Ellipsoids, Datums, and Geoids

> Why wouldn't a "simple" Ellipsoid be adequate for a determination of elevation?

I'll try that one. The equipotential along the geoid is to determine the elevation as you would run it using a level @ perpendicular to the plumb line. That will determine how water would flow and why you need the elevation a commone geopotential (in this case the geoid) to determine water flow. This "geoid" is not parallel, nor a perfect shape. It varies due to gravitational pull direction. The calculatable "ellipsoid" height and the separation to the geoid at any given point is used to come up with a common horizontal location. Having height differences to a common ellipsoid helps in determining a horizontal location, but does not provide a true elevation that would effect the flow of water.

I hope I said that intelligibly.

Thanks Tom. That helps.

What you said got me to thinking that two points at exactly the same height above an ellipsoid might have different gravitational pulls, and because of that, water would flow from one to the other. That would definitely be a good argument for the latest Geoid.

Dave

Yes...I think I agree with that. I would say that that is essentially the whole purpose of having a geoid. Otherwise we would just draw a great big circle and measure up or down to the simple sphere. (That is what the ellipsoid is, except not quite as simple of geometric figure as a circular sphere, but more closely compares to the geoidal shape).

> Trying to nail down a few concepts.
mis dos pesos...

>
> Why does a Horizontal Datum need a Reference Ellipsoid?
an ellipsoid is a mathematical model of the shape of the earth, in an oblate ellipsoidal axis of revolution

Can a Datum be both a Horizontal Datum and a Vertical Datum?
maybe, let us check to see if there is one somewhere

Is a Geoid just a Vertical Datum?
the geoid is a gravity map, not smooth at all. similar to a potato

Is there any way a Geoid can influence Horizontal Position?
sure, trying to traverse near the base of a large mountain is one example
>
> Why wouldn't a "simple" Ellipsoid be adequate for a determination of elevation? I don't understand the obsession with Mean Sea Level, and the (seeming) overcomplications of new Datums and Geoids.
our new, geoid12a, is a hybrid geoid model that was computed from several different modes, and is improved from the older models

>
> Are NAD83, GRS80, and WGS84 Ellipsoids or Horizontal Datums? Are they also Vertical Datums?

nad 83 horiz datum, grs80 and wgs 84 are both ellipsoids, their origins are somewhere near 2 m different, i believe, but for practical purposes of surveys should not reflect a huge difference in typical work.

where's Loyal when we need his wisdom?
>
> Dave

Doctor Earl Burkholder has a software that is a 3D geodetic transformation tool, basically. Vectors are delta x, delta y, delta z. so by some definition, that might/maybe/could be called both a vertical and horizontal datum. earth centered, earth fixed.

The Geoid, is the definition of the shape of the Earth based on a Gravity model. Since the Geoid is so irregular this is no way of defining it mathematically. The best fit mathematical figure for the Geoid is an ellipsoid of revolution. Since we can handle the math associated with an ellipsoid we use it as a mapping surface. The Ellipsoid is a best fit approximation of the Geoid so the 2 aren't necesarily coincident and there are places where the separation is pretty big.

In order to get into this stuff in depth, you're going to have to study things like orthometric height, ellipsoid heights, deflection of the vertical , normal height etc.

The Ellipsoid is a best fit approximation of the Geoid so the 2 aren't necesarily coincident and there are places where the separation is pretty big.

i believe the ellipsoid is an approximate shape of the earth, the oblate ellipsoid specifically. something like 3 tenths of a percent fatter at the equator.
the geoid is a representation of geopotential, or gravity. so, since large mountain ranges can change gravity/verticality we often have to account for these effects.

ralph, are we saying the same thing?

