Developing global maps of carbon dioxide (CO₂) mole fraction (in units of parts per million) near the Earth’s surface can help identify locations where major amounts of CO₂ are entering and exiting the atmosphere, thus providing valuable insights into the carbon cycle and mitigating the greenhouse effect of atmospheric CO₂. Existing satellite remote sensing data do not provide measurements of the CO₂ mole fraction near the surface. Japan’s Greenhouse gases Observing SATellite (GOSAT) is sensitive to average CO₂ over the entire column, and NASA’s Atmospheric InfraRed Sounder (AIRS) is sensitive to CO₂ in the middle troposphere. One might expect that lower-atmospheric CO₂ could be inferred by differencing GOSAT column-average and AIRS mid-tropospheric data. However, the two instruments have different footprints, measurement-error characteristics, and data coverages. In addition, the spatio-temporal domains are large, and the AIRS dataset is massive. In this article, we describe a spatio-temporal data-fusion (STDF) methodology based on reduced-dimensional Kalman smoothing. Our STDF is able to combine the complementary GOSAT and AIRS datasets to optimally estimate lower-atmospheric CO₂ mole fraction over the whole globe. Further, it is designed for massive remote sensing datasets and accounts for differences in instrument footprint, measurement-error characteristics, and data coverages. This article has supplementary material online.

Global maps of total-column carbon dioxide (CO₂) mole fraction (in units of parts per million) are important tools for climate research since they provide insights into the spatial distribution of carbon intake and emissions as well as their seasonal and annual evolutions. Currently, two main remote sensing instruments for total-column CO₂ are the Orbiting Carbon Observatory-2 (OCO-2) and the Greenhouse gases Observing SATellite (GOSAT), both of which produce estimates of CO₂ concentration, called profiles, at 20 different pressure levels. Operationally, each profile estimate is then convolved into a single estimate of column-averaged CO₂ using a linear pressure weighting function. This total-column CO₂ is then used for subsequent analyses such as Level 3 map generation and colocation for validation. In principle, total-column CO₂ in these applications may be more efficiently estimated by making optimal estimates of the vector-valued CO₂ profiles and applying the pressure weighting function afterwards. These estimates will be more efficient if there is multivariate dependence between CO₂ values in the profile. In this article, we describe a methodology that uses a modified Spatial Random Effects model to account for the multivariate nature of the data fusion of OCO-2 and GOSAT. We show that multivariate fusion of the profiles has improved mean squared error relative to scalar fusion of the column-averaged CO₂ values from OCO-2 and GOSAT. The computations scale linearly with the number of data points, making it suitable for the typically massive remote sensing datasets. Furthermore, the methodology properly accounts for differences in instrument footprint, measurement-error characteristics, and data coverages.

The fraction of land area over the Continental United States experiencing extreme hot and dry conditions has been increasing over the past several decades, consistent with expectation from anthropogenic climate change. A clear concurrent change in precipitation, however, has not been confirmed. Vapor pressure deficit (VPD), combining temperature and humidity, is utilized here as an indicator of the background atmospheric conditions associated with meteorological drought. Furthermore, atmospheric conditions associated with warm season drought events are assessed by partitioning associated VPD anomalies into the temperature and humidity components. This approach suggests that the concurrence of anomalously high temperature and low humidity was an important driver of the rapid development and evolution of the exceptionally severe 2011 Texas and the 2012 Great Plains droughts. By classification of a decade of extreme drought events and tracking them back in time, it was found that near surface atmospheric temperature and humidity add essential information to the commonly used precipitation-based drought indicators and can advance efforts to determine the timing of drought onset and its severity.

We review the singular value decomposition (SVD) framework and use it for quantifying and discerning vertical information in greenhouse gas retrievals from column integrated absorption measurements. While the commonly used traditional Bayesian optimal estimation (OE) assumes a prior distribution in order to regularize the inversion problem, the SVD approach identifies principal components that can be retrieved from the measurement without explicitly specifying a prior mean and prior covariance matrix. We review the SVD method, explicitly recognize the use of an uninformative prior and show it to incur no bias from the choice of the prior. We also make the connection between the SVD method and the pseudo-inverse, which makes it more intuitive and easy to understand. We illustrate the use of the SVD method on an integrated path differential absorption CO₂ lidar measurement model and verify our derivations and bias-free properties versus optimal estimation using numerical simulations. In contrast, traditional OE retrievals exhibit bias when the prior mean used in the retrieval differs from the true mean. Hence, the SVD method is particularly useful for situations in which knowledge of the prior mean and prior covariance of the true state (e.g., greenhouse gas profiles) is inadequate.

Optimal Estimation (OE) is a popular algorithm for remote sensing retrievals, partly due to its explicit parameterization of the sources of error and the ability to propagate them into estimates of retrieval uncertainty. These properties require specification of the prior distribution of the state vector. In many remote sensing applications, the true priors are multivariate and hard to characterize properly. Instead, priors are often constructed based on subject-matter expertise, existing empirical knowledge, and a need for computational expediency, resulting in a “working prior.” This paper explores the retrieval bias and the inaccuracy in retrieval uncertainty caused by explicitly separating the true prior (the probability distribution of the underlying state) from the working prior (the probability distribution used within the OE algorithm), with an application to Orbiting Carbon Observatory-2 (OCO-2) retrievals. We find that, in general, misspecifying the mean in the working prior will lead to biased retrievals, and misspecifying the covariance in the working prior will lead to inaccurate estimates of the retrieval uncertainty, though their effects vary depending on the state-space signal-to-noise ratio of the observing instrument. Our results point towards some attractive properties of a class of uninformative priors that is implicit for least-squares retrievals. Furthermore, our derivations provide a theoretical basis, and an understanding of the trade-offs involved, for the practice of inflating a working-prior covariance in order to reduce the prior’s impact on a retrieval (e.g., for OCO-2 retrievals). Finally, our results also lead to practical recommendations for specifying the prior mean and the prior covariance in OE.

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.