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Question About Map Datum

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NAD 83 and WGS 84 for all practical purposes which you are using them for are one in the same. Your handheld GPS cannot distinguish between the two datums. So no worries.




I did not find my First Benchmark today untill I changed my gps legend setting to NAD83


When I had it sent for WGS 84 the gps was leading me a few blocks in the wrong direction.


Once I change it to NAD 83 it pointed right to the sign post that the description side it was at.

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Millbank -


I saw your post about your first find today, and I noted that it had SCALED coordinates. I has been my experience that a handheld GPS GOTO function will never point directly to a mark with scaled coordinates (unless by a complete fluke of errors).


The difference between the published coordinates and the actual location for a mark with scaled coordinates may be up to 600 feet. Most of the time, the actual deviation is much better than that - typically 100 - 150 feet.


If my handheld ever pointed directly to a mark with scaled coordinates (and got the distance right to within a few feet), I would chalk it up to an improbable, random error.


In my experience, the difference between NAD83 and WGS84 is, for all intents and purposes, 0. Anytime I've noted the difference, it was a fraction of the normal variability of the ever-changing distance measurement of the handheld itself.


I think that your experience in recovering your first benchmark is attributable to some other phenomenon than your change from WGS84 to NAD83.




p.s. - this topic much discussed in the past. though I am not a professional surveyor, I think CallawayMT and the other pros will agree, at least with regard to my general conclusions.

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408 benchmarks found, you people have been busy.


It also looks like you both enjoy finding benchmarks more then caches.


Do you have a different account for caches or do you just look for benchmarks.


If you only look for benchmarks may I ask why?


I must say finding my first benchmark disk today was really exciting.

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Millbank -


I don't look for caches because they just don't interest me.


I spend a certain amount of time and $$ (mostly gas but some Caladryl) planning to search for benchmarks, searching for benchmarks, and logging my results to Geocaching and NGS. The scope of that activity pretty much satisfies my desire to go out and about and hunt for things.


Someday, I will hunt for a cache. It will be the day after I or someone else has found or failed to find the last benchmark.




p.s. I think that sixthings and I are the only two benchmark hunters with more than 100 benchmarks and exactly 0 caches.

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Seventhings: If you ever get up to NY check out this benchmark. It is my first cache that I made a virtual. You can mark it as a benchmark if you don't want to mess your record up with other kind of finds. GC2A3E Also known as KU3344 the most interesting benchmark around these parts. LOts of people have come by to check the acuracy of their GPS's and enjoy the activities. :(

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If you only look for benchmarks may I ask why?


For the most part I do prefer the benchmarks, even though I do this for a living, I enjoy just getting out and looking for special or older marks. I log benches as a sort of map of where I have been lately; as I do a lot of traveling with work and also after work.


I enjoy looking for benchmarks and other survey marks, because I can really appreciate the work and especially some of the timing that went into the setting and surveying of these marks. For instance if you look at some of my finds you will find some MORC(Missouri River Commission) monuments; these were set in the 1880's around here in Montana. I go to these and think about the hardships that went into the survey of these and really appreciate their work that was done back in those days!


One more thing for you Milbank, are you sure you weren't switching between NAD27 and NAD83 or WGS84, because you would have not been looking in a new area in your switch between NAD83 and WGS84.


Anyway happy hunting, and remember those old timers when you are out there recovering those old marks.

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I have my GPS units set to NAD83, always have.


When USGS wanted positions on map features, they want the receiver set to NAD83.



Page 249




Charles R. Schwarz


This chapter addresses the differences between the North American Datum of 1983 and the World Geodetic System of 1984 (WGS 84) of the U.S. Defense Mapping Agency (DMA). Both NAD 83 and WGS 84 were defined (in words) to be geocentric, and oriented as the BIH Terrestrial System. In principle, the three-dimensional coordinates of a single physical point should therefore be the same in both systems; in practice, small differences are sometimes found. The original intent was that both systems would also use the Geodetic Reference System of 1980 (GRS 80) as a reference ellipsoid. As it happened, the WGS 84 ellipsoid differs very slightly from GRS 80.




To understand the sources and importance of these differences, it is necessary to take a close look at the concept of a datum and at how the coordinates in a datum are actually computed. The concept of a horizontal geodetic datum actually involves several ideas. A definition almost always begins with some form of specification of a reference surface. This involves the specification of the dimension of a reference ellipsoid, as well as quantities which determine the origin and orientation of the ellipsoid with respect to the Earth. (See, for instance, National Geodetic Survey, 1986.)


