Assessing the limits of lidar aerosol inversions using a probabilistic machine learning approach

Abstract. Aerosol-cloud interactions represent a major source of uncertainty in climate models and addressing this requires accurate, vertically-resolved observations of aerosol microphysical properties such as effective radius and number concentration. While Raman and High Spectral Resolution lidars provide vital bulk optical measurements, fundamentally they do not measure these quantities directly; retrieving microphysical properties from these observations is a mathematically ill-posed and non-unique inverse problem. Existing retrieval algorithms—including traditional physics-based inversions, semi-empirical parametrization methods, and recent empirical machine learning approaches—typically force a deterministic, single-point solution. This masks fundamental uncertainties and relies on opaque priors. In this study, we introduce a machine learning framework that embraces the inherent non-uniqueness of the lidar inversions. Trained on a dataset of in situ aerosol size distributions coupled with Mie theory, our model predicts the Probability Density Function (PDF) of possible aerosol microphysical states rather than a single estimate. We leverage this framework to evaluate the theoretical capabilities and error sensitivities of four distinct lidar architectures, ranging from advanced multi-wavelength Raman configurations (6β+2α, 3β+2α) to spaceborne-relevant systems (1β+1α at 355 nm, 3β). Under idealized, low-noise conditions, advanced multi-wavelength systems best constrain the microphysical solution space. However, under realistic observational uncertainties, the accuracy of these complex architectures degrades, whereas simpler configurations with direct extinction measurements (e.g., 1β+1α) prove significantly more robust. Ultimately, this best-case analysis establishes that lidar has the potential to constrain effective radius to approximately a factor of 2 and concentration to an order of magnitude, demonstrating that probabilistic retrievals can play an important role in providing mathematically transparent observational constraints for global climate models.