Estimation of the Concentration of XCO₂ from Thermal Infrared Satellite Data Based on Ensemble Learning

Abstract

Global temperatures are continuing to rise as atmospheric carbon dioxide (CO₂) concentrations increase, and climate warming has become a major challenge to global sustainable development. The Cross-Track Infrared Sounder (CrIS) instrument is a Fourier transform spectrometer with 0.625 cm⁻¹ spectral resolution covering a 15 μm CO₂-absorbing band, providing a way of monitoring CO₂ with on a large scale twice a day. This paper proposes a method to predict the concentration of column-averaged CO₂ (XCO₂) from thermal infrared satellite data using ensemble learning to avoid the iterative computations of radiative transfer models, which are necessary for optimization estimation (OE). The training data set is constructed with CrIS satellite data, European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) meteorological parameters, and ground-based observations. The training set was processed using two methods: correlation significance analysis (abbreviated as CSA) and principal component analysis (PCA). Extreme Gradient Boosters (XGBoost), Extreme Random Trees (ERT), and Gradient Boost Regression Tree (GBRT) are used for training and learning to develop the new retrieval model. The results showed that the R² of XCO₂ prediction built from the PCA dataset was bigger than that from the CSA dataset. These three learning models were verified by validation sets, and the ERT model showed the best agreement between model predictions and the truth (R² = 0.9006, RMSE = 0.7994 ppmv, MAE = 0.5804 ppmv). The ERT model was finally selected to estimate the concentrations of XCO₂. The deviation of XCO₂ predictions of 12 TCCON sites in 2019 was within ±1 ppm. The monthly averages of XCO₂ concentrations in close agreement with TCCON ground observations were grouped into four regions: Asia (R² = 0.9671, RMSE = 0.7072 ppmv), Europe (R² = 0.9703, RMSE = 0.8733 ppmv), North America (R² = 0.9800, RMSE = 0.6187 ppmv), and Oceania (R² = 0.9558, RMSE = 0.4614 ppmv).

1. Introduction

Since the beginning of industrialisation, humanity’s pursuit of sustainable development has led to increasing greenhouse gas emissions. This significant rise in worldwide atmospheric carbon dioxide concentrations has escalated from 280 ppmv before the industrial revolution to 413.2 ppmv in 2020 [1]. The present extent of human-induced pollution and the unregulated release of greenhouse gases into the atmosphere have the potential to exacerbate signs of global climate change such as global warming, shifts in precipitation patterns, the thawing of glaciers, and the escalation of sea levels [2]. These issues have caused significant concern in the international community. In response to the challenge of climate change, the United Nations Paris Agreement was adopted at the 2015 Paris Climate Change Conference. The primary aim of the agreement is to restrict the rise in global average temperature, keeping it well below 2 °C, or even 1.5 °C [3]. Concerted efforts must be initiated to reduce carbon emissions and increase carbon sequestration through a range of socio-economic and technological interventions [2].

Concentrations of atmospheric trace gases are observed using spectrometers or air-sampling instruments. However, column-averaged concentrations are usually retrieved from spectrometers on the ground or onboard space aircraft. Ground-based measurements are effective in precisely determining trace gas concentrations. Nonetheless, the assessment of CO₂ levels is limited by sparse spatial and temporal coverage [4]. In contrast, spaceborne measurements characterized by high spatiotemporal resolution are widely regarded as the most efficacious means of capturing spatial and temporal variations in CO₂ distributions [5]. Satellite observations are suitable for “bottom-up” inversion to improve the accuracy of carbon sink estimations [6].

Thermal infrared (TIR) detectors [7] and near-infrared (NIR) detectors [8] are two primary methods of monitoring the concentration of CO₂ in space. Thermal infrared hyperspectral sensors receive thermal radiation from the Earth’s surface, and are sensitive to the CO₂ absorption in the mid to upper troposphere. In contrast, short-wave infrared detectors receive solar radiation reflected from surfaces, having sensitivities to CO₂ absorption near the surface, but being affected by clouds and water vapour [9]. CrIS onboard NOAA-20, launched in 2017 and featuring accurate radiometric and spectral calibration, can provide observations in long time series. When considering a machine learning model to estimate CO₂ concentrations, a sufficient number of samples can improve the model’s ability to generalize, reduce the risk of overfitting, and consequently improve the model’s predictive accuracy [10]. CrIS has much wider range than these SW IR sensors, and can provide more observations for modelling.

