I've been stuck on a problem the last few weeks that I'm hoping somebody more knowledgable here might be able to help answer. I'm trying to pull out a realistic estimate of vertical motion from WRF model output. Unfortunately, the output that I'm using does not contain a w-wind or omega field, but I do have 3D U, V, T, and HGT (along with some of the standard 2D fields).

Using the 3D fields, I've tried solving for the forcing terms in the traditional QG-Omega equation, but ran into difficulties trying to invert the laplacian in order to isolate omega. I figure there must be an easier way to do this that I'm missing such as vertically integrating the continuity equation, but I'm finding it very difficult to actually find any information on what the best practices for estimating omega/w-wind are.

My questions are:

1. Would anybody be able to offer some insight into how this quantity is calculated within the WRF model? This leads into question #2:

2. Is there a way of solving for this or approximating it by post-processing model output?

Any papers, resources, or implemented solutions to this problem (in a language like Python) would be much appreciated! Thank you!