By "high frequencies" I assume you mean wavelengths that are short compared to the obstacle - all scattering solutions are relative to the obstacle size.

Many people have produced electromagnetic scattering solutions for spheres - see https://en.wikipedia.org/wiki/Mie_scattering for an overview of Fourier-Bessel type wave solutions. These however are all flawed. If you would like an explanation of the flaws of this type of solution in the context of acoustic scattering from a rigid cylinder, see my paper at https://www.researchgate.net/publication/257308428_What's_wrong_with_scattering_theory .

While cylinders differ somewhat from spheres and the boundary conditions for electromagnetic waves differ from the boundary conditions for sound waves, the same principles apply regarding conservation of energy, causality, continuity of transmitted waves, critical angles for transmitted waves, interior reverberation of transmitted waves and creeping wave propagation velocity.

If you would like to see a partial acoustic wave scattering solution for the insonified side of a rigid cylinder, a solution by a different method that does not have these flaws, see my paper at https://www.researchgate.net/publication/390322927_Acoustic_scattering_solution_by_a_modified_method_of_characteristics_for_a_plane_wave_with_normal_incidence_on_the_side_of_a_long_rigid_cylinder . The solution has not yet been extended to the diffracted component of the wave.

If you are only interested in short-wave solutions, it might be better to focus on the geometrical theory of diffraction and its descendants. These are more tractable algebraically, simpler to evaluate and more physically justifiable than Fourier-Bessel type solutions. Geometric solutions are not inherently well-suited however to modelling resonance effects.

With regard to the specifics of your research topic, you are dealing with dielectric scattering rather than scattering by conductive obstacles, but combined with molecular resonance effects. My inclination would be to take a geometric approach to the problem and try to combine that with known electromagnetic resonance spectra of water molecules. I would expect these resonance effects to be isotropic in statistical terms, even if they are not for individual molecules or droplets. I don't know if this has already been attempted - perhaps someone more familiar with electromagnetic scattering literature might offer advice on this.

I expect that almost everyone in this field who reads this answer will disagree with my assessment of Fourier-Bessel type solutions, and I am probably kicking a hornet's nest by posting this, but I urge them to read the first paper I cited before trying to shout me down. Then, by all means, tell me what's wrong with my reasoning.

The second paper cited has just been updated. I spotted some minor errors on p7 and p9. They are housekeeping rather than anything consequential. The corrections are listed at the end. My apologies for any inconvenience caused.

One more update has been made on the second paper - two equations with alternate solution forms have been added on p13. Their equation numbers have been given suffixes so that the other equation numbers are unaffected.

In terms of prior work, you might also find it useful to use the search terms "aerosol" and "atmospheric turbidity" and search for papers that cite this paper:

C. Gueymard, “Importance of atmospheric turbidity and associated uncertainties in solar radiation and luminous efficacy modeling,” in SOLARIS 1—Measurement and Modeling of SolarRadiation, Edinburgh, January 2003

Gueymard's work doesn't focus on the mechanics of scattering theory, but in other respects it is relevant to your topic.