22.1.1 A Datum as a Coordinate System


A three-dimensional Cartesian coordinate system is associated with every geodetic datum. This coordinate system must be fixed in the physical earth. This specification of the origin and orientation of the coordinate system can be expressed in several ways. With local horizontal datums, these quantities were fixed by specifying the geodetic coordinates of an initial point and at least one azimuth. With the use of satellite geodesy, the origin and orientation of the coordinate system are determined (usually overdetermined) by specifying the three-dimensional coordinates of a number of points. A coordinate system can also be specified by describing the relationship between it and another coordinate system. This is the case with NAD 83 and WGS 84. Both are defined (in words) in terms of their relationship to the NWSC 9Z-2 coordinate system. Both transformations are attempts to realize the BIH Terrestrial System (BTS). The two transformations are exactly the same because DMA and NGS coordinated their efforts in this regard. Thus, the NAD 83 and WGS 84 coordinate systems are identical.


22.1.2 A Datum as Ellipsoid


The WGS 84 ellipsoid differs very slightly from the GRS 80 ellipsoid which was used for NAD 83. The differences can be seen in tables 22.1 and 22.2. These differences arise because DMA used the normalized form of the coefficient of the second zonal harmonic of the gravity field as a fundamental constant, while GRS 80 had used the unnormalized form. Furthermore, the normalized value used by DMA was obtained by using the mathematical relationship


and rounding the result to eight significant figures (Defense Mapping Agency' 1987). Thus quantities depending directly on the form factor, such as the flattening, generally differ after the eighth significant digit, while linear quantities, such as the semiminor axis, generally differ after the tenth significant digit. These differences, while small, can cause confusion among users who attempt to compare computations in the two systems. Most analysts agree that these differences will be of no significance for practical applications.


22.1.3 A Datum as Coordinates


The specification of a reference surface defines a datum only in an idealized sense. This specification is usually supplemented by a second definition which states that a horizontal geodetic datum is composed of the adopted horizontal coordinates of a set of physical points in that datum. This is the operational definition. It is from this second definition-the adopted coordinates-that we actually determine the origin and orientation of a datum. In this sense, the first definition is more a statement of intention than a statement of reality.


There are other qualities connoted by the concept of a datum. The idea that there are adopted coordinates implies that a datum is stable-the coordinates seldom change. Furthermore, a datum must be extensible-there must be some way of computing the coordinates of new points. Often there are preferred or expected ways to determine these new coordinates. For instance, it is expected that new NAD 83 points will be established by running new horizontal surveys using theodolites and distance measuring equipment. It is also expected that if one uses Global Positioning System (GPS) observations in the single point positioning mode, together with a satellite ephemeris given in the WGS 84 coordinate system, then the resulting coordinates will also be in WGS 84.


The idea of extending a datum by adding new points implies that there are some fundamental points from which the process is begun. By definition, these are the points that participate in the initial network adjustment, irrespective of accuracy or order. All of the points that participated in the NAD 83 adjustment are thus fundamental points of that datum. New points that will be added are not. In most geodetic datums, the distinction between fundamental and non-fundamental points has been lost. Typically a new point surveyed to first-order accuracy and adjusted into the network has been treated as equal in usefulness to a fundamental first-order point, and superior to a fundamental second-order point. This common, but incorrect, practice has often misled users as to the accuracy of a point's coordinates.


Some physical points are fundamental to both NAD 83 and WGS 84. The coordinates of these points in the two systems may differ because the two adjustments which produced the coordinates of the two sets of fundamental points were based on two different sets


of observations. For instance, a Doppler survey may have been performed at a point by either DMA or NGS, and the data may have been exchanged, so that both agencies had exactly the same data set. Furthermore, the two agencies agreed on all the details of data processing, so that both agencies determined the same set of Doppler-derived three-dimensional coordinates. Even further, the agencies agreed extly on how to transform the Doppler-derived NWSC 9Z-2 coordinates into the BIH Terrestrial System. However, in the NAD 83 adjustment these coordinates received corrections due to interactions with other observations (mostly classical triangulation and traverses), while no such corrections were made in the determination of the WGS 84 coordinates. These corrections can amount to a meter or more. However, both adjustments are still thought to be valid. The differences of coordinates are thought to be simply the effect of small random measurement errors in the two sets of observations. Even though differences as large as several meters are found occasionally, the expected value of these differences is zero.


Other physical points are derived, rather than fundamental. For these points, coordinates in the two datums may differ for two reasons:


1. The two coordinate determinations are based on different fundamental points.


2. The observations used to extend the datum may differ.


The method of labeling the datum for derived points is mainly a matter of convention. The actual physical observations (such as angles or distances) are themselves independent of any datum. When a new point is surveyed for the purpose of determining its coordinates, the survey must be tied to one or more old points. If the coordinates of the old point in the NAD 83 system are used in the computations, the coordinates of the new point are also said to be in NAD 83. Similarly, if the coordinates of the old point in WGS 84 are used, the coordinates of the new point are said to be in WGS 84.




