Prevent frontogenesis from returning nans

[sgdecker]

Description Of Changes

Previously, frontogenesis could return nans when there was a constant theta field (division by zero would occur) or if round-off error resulted in the argument to arcsin being slightly outside the valid domain of the function (-1 to 1). In this commit, edits are made to set points to zero where nans occur due to division by zero (the frontogenesis is zero when the magnitude of the theta gradient is zero anyway) and to use np.clip to ensure the argument to arcsin is valid.

I could not come up with a simplified test case that triggers the round-off error issue with arcsin, but I do include a test case for the constant theta situation. Because the test case results in a division by zero by design, it is currently failing since that triggers a RuntimeWarning.

Checklist

• Closes Frontogenesis should not return nan #3678
• Tests added
• Fully documented

[sgdecker]

Ideas on how to make my test pass would be greatly appreciated!

[dopplershift]

Thanks @DWesl for the helpful comments that made the final version of this really nice.

[DWesl]

If you're interested in eliminating all trig:

We have $\tan(2 \psi) =\frac{shrd}{strd}$, which implies $\cos(2\psi)=\frac{strd}{\sqrt{shrd^2+strd^2}}$. We use psi next line to find $\cos(\psi)$ and $\sin(\psi)$.

We show later that $\cos(2\psi) = 1 - 2 \sin^2(\psi) = 2 \cos^2(\psi) - 1$. Rearranging those identities gives
$\cos(\psi) = \sqrt{\frac{1 + \cos(2 \psi)}{2} }$
$\sin(\psi) = \sqrt{\frac{1 - \cos(2 \psi)}{2} } = \sqrt{1-\cos^2(\psi)}$
This lets you replace three trig functions and a multiplication with three or four multiplications, three additions, three square roots, and a division, and four trips through the data with eight. I have no idea whether the eliminating the trig calls makes up for the extra trips through the data.

[dopplershift]

I ran through that too and wasn't wild about all the square roots. I'm not passionate about trying it but if someone wants to see about performance/accuracy, I'd entertain it.