Study on Atmospheric Stratified Iterative Inversion Algorithm Based on Fernald Algorithm

Objective Accurate retrieval of the vertical profile of atmospheric aerosol and cloud extinction coefficients is essential for understanding climate change, improving weather forecasting accuracy, and monitoring air quality. However, traditional lidar inversion algorithms such as the Fernald algorithm rely on several simplifying assumptions, including a constant lidar ratio, a fixed calibration height with known aerosol backscatter, and predefined integration paths. These assumptions introduce significant errors, particularly under complex atmospheric conditions where cirrus clouds coexist with varying aerosol layers. This study aims to address these limitations by proposing a stratified iterative inversion algorithm that improves the accuracy and stability of lidar-based atmospheric extinction profile retrievals. Methods The proposed approach builds upon the classic Fernald inversion framework by introducing a stratified iterative refinement strategy. First, cloud layers are automatically identified using a combination of slope analysis and an adaptive threshold method applied to smoothed lidar backscatter signals. The slope algorithm detects cloud base heights by searching for regions with consecutively increasing signal slopes over at least five adjacent bins, while the adaptive threshold distinguishes cloud tops based on background noise levels. Once cloud boundaries are established, the algorithm applies a bisection-based iterative adjustment of the lidar ratio within the cloud regions. The iterative process minimizes discrepancies in backscatter coefficients between cloud base regions under cloudy conditions and reference values obtained from adjacent clear-sky measurements. This approach ensures consistent aerosol backscatter estimates while adaptively refining cloud lidar ratios without requiring external multi-wavelength or Raman lidar data. To quantify error sources in the traditional Fernald algorithm, detailed sensitivity analyses were conducted. Simulated lidar signals were generated by combining measured extinction profiles with known lidar system parameters, including background radiation and photon-counting noise. Retrieval errors were analyzed by systematically varying three key parameters: integration direction (forward vs. backward), calibration backscatter coefficient errors, and lidar ratio settings. For forward integration, calibration near the surface often leads to amplified errors due to strong aerosol concentration variability, while backward integration from high-altitude low-aerosol regions exhibits better error convergence properties. Results and Discussions Experimental results demonstrate that the proposed stratified iterative algorithm significantly improves retrieval accuracy in mixed aerosol-cloud scenarios. When applied to high-concentration aerosol layers (0?5 km altitude), the relative inversion error decreased from a maximum of 50% (using the traditional Fernald method) to only 5%. For low-concentration aerosol regions near cloud bases (5?7.5 km), errors reduced from 60% to 2%, while in cloud regions (7.5?9 km), errors decreased from 90% to 8%. These improvements are attributed to the algorithm's ability to automatically identify cloud positions and iteratively optimize the cloud lidar ratio. Moreover, the algorithm maintains high retrieval stability even under noisy conditions, thanks to its use of backward integration, which inherently suppresses error propagation. Compared with traditional approaches that apply a single, fixed lidar ratio throughout the profile, the proposed algorithm dynamically adjusts cloud-region lidar ratios in response to local scattering properties while preserving reference backscatter consistency. In addition to simulation experiments, real lidar measurements collected over Anhui Province on 20 January 2017 further validate the algorithm. The stratified iterative algorithm successfully identifies thin cirrus layers at around 8 km altitude, avoiding misclassification of near-surface aerosol layers as cloud. The retrieved extinction coefficient profiles show uniform, physically realistic aerosol and cloud distributions, free from the unphysical negative extinction values observed in traditional Fernald inversions without lidar ratio refinement. Conclusions This study develops and validates an atmospheric stratified iterative inversion algorithm based on the classic Fernald algorithm. By combining slope analysis, adaptive thresholding, and iterative lidar ratio optimization, the algorithm enables accurate retrieval of aerosol and cloud extinction profiles even under complex atmospheric layering. Key advantages include error convergence via backward integration, adaptive lidar ratio estimation without auxiliary instruments, and reduced sensitivity to calibration uncertainties. The approach reduces inversion errors by an order of magnitude compared to traditional algorithms and is particularly suited for real-time, single-wavelength elastic lidar applications in operational atmospheric monitoring. Future work will explore extending this framework to multi-wavelength inversions and integrating machine learning approaches for real-time lidar ratio estimation, further enhancing the capabilities of atmospheric remote sensing.