The physical retrieval model has commonly been used to estimate the concentrations of CO₂ from satellite measurements. Zhang et al. [11] conducted a CO₂ optimal estimation using CrIS full resolution spectral data, with an R² of 0.72 and an RMSE of 0.45 ppmv when compared with measurements from the Civil Aircraft for the Regular Investigation of the Atmosphere Based on an Instrument Container (CARIBIC). The iterative inverse process is prone to nonconvergence due to the nonlinear radiation transfer equation and the difficulty of obtaining accurate atmospheric state parameters [12]. Zhao et al. [13] proposed a two-step machine learning model based on Greenhouse gases Observing SATellite (GOSAT) clear sky radiances, achieving a mean error (ME) of 0.09 ppmv and an RMSE of 3.13 ppmv, compared to GOSAT Level 2 product data. David et al. [14] proposed a neural network model (NN) for CO₂ concentration estimation, with a precision of 0.8 ppmv, indicating that when trained on a representative dataset, the NN model offers slightly superior accuracy compared to the fully physical algorithm. This work demonstrated that both machine learning and neural network models can achieve high accuracy in predicting CO₂ concentrations.

Ensemble learning is a meta-method that improves the performance of a model by combining multiple machine learning models, and mitigates the risk of overfitting often seen in machine learning algorithms when dealing with challenges like imbalanced, multidimensional, and noisy data [15]. This approach can improve the overall forecast accuracy and stability. In this paper, we employed three models to predict the concentration of XCO₂ from thermal infrared satellite data using ensemble learning. The dataset used for training was constructed using CrIS satellite data, ERA5 meteorological parameters, the normalised difference vegetation index (NDVI), surface parameters, DEM, and ground-based observations; the training set was processed using two methods: correlation significance analysis and principal component analysis (PCA). Comparing between model predictions and the truth in three ensemble learning algorithm models, we identified the most suitable model for estimating CO₂ concentrations using thermal infrared data. This research provides a precise and efficient model algorithm for CO₂ concentration estimation.

2. Data Sources and Processing

2.1. Data Sources

We used column-averaged concentrations of CO₂ from TCCON sites as reference benchmarks to build the dataset and validate the accuracy of the model [16]. Parameters were derived from CrIS, ERA5, and products from other satellites for describing representative features in spectral, spatial-temporal, meteorological and surface domains.

2.1.1. TCCON Data

The Total Carbon Column Observing Network (TCCON) is a global observational network that gathers high-precision atmospheric greenhouse gas (primarily CO₂ and CH₄) concentrations from ground-based Fourier transform spectrometers. TCCON was established in 2004, and has expanded from its initial 3 sites to the current 26 official sites [17]. Figure 1 illustrates the distribution of TCCON sites, primarily located in North America, Europe, and the East Asia.

The concentrations of XCO₂ were processed with the Gas Fit (GFIT) algorithm, a non-linear least-squares fitting method [18], which involves generating a synthetic spectrum by fine-tuning a priori profiles to achieve the closest match with the observed spectrum. The total column amounts of CO₂ were integrated from the adjusted CO₂ profile, and the concentrations of XCO₂ were divided by the total column amount of dry air [19]. This study used the latest version of the TCCON data (GGG 2020) [20], from all 26 sites in 2019. The detailed information of TCCON sites is listed in

Table 1. Information for TCCON stations used for validation.

Name	Lon	Lat	Number	Name	Lon	Lat	Number
Xianghe	116.96	39.8	16,075	Rikubetsu	143.77	43.46	3976
Hefei	117.17	31.91	3002	SaintDenis	26.63	67.37	9825
Zugspitze	10.98	47.42	3567	Paris	2.36	48.85	21,442
Wollongong	150.88	−34.41	19,508	ParkFalls	−90.27	45.94	21,986
Tsukuba	140.12	36.05	13,990	Trainou	2.11	47.97	15,753
NyAlesund	11.92	78.92	4736	Lamont	−97.49	36.6	28,766
Lauder	169.68	−45.04	42,984	Eureka	−86.42	80.05	7652
Karlsruhe	8.44	49.1	8229	EastTrout	−104.99	54.36	39,992
Saga	130.29	33.24	15,147	Edwards	−117.88	34.96	57,555
Izana	−16.48	28.3	12,940	Darwin	130.89	−12.43	12,838
Garmisch	47.48	11.06	8803	Caltech	−118.13	34.14	36,000
Bremen	8.85	53.1	1451	Burgos	120.65	18.53	32,649
Sodankyla	26.63	67.37	13,050	Nicosia	33.38	35.14	10,476

.

