Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Add conversion routines between ellipsoidal-harmonic and geodetic coordinates #186

Closed
wants to merge 4 commits into from

Conversation

MarkWieczorek
Copy link
Contributor

@MarkWieczorek MarkWieczorek commented Apr 10, 2024

This PR adds two conversion routines, to and from geodetic and ellipsoidal-harmonic coordinates:

  • Ellipsoid.geodetic_to_ellipsoidal_harmonic()
  • Ellipsoid.ellipsoidal_harmonic_to_geodetic()

These will be required when computing the normal gravitational potential above the reference ellipsoid in issue #151.

The routines work, but I am worried about the precision. The conversion from geodetic to ellipsoidal uses the same code as in the normal_gravity method, which is based on the equations in Lakshmanan (1991). The inverse is just a a couple atans for the latitude, and the ellipsoidal height is computed as the difference of the prime_vertical_radius of the two ellipsoids. Even if I can understand why the height might lose precision this way, the latitude shouldn't.

Here are a couple of examples:

In [2]: longitude, reduced_latitude, u = boule.WGS84.geodetic_to_ellipsoidal_harmonic(0, 45., height=0)

In [3]: boule.WGS84.ellipsoidal_harmonic_to_geodetic(longitude, reduced_latitude, u)
Out[3]: (0, 45.0, 0.0)

In [4]: longitude, reduced_latitude, u = boule.WGS84.geodetic_to_ellipsoidal_harmonic(0, 45., height=1.e-8)

In [5]: boule.WGS84.ellipsoidal_harmonic_to_geodetic(longitude, reduced_latitude, u)
Out[5]: (0, 44.99999999999992, 9.930249518419041e-09)

In [6]: longitude, reduced_latitude, u = boule.WGS84.geodetic_to_ellipsoidal_harmonic(0, 45., height=1)

In [7]: boule.WGS84.ellipsoidal_harmonic_to_geodetic(longitude, reduced_latitude, u)
Out[7]: (0, 44.999999969779665, 0.9999999988228683)

In [8]: longitude, reduced_latitude, u = boule.WGS84.geodetic_to_ellipsoidal_harmonic(0, 45., height=1000)

In [9]: boule.WGS84.ellipsoidal_harmonic_to_geodetic(longitude, reduced_latitude, u)
Out[9]: (0, 44.99996978922941, 1000.0002619091734)

In [10]: longitude, reduced_latitude, u = boule.WGS84.geodetic_to_ellipsoidal_harmonic(0, 45., height=10000)

In [11]: boule.WGS84.ellipsoidal_harmonic_to_geodetic(longitude, reduced_latitude, u)
Out[11]: (0, 44.999698744381085, 10000.026154076979)

Maybe this is good enough. I suspect that the loss of precision comes from the Lakshmanan equations (which have some subtractions of similarly sized numbers). Perhaps there is nothing we can do about it, but if this is the case, then it affects the Normal gravity routine.

Relevant issues/PRs:
Related to #151


beta_p = np.degrees(np.arccos(np.sqrt(cosbeta_p2)))

return longitude, beta_p, b_p

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This is a bit strange because in the docstring they have other names :)

Copy link
Contributor Author

@MarkWieczorek MarkWieczorek Apr 11, 2024

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

I could change this to just u and reduced_latitude. The only reason I did it this way was that these are the names of the parameters in the paper we cite, and they are also the names of the variables used in the normal gravity routine. When writing this, I originally used u and then changed it at the end, so I don't have any preference either way...

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

it makes sense. Perhaps change just the docstring so you don't have surprise ;-) but it is a nit

@MarkWieczorek
Copy link
Contributor Author

This PR was incorporated into #187

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
None yet
Projects
None yet
Development

Successfully merging this pull request may close these issues.

None yet

2 participants