AecroFormer: First Noise-Robust Aerosol Microphysical Retrieval With Transformer Framework for Multiwavelength Raman Lidar Data

In this study, we present AecroFormer, a novel neural network model for aerosol microphysical retrieval from multi-wavelength Raman lidar observations. Integrating Multi-Head Attention (MHA) into a lightweight MLP backbone, AecroFormer addresses the limitations of traditional retrieval methods in terms of accuracy, noise sensitivity, and computational efficiency. The model effectively captures the nonlinear and coupled relationships inherent in inversions based on Mie light-scattering theory, which assumes spherical particle geometry. It is trained on 1.1 million synthetic samples using various channel combinations (e.g., 3β+3α, 3β+2α), where β represents particle backscatter coefficients and α represents particle extinction coefficients at one or more of the commonly used observation wavelengths (355, 532, and 1064 nm). Under 10% Gaussian noise, AecroFormer achieves mean absolute errors below 0.07 (m<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub>) and 0.015 (m<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub>) of the real and imaginary part of the complex refractive index of aerosol particles. AecroFormer keeps the relative error of the effective radius (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub>) of the investigated monomodal particle size distributions below 30%. The per-point inference time is 7.4×10⁻⁵ seconds. The 3β+2α configuration is identified as the minimal viable Raman lidar setup, with extinction channels critical for constraining refractive index–related parameters. Validation is limited by the availability of suitable datasets. However, we identified one published case that enabled testing the AecroFormer concept using real lidar and in-situ aircraft observations, confirming its physical consistency under realistic atmospheric conditions. Overall, AecroFormer offers a robust, generalizable, and efficient solution for lidar-based aerosol retrieval, demonstrating strong potential for operational deployment.