2.1.2. CrIS

The Joint Polar Satellite System-1 (JPSS-1) satellite was successfully launched into space from Vandenberg Air Force Base on 18 November 2017. Mounted on the satellite, the CrIS (Cross-track Infrared Sounder) is a Fourier-transform infrared spectrometer equipped with a total of 2211 infrared detection channels. ATMS (Advanced Technology Microwave Sounder) is a microwave sensor with 22 channels, operating within a frequency range from 23 GHz to 183 GHz. The CLIMCAPS (Community Long-Term Infrared Microwave Coupled Product System) algorithm was employed for the analysis of the infrared and microwave well-calibrated radiance of this CrIS/ATMS. Due to the significant impact of clouds on observations from the infrared detector, cloud-clearing processing was applied, yielding cloud-cleared radiance L2 products, which provides radiation that is free of cloud and fog interference. The data are generated at 6 min intervals, covering 30 positions horizontally and having 45 data points along the orbit. With a spatial resolution of 50 km, this dataset has one of the highest spatial and temporal resolutions of the data sets currently available for meteorological analysis [21,22,23].

2.1.3. ERA5

The European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) is a fifth-generation global climate reanalysis dataset. It provides high-spatial-resolution and high-temporal-resolution meteorological fields worldwide, including various meteorological and cloud parameters such as temperature, precipitation, wind speed, and atmospheric pressure. ERA5 features a spatial resolution of 0.25° and a temporal resolution of 1 h, establishing its status as the most high-resolution global meteorological reanalysis dataset available to date [24].

To further investigate the influence of cloud and meteorological features on CO₂ concentration, this study acquired meteorological parameters including temperature, wind components (U and V), and vertical velocity within the pressure range of 100 to 1000 hPa. Additionally, data related to cloud features were collected, including boundary layer height (blh), cloud base height (cbh), total cloud cover (tcc), and total precipitation (tp). Furthermore, gas-related data, such as total ozone column concentration (tco₃) in the atmosphere, were also obtained.

2.1.4. Other Parameters

The normalized difference vegetation index (NDVI) is an indicator used to assess the extent of vegetation coverage and its growth conditions. The concentration of CO₂ is highly affected by the condition of surface vegetation [25]. In this work, NDVI values were extracted from MODIS (MOD13Q1 [26]) with a spatial resolution of 250 m and a temporal resolution of 16 days.

Surface parameters such as surface emissivity and skin temperature are crucial for upward atmospheric radiation [27,28]. In this work, the surface reflectance was extracted from MODIS (MOD09GA [29]), in the infrared band (620–670 nm) with a spatial resolution of 500 m.

There is also a certain relationship between site elevation and XCO₂ concentration. Additionally, the elevation was extracted from Global Land One km Base Elevation (GLOBE) (GLOBE Topography [30]) with a spatial resolution of 1 km.

2.2. Data Processing

TCCON carries out continuous measurements of data at 90 s intervals on a daily basis. For each TCCON site, we calculated the mean and standard deviation of XCO₂ concentrations. Then, we removed the data that exceed three times the standard deviation. Finally, we recomputed the mean of the remaining values to obtain the corrected daily XCO₂ concentration for each site [13]. The processing of parameters as trained by CrIS included the following operations. (1) The reciprocal of the cosine of the solar zenith angle and the zenith angle were found, respectively, and the sine of the difference between the solar azimuth angle and the satellite azimuth angle was found. (2) The spectral channels were selected in the range of 648.75 cm⁻¹ to 1096.875 cm⁻¹, giving a total of 717 channels. Due to variations in the temporal and spatial resolutions of the parameters involved in the modelling process, it was necessary to perform spatiotemporal matching. This involved standardizing the data to a daily temporal resolution and a spatial resolution of 1° [17]. We performed daily averaging on the hourly data provided by ERA5 meteorological reanalysis. The MODIS NDVI and surface reflectance data have different temporal resolutions (16 days and daily, respectively). These parameters used daily column-averaged CO₂ concentrations from TCCON sites as reference benchmarks to build the dataset. The specific information of the features used for model training is listed in

Table 2. The specific feature information used in model training.

