 1 is the n × 1 unit vector. The deterministic trend component (the temporal trend of XCH 4 as shown in Equation (2) and Figure 3) is tightly constrained since a lot of data available. As indicated by the fitted parameters, the uncertainties are very small compared to the predictive variance in the residual component. Therefore, the uncertainty in the regression mean term is not considered here.
To reduce the computational complexity and maintain local variability, data used in the prediction were searched within an appropriate space-time kriging neighborhood centered on the predicting point [22]. The kriging neighborhood used is a moving cylinder in space and time as described in Zeng et al. [44]. The radii of the search range are initially set to 300 km in space and 20 time-units. The 10 km and 1 time unit for each search process is used as the increment lags if the number of observations is less than 20 within the cylinder neighborhood. At the same time, we set the search range radii limits to 500 km and 40 time-units.

Precision Evaluation of the Mapping-XCH 4 Dataset
We evaluated the performance of the mapping XCH 4 dataset using cross-validation and compared it with TCCON measurements and CH 4 data simulated by the atmospheric transport model.
Cross-validation, which is a widely used method for evaluating the prediction accuracy of statistical models [51], can be used to evaluate the prediction accuracy of the spatiotemporal geostatistical method. Cross-validation is implemented by first removing the observation data and then making its prediction using the remaining data. As a result, two datasets, the predicted dataset ∧ Z s j, t j, j = 1, 2,..., N and the corresponding original dataset Z s j, t j, j = 1, 2,..., N, can be obtained. We selected four evaluation criteria, the correlation coefficient (R) between two datasets, the mean absolute prediction and the percentage of prediction error less than 15 ppb, and the population mean prediction error ME = 1 to evaluate the results [52]. Additionally, we also discussed the performance of the Mapping-XCH 4 dataset in detecting the spatial and timely variations from 2009 to 2020 over Monsoon Asia.  Figure 5, present a significant correlation coefficient (R 2 ) of 0.97 which indicate small prediction biases between the observed XCH 4 and the predicted XCH 4 data, where the mean MAE is generally 7.76 ppb and the standard deviation (STD) is 6.91 ppb. Figure 5a demonstrates a systematic bias where the observed XCH 4 tends to be larger than the predicted XCH 4 mostly at high concentrations, while it is smaller than the predicted XCH 4 mostly at lower concentrations. This is likely related to the effects of the sensor capability and sensitivity in GOSAT observations for areas with extremely high and low concentrations. The statistical results of cross-validation for the five regions are show in Table 2. It can be seen from Table 2 that the number of predicted data with MAE less than 15 ppb accounts for greater than 83 percent of all validated samples (N). The biases in Eurasia and North America are larger than those in the other regions likely due to the diverse and active surface XCH 4 emissions in the two areas. statistical results of cross-validation for the five regions are show in Table 2. It can be seen from Table 2 that the number of predicted data with MAE less than 15 ppb accounts for greater than 83 percent of all validated samples (N). The biases in Eurasia and North America are larger than those in the other regions likely due to the diverse and active surface XCH4 emissions in the two areas.  We can obtain the corresponding kriging variance as indicated in Equation (7) for each geostatistical prediction to evaluate the uncertainty of Mapping-XCH4 dataset. The kriging variance depends on both the density of XCH4 retrievals and the data homogeneity surrounding the prediction position. The denser the observations and more homogeneous the XCH4 variation surrounding the prediction position are, the lower the prediction uncertainty [53]. Figure 6a demonstrates the spatiotemporal variation in the kriging standard deviations (Kstd), which is the root of the kriging variance of the Mapping-XCH4 dataset from 2009 to 2020. Figure 6a shows that the uncertainty of Mapping-XCH4 is larger in mid-high latitudes, 35°N-65°N, and around the tropical region, 10°S, where Kstd ranges from 14 ppb to 17 ppb, and seasonally presents a maximum in December or January each year in these areas. In mid-low latitudes, the uncertainty is lower, and Kstd presents a maximum in July or August each year. These high uncertainties are likely due to fewer available observations, which can be seen in Figure 1, less homogeneous variation in XCH4 surrounding the prediction location induced by the effects of atmospheric conditions such as  We can obtain the corresponding kriging variance as indicated in Equation (7) for each geostatistical prediction to evaluate the uncertainty of Mapping-XCH 4 dataset. The kriging variance depends on both the density of XCH 4 retrievals and the data homogeneity surrounding the prediction position. The denser the observations and more homogeneous the XCH 4 variation surrounding the prediction position are, the lower the prediction uncertainty [53]. Figure 6a demonstrates the spatiotemporal variation in the kriging standard deviations (Kstd), which is the root of the kriging variance of the Mapping-XCH 4 dataset from 2009 to 2020. Figure 6a shows that the uncertainty of Mapping-XCH 4 is larger in mid-high latitudes, 35 • N-65 • N, and around the tropical region, 10 • S, where Kstd ranges from 14 ppb to 17 ppb, and seasonally presents a maximum in December or January each year in these areas. In mid-low latitudes, the uncertainty is lower, and Kstd presents a maximum in July or August each year. These high uncertainties are likely due to fewer available observations, which can be seen in Figure 1, less homogeneous variation in XCH 4 surrounding the prediction location induced by the effects of atmospheric conditions such as clouds, water vapor, aerosols, etc., and observation of the geometry of the sun-target-sensor geometry.

