Yes, it is possible but the inverse problem to be solved is rather complicated and the solution is not necessarily unique. For example please consider the following paper:

Article Features of retrieval of microstructural parameters of aeros...

The literature discussing all problems related to your question is very extensive and I would suggest to retrieve the basic papers from the huge web resources.

Cher Hang Nguyen ,

Oui, il est possible de convertir l'AOD ou l'AOT en concentration d'aérosols. La méthode consiste, tout d'abord, à établir un lien entre les concentrations observées en un lieu et les AOD ou AOT ; puis en déduire (Convertir/Calculer/Estimer) les valeurs des AOD ou AOT en concentration d'aérosols. Toutefois, la principale difficulté est (souvent) la compréhension des fondements théoriques et pratiques des méthodes utilisées. Mais, la littérature dans ce domaine étant abondante, il faudra donc chercher à t'approprier les bases théoriques et pratiques pour y arriver. Je vous recommande quelques papiers à lire :

- Article Estimation of Aerosol and Air Quality Fields with PM MAPPER-...

- Article Discuss on Satellite-Based Particulate Matter Monitoring Technique

- https://core.ac.uk/download/pdf/199242098.pdf

- Article Satellite Remote Sensing of Particulate Matter Air Quality: ...

Bonne lecture et bonne application.

I would say that you need a vertical profile of the aerosol and a Volume Size distribution of the aerosol too to start. Then depending on which concentration, you would also need mass density of the aerosol.

have a look at Article Estimating marine aerosol particle volume and number from Ma...

Sayer, A. M., Smirnov, A., Hsu, N. C., Munchak, L. A., and Holben, B. N.: Estimating marine aerosol particle volume and number from Maritime Aerosol Network data, Atmos. Chem. Phys., 12, 8889–8909, https://doi.org/10.5194/acp-12-8889-2012, 2012.

yes, you can but it depends on the level uncertainty you are willing to deal with. Accurate mass concentration retrievals depend on a number of conditions that are not always fulfilled (such as location of the aerosol layer and RH conditions) and this is assuming that the satellite retrieval is accurate. None of these conditions are a sure thing and highly variable depending the location. And also, it is the fact that satellite derives column integrated information which is tricky to compare with single point surface PM concentration measurements.

YES, if you have spectral information of AOD, you can convert it in to aerosol concentration.

I think you can find an empirical equation in order to achieve that, but the accurcy of the results might be not sufficent!!!

see the following paper it will help you!!

https://www.jstor.org/stable/26186568

Good Luck

you need to assume aerosol extinction profile, fit its column intigrated value to AOD, then you can have aerosol extinction coefficient at any altitude, then apply aerosol mass extinction coefficient based on site.

Yes it is possible to model AOD to surface level PM of any other aerosol. The attached paper may be helpful.