Multivariate Spatial Data Fusion for Very Large Remote Sensing Datasets

Global maps of carbon dioxide (CO2) mole fraction (in units of parts per million) in the lower atmosphere are important tools for climate research since they can help identify sources and sinks of CO2. No satellite instrument currently provides estimates of the lower-atmosphere CO2, though inferences are possible using data from existing instruments. Two remote sensing instruments, the Orbiting Carbon Observatory 2 (OCO-2) and the Greenhouse gases Observing SATellite (GOSAT), both observe column-averaged CO2. These data are then used as inputs into flux inversion, which combines a transport model, a priori atmospheric information, and satellite-derived column-averaged CO2 to produce estimates of sources and sinks. Here, we demonstrate a method for improving inferences for column-averaged CO2 using OCO-2 and GOSAT. Both instruments 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 pressure weighting function. However, CO2 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.