# Review of Satellite Remote Sensing of Carbon Dioxide Inversion and Assimilation
## 3 Carbon Satellite Remote Sensing Inversion Techniques
### Optimal Estimation Algorithm  
Optimal estimation algorithms need to determine the cost function first and then use different optimization strategies to minimize the cost function. The National Institute for Environmental Studies (NIES) of Japan developed the NIES-FP inversion algorithm using an optimal estimation approach. This algorithm retrieves the column abundances of CO\({}_{2}\) and CH\({}_{4}\) from short-wavelength infrared spectra collected by the TANSO-FTS [69]. It features an unbiased cloud-detection algorithm [70] that utilizes the TANSO-CAI cloud product for cloud screening and refines the atmospheric light path by simultaneously inverting aerosol, surface, and gas parameters at observational pixels. As the standard algorithm for GOSAT data products, it has demonstrated high accuracy in GHG inversions, achieving errors within 1% [71]. Recently, [PERSON] et al. [72] introduced a new version, V03.xx, of the NIES SWIR L2 product algorithm. The ACOS retrieval algorithm, initially developed by NASA's science team for the OCO satellite, was adapted for use with the GOSAT satellite following the OCO mission's failure [73]. This physics-based algorithm features distinct approaches in cloud filtering, state vectors, forward modeling, and inversion strategies [73; 74]. It utilizes optimal estimation to refine input parameters of the forward model, aiming to match the simulated spectrum to the observed spectrum while adhering to a priori constraints. To minimize the cost function, the algorithm employs a modified Levenberg-Marquardt method [45]. The ACOS team continues to work on inverting the GOSAT L1B product, with the ACOS Level 2 Full Physics Field (L2 FP) retrieval algorithm recently updated to version 10 [75]. This updated version is used to analyze multi-year observational data from OCO-2 and OCO-3, providing accurate XCO\({}_{2}\) measurements. The UoL-FP algorithm, developed by [PERSON] et al. [76] from the University of Leicester, UK, is a comprehensive physics-based algorithm designed for CO\({}_{2}\) inversion using data from OCO and OCO-2. This algorithm utilizes the LIDORT radiative transfer model, which  
Figure 13: Block diagram of the implementation process of the WFM-DOAS algorithm. solves the radiative transfer equations through an additive eigenmatrix approach. To address polarization effects, it incorporates a fast second-order scattering vector radiative transfer model. The inversion method employed by UoL-FP relies on the best-estimation technique [77]. The RemoTeC algorithm, developed by the Dutch Space Research Institute SRON and KIT, comes in two versions: SRPR (proxy retrieval) and SRFP (full physics) [78; 79]. The SRFP version utilizes the linearized radiative transfer model LINTRAN to retrieve gas concentrations and accounts for multiple scattering effects [67]. It retrieves CO\({}_{2}\) and CH\({}_{4}\) concentrations along with aerosol properties, including optical thickness, elevation, and particle scale. In contrast, the SRPR version simplifies the model by neglecting scattering effects and aerosol influences [80]. RemoTeC is employed for greenhouse gas retrieval from GOSAT, XCO\({}_{2}\) retrieval from OCO-2, and methane retrieval from TROPOMI, as part of ESA's Climate Change Initiative (CCI). The RemoTAP algorithm, also developed by SRON, can simultaneously retrieve aerosol and trace gases by integrating measurements from both the CO\({}_{2}\) imager (CO2I) and the multi-angle polarimeter (MAP). Originating from the SRON aerosol retrieval algorithm (or SRON-MAP algorithm) that uses MAP measurements, RemoTAP has been recently extended to include spectroscopic measurements and the capability to retrieve trace gas columns [24]. This extension builds on the RemoTeC algorithm, which infers trace gases from spectrometer data.