> Why does a Horizontal Datum need a Reference Ellipsoid? Can a Datum be both a Horizontal Datum and a Vertical Datum? Is a Geoid just a Vertical Datum? Is there any way a Geoid can influence Horizontal Position?
>
A horizontal datum needs a reference ellipsoid to define what horizontal is. I would say that all modern datums are both horizontal and vertical as they contain 3 dimensional elements. The geoid is synonymous with sea level (there will be some debate on this as the technical term is equipotential surface, but this is the clearest way to consider it in my opinion). The geoid affects horizontal terrestrial surveys somewhat, particularly in celestial observations, but has no affect (at the surveyor's level) on GPS based surveys of horizontal positions.

> Why wouldn't a "simple" Ellipsoid be adequate for a determination of elevation? I don't understand the obsession with Mean Sea Level, and the (seeming) overcomplications of new Datums and Geoids.
>
$#!t still runs downhill and payday is still Friday.

> Are NAD83, GRS80, and WGS84 Ellipsoids or Horizontal Datums? Are they also Vertical Datums?
>
As has been mentioned GRS80 and WGS84 are ellipsoids (mathematical shapes). Unfortunately "WGS84" is also used to describe the DOD's mystery datum which has been reverse engineered as ITRF. NAD83 is a datum as well. While GRS80 and WGS84 (the ellipsoids) are very similar, their positions in space (the datum) differ by 2 meters (3d).

Datums/Realizations are the real points on the ground with published values (benchmarks and control monuments) and have errors while Ellipsoids are purely mathematical and are error free.

Thanks, Moe.

On whether a Geoid can influence horizontal position, certainly leveling a total station or plumbing a GPS rod will affect measurement next to a mountain. But I meant more, compared to say Geoid 03, will loading Geoid 12A into Survey Controller affect horizontal measurement? I'm pretty sure it will affect elevation, or more accurately, Orthometric Height.

I can find definitions of these concepts. Most of them are not user-friendly and seem to be written by lawyers. What I'd like to understand is how they fit together--Ellipsoid >> Datum >> Geoid >> Projection. Some say that NAD83 is a datum and some say an ellipsoid. Datum or Ellipsoid, why would it need to lean on another ellipsoid, GRS80? How does a Datum "reference" an Ellipsoid? GPS uses WGS84, in spite of it being very close to GRS80. I'd like to read about why that was. And when is the next WGS(XX) going to pull the rug out from under us? :-S

Dave

> Why does a Horizontal Datum need a Reference Ellipsoid?

I think it's the other way round - a reference ellipsoid needs to be anchored and oriented with respect to the earth - that is what the datum part does, it defines the position and orientation of the ellipsoid. So the ellipsoid needs a datum.
The 2 together - datum and ellipsoid creates the 2D reference frame.

Add a geoid and you get a 3D reference frame.

I believe you could call a geoid a vertical datum as it is establishing the "zero surface".

My understanding is that NAD83 is a 3D reference frame based on the GRS80 ellipsoid and the latest geoid model.

WGS84 is the name of both the ellipsoid and the reference frame created from it.

I think the difference between the WGS84 and the GRS80 ellipsoids comes down to the different datums used to anchor and orientate them.

That's what I think, anyway!

Great answers are being posted. When you have time, you might want to look at NOAA and NGS's FAQs, articles, and webinars/presentations. Here are a few links:

What is a datum?

Datums and Transformations from Coast Survey (more vertical datum information)

National Ocean Service's Geodesy tutorial pages

Introduction to Geodetic and Vertical Datums by Dave Doyle (search on Doyle)

I hope this information is useful,
Melita

> The Ellipsoid is a best fit approximation of the Geoid so the 2 aren't necesarily coincident and there are places where the separation is pretty big.
>
>
> i believe the ellipsoid is an approximate shape of the earth, the oblate ellipsoid specifically. something like 3 tenths of a percent fatter at the equator.
> the geoid is a representation of geopotential, or gravity. so, since large mountain ranges can change gravity/verticality we often have to account for these effects.
>
> ralph, are we saying the same thing?

