Retrieval algorithm of aerosol extinction, scattering and absorption coefficient profiles based on MAX-DOAS

Uncertainty in aerosol radiative forcing is partly driven by poorly constrained vertical profiles of aerosol optical properties. We developed a multi-axis differential optical absorption spectroscopy (MAX-DOAS) algorithm based on optimal estimation, coupling vector linearized discrete ordinate radiative transfer model with the Henyey-Greenstein phase function to retrieve aerosol extinction profiles and single-scattering albedo (SSA) from multi-angle, multi-wavelength observations; scattering and absorption profiles are then derived. Total uncertainties are 11.55–16.63% for 360 nm extinction and 12.51–16.55% for SSA. Synthetic tests with exponential, box-shaped, and Gaussian extinction profiles confirm that retrieval errors fall within these bounds. Continuous observations in Hefei (December 2024–November 2025) show winter maxima and summer minima in extinction, scattering, and absorption, with bimodal autumn–winter and weak spring–summer diurnal variations. Screening based on free-tropospheric extinction fraction, relative humidity, and the near-surface PM2.5/PM10 ratio limits potential biases from vertical SSA inhomogeneity. At Shouxian, retrieved scattering and absorption agree with in situ measurements (r = 0.77 and 0.75, respectively). These results establish a systematically validated and feasible approach for using MAX-DOAS to simultaneously retrieve the vertical distributions and spatiotemporal evolution of multiple aerosol optical properties.