A dual-pass carbon cycle data assimilation system to estimate surface CO₂ fluxes and 3D atmospheric CO₂ concentrations from spaceborne measurements of atmospheric CO₂

Abstract. Here we introduce a new version of the carbon cycle data assimilation system, Tan-Tracker (v1), which is based on the Nonlinear Least Squares Four-dimensional Variational Data Assimilation algorithm (NLS-4DVar) and the Goddard Earth Observing System atmospheric chemistry transport model (GEOS-Chem). Using a dual-pass assimilation framework that consists of a carbon dioxide (CO₂) assimilation pass and a flux assimilation pass, we assimilated the atmosphere column-averaged CO₂ dry air mole fraction (XCO₂), while sequentially optimizing the CO₂ concentration and surface carbon flux via different length windows with the same initial time. When the CO₂ assimilation pass is first performed, a shorter window of 3 days is applied to reduce the influence of the background flux on the initial CO₂ concentration. This allows us to obtain a better initial CO₂ concentration to drive subsequent flux assimilation passes. In the following flux assimilation pass, a properly elongated window of 2 weeks absorbs enough observations to reduce the influence of the initial CO₂ concentration deviation on the flux, resulting in better surface fluxes. In contrast, the joint assimilation system Tan-Tracker (v0) uses the same assimilation window for optimization of CO₂ concentration and flux, making the uncertainties in CO₂ concentration and flux indistinguishable. The proper orthogonal decomposition (POD)-4DVar algorithm applied with the older system is only a rough approximation of the one-step iteration of the NLS-4DVar algorithm; thus, it can be difficult to fully resolve the nonlinear relationship between flux and CO₂ concentration. In this study, we designed a set of observation system simulation experiments to assimilate artificial XCO₂ observations, in an attempt to verify the performance of the newly developed dual-pass Tan-Tracker (v1). Compared with the a priori joint system, the dual-pass system provided a better representation of the spatiotemporal distribution of the true flux and true CO₂ concentration. We performed sensitivity tests of the flux assimilation window length and number of NLS-4DVar assimilation iterations. Our results indicated that the appropriate flux assimilation window length (14 days) and the appropriate number of NLS-4DVar maximum iterations (three) could be used to achieve optimal results. Thus, the Tan-Tracker (v1) system, based on a novel dual-pass assimilation framework, provides more accurate surface flux inversion estimates and is ultimately a better tool for carbon cycle research.