A High-Resolution MCMC Method for Aerosol and Trace Gas Profile Retrieval from MAX-DOAS Observations

Correspondence to: Pinhua Xie (phxie@aiofm.ac.cn), Xin Tian (xtian@aiofm.ac.cn)

Boundary layer processes detected by Multi-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS) often occur at fine vertical scales, which necessitates high-resolution profile retrieval. This study introduces a Markov Chain Monte Carlo (MCMC) approach that uses an Ensemble Sampler with dynamically adjusted parallel sampling chains to ensure effective mixing in high-dimensional spaces. MCMC globally explores the parameter space, directly evaluates the full nonlinear forward model, and generates complete posterior probability distributions. Meanwhile, the study uses a two-stage decoupling strategy based on O₄ observations. In the first stage, to avoid under-constraint and overfitting issues, MCMC retrieves aerosol extinction profiles at 100-meter resolution from O₄ slant column densities. In the second stage, the posterior aerosol field is used as a fixed constraint to retrieve trace gas concentration profiles at 50-meter resolution. This approach reduces the high-dimensional joint optimization to sequential low-dimensional subproblems, which decreases parameter correlations and enhances MCMC sampling efficiency. The two-stage decoupling also allows MCMC to adopt optimal parallel sampling chain configurations for each stage’s dimensional state vector, ensuring stable retrieval of high-dimensional posterior distributions at fine vertical grids. Comparison with CALIPSO satellite data shows that MCMC-retrieved aerosol profiles achieve an R² of 0.875 and an RMSE of 0.11 km^-1. Validation against sun photometer CE318 observations reveals that the MCMC-retrieved aerosol optical depth (AOD) achieves an R² of 0.935 with a relative bias of 10.9%, confirming the algorithm's accuracy. Compared to algorithm model data from AIOFM, AUTH, and Suwon obtained from the CINDI-3 comparison activity, NO₂ vertical profiles achieve an R² of 0.9 with a relative bias of 11%. Further validation with ground-based near-surface NO₂ concentration measurements reveals that MCMC-retrieved NO₂ concentrations at 50-meter trace gas resolution result in an R² of 0.912 and an RMSE of 2.95 ppb, compared to an R² of 0.825 and an RMSE of 3.85 ppb at 200-meter resolution. Increasing the vertical resolution improves the NO₂ correlation by 11% and reduces the RMSE by 23%. Therefore, MCMC effectively addresses challenges associated with nonlinearity, non-Gaussian posterior distributions, and high-dimensional sampling, leading to improved vertical resolution in MAX-DOAS profile retrieval.