What's the difference between a horizontal datum and a reference frame?
Earth Centered,Earth Fixed XYZ Is A Reference Frame
Three directions at 90°, three distances encompasses all of space; very simple.
A datum is generally much more complicated behind the scenes in order to simplify calculations on the datum.
In order to transform GPS XYZ to a more useable format for much of surveying two concurrent datums are required, for instance;
"Lat/Lon" and "Elliptical elevation", or
"SPC N,E" and "Orthometric elevation".
Datums are a subset of reference frames.
Paul in PA
> What's the difference between a horizontal datum and a reference frame?
I would say...
A datum is perfect - a reference frame is a datum dragged kicking and screaming into the real world so people can use it.
It is the actual physical realization, useable control points, of a perfect but theoretical concept.
A datum has no error - a reference frame inevitably does.
James,
If you can understand that link, then you're one whole hell of a lot smarter than I am:
Dave
Colin,
"A datum is perfect..."
According to James' link, a Reference Frame fixes a flawed Datum. So now I'm doubly stumped.
What I need is for someone to take a big fat crayon and spell it out, slowly, for me. 
Dave
Adapted from the notes of a presentation by Dr. Richard Snay, retired National Geodetic Survey geodesist:
A HORIZONTAL DATUM is a reference surface (an ellipsoid) that consists of 5 quantities:
- 2 constants to define the size and shape of the reference ellipsoid (could be major axis, semi-major axis, flattening).
- Latitude, Longitude of an initial point.
- Azimuth of a line from the initial point to define the ellipsoid's orientation.
* Example: NAD83 reference ellipsoid.
A REFERENCE SYSTEM is a collection of fundamental rules and parameters describing the positions of points in space.
* Example: NAD83, WGS84.
A REFERENCE FRAME is the real-world realization of a reference system. It is consists of a network of physical stations on the ground with adopted coordinates.
* Example: NAD83(1986), NAD83(2011) epoch 2010.00, WGS84(G1150).
The year of the adjustment is indicated in parenthesis and NGS now adds the reference epoch, the date for which the coordinates are valid.
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So, a horizontal datum is a defined ellipsoid. A reference system aims to use that horizontal datum. The reference frame is the materialization of that reference system. NAD83 is a reference system that has several associated reference frames.
BTW, when a new NAD83 reference frame is realized, the underlying horizontal datum (ellipsoid) has not changed. What has changed are the ground stations' coordinates.
Also, re: ECEF XYZ. This is a coordinate system and may be used on any horizontal datum, just like Lat/Long/Ellipsoid Height. Because horizontal datums' ellipsoids are set at slightly different origin points in the earth, a ground station will have different coordinate positions between datums.
Hope that helps! Can be pretty dense stuff.
-Ben Erickson
Earth Centered,Earth Fixed XYZ Is A Reference Frame
Paul,
"...very simple."
If I had the power to strike any word from the English Language, I would start with the word "simple".
OK, so if Datums are a subset of Reference Frames, what else is subsumed under the concept of a Reference Frame?
Dave
I wholeheartedly recommend Basic GIS Coordinates by Jan Van Sickle. It covers all that stuff in a language even I can understand...I think you would find it a good read. I could mail it you if you promise to send it back!
Dear Dave,
Dave asked:
"What's the difference between a horizontal datum and a reference frame?"
Let's look at this in two steps. First, the relation of datum and frame.
Then, second, the realization of a horizontal datum in a 3-dimensional
system. I think that will get to your question.
I *strongly* recommend looking at Appendix A of the GEOCON Technical
Report. (The answer is also found in the International Earth Rotation
Service (IERS) Conventions, 2010.)
http://www.ngs.noaa.gov/GEOCON/techreport.pdf
In short, there is a hierarchy of abstraction.
Most abstract is the Ideal Reference System. This is the ideal notions
of geometry such as a generic ellipsoid, generic 3D Cartesian system,
generic orientation, rotation, etc... Think geometry.
