# Review of Satellite Remote Sensing of Carbon Dioxide Inversion and Assimilation
## 3 Carbon Satellite Remote Sensing Inversion Techniques
### Orthogonal Modelling and Inversion Principles
#### 3.1.2 Selection of Forward Modelling  
In hyperspectral satellite remote sensing, the forward model is a numerical simulation model that describes the remote sensing observation process of a satellite instrument. The radiative transfer model is the core of the forward model, and the concentration inversion is based on the molecular absorption features generated during the radiative transfer process. As an important component of the forward model, the model is designed to simulate the full physicochemical processes of the atmospheric radiation field, which include the properties of incident sunlight, its transmission, reflection, refraction, scattering, and radiation in the atmosphere, as well as thermal radiation from the ground and bi-directional surface reflections. Theoretically, the intensity of radiation observed by satellite instruments at the top of the atmosphere can be fully determined by these parameters and boundary conditions when a certain observational coordinate system is established. Atmospheric radiative transfer model calculation parameters generally include absorption, emission, and scattering. The following are descriptions and principles of several atmospheric radiative transfer models:  
4A/OP: It is a physical radiative transfer model developed by the LMD Laboratory based on a fast line-by-line integration model. It can be used to simulate atmospheric absorption and scattering for the thermal infrared spectral region. It contains a database of atmospheric absorption GEISA [46] constructed using a wavelength-by-wavelength, layer-by-layer model. With this database, 4A allows the calculation of direct transmittance in each layer of the atmosphere and the calculation of radiation at different altitudes. 6S: The 6S model was developed by [PERSON] et al. [47] of the University of Maryland, USA, in 1997 based on the 5S. The 6S model consists of the following five main parts: the sun, the geometrical relationship between the features and sensors, the atmospheric model, the aerosol model and spectral properties of sensors, and the reflectance of the ground surface. The solving of the radiation equations takes into consideration the multiple scattering and the interactions between the molecular scattering and the aerosol scattering. The 6S model mainly serves the MODIS atmospheric correction algorithm, which can accurately simulate satellite observations in the visible band. LOWTRAN: LOWTRAN 7 is a single-parameter, spectral band mode atmospheric transport model developed by the American Geophysical Laboratory, which is a software package for calculating atmospheric transmittance and radiation, and supplemented by molecular line parameters obtained from theoretical calculations. LOWTRAN mainly consists of three algorithms: multi-scattering processing, transmittance calculation, and geometric paths of light rays, which are fast in calculation speed and widely applied for modeling atmospheric forcings and backgrounds. However, it also has inherent defects, such as the two-stream approximation for dealing with scattering problems limits its computational accuracy, and the direction-dependent irradiance calculation is not highly accurate. MODTRAN: MODTRAN is an atmospheric radiative transfer model developed by the United States Air Force, which is an improved model of LOWTRAN with the basic structure and framework of the program remaining intact, and the absorption band mode parameters calculated using the latest HITRAN database. In addition, by further refining the wave number interval of the K-distribution, the latest version of MODTRAN 5.0 has improved the spectral resolution to 0.1 cm\({}^{-1}\). SCIATRAN: An integrated atmospheric radiative transfer and inversion model developed by the University of Bremen, Germany, for SCIAMACHY. It is based on GOMETRAN and can calculate atmospheric radiative intensity, weight function, atmospheric mass, column concentration, and radiative flux simultaneously.