Reconstructing the wind field from vorticity and divergence over finite domains

[winash12]

What should we add?

We suggest to add the following new functionality which implements a reconstruction of the wind field from vorticity and divergence over a limited domain. It can be used to quantify, among others, how clouds induce a far-field circulation around them – see for example [Oertel and Schemm 2021](https://doi.org/10.1002/qj.3992 .)

Specifically equation (8) and (9) of that paper.

How
We suggest to follow the notebook [Clark Evans notebook](https://github.com/evans36/miscellany/blob/main/Vorticity%20and%20Divergence%20Inversion.ipynb .) The interface will support xarray data structures as is used by other APIs of MetPy.

What's next

While I am looking to implement a first version of this myself I do welcome support and inputs.

Specifically the first version of this functionality will cover these aspects

1. A rewrite of the Clark Evans notebook with a vectorized approach of the original implementation by possibly eliminating two of the four for loops.
2. In addition to reconstructing the wind field compute the stream function and velocity potential (Equation (6) and (7) of the first reference)
3. It is expected to keep this simple and only apply it for finite domains and finite differences.

Future versions could possibly include

1. spectral methods for computing vorticity and divergence as well as icosahedral computations of vorticity and divergence(finite domain data from ICON or GFDL)
2. 3d inversions.

Reference

1. Oertel, A, Schemm, S. Quantifying the circulation induced by convective clouds in kilometer-scale simulations. Q J R Meteorol Soc. 2021; 1752–1766.

DOI: 10.1002/qj.3992

[winash12]

@dopplershift We have a preliminary version of the vectorized code that reproduces the Clark Evans notebook. What indeed are the next steps ?

[dopplershift]

The first step is to open a draft PR so we can see concretely the code and give better design feedback, including addressing some of the issues above.