In the middle is the Reference System. This adds physical environment
and physical theory. Imagine precession, nutation, polar motion,
crustal motion. However, no actual measurements, no coordinates. Physics.
The least abstract is the Reference Frame. This is the materialization
of the Reference System. This provides the quantitative description
of positions and motions on the Earth.
This hierarchy dates back to 1980, and is endorsed by the IERS and, I
believe, the International Association of Geodesy (IAG).
The IERS Conventions (2010) define datum:
datum: A geodetic reference frame. In surveying and geodesy, a
datum is a set of reference points on the Earth's surface, and (often)
an associated model of the shape of the Earth (reference ellipsoid)
used to define a geographic coordinate system.
Thus, a geodetic datum is a set of coordinates that are a
materialization of a coordinate reference system.
There is confusion regarding these terms. Some believe a datum is
an Ideal Reference System. Others interchange the names of Reference
System and Reference Frame. Some think that Reference System and
Reference Frame are interchangable. This is why I'm going over the
basics. But, fair warning, when you talk to someone, they may be
coming from a different (non-standard) understanding.
A Reference Frame/Datum is the materialization. These are coordinates
on points. Will the observation/materialization be perfect? No.
That said, the Reference Frame/Datum itself is promulgated as a
standard. So, despite its imperfections, it may generally be used
as a basis for subsequent computations.
Now, horizontal datum.
This is just the latitude & longitude subset of a
Reference Frame/Datum. However, back in the day (pre-satellite),
it was obtained in a 2-D process.
Lets think about NAD 27.
At the ideal level, the Earth was modeled as an ellipsoid, the
coordinates would be computed as body-fixed.
At the reference system level, no crustal motion. To satisfy
the ideal, a set of requirements fall out: need an origin on
the ellipsoid (MEADES RANCH), need a network orientation (by
an azimuth). Scale to be provided at the measurement level by
taped baselines. No geoid, no deflections of the vertical.
At the Reference Frame/Datum level -- now the actual choices
are made, measurements selected and combined by least squares.
Here we select the specific ellipsoid (CLARKE 1866), the lat and long
for MEADES RANCH, the azimuth at MEADES RANCH. Then, the reduction
of distances to the ellipsoid (plus infrequent reduction of
directions in mountainous areas), combination, data cleansing,
rejections, the least squares computation of the framework, and
subsequent computation of lower order control points.
I should mention that at the reference system level, the notional
NAD 27 would be approached by a reduction method -- where the
key measurements (typically distances) would be brought down to
the ellipsoid. This is in contrast to a more modern approach
called the projective method -- where all measurements are
considered in their full 3-D glory. (c.f. Wolf in the '60's),
but where it is possible to only allow the horizontal coordinates
to adjust. (c.f. NGS Program ADJUST). The projective method was
used for NAD 83(86).
Hope this helps.
Time and Gravity
Time may be a necessary describer. If not in ITRF most definitely in NAD 83
Gravity is defined as down, but down to where is why elliptical or more complicated solutions are required. Most definitely required in ortho elevations from the geoid.
Paul in PA
Ben,
Thank you. A clear, succinct explanation. Well done.
Dave
Colin,
Thanks very much for the offer. It sounds like a book I'd like to have in my library, so I'll nose around today and see if I can buy a copy.
Dave
Dennis,
Thank you. And thanks for the link, too.
Crustal motions. That helps to understand the neccessity for a Frame.
Dave
Dave,
I know I threw a lot of material up on that post.
So let me address your last comment regarding
Reference Frame and crustal motion.
By the IERS Conventions, a Datum is a Reference Frame.
I know there are some that disagree, but I know where
the IERS is coming from. Materialization is where the
rubber hits the road, where the coordinates are computed.
At the Datum (Reference Frame) layer, you would compute
crustal motion velocities. At the Reference System layer
you have the physics of crustal motion. You decide you will
model constant velocity, if you include episodic motion,
what tectonic plates and subplates are in the model. Or you
might put a unique velocity on each point. But, the actual
numbers materialize in the Datum (Reference Frame) layer.
