Revisit GAHM isotach perturbations

[WPringle]

Given a Rmax perturbation the GAHM isotachs are currently perturbed by the same absolute amount [n mi]

Let's revisit to see if we can adjust with more physical/theoretical basis , by e.g., preserving the "B" parameter of the GAHM model.

[WPringle]

Update on exploring... Here is an example for a 34-kt isotach at some time of Hurricane Florence:

The original Vr is in blue then I adjusted Vmax by increasing by 10% and reduced Rmax by 10%.
Conserving the B parameter that was found to fit Vmax and r34 in the original curve, we get the new curve and r34

[WPringle]

The equation used is simplified Holland model without Coriolis term. I think for our purposes here it can be a reasonable approximation:

alpha = (Rmax./r)^B;
Vr = Vmax*sqrt(exp(1-alpha).*alpha);

[WPringle]

Another question is are the Rmax values in the track file actually used in GAHM? @pvelissariou1

Based on https://wiki.adcirc.org/Generalized_Asymmetric_Holland_Model and discussion with Taylor Asher it seems the Rmax is actually computed within GAHM for each quadrant.

One idea to test things by @andybpenny is to zero out all the radii values and run GAHM vs including the radii values and running with GAHM.

Presumably zeroing out the radii would result in a non-asymmetric GAHM type implementation but has advantage over classical Holland model in that it actually captures the true Vmax at low Rossby numbers:

where

[WPringle]

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