Aiming at the key challenges of crowd counting in foggy environments, such as long-range target blurring, local feature degradation, and image contrast attenuation, this paper proposes a crowd-counting method with a physical a priori of atmospheric scattering, which improves crowd counting accuracy under complex meteorological conditions through the synergistic optimization of the physical mechanism and data-driven.Specifically, first, the method introduces a differentiable atmospheric scattering model and employs transmittance dynamic estimation and scattering parameter adaptive calibration techniques to accurately quantify the nonlinear attenuation laws of haze on targets with different depths of field.Secondly, the MSA-KAN was designed based on the Kolmogorov-Arnold Representation Theorem to construct a learnable edge activation function. By integrating a multi-layer progressive architecture with adaptive skip connections, it significantly enhances the model's nonlinear representation capability in feature-degraded regions, effectively suppressing feature confusion under fog interference.Finally, we further propose a weather-aware GCN that dynamically constructs spatial adjacency matrices using deep features extracted by MSA-KAN. Experiments on four public datasets demonstrate that our method achieves a 12.2\%-27.5\% reduction in MAE metrics compared to mainstream algorithms in dense fog scenarios.