Variable Abbreviation	Full Name of the Variable	Unit	Temporal Resolution	Spatial Resolution	Data Sources
XCO2	Column-averaged CO2 dry air mole fraction	ppmv	-	-	TCCON
lon	Longitude		6 min	50 km × 50 km	Cloud-cleared radiances V2
lat	Latitude
month	Month	m
dd	Days	d
band	Radiance	mw/(m2 sr cm−1)
sza	Solar zenith angle	-
saa	Solar azimuth angle	degree
za	Zenith angle	-
aa	Azimuth angle	-
P1 *	100 hpa	hPa	1 h	0.25° × 0.25°	ERA5
T1 *	Temperature at 100 hpa	K
U1 *	U-component of wind at 100 hpa	m/s
V1 *	V-component of wind at 100 hpa	m/s
W1 *	Vertical velocity at 100 hpa	pa/s
blh	Boundary layer height	m
cbh	Cloud bottom height	m
tp	Total precipitation	-
cl	Lake cover	-
tcc	Total cloud coverage	-
skt	Skin temperature	K
t2m	2 m Temperature	K
tco3	Total column ozone	kg/m−2
NDVI	Normalized difference vegetation index	-	16 d	250 m × 250 m	MOD13Q1
SR	Surface reflectance	%	1 d	500 m × 500 m	MOD09GA
DEM	Digital elevation model	m	-	-	GLOBE Topography

* T, U, V, and W at different vertical air pressures from 100–1000 hPa.

.

3. Methodology

Machine learning is a branch of artificial intelligence whose primary aim is to enable computers to automatically learn from data and use the acquired knowledge for prediction or decision making [31]. Models in machine learning are mathematical algorithms that learn from data to make predictions, classifications, or decisions on unseen data by identifying patterns and relationships in the information; many machine learning models have been developed and are widely used, including neural networks (NNs), random forest (RF), support vector machines (SVMs), convolutional neural networks (CNNs), etc. [32]. Ensemble learning has shown good consistency in gas concentration inversion studies [33]. This study analyses and compares three ensemble learning algorithms: Gradient Boosting Decision Trees (XGBoost), Gradient Boosting Regression Trees (GBRT), and Extremely Randomized Trees (ERT), with the aim of selecting the optimal estimation model.

3.1. Ensemble Learning Methods

Ensemble learning is a machine learning approach whose core idea is to enhance the overall performance and robustness of a model by combining the predictions of multiple individual models [34]. Ensemble learning methods are primarily divided into two main categories: bagging and boosting. Bagging involves the creation of many subsamples through random sampling with replacement. Each of these subsamples is then utilized to train an individual base model. The final prediction results from these models are combined through averaging or voting [35]. By contrast, boosting modifies the weights of the samples in each iteration, based on the prediction errors from the previous stage; the final ensemble model is ultimately obtained by aggregating the predictions of all the base models through weighted combination [36]. By combining predictions from several models, ensemble learning can efficiently employ different models’ strengths, address individual models’ weaknesses, and improve prediction accuracy and generalization capabilities. This approach has been demonstrated in practical applications to significantly enhance model performance, making it adaptable to a broader range of data and problems [37].

Extreme Gradient Boosting (XGBoost) stands out as an optimized distributed gradient boosting algorithm, notable for its expedited computational performance compared to contemporary popular machine learning models. This model incorporates a regularization term within the loss function to manage the model’s complexity. The adjusted loss function is elucidated through the utilization of the two-dimensional Taylor formula. This strategic refinement effectively addresses the issues of overfitting inherent in conventional gradient boosting models, concurrently augmenting the model’s accuracy and its generalization capabilities [38]. Gradient Boosted Regression Trees (GBRT) constitute a supervised machine learning technique that was first conceptualized by Friedman in 2001. It embodies the concept of a robust learner, weighted by an ensemble of multiple weaker learners. Each of the weaker learners is represented as an individual regression decision tree, and every subtree is oriented toward learning in the direction of the negative gradient associated with the residuals from the preceding tree. Through continuous iterations aimed at minimizing the loss function, the GBRT prediction model is systematically forged. The algorithm predominantly comprises the stages of expanding regression decision trees, judiciously pruning these trees and harmoniously amalgamating them into a coherent ensemble [39]. Compared with traditional random forest, Extremely Randomized Trees (ERT) employ the entire dataset to train individual decision trees. This ensures the effective utilization of training samples and contributes to a reduction in the final prediction bias. To maintain distinct structural variations among each decision tree, ERT introduces increased randomness to node splitting. Specifically, it involves the random selection of division thresholds for each feature from the sub-dataset, and the optimal partition attribute is chosen based on the best division according to the specified threshold feature [40].