Evaluation of the
The magnitude of annual average Kstd, which is shown in Figure 6b, generally presents larger and strip variation in Eurasia compared with the other regions. In particular, Mapping-XCH 4 shows higher uncertainties in the southern area of Asia, where Kstd is up to 16 ppb. These results are likely induced by the available GOSAT observations, as shown Figure 1, and inhomogeneous XCH 4 variation and atmospheric conditions in these areas. clouds, water vapor, aerosols, etc., and observation of the geometry of the sun-target-sensor geometry. The magnitude of annual average Kstd, which is shown in Figure 6b, generally presents larger and strip variation in Eurasia compared with the other regions. In particular, Mapping-XCH4 shows higher uncertainties in the southern area of Asia, where Kstd is up to 16 ppb. These results are likely induced by the available GOSAT observations, as shown Figure 1, and inhomogeneous XCH4 variation and atmospheric conditions in these areas.

Comparison with TCCON Measurements
XCH4 from TCCON measurements has high accuracy and can be used for validation of the Mapping-XCH4 [54]. In this study, we selected 22 representative TCCON sites where XCH4 measurements were available from 2015 to 2019. We took 1° × 1° grid and one month as a space-time unit to calculate the mean values of TCCON. Figure 7 shows the biases of Mapping-XCH4 by the comparison of the XCH4 measurements (X-axis) over TCCON sites plotted in different colors and the Mapping-XCH4 (Y-axis) that coincide with TCCON sites in geolocation and time. As seen from Figure 7, the correlation coefficient (CORR), indicating consistency between Mapping-XCH4 and TCCON data, is as high as 0.92, and the mean absolute error (MAE), mean error (ME), and standard deviation (STD) are 8.1 ppb, 1.07 ppb, and 11.42 ppb, respectively.

Comparison with TCCON Measurements
XCH 4 from TCCON measurements has high accuracy and can be used for validation of the Mapping-XCH 4 [54]. In this study, we selected 22 representative TCCON sites where XCH 4 measurements were available from 2015 to 2019. We took 1 • × 1 • grid and one month as a space-time unit to calculate the mean values of TCCON. Figure 7 shows the biases of Mapping-XCH 4 by the comparison of the XCH 4 measurements (X-axis) over TCCON sites plotted in different colors and the Mapping-XCH 4 (Y-axis) that coincide with TCCON sites in geolocation and time. As seen from Figure 7, the correlation coefficient (CORR), indicating consistency between Mapping-XCH 4 and TCCON data, is as high as 0.92, and the mean absolute error (MAE), mean error (ME), and standard deviation (STD) are 8.1 ppb, 1.07 ppb, and 11.42 ppb, respectively.  Overall verification results by TCCON sites (Appendix A Table A1), the MAE is generally 8.10 ppb, while the largest MAEs are over Paris and Zugspitze located in Eurasia, which are 10.61 ppb and 14.60 ppb, respectively