Abstract
Satellite remote sensing of trace gases such as carbon dioxide (CO$_2$) has increased our ability to observe and understand Earth's climate. However, these 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 satellite instrument, since Level 2 retrievals are generally not co-located with ground-based remote sensing instruments. 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 validate statistically 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 ground-based 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 compares better with TCCON data than that based on Version 7r.
Highlights
Level 2 retrievals from satellite remote sensing instruments are typically retrieved irregularly in space and time
We have presented statistical approaches to generating Level 3 products that contain maps of predictions and prediction standard errors, from satellite remote sensing retrievals
When both data size and signal-to-noise ratio (SNR) are an issue, we showed that reduced-rank methods such as fixed rank kriging (FRK) are a viable and attractive way forward
Summary
Level 2 retrievals from satellite remote sensing instruments are typically retrieved irregularly in space and time. Statistical techniques tend to be more computationally intensive, on the one hand, but on the other hand, they allow for uncertainty quantification This is indispensable when validating satellite remote sensing products to ground-based measurements or to other transport-model outputs, as it puts into context the magnitudes of any observed discrepancies. The modelled covariances of the local spatial processes may together yield invalid covariance matrices Another class of statistical techniques that are designed to work with large datasets is based on dimensionality reduction. In our discussion of Level-3 product generation, we go one step further and assume that the covariance function of the process is known This simplification is made so that we can focus on the issue of prediction and how various model assumptions and local methods affect the quality of the inferences we can make.
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