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SCIENCE CHINA Earth Sciences, Volume 60 , Issue 2 : 286-296(2017) https://doi.org/10.1007/s11430-015-0247-9

An improved constraint method in optimal estimation of CO2 from GOSAT SWIR observations

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  • ReceivedJul 5, 2016
  • AcceptedSep 7, 2016
  • PublishedNov 21, 2016

Abstract

We propose an algorithm that combines a pre-processing step applied to the a priori state vector prior to retrievals, with the modified damped Newton method (MDNM), to improve convergence. The initial constraint vector pre-processing step updates the initial state vector prior to the retrievals if the algorithm detects that the initial state vector is far from the true state vector in extreme cases where there are CO2 emissions. The MDNM uses the Levenberg-Marquardt parameter γ, which ensures a positive Hessian matrix, and a scale factor α, which adjusts the step size to optimize the stability of the convergence. While the algorithm iteratively searches for an optimized solution using observed spectral radiances, MDNM adjusts parameters γ and α to achieve stable convergence. We present simulated retrieval samples to evaluate the performance of our algorithm and comparing it to existing methods. The standard deviation of our retrievals adding random noise was less than 3.8 ppmv. After pre-processing the initial estimate when it was far from the true value, the CO2 retrieval errors in the boundary layers were within 1.2 ppmv. We tested the MDNM algorithm’s performance using GOSAT L1b data with cloud screening. Our preliminary validations comparing the results to TCCON FTS measurements showed that the average bias was less than 1.8 ppm and the correlation coefficient was approximately 0.88, which was larger than for the GOSAT L2 product.


Funded by

The authors are grateful for the data shared by the GOSAT User Interface Gateway(GUIG)

TCCON data obtained from the TCCON Data Archive and hosted by the Carbon Dioxide Information Analysis Center (CDIAC^ tccon.onrl.gov). the State Key Program of the National Natural Science Foundation of China(41130528; the National Natural Science Foundation of China(Grant No. 41401387; the Green Path Program of the Beijing Municipal Science,Technology Commission (Grant No. Z161100001116013)


Acknowledgment

The authors are grateful for the data shared by the GOSAT User Interface Gateway (GUIG), and the TCCON data obtained from the TCCON Data Archive and hosted by the Carbon Dioxide Information Analysis Center (CDIAC, tccon.onrl.gov). This work was supported by the State Key Program of the National Natural Science Foundation of China (Grant No. 41130528); the National Natural Science Foundation of China (Grant No. 41401387); the Green Path Program of the Beijing Municipal Science and Technology Commission (Grant No. Z161100001116013).


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  • Figure 1

    Sample CO2 retrievals using two methods. (a) Sample retrievals using MDNM. (b) Sample retrievals using the γ-Rodgers method. (c) Differences between the true state vector, a priori constraint vector, and estimated state vector of CO2 concentration and the true state vector, when using the MDNM algorithm. (d) Differences between the true state vector, a priori constraint vector, and estimated state vector of CO2 concentration and the true state vector, when using the γ-Rodgers method. In (a) and (b), thick solid lines represent the true state vector; dotted lines are the a priori state vectors, and thin solid lines are the estimated profiles.

  • Figure 2

    Sample CO2 retrievals using two methods. (a) Sample retrievals using MDNM. (b) Sample retrievals using the γ-Rodgers method. (c) Standard deviation of estimated state vectors of CO2 concentrations to the true state vector, when using the MDNM. (d) Standard deviation of estimated state vectors to the true state vector, when using the γ-Rodgers method. In (a) and (b), thick solid lines represent the true state vector; dotted lines represent the a priori state vectors, thin solid lines represent the estimated profiles, and “○” shows the distribution of retrieved CO2 concentrations in each atmospheric layer.

  • Figure 3

    Sample CO2 retrievals using MDNM without initialization. (a) Sample retrievals; (b) differences between the true state vector, a priori constraint vector, and estimated state vector of the CO2 concentration and the true state vector, when using the MDNM.

  • Figure 4

    Sample CO2 retrievals using initialization step with the MDNM. (a) Sample retrievals; (b) differences between the true state vector, the initialized a priori constraint vector, and the estimated state vector of CO2 concentration and the true state vector, when using the MDNM. In (a), the thick solid line represents the true state vector; the dotted line represents the a priori state vector; the thin solid line represents the estimated profile, and the dashed line is the initialized a priori vector.

  • Figure 5

    Simulated spectrums in the 2 micron and oxygen-A band. Deep blue lines in (a) and (b) are observations without cloud scattering; and the magenta and green lines represent spectrums scattered by two different cirrus clouds; deep blue lines in (c) line represents observations without scattering; and the magenta and green lines represent spectrums scattered by two different aerosols.

  • Figure 6

    GOSAT observed spectrums in band 3 and band 1; the red line is the P polarization spectra and the green line represents the S polarization spectra. (a) and (b) show the observations in cloud-free scene; (c) and (d) show the observations in cloudy scene.

  • Figure 7

    Comparisons of satellite retrieved XCO2 to FTS measurements at Parkfalls, TCCON. The first panel contains the correlation scatter plots with the correlation coefficients, average bias, standard deviation of the bias, and a unit-slope line (red). The second panel gives the daily trend from 2010–2012. (a) and (c) show MDNM-based retrieval compared with FTS measurements; (b) and (d) show GOSAT Level 2 product compared with FTS measurements.

  • Figure 8

    Comparisons of satellite retrieved XCO2 to FTS measurements at Lamont, TCCON. The first panel contains the correlation scatter plots with the correlation coefficient, average bias, standard deviation of the bias, and a unit-slope line (red). The second panel gives the daily trend from 2010–2012. (a) and (c) show MDNM-based retrieval compared with FTS measurements; (b) and (d) show GOSAT Level 2 product compared with FTS measurements.

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