Seamless mapping of long-term (2010-2020) daily global XCO 2 and 1 XCH 4 from GOSAT, OCO-2, and CAMS-EGG4 with a 2 spatiotemporally self-supervised fusion method

. Precise and continuous monitoring on long-term carbon dioxide (CO 2 ) and methane (CH 4 ) over the globe is of great 14 importance, which can help study global warming and achieve the goal of carbon neutrality. Nevertheless, the available 15 observations of CO 2 and CH 4 from satellites are generally sparse, and current fusion methods to reconstruct their long-term 16 values on a global scale are few. To address this problem, we propose a novel spatiotemporally self-supervised fusion method 17 to establish long-term daily seamless XCO 2 and XCH 4 products from 2010 to 2020 over the globe at grids of 0.25°. A total of 18 three datasets are applied in our study, including GOSAT, OCO-2, and CAMS-EGG4. Attributed to the significant sparsity of 19 data from GOSAT and OCO-2, the spatiotemporal Discrete Cosine Transform is considered for our fusion task. Validation 20 results show that the proposed method achieves a satisfactory accuracy, with the 𝜎 (R

Quality Flag" and "XCH4 Quality Flag" are exploited to filter bad data. Relevant information of XCO2 and XCH4 products 118 from GOSAT is shown in Table 1.
119 Apart from GOSAT, the ACOS XCO2 retrieval algorithm is also applied to OCO-2 observations (Kiel et al., 2019), which 122 utilizes the same bands of the Oxygen-A, CO2 weak, and CO2 strong. OCO-2 provides a global XCO2 product at a high spatial 123 resolution of 1.29×2.25 km 2 with a revisit time of 16 days. After 2015, the XCO2 product from OCO-2 is used for fusion 124 instead of GOSAT due to its more observation counts and better accuracy. In this study, the scientific data record of "XCO2"

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in OCO2_L2_Lite_FP (level 2, bias-corrected) is applied in the fusion with CAMS-EGG4 using the developed method.

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Moreover, the quality assurance (QA) record of "XCO2 Quality Flag" is adopted to filter bad data. Since the OCO-2 XCO2 127 product of the latest version (V11r) is still on processing, both data of V10r and V11r are considered in our study. Related 128 information of XCO2 product from OCO-2 is given in Table 1.

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In our study, the XCO2 and XCH4 measurements provided by an international in-situ network, which is named after TCCON  Data pre-processing is an important procedure to ensure the rationality and reliability of fused results. In this study, the values 153 of "QA=0" in XCO2 and XCH4 from GOSAT and OCO-2 are discarded, which filters the bad data. Besides, the CAMS-EGG4

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XCO2 and XCH4 at a temporal resolution of 3 hours are averaged in a single day to produce daily datasets. Finally, the spatial 155 resolutions of XCO2 and XCH4 from GOSAT, OCO-2, and CAMS-EGG4 ought to be adjusted to the same value. A globally 156 covered grid of 721×1441 (0.25º) is employed in our study. The XCO2 and XCH4 from GOSAT, OCO-2, and CAMS-EGG4 3.2 Spatiotemporally self-supervised fusion method

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Since the sparsity of data from GOSAT and OCO-2 is significant in space-time domain (see Fig. 1), it is difficult to perform 162 fusion procedures for them. In contrast, frequency domain is more suitable because of its concentrated signal distribution. DCT

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is an efficient algorithm to transform signal into frequency domain (Rao and Yip, 2014), which has been widely applied in   198 where ‖ ‖ signifies the Euclidean norm; represents the binary mask showing the data is whether available or not; and

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∇ indicate a smoothing factor and the Laplace operator, respectively. This equation can be solved by iterations via Eq. (6):

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where is a relaxation factor to accelerate convergence; indicates a 3-dimensional filter related to the smoothing term,

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which is defined in Eq. (7): 205 Here, represents the d th value along the k th dimension (k = 1, 2, and 3); denotes the size of along the k th dimension.

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Namely, , , and stand for u, v, and w (see Eq. (1)), respectively. In this study, the number of total iterations, , and 207 are empirically configured to 100, 1.5, and a range from 10 3 to 10 -1 (spaced with 100 intervals), respectively. It is worth 208 noting that is initialized through the temporal nearest neighbor interpolation. Regarding the grids where the data is missing 209 during the whole temporal sequence, is initially set to 1. More details about the solution steps can be found in Garcia (2010).

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As shown in Fig. 3, the XCO2 from OCO-2 and XCH4 from GOSAT perform better than those from CAMS-EGG4, with larger

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As observed in Fig. 8 and 9, a large overestimation generally exists in the CAMS-EGG4 XCO2 from 2010 to 2014 and in 2020,    In our study, a novel spatiotemporally self-supervised fusion method, i.e., S-STDCT, is proposed to acquire long-term daily 345 seamless globally distributed XCO2 and XCH4 products from 2010 to 2020 at the grids of 0.25°. A total of three datasets are 346 adopted, which include GOSAT, OCO-2, and CAMS-EGG4. Since the data from GOSAT and OCO-2 is greatly sparse in Author contributions

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YW designed the study, collected and processed the data, analyzed the results, and wrote the paper. QQY and TWL provided 361 constructive comments on the paper. YJY, SQZ, and LPZ revised the paper. All authors contributed to the study.

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The contact author has declared that none of the authors has any competing interests.

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Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and 366 institutional affiliations.

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The authors would like to express gratitude to the Goddard Earth Science Data and Information Services Center for providing