Two major projects that investigate the climate system's response to natural and anthropogenic aerosols forcings are:
1. the PDRMIP - Precipitation Driver and Response Model Intercomparison Project
2. the AerChemMIP - the Aerosol Chemistry Model Intercomparison Project, which is part of CMIP6
The key papers are:
1. https://journals.ametsoc.org/view/journals/bams/98/6/bams-d-16-0019.1.xml
2. https://acp.copernicus.org/articles/special_issue1057.html