I think when you choose your ellipsoid you're trying to best fit the Geoid, as the Geoid model improves you would probably have to adjust your ellipsoid. Large Mountain ranges have an effect because of their underlying mass. Gravity is not a straight line vector. It is affected by among other things "Free air anomalies" So it is best defined mathematically as Space Curve. It may or may not have the same value at any point in space ( I don't think it has to get that technical).
I think the term Hybrid used by NGS is just that, I believe these hybrid geoids are more akin to leveling surfaces. Where they hold some arbitrary point as a contraint (I believe it's father's point) and best fit a whole lot of things like passive bench marks etc.
I haven't really looked into it in depth recently, but that was my take on it the last time I read up on it.
It depends on who you talk to, some say "good enough", but in a pure Geodetic Sense sea level may approximate the Geoid but it does not define the Geoid.

Hopefully Base9 and Mulcare will jump in here and straighten this out.

:good:

straight from the source!

Thanks, Ralph.

"In order to get into this stuff in depth, you're going to have to study things like orthometric height, ellipsoid heights, deflection of the vertical , normal height etc."

Exactly my intent. For the last week I've spent most waking hours scouring the Innertoobs for info--Penn State, NOAA, Sinc's old articles, etc...

Most of my questions are practical. How does a Geoid affect a GPS measurement? If not a mathematical surface, is Geoid 12A a TIN surface? Who went out and measured gravity all over the planet to fine-tune the latest Geoid and what kind of grid pattern did they use?

Dave

A couple of quick (SHORT version) comments:

WGS84 (all realizations), is/are both a DATUM and an associated ELLIPSOID. The geometric difference between the WGS84 & GRS-80 Ellipsoids is trivial for most practical purposes.

GRS80 is ONLY an ELLIPSOID definition (there's more to it than that, but for our purposes today, the statement should suffice), and is used as the reference ellipsoid of ITRF2008, IGS08, and NAD83 (and all realizations of the ITRF, IGS, and NAD83).

The geocentric origin (center of the “Earth”) used by ITRF/IGS08 and WGS84(G1674) is for all practical purposes coincident.

The geocentric origin of NAD83 (all realizations) is ABOUT 2 meters (3-dimensionally) from the current WGS84/ITRF/IGS origin, and WAS (more or less) coincident with the ORIGINAL WGS84 (which has been updated to conform [more or less] with the ITRF/IGS origin over the years).

BTW...Two “points” with the same geopotential number, will NOT (necessarily) have the same Gravity Value.

AND...Two “points” with the same NAVD88 Orthometric Height, will NOT necessarily) be “LEVEL” (in the hydrodynamic sense) with each other. Nor will they (necessarily) have the same geopotential number (they might though). Now NAVD88 Dynamic Heights are another story.

Back to work...
Loyal

Thanks, Melita!

Good links. Just the sort of thing I've been looking for.

Dave

Thanks, Shawn,

"$#!t still runs downhill and payday is still Friday."

I guess geodesists need a paycheck too. 😀

Dave

Thanks, Colin.

"The 2 together - datum and ellipsoid creates the 2D reference frame. Add a geoid and you get a 3D reference frame."

I like that description! That makes sense.

Dave

> Thanks, Ralph.
>
> "In order to get into this stuff in depth, you're going to have to study things like orthometric height, ellipsoid heights, deflection of the vertical , normal height etc."
>
> Exactly my intent. For the last week I've spent most waking hours scouring the Innertoobs for info--Penn State, NOAA, Sinc's old articles, etc...
>
> Most of my questions are practical. How does a Geoid affect a GPS measurement? If not a mathematical surface, is Geoid 12A a TIN surface? Who went out and measured gravity all over the planet to fine-tune the latest Geoid and what kind of grid pattern did they use?
>
> Dave

In the U.S. I believe it's done by Volunteer students. A few years back Loyal introduced me to some program where they needed some people to undertake this task, I in turn presented it to Dr. Laramie Potts at NJIT to see if they could take care of it.
It involves taking a gravity reading and recording the measurements.
I think the new thing is going to be
Grav-D

BTW There were a whole lot of places out there with no readings whatsoever, They just had to wing it :). Think about how big an undertaking this is to do correctly. I think as technology evolves so will the refinement in the Geoid's definition.