensing of trace gases such as carbon dioxide (CO_2) has led to a revolution in our ability to observe and understand Earth's climate. However, remote sensing data, specifically Level 2 retrievals, tend to be irregular in space and time, and hence spatio-temporal prediction is required to infer values at any location and time point. Such inferences are not only required to answer important questions about our climate, but they are also needed for validating the remote sensing instrument, since Level 2 retrievals are generally not co-located with in-situ measurements. Here, we discuss statistical approaches to construct Level 3 products from Level 2 retrievals, placing particular emphasis on the strengths and potential pitfalls when using statistical prediction in this context. Following this discussion, we use a spatio-temporal statistical modelling framework known as Fixed Rank Kriging (FRK) to obtain global predictions and prediction standard errors of column-averaged carbon dioxide based on Version 7r and Version 8r retrievals from the Orbiting Carbon Observatory-2 (OCO-2) satellite. The FRK predictions allow us to statistically validate the Level 2 retrievals globally even though the data are at locations and at time points that do not coincide with validation data. Importantly, the validation takes into account the prediction uncertainty, which is dependent both on the temporally varying density of observations around the in-situ measurement sites and on the spatio-temporal high-frequency components of the trace gas field that are not explicitly modelled. Here, for validation of remotely sensed CO_2 data, we use observations from the Total Carbon Column Observing Network. We demonstrate that the resulting FRK product based on Version 8r is an improvement over that based on Version 7r, in terms of both prediction accuracy and uncertainty quantification.
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