Formula for vertical levels?

[navidcy]

Are the vertical levels here defined recursively?

regional-mom6/regional_mom6/regional_mom6.py

Lines 248 to 279 in abf630d

	def dz(npoints, ratio, target_depth, min_dz=0.0001, tolerance=1):
	"""Generate a hyperbolic tangent thickness profile for the
	experiment. Iterates to find the mininum depth value which gives
	the target depth within some tolerance
	Args:
	npoints (int): Number of vertical points
	ratio (float): Ratio of largest to smallest layer
	thickness. Negative values mean higher resolution is at
	bottom rather than top of the column.
	target_depth (float): Maximum depth of a layer
	min_dz (float): Starting layer thickness for iteration
	tolerance (float): Tolerance to the target depth.
	Returns:
	numpy.array: An array containing the thickness profile.
	"""
	profile = min_dz + 0.5 * (np.abs(ratio) * min_dz - min_dz) * (
	1 + np.tanh(2 * np.pi * (np.arange(npoints) - npoints // 2) / npoints)
	)
	tot = np.sum(profile)
	if np.abs(tot - target_depth) < tolerance:
	if ratio > 0:
	return profile
	return profile[::-1]
	err_ratio = target_depth / tot
	return dz(npoints, ratio, target_depth, min_dz * err_ratio)

And maximum rate of change of the vertical spacing occurs at the mid-depth (exactly)?

[navidcy]

cc @kialstewart

[navidcy]

note to self after chatting w @kialstewart: 10.1016/j.ocemod.2017.03.012 might be relevant; see section 2

[ashjbarnes]

Ok so I took Kial's formula, but modified it so that the free parameter is different. From memory I think you give it number of layers, depth, ratio of the biggest to smallest ratio and then it chooses where to place the first layer.

Vertical levels aren't defined recursively, but the equation is solved by recursively searching for the solution. After I wrote this code I realised that you can solve it directly but it worked and apparently I never bothered changing it.

[ashjbarnes]

What would resolve this @navidcy? This is the vertical coordinate that I use for my experiments and so currently is the only one implemented. Future updates will implement more grid generation options - see issue #69 so this one isn't intended to be perfect or one size fits all

[navidcy]

A description in the docstring explaining how these levels are computed?

My problem wasn't that it wasn't as generic as possible. My main issue was that I couldn't understand what was happening.