Automated Trough/Ridge Axis Calculation

[winash12]

https://www.dtn.com/what-are-troughs-and-ridges/ From this link we need to calculate the trough axis (the dotted line) and it's tilt. What direction is it tilted ? This is very useful in operational forecasting.

In order to accomplish this coding effort here is what we need to do -

1. Geopotential heights at a given level from GFS or ERA or any other source
2. Contour them or in other words make a contour plot of the geopotential heights. Standard python allows you to do this
3. Calculate the curvature of the contours- what does that mean exactly ? There are two ways to calculate the curvature. One is to use a least squares method to fit a circle at each point of the contours and then the obtain the radius of the circle. The inverse of the radius is the curvature. The other way to calculate the curvature is to do a smoothing spline on the contours and then take a finite second derivative of the smoothed spline and the curvature is the numerical second derivative of the curve.
4. Calculate the maxima/minima of the curvature of each of the contours
5. Then link the points of each maxima and then form an axis of either the trough or the ridge. Here we need to do an objective analysis that identifies the maxima or minima of the ridge.

INPUT - geopotential height at a particular isobaric or isoentropic level OUTPUT - latititude,longitude list of points containing the coordinates of curvature maxima of the contours. Angle containing the tilt of the trough axis.

[dopplershift]

Sounds like a plan. I look forward to having a pull request to review.