WOMBAT v2.S: A Bayesian inversion framework for attributing global CO$_2$ flux components from multiprocess data

Contributions from photosynthesis and other natural components of the carbon cycle present the largest uncertainties in our understanding of carbon dioxide (CO$_2$) sources and sinks. While the global spatiotemporal distribution of the net flux (the sum of all contributions) can be inferred from atmospheric CO$_2$ concentrations through flux inversion, attributing the net flux to its individual components remains challenging. The advent of solar-induced fluorescence (SIF) satellite observations provides an opportunity to isolate natural components by anchoring gross primary productivity (GPP), the photosynthetic component of the net flux. Here, we introduce a novel statistical flux-inversion framework that simultaneously assimilates observations of SIF and CO$_2$ concentration, extending WOMBAT v2.0 (WOllongong Methodology for Bayesian Assimilation of Trace-gases, version 2.0) with a hierarchical model of spatiotemporal dependence between GPP and SIF processes. We call the new framework WOMBAT v2.S, and we apply it to SIF and CO$_2$ data from NASA's Orbiting Carbon Observatory-2 (OCO-2) satellite and other instruments to estimate natural fluxes over the globe during a recent six-year period. In a simulation experiment that matches OCO-2's retrieval characteristics, the inclusion of SIF improves accuracy and uncertainty quantification of component flux estimates. Comparing estimates from WOMBAT v2.S, v2.0, and the independent FLUXCOM initiative, we observe that linking GPP to SIF has little effect on net flux, as expected, but leads to spatial redistribution and more realistic seasonal structure in natural flux components.