3.2. Model Evaluation Methodology

The model’s performance was evaluated using the squared coefficient of determination (R²), which determines the extent to which the model explains the variance in the observations [41]. Furthermore, the root mean square error (RMSE) was used to illustrate the standard deviation of residuals (prediction error) [42], whereas the mean absolute error (MAE) calculated the average absolute difference between model predictions and observed values [43]. The TCCON observation was set as y_i, $\overline{y}$_i is the mean of the TCCON observation, $\widehat{y}$_i is the model prediction, and n is the number of samples.

$R^2$ is computed as follows:

$$R^2=1-\frac{{\displaystyle {\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}}{{\displaystyle {\sum }_{i=1}^{\mathrm{n}}{(y_i-{\overline{y}}_i)}^2}}$$

(1)

The $RMSE$ is the square root of the mean of the squared deviations between predicted values and observed values. The formula is as follows:

$$RMSE==\sqrt{\frac{{\displaystyle {\sum }_{i=1}^{\mathrm{n}}{(y_i-{\widehat{y}}_i)}^2}}{n}}$$

(2)

The $MAE$ is the mean of the absolute disparities between predicted values and observation values. The formula is as follows:

$$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|y_i-{\widehat{y}}_i\right|}$$

(3)

3.3. Technical Flowchart

The estimation process of the concentration of XCO₂ from thermal infrared satellite data based on ensemble learning in the thermal infrared is shown in Figure 2. Firstly, the data were standardized to a daily temporal resolution and a unique spatial resolution of 1°. Due to the large number of features, two methods were employed to construct datasets to select the optimal feature parameters: correlation significance analysis and principal component analysis. The datasets were randomly divided into training sets (80%), testing sets (10%), and validation sets (10%). Three different ensemble learning models (ERT, XGBoost, GBRT) were employed and compared over two datasets. The final objective is to choose the model with the lowest RMSE in the estimation of XCO₂ concentration.

4. Feature and Model Experiments

This study employed correlation and significance analysis and principal component analysis (PCA) to select the characteristic variables. Improving training speed by reducing features and reducing interference noise to reduce the risk of overfitting improves model effectiveness, we chose a training set that is more suitable for building an ensemble learning model. The experiments were carried out using XGBoost, GBRT, and ERT with two datasets.

4.1. Correlation and Significance Analysis

Correlation and significance analysis can be employed to filter out unimportant features, reduce the number of features, enhance model accuracy, and reduce runtime. The Pearson correlation coefficient is typically denoted as “r”, and is used as a statistical measurement to assess the strength of the linear relationship between two continuous variables [44]. Significance is commonly represented using p-values and is also used to filter out unimportant features [45].

In Figure 3, the heat map of correlation coefficients shows a positive correlation in red and a negative correlation in blue, and the number of stars shows the level of significance. Sensitivity was assessed in each case by examining the correlation coefficient^® and its level of statistical significance (p-value). XCO₂ showed a positive correlation with lat, DEM, blh, cl, and tco₃, with a significance of 0.01. Among these factors, tco₃ has the highest positive correlation, which is 0.27. XCO₂ showed a negative correlation with lon, month, dd, NDVI, skt, and t2m, and NDVI showed the highest negative correlation of −0.21. Other features exhibited low or no correlation with XCO₂, so they were all removed. Ultimately, lat, lon, month, dd, NDVI, skt, t2m, DEM, blh, cl, and tco₃ were retained. The selection of spectral bands involved choosing two channels around 15 µm that are sensitive to CO₂ but not sensitive to other variables, based on the Jacobian function, as mentioned in [11]. Figure 4 illustrates the selected bands, denoted by red lines. The final selected two spectral bands corresponded to radiance at wavelengths of 668.75 cm⁻¹ and 701.875 cm⁻¹.

