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

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 gamma, which ensures a positive Hessian matrix, and a scale factor alpha, 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 gamma and alpha 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.