Background info
The prior thread on what I presume to be the same project is [msg=171761]here[/msg]
The ultimate goal stated there was to find the tilt of the water table between wells over a moderate size area in order to estimate its flow. So absolute elevation is not so important, but differences between wells is critical.
At the 2 cm level, the nuances of geoid models, orthometric corrections, and the very definition of height become important. I'm not smart enough to be sure how to define what they want, even given perfect ellipsoid OR Helmert Orthometric heights at each well. My best guess is that they really need Dynamic Height. In any case, having a decent gravity/geoid model is important.
Background info
It's not the same project, but in general that kind of accuracy is what we're going for in a lot of our projects. In this case it's surface water levels along with well water levels that we're measuring. I think part of the desire for 2 cm vertical accuracy comes from in the past where, through traditional leveling, vertical accuracies of 0.1 ft were possible. The desire is to get similar to that using GPS to avoid the time and difficulty of leveling.
Background info
Does someone on your projects understand the things I alluded to, for instance how to find dynamic height from orthometric height or raw leveled data, and why dynamic height is the likely choice for hydrological work?
Background info
That I don't know. I'll have to ask. I did save the examples you posted from the previous thread, though. Thanks for those.
> If we have HARN points with published elevations of First Order vertical accuracy and known errors (I'm thinking of the network and local accuracies on the NGS datasheets), why do we need to survey the HARNs in advance and establish a control network when we already know what the elevations and accuracies are?
The HARN designation is irrelevant to your goal of vertical accuracy, so it doesn't matter if you have HARN stations or not. What you want is reliable NAVD88 orthometric heights. If your HARN stations happen to be First Order NAVD88 benchmarks and they're not in a subsiding area, you're one step closer to your goal.
Next, as Cliff Mugnier said, you need to know what the geoid is doing between your reference bench marks and your site(s) of interest. If the model (e.g. GEOID09a) is known to be accurate, you're another step closer. If it isn't you need to improve it. If you don't know, you need to find out. The best way to do the latter is by running geodetic levels from known bench marks to your area of interest, but that tends to be expensive. Next best might be to run some crosses (geodetic level lines run at right angles to each other) with, say 10km legs, and distributed across the area between the known bench marks and your area of interest (in effect, sampling the reliability of the model). Still pretty expensive, though. Third best is to run GPS sessions on legacy bench marks (e.g. NGVD29, USGS, or local agency) distributed across the "unknown zone" to see if you can discern a reliable pattern to validate the model. (Sort of like the USACE CEPD approach.) Again, this can consume a lot of time both in the field and in the office.
With regard to L1-only: NGS-58 and 59 allow L1 for vectors up to 10km (L1-fixed is the gold standard). After that, you have to use L1/L2 to get iono-free fixed solutions. Since you need dual-frequency for a primary 40-km network, you're out of luck with L1-only unless you want to bridge the entire span from your reference bench marks to your project site(s) with a 7-10 km L1 network (as Paul suggested). Way too much work to avoid using L1/L2, in my opinion.
Also: In my experience, the 30-minute sessions called for by NGS-58 and 59 are too short unless conditions are ideal, which they rarely are. We routinely use 1-hour sessions for 7-10 km vectors in height mod projects, and a significant percentage of those still fail the QC test. More than a few times I've seen a group of repeat vectors spread across Day 1 that agree within a few millimeters, and another group on Day 2 that agree within millimeters, but between days there's a 4 cm difference. Which group is correct? Time to reobserve...
Reliable elevation transfer over long distances via GPS isn't for the faint of heart. (And if you're wondering which way the water is going to go, note what Bill said.) Trying to get by with inadequate equipment is likely to turn the exercise into a big waste of time and a false sense of reliability. With old-school L1/L2 geodetic receivers going for less than $500 on eBay, why futz around with L1-only?
Background info
A quick lesson in heights, as I think I understand them. I know just enough to be dangerous, so welcome corrections.
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Still water stands at constant gravitational potential over its entire surface.
A particular constant gravitational potential surface, chosen near sea level, is called the geoid. The geoid wanders up and down with respect to the ellipsoid model of the earth depending on the irregular composition of the earth and the resulting small changes in gravity.
Dynamic height is just a units conversion from gravitational strength, to get a more familiar representation in feet or meters. Thus still water stands at a nearly (precisely?) constant dynamic height. The conversion factor is a standard reference value of gravity. Dynamic heights are not truly feet or meters, but the approximate relationship to true distances is useful for some purposes. It is sort of a flexible measuring tape that changes with gravity. Dynamic height is given on NGS data sheets for vertical control marks, as well as the Helmert orthometric height.
Ellipsoidal height as measured by GPS and orthometric height are both in standard units of true feet or meters, but measured from different starting points. The difference between them depends on the geoid shape.
We can't really know where the geoid is, somewhere under the land surface through varying density of rock, but use a model to "find" it from surface gravity data (Helmert orthometric height). That data is currently a little crude for converting between GPS (ellipsoidal) heights and orthometric heights, but will get better via the NGS 10-year project GRAV-D.
Dynamic height differences do not match ellipsoidal or orthometric differences when applied to points with gravity that differs from the reference value. Two surfaces, each of constant dynamic height, are not the same distance apart unless the gravitational field is uniform.
As a thought experiment, imagine two mine shafts, one 20 miles north of the other, and connected by an underground tunnel. Place a trough of still water in the tunnel and another at the surface. Measure the difference in height between the water levels at one end with a calibrated pole (orthometric height difference or ellipsoidal height difference). Then go to the other end and you will find that your measurement does not match by a few centimeters. The dynamic height difference (gravitational potential) between the water levels at one end is the same as the dynamic height difference (gravitational potential difference) at the other end. The orthometric height differences do not match.
Why do we use orthometric heights for so many purposes, when it doesn't quite represent how water will flow? Because the feet and meters are standard and easy to work with, and the difference in water behavior (running "uphill") is negligible for typical projects. That's why NGVD29 and NAVD88 are in orthometric height. The difference may not be negligible for precise studies of water tables over a state. The Great Lakes Datum is in dynamic height because it is used for the behavior of water over a huge area.
Precise optical leveling over long distances needs to account for changes in gravity along the route. When you sight the level you are following (close enough) a constant dynamic height. When you measure up or down on the level rod, you are working with orthometric height differences (or ellipsoidal height differences for that matter). The discrepancy between dynamic height and orthometric height accumulates on long routes, and there is a formula for applying the "orthometric correction" to the measurements. Perfect measurements over different routes will get different answers if the correction is not applied. A correction can also be calculated to remain in dynamic height, but that is less common for surveyors to do.
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And please, everyone, educate me where I've strayed.