4.2. Principal Component Analysis

Principal component analysis (PCA) is a widely used method for data dimensionality reduction and extracting essential information [46]. This process involves finding a new set of orthogonal feature vectors, also known as principal components, that capture the variability in the original data in a particular way, allowing for an efficient representation of the data in lower dimensions while maximising the retention of information in the data. By selecting an appropriate number of principal components, it is possible to achieve dimensionality reduction in the data, reducing redundancy and enabling a deeper understanding and analysis of the data [47].

In this work, principal component analysis was conducted on 717 channels within the spectral range of 648.75 cm⁻¹ to 1096.875 cm⁻¹ which had information on CO₂ absorption, and the first three principal components scores were computed to represent the information from 717 channels. Similarly, principal component analysis was conducted on meteorological data on ten pressures (100–1000 hPa), and temperature (T), vertical wind speed (U), horizontal wind speed (V), vertical wind speed (W) on these ten pressures, and the first three principal components were selected to represent meteorological data. Additionally, one principal component was chosen to represent satellite observed geometry information. Additionally, surface parameters such as NDVI, SR, and DEM have become crucial for the upward atmospheric radiation. The initial dataset was constructed by employing spatial–temporal and spectral characteristics as reference benchmarks. This study investigates the influence of additional parameters on model correctness through the utilization of the ERT model. Figure 5 illustrates the values of R², RESE, and MAE for the ERT model that was trained using various features. The results demonstrated that the features such as NDVI, SR, and PCA scores of the observed geometry information of satellites (abbreviated as SOA) resulted in a noteworthy enhancement of the R² value of the model. Furthermore, a decrease in RMSE and MAE values suggested a favourable impact of these features on the overall performance of the model. The first three principal components score of meteorological data and DEM exhibited a minimal or negligible impact on the accuracy of the model. Consequently, these features were excluded from the dataset.

4.3. Model Training Comparison

Three distinct ensemble learning models, namely ERT, XGBoost, and GBRT, were utilized for training. The determination of the optimal selection of primary parameters for the three ensemble learning models was achieved by optimizing model parameters. The model parameter settings can be found in

Table 3. Detailed settings of model parameters.

Model	n_Estimators	Max_Depth	Min_Samples_Split	Min_Samples_Leaf
ERT	400	30	5	1
GBRT	300	25	5	5
XGBoost	400	30	8	0.2

. The adjustment of parameter configurations will improve the performance of the model during both the training and prediction stages, hence guaranteeing more precise and dependable forecasting outcomes [48].

Figure 6 showed a scatter plot of the XCO₂ concentration of the three different ensemble learning models (ERT, XGBoost, GBRT), with datasets derived from the testing dataset. Comparing these three models, the R² of XCO₂ prediction built from the PCA was found to be significantly higher than that from the correlation and significance analysis. The ERT model demonstrated the best agreement (as shown in

Table 4. The various evaluation metrics of the model training results.

Model	R2	RMSE (ppmv)	MAE (ppmv)
ERT (PCA)	0.9231	0.7552	0.5568
ERT (CSA)	0.9029	0.8026	0.5704
GBRT (PCA)	0.9067	0.7907	0.5812
GBRT (CSA)	0.8938	0.8458	0.6163
XGBoost (PCA)	0.8995	0.8382	0.6371
XGBoost (CSA)	0.8701	0.9368	0.6777

), with an R² of 0.9231, an RMSE of 0.7552 ppmv, and a MAE of 0.5568 ppmv. The result showed that the R² of the ERT model was higher, and the RMSE and MAE were lower than those of the other models.

5. Validation

Figure 7 shows a scatter plot of predicted XCO₂ concentration in the validation set. These three learning models were validated using validation sets. The results show that the R² values were 0.9006, 0.8720, and 0.8769 for ERT, GBRT, and XGBoost, respectively. The RMSE values were 0.7994, 0.9068, and 0.8897, and the MAE values were 0.5804, 0.6705, and 0.6624(as shown in

Table 5. Validation results of the three models.