Hope this helps some more ....
Dennis,
I'm swimming through your white paper right now. I've gone under a couple of times, but I'll keep after it. 
So to become a Reference Frame, a Datum needs points on the ground, their location and velocities, a point in time, and an official recognition of those facts. I think I've got it.
Dave
Dave,Horizontal Datums and Reference Frames
Dave,
OK, in the hierarchy:
A Datum is a Reference Frame.
A Reference Frame is a Datum.
They both have coordinates (and maybe velocities).
You used the word "become"; that's good.
Becoming represents less abstraction, more materialization.
We add stuff to the Ideal to get to the Reference System.
And we add stuff to the Reference System to get to the Reference Frame.
And, the Datum is the Reference Frame.
The Ideal Reference System is mostly geometry (e.g. an ellipsoidal
coordinate system). If we add physics to it, we get a Reference System.
This physics would include models of our measurements. This is the link
between our real world activities and the values of our coordinates.
When we actually add the measurements, then we can compute coordinates.
This is when we get the Reference Frame. (And, Datum = Reference Frame).
Now, it may be the case that we need to *define* some numbers, because
our measurements, by themselves, don't do the whole job. These extra
numbers (or procedural rules) are part of the step of going from Reference
System to Reference Frame. These are synonymous with Datum. Hence, in
NAD 27, MEADES RANCH is the datum point. These extra elements, and the
associated results, are denoted a Conventional Reference Frame.
Oh, by the way, regarding that white paper -- that is for GEOCON. The
Appendix was the key item. You might want to look at the Operating
Instructions and the User Guide if you are interested in GEOCON itself.
Couple other notes to support Dennis's line of thought.
NGS's Geodetic Glossary ( http://www.ngs.noaa.gov/CORS-Proxy/Glossary/xml/NGS_Glossary.xml ) has a second entry for geodetic datum (AKA horizontal datum).
Datum, geodetic: (2) The datum [reference ellipsoid], together with the coordinate system and the set of all points and lines whose coordinates, lengths, and directions have been determined by measurement or calculation.
To me, this is more of a colloquial name than a strict definition that datum=reference frame (i.e. "the NAD83(2011) epoch 2010.00 datum"). However, IERS produces the global ITRS reference system, which has different goals than NAD83. When a new ITRS frame is realized, the parameters of the datum actually do change (unlike NAD83), so I can see how one could tie the idea of datum and reference frame together regarding IERS's work.
-Ben
Ben,
Thanks for the input. 🙂
Dave,
Yes, there is the NGS Geodetic Glossary. It was a compilation of
definitions found in general use -- and it preceded the 1980 work
of Mueller and the IERS Conventions. As you see, it gives two (2)
definitions of datum. One is just a collection of a handful of
defining numbers, and the other is the actual materialization.
It was because of the variety of definitions, not just datum, but
also reference frame and reference system, that everything was
systematized in the 80's.
So, this is one of the "dirty" secrets about a geodetic datum.
It has two different meanings in use. (This is one reason why I
warned you at the start about different definitions.) The IERS
Conventions do not distinguish between a set of defining parameters
and the resultant Conventional Reference Frame. By the same token,
they do not distinguish between a set of measurements and the
resultant Conventional Reference Frame.
Now, Ben brings up a further point regarding an ITRF vs. the NAD83.
NAD (post 1986) represents a densification network within an
ITRF framework. This is done with a set of fiducial points which
are CORS (no surprise). Those points change coordinates under
different ITRF materializations, and they change coordinates under
different NAD materializations. NGS does attempt to retain the
original origin and orientation of NAD83 by a fitted transformation
of these fiducial control points. The final sections of my GEOCON
Technical Report address the fact that something got missed in
the fitting process for the NAD83(2011) epoch 2010.00. Since you are
reading the Report, this may help explain what is going on there.
Good question Dave, and great answers Dennis and Ben. Much appreciated.
It explains the confusion very well that some of these terms have been used interchangeably.
