Yes, there are quite a few relevant papers. Here's a preliminary study from 2006 regarding weather forecasting using surface pressure measurements on the synoptic scale: http://journals.ametsoc.org/doi/abs/10.1175/BAMS-87-2-175

A number of papers have been published since as that work has continued. So we know that surface pressure data is useful on a large scale; is it useful on a micro- or mesoscale? A few researchers are actively writing and publishing papers on this topic. Cliff Mass at the University of Washington, along with his colleagues and students, are leading the charge.

https://ams.confex.com/ams/94Annual/webprogram/Paper236282.h...