Model	R2	RMSE (ppmv)	MAE (ppmv)
ERT	0.9006	0.7994	0.5804
GBRT	0.8720	0.9068	0.6705
XGBoost	0.8768	0.8897	0.6624

). The ERT had the highest R² and the lowest RMSE and MAE. Combining these with consideration of three model evaluation indicators, the ERT model showed the best agreement in model validation, with high prediction accuracy and minimal prediction errors. Thus, the ERT model was finally selected to estimate the concentrations of XCO₂.

The mean and standard deviation of the XCO₂ concentrations obtained from 12 TCCON stations in the validation set were compared with the XCO₂ concentrations predicted by the ERT model in Figure 8. The Xianghe station in China exhibited the highest concentration of XCO₂, as indicated by a model projected value of 412.33 ppmv and an observed value of 412.17 ppmv. The Lauder station in New Zealand exhibited the lowest concentration of XCO₂, as evidenced by the observed value of 406.86 ppmv compared to the model projected value of 406.96 ppmv. The mean and standard deviations of XCO₂ concentrations at various stations were within ±1 ppmv. The results indicate that the XCO₂ concentrations at various longitudes and latitudes were accurately predicted by the ERT model.

Based on the global distribution of TCCON sites, the results of ground-based observations and model predictions were categorized into four groups: such as Asia, Europe, South America, and Oceania. The model predicted results were compared with the monthly means and standard deviations of the TCCON measurements (as shown in Figure 9). The R² and RMSE values for the monthly mean values of TCCON observations and model predictions are as follows in the four regions: Asia (R² = 0.9671, RMSE = 0.7072 ppmv), Europe (R² = 0.9703, RMSE = 0.8733 ppmv), North America (R² = 0.9800, RMSE = 0.6187 ppmv), and Oceania (R² = 0.9558, RMSE = 0.4614 ppmv). The monthly averages of XCO₂ concentrations of model prediction and TCCON observations are generally consistent in the four regions. The concentration of XCO₂ at the sites located in Asia, Europe, and North America demonstrate a declining pattern throughout June to August, followed by a steady increase in the subsequent months from August to December.

The model prediction exhibits significant agreement with the TCCON observations in most months, notably in the trends of XCO₂ concentration seasonal fluctuations during the summer and autumn. The results suggest that the model exhibits a strong ability to estimate XCO₂ concentrations on a monthly basis. However, the accuracy of model predictions in the Oceania region is limited due to a lack of samples.

6. Conclusions

In this work, three ensemble learning models were used for the prediction of column-averaged CO₂ concentrations from thermal infrared satellite data. These estimations were based on data obtained from the CrIS satellite, ERA5 meteorological parameters, and ground-based observations. The study involved a comparison of datasets generated using two methodologies in order to identify the most suitable model. Research indicates the following conclusions:

(1) The primary determinants affecting the evaluation of the concentration of XCO₂, as studied through correlation and significance analysis, encompass latitude, NDVI, and TCO₃. The correlations between XCO2 and these variables are 0.18, −0.17, and 0.26, showing a strong correlation between the concentration of CO₂ and the seasonal variation in biomass. The PCA showed that the features such as NDVI, SR, and PCA scores of the observed geometry information of satellites could raise up the R² of the model. The NDVI showed a substantial influence on both datasets and warranted careful consideration as a pivotal feature in forthcoming CO₂ retrieval procedures.

(2) The dataset constructed using PCA leads to improved accuracy in the estimation of XCO₂ concentrations. The ERT model demonstrated the highest estimation accuracy based on several evaluation indicators, including an R² value of 0.9231, an RMSE value of 0.7552 ppmv, and an MAE value of 0.5568 ppmv.

(3) The model predictions agree well with the measurements from the TCCON sites in industrial regions, including Xianghe, Saint Denis and Caltech, showing higher XCO₂ concentrations than other sites. The examination of monthly trends indicates the existence of seasonal variations in XCO₂ levels across multiple sites in Asia, Europe, and North America. It is worth noting that the lowest concentration of XCO₂ appears in August. TCCON station observations have high precision, but the scarcity of globally effective observation sites results in very limited observational data. Looking ahead, as the number of observation sites continues to grow, our model presents a valuable tool for estimating regional CO₂ concentrations. Furthermore, it enables the analysis of spatiotemporal variations in CO₂ concentrations, particularly focusing on key urban areas. This research contributes to the broader understanding of carbon dioxide dynamics, aiding in the development of targeted strategies for environmental management and policy formulation.