[Proj] GeographicLib geoid calculations

[Noel Zinn (cc)]

Regarding Charles Karney's point (1) below, there are Mean Sea Surface 
models available.  DTU10 is a recent MSS from Denmark.  Follow the link 
below to research/download:

http://www.space.dtu.dk/English/Research/Scientific_data_and_models/Global_Mean_sea_surface.aspx

The difference between the (level) geoid and the (non-level) MSS is Dynamic 
Ocean Topography (DOT).

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

-----Original Message----- 
From: Charles Karney
Sent: Thursday, October 18, 2012 9:30 AM
To: proj at lists.maptools.org
Subject: Re: [Proj] Fw: Re: GeographicLib geoid calculations

> --- Alkuperäinen viesti ---
> Aihe: Re: GeographicLib geoid calculations
> Päiväys: 18.10.2012 12:51
> Lähettäjä: support.mn at elisanet.fi
> Charles Karney [charles.karney at sri.com] kirjoitti:
>> The errors for various geoid models and various grid sizes are listed in
>>
>>     http://geographiclib.sf.net/html/geoid.html#geoidinterp
>>
>> For example for the 15' EGM96 grid using cubic interpolation the max and
>> RMS errors are 169mm and 7mm.  However, I would normally recommend the
>> 5' EGM95 grid or the 2.5' or 1' EGM2008 grid.
>>
>
> Looks like the bilinear interpolation destroys the accuracy?

Well, not necessarily!!  Higher order interpolation will more faithfully
follow the spherical harmonic model of the geoid.  However most people
who use geoid heights are merely doing vertical datum shifts; and then
you need to ask how others are doing the interpolation.  (For example, I
was recently tasked with creating bare-earth DEMs from lidar data with
the lidar z being height over the ellipsoid and and the DEM being
referenced to EGM96.  However, I was required to use the 15' grid +
bilinear interpolation for EGM96 in order to conform to what others were
doing.)

It might be worth making a few other remarks about the geoid:

(1) The geoid is not mean sea level.  MSL includes local topographic
effects due to currents and the shape of the sea bed.  Marine charts
obvious will need to account for these (and they include tidal effects
with mean low tides or whatever).

(2) The normal to geoid does not give you the direction of gravity on
land.  In calculating the geoid separation, a fudge is added to the
gravity field to account for the mass of the terrain above the geoid
(the zeta-to-N correction).

(3) The NGA code which computes the EGM2008 uses different masses for
the real earth and reference ellipsoid.  This leads to a 1/r effect
which is ignored.  (There is an additional bug in the code which affects
the calculation of the deflection from the normal.  I've pointed this
out to the authors --- and gotten no response!)

(4) If you're really interested in the gravity field then use the
EGM2008 gravity model (or more recent models) directly.  If working with
sensitive equipment,  you might need to account for the mass of the
atmosphere (included in EGM2008!), the buoyancy of your instruments,
earth and ocean tides, etc.

It's best to view the geoid height as "just" a datum shift.  It's
computed to approximate a surface of constant potential and the whole
procedure has various warts.  But these defects don't matter as long as
you make clear what geoid model you used and how you interpolated into
it.

   --Charles
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