# Review of Satellite Remote Sensing of Carbon Dioxide Inversion and Assimilation
## 3 Carbon Satellite Remote Sensing Inversion Techniques
### Optimal Estimation Algorithm
#### 3.2.4 Empirical Algorithms
Compared to parametric regression models, neural networks are better equipped to handle spatiotemporal variability and model complex nonlinear relationships, leading to superior prediction performance [95]. However, their application in CO\({}_{2}\) modeling remains limited. Additionally, due to the complex effects of clouds on thermal infrared outgoing radiation, neural networks are typically effective only for inversion under clear sky conditions. [PERSON] et al. [96] developed a rapid neural network-based algorithm for IASI sensors, enabling nearly real-time inversion of CO and CH\({}_{4}\). [PERSON] et al. [97] utilized a neural network algorithm to invert the \(5^{\circ}\times 5^{\circ}\) distribution of CO\({}_{2}\) over the global tropical oceans using clear-sky data from IASI. They compared their 2008 inversion results with previous CONTAIL flight data, confirming consistent temporal and spatial distribution trends. [PERSON] [98] introduced a new, fast algorithm for the radiative transfer model of the hyperspectral thermal infrared atmosphere, leveraging radial basis function (RBF) neural network techniques. This multilayer neural network, trained for specific bands, efficiently calculates radiative transfer brightness at the top of the hyperspectral thermal infrared atmosphere. [PERSON]'s experimental results demonstrated that this algorithm not only achieves high computational accuracy but also increases processing speed by over 100 times compared to traditional radiative transfer models. [PERSON] et al. [99] employed a feed-forward neural network (FFNN) with a sigmoid function, using variables such as moon phase,latitude, longitude, sea surface temperature, sea surface salinity, and chlorophyll-a concentration (CHL) to model XCO\({}_{2}\) concentrations over the ocean. [PERSON] et al. [100] used a multilayer perceptron (MLP) to simulate monthly XCO\({}_{2}\) coverage based on data from the Orbiting Carbon Observatory-2 (OCO-2) and eight environmental variables, highlighting the application of machine learning in satellite XCO\({}_{2}\) retrieval. [PERSON] et al. [101] proposed a novel retrieval algorithm for rapid XCO\({}_{2}\) extraction from GOSAT observation spectra, employing an empirical orthogonal function approach with GOSAT training sets and ground observations. [PERSON] et al. [102] developed a BRDF model [103] for inversion using single observations from MODIS surface two-way reflectance distribution function (BRDF) data. Their model, applied to the urban area of Beijing over five years (2011-2016), facilitates the simultaneous inversion of surface BRDF parameters and atmospheric CO\({}_{2}\) content. [PERSON] et al. [104] introduced an alternative method using artificial neural network (ANN) techniques to estimate XCO\({}_{2}\) from OCO-2 spectral measurements. The model was trained on real nadir-mode measurements collected during cloud-free conditions in even-numbered months and was subsequently evaluated using similar observations from odd-numbered months. Unlike the initial version of the model [105], which did not incorporate surface pressure as an input, this updated model integrates surface pressure data from numerical weather models and XCO\({}_{2}\) data from atmospheric transport simulations. Figure 14 illustrates the neural network architecture, which uses three-band spectra and observation geometry (including solar and field of view zenith angles: SZA and VZA, and relative azimuth angle: AZI) as inputs. Some versions of the model also include surface pressure (Psurf) as an additional input. [PERSON] et al. [106] introduced a two-step machine learning approach for atmospheric XCO\({}_{2}\) retrieval using a multilayer perceptron neural network. This method, applied to satellite spectral measurements, aims to efficiently retrieve atmospheric CO\({}_{2}\) column densities. The approach involves creating a database of pressure-based line-by-line (LBL) CO\({}_{2}\) absorption coefficients sourced from the HITRAN spectral database [107; 108].