A dual-pass carbon cycle data assimilation system to estimate surface CO<sub>2</sub> fluxes and 3D atmospheric CO<sub>2</sub> concentrations from spaceborne measurements of atmospheric CO<sub&

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.