Updating the Vertical Vorticity Constraint

In Dahl et al. (2019) (https://doi.org/10.1175/JTECH-D-18-0211.1), the vorticity constraint for the DDA was updated so that instead of using Ut and Vt as a proxy for the vorticity tendency in the cost function, the vorticity tendency field was calculated before running the DDA and that field was then held constant for calculating the vorticity cost function during the DDA. This gave much better results than using the old method. Could this be implemented into PyDDA? If so, I think it would also be good to provide functions to calculate the vorticity tendency like it was done in Dahl et al. (2019).

I am one of the co-authors on the Dahl et al. (2019) paper and also worked with technique for my dissertation so I am very familiar with the changes. I could possibly try to work on this when I get the chance but I don't know when that would be.

Start by comparing PyDDA's current vertical vorticity constraint with the method described in Dahl et al. (2019), focusing on how Ut and Vt are used in the cost function. Define the vorticity-tendency calculation functions and the process for calculating the field before the DDA and holding it constant during optimization. Done means the updated constraint and supporting functions are implemented and produce the improved behavior described in the paper.