| 06 May 2026
A new Monte Carlo treatment of multiple scattering of light by black carbon aggregates with varying levels of compactness
Abstract. We use a specially designed Monte Carlo (MC) model that includes individual Mueller matrix selection in each scattering event to conduct a comprehensive theoretical investigation of the intensity and polarization of light multiply scattered by an atmospheric layer embedded with black carbon (BC) particles with varying compactness. We find that the spatial distributions of the degree of linear and circular polarization are sensitive to BC particle shape, and that depolarization is more dominant for spherical BC particles than for fractal aggregates. We also find that the layer transmittance is highest for the more spherical BC particle shapes and lowest for the extended fractal aggregates, with an overall difference of approximately 10 % relative to the incident intensity between the highest and lowest values of transmittance. We find that the reflectance exhibits a similar tendency, and that correspondingly, the layer absorptance is lowest for the more spherical BC shapes and highest for the extended fractal aggregates. In addition, we compare the results obtained from our MC simulations with those obtained with the delta-Eddington approximation for the same optical thickness, single scattering albedo, asymmetry factor, and incident zenith angle. We find that there is a relatively small difference between our results and the delta-Eddington results with respect to the layer transmittance and the layer absorbance, but that the layer reflectance obtained with our MC simulations is up to 50 % lower than that obtained with the delta-Eddington approximation. These results could have important implications for radiative forcing estimations, climate modeling, and remote sensing implementations.
This manuscript investigates polarized multiple scattering by black carbon aggregates with different morphologies using a Monte Carlo radiative-transfer model in which a specific Mueller matrix is selected for each scattering event. The topic is relevant to aerosol optics, polarized radiative transfer, and potentially remote sensing. The manuscript contains a substantial amount of numerical work and several interesting polarization patterns. However, I still have several concerns regarding the physical basis and validation of the proposed methodology. In my view, these issues should be addressed before the main conclusions can be fully supported. I therefore recommend major revision.
Comment #1: My main concern is the treatment of particle orientation in the proposed “individual Mueller matrix selection” method. Rather than using a Mueller matrix averaged over particle orientations, the model randomly selects a particular particle realization and orientation for each scattering event and applies the corresponding Mueller matrix. The authors argue that this treatment is more representative of the physical interaction between a photon and an individual particle.
Based on my understanding, if the individual-event method and the conventional pre-averaged method represent exactly the same random particle population, I would expect the two methods to converge toward the same ensemble-mean result when the orientation-dependent extinction, scattering, and phase-matrix properties are weighted consistently. However, the manuscript reports that the two approaches give systematic differences, which can reach to even 10% as shown in Appendix A. The difference might represent genuine physics, but it might instead arise because the authors are not weighting the orientations in exactly the same way as the conventional orientation average.
In particular, the authors should demonstrate that the orientation-sampling procedure gives the correct statistical weighting to particles with different orientation-dependent optical properties. Otherwise, the difference you see compared with the standard orientation-averaged method may just come from giving different particle orientations the wrong statistical weights.
Based on this concern, there are several additional questions listed below:
Comment #2: The main novelty of the manuscript concerns multiple scattering, but the comparison between the new individual-selection method and the conventional orientation-averaged method in Appendix A is limited to single scattering and one realization of the most extended aggregate. This makes it difficult to evaluate how much the proposed treatment actually affects the multiple-scattering results presented in the main text. I suggest repeating a representative subset of the full Monte Carlo calculations using both methods. For example, comparisons for one compact and one extended aggregate at an optical thickness of approximately 1, considering unpolarized, linearly polarized, and circularly polarized incident light, would be useful. Comparing quantities such as transmittance, reflectance, and selected polarization distributions would provide a much clearer demonstration of the practical impact of the proposed method.
Comment #3: What is the justification of using Delta-Eddington method as a validation benchmark. I am not fully convinced that the delta-Eddington approximation provides an adequate benchmark for validating the Monte Carlo model, since delta-Eddington is itself an approximate radiative transfer treatment. The polarized-Monte-Carlo methodology cited by the authors has historically been compared against adding-doubling solutions, and such comparisons can achieve approximately percent-level agreement. Established polarized adding-doubling approaches provide a natural independent benchmark.
Comment #4: Please carefully check the manuscript to ensure that all symbols and variables are clearly defined when they first appear and are used consistently throughout the text.