# Review of Satellite Remote Sensing of Carbon Dioxide Inversion and Assimilation
## 4 Carbon Flux Data Assimilation and Inversion Studies
### History of the Development of the Data-Asimilation System for Atmospheric CO\({}_{2}\)  
The atmospheric CO\({}_{2}\) data-assimilation method belongs to the \"top-down\" approach for estimating surface carbon sources/sinks. It involves comparing simulated and observed atmospheric CO\({}_{2}\) concentrations and using optimization algorithms to adjust carbon source/sink data, thereby inferring global or regional carbon source/sink distributions. This method is an important approach for carbon source/sink estimation, providing an effective means for estimating carbon fluxes in regional and global ecosystems. Early atmospheric carbon data-assimilation models had many issues. Due to the limited number of CO\({}_{2}\)-observation sites, their temporal resolution was yearly, and the Transcom carbon-assimilation framework divided the world into 23 regions with coarse spatial resolution. In the case of difficulty in improving the density of ground-based atmospheric CO\({}_{2}\) observations, researchers began to improve and optimize the atmospheric CO\({}_{2}\) data-assimilation framework. [PERSON] et al. [114] subdivided the regions and introduced a nested model based on the Transcom system, which improved the spatiotemporal resolution of carbon source and sink inversion. In order to comprehensively understand the global carbon cycle and the spatiotemporal evolution mechanism of carbon sources and sinks, the National Oceanic and Atmospheric Administration (NOAA) of the United States developed the world's first global carbon-tracking-assimilation system (Carbon Tracker, CT) in 2007 [115]. It assimilates global ground and aircraft CO\({}_{2}\) concentration observations to optimize weekly global ecosystem carbon fluxes. The system uses a nested atmospheric transport model (1\({}^{\circ}\)\(\times\) 1\({}^{\circ}\) for North America and 3\({}^{\circ}\)\(\times\) 2\({}^{\circ}\) for other regions) and assimilates global ground and aircraft CO\({}_{2}\) concentration observations to optimize weekly global ecosystem carbon fluxes. In addition, the team developed the Carbon Tracker-Lagrange carbon-assimilation system based on the Lagrangian particle dispersion model [116]. In 2005, the European Centre developed the CAMS carbon-assimilation system based on the LMDz model, using the variational assimilation method [117]. Currently, many countries and regions around the world have transplanted and improved the Carbon Tracker system, establishing localized carbon-assimilation inversion systems such as CT-Australasia, CT-Asia [118], CT-Europe [119], and CT-China [120]. However, the CT system uses the Ensemble Kalman Filter (EnKF) method. Theoretically, a single assimilation window can only assimilate observations from one time point and one type of observation data, which limits the effective utilization of rich information from multiple sources and frequencies of observational data. On the other hand, the CT system overlooks the impact of initial errors in atmospheric CO\({}_{2}\) concentration on the optimization results. The simulation errors in CO\({}_{2}\) concentration accumulate with the forward integration of the atmospheric transport model, increasing the uncertainty of the results. Additionally, mismatches between models and observational data and high computational costs present challenges. Despite these issues, modern systems like Carbon Tracker significantly enhance the accuracy of carbon flux estimates by integrating global observational data and employing higher resolution models, though the scarcity of observational data in some regions remains a concern. Based on the Carbon Tracker system and its improved carbon-assimilation inversion systems, researchers from various countries have conducted numerous estimations of carbon sources and sinks. [PERSON] et al. [121] improved the core module of the CT-Europe system and used the newly improved carbon-assimilation inversion system to estimate global carbon fluxes, revealing the distribution of carbon sinks in terrestrial and marine ecosystems. [PERSON] et al.