NAD 83 and WGS 84 should be thought of" a! geographically overlapping datums (in the sense of datum as adopted coordinates). There will be points with coordinates in both datums. The action to take when confronted with two sets of coordinates for a single point is up to the user. If neither position determination contains a blunder, then the differences of coordinates should be small. In fact, the expected size of these differences can be computed from the uncertainties of the two determinations. If the differences are smaller than the accuracy required, then the user may select either determination (or some combination of the two).


"Small" differences must be properly understood here. The actual difference between coordinates may quite possibly be a meter or more. Although this might be disturbing to some, this is actually the magnitude of the uncertainty of the differences that would be computed from the uncertainties of the two coordinate determinations. It reflects the fact that the two coordinate determinations are independent and uncorrelated.


22.2.1 Mixing Coordinates


Surveyors are familiar with the limitations imposed when mixing the results of two independent surveys (or two datums) in a single positioning problem. Within a single survey, the relative coordinates of nearby points are much more accurate than the coordinates of either. This is not the case if the two sets of coordinates come from different surveys.


Suppose that within a local area there is both an NAD 83 point and a WGS 84 point. Suppose also that a survey is run to determine the distance between the points. The measured distance could differ from the value computed from the coordinates by a meter or more. Some might find this difference to be disturbing, but it is only a reflection of the fact that the variance of relative coordinates from two different surveys is much larger than the variance of the relative coordinates of two points from the same survey.


We thus say that the most common reason that we find differences between the NAD 83 and the WGS 84 coordinates of a point is that we are dealing with two independent determinations of the same thing. Both determinations are affected by the small statistical variations which are inherent in any measurement process. Each has its own associated standard deviation, but each is valid in its own way. The user may chose either, but must be careful about mixing coordinates.


22.2.2 Area of Validity


Some investigators have suggested that a difference between NAD 83 and WGS 84 is that NAD 83 is valid only within North America, while WGS 84 is valid worldwide. This is incorrect. If one has an accurate method of extending NAD 83 outside of North America, then there is no reason not to do so, nor is there any reason to think that the resulting coordinates would differ from WGS 84 coordinates. In fact, as


part of the NAD 83 adjustment, Doppler observations were used to extend the datum outside of the contiguous survey networks to isolated areas such as Greenland, Puerto Rico, and Hawaii.


22.2.3 Extending the Datum Offshore


The case of a ship navigating offshore is of particular interest to the hydrographic and bathymetric surveying activities of the National Ocean Service. If the ship navigates with a radio navigation system using shore-based transmitters, and if the coordinates of the transmitters are known in NAD 83 coordinates, then the navigated position will also be in NAD 83. The ship may also navigate with a satellite-based system which yields coordinates in the WGS 84 system. We expect both navigation systems to provide the same coordinates at each instant of time; but due to unavoidable measurement errors we may find small differences. The existence of such differences should not be interpreted to mean that there is a difference in the two datums. Unless there is some reason to suspect that one or the other navigation system is producing serious errors, the differences between the coordinates produced by the two systems should be attributed simply to measurement error. The navigator may choose to use either set of coordinates. Only the navigator with extraordinarily demanding accuracy requirements will need to worry about computing some combination of the two sets of coordinates.


22.2.4 Computational Differences


There are some differences between NAD 83 and WGS 84 which may arise because of approximations made in a particular method of computing coordinates. For most applications, the effect of these approximations is considerably smaller than the effect of observational errors. These differences are important only if one is testing the accuracy of a set of equations or a method of computing coordinates.


One such set of approximations concerns the different ellipsoids used for NAD 83 and WGS 84. This difference has no effect on the three-dimensional coordinates of a point computed by satellite surveying. If such a set of three-dimensional Cartesian coordinates is converted to latitude and longitude using the two coordinate systems, there would be no difference in the longitudes, and the latitude difference would be which reaches a maximum value of 0.000003 second of arc (or 0.0001 meter) at a latitude of 45 degrees. It is assumed that most users will ignore this very small difference.


Another approximation concerns the datum shifts computed for map sheets. The National Geodetic Survey has computed a latitude and longitude shift for every map sheet published by the U.S. Geological Survey. These pairs of numbers were computed by meaning the actual shifts from NAD 27 to NAD 83 at all points falling on the map sheet. These mean shifts are then assumed to be correct for the entire map sheet. Thus a very small error, amounting to the difference between the actual datum shift and the mean datum shift for the map sheet, is committed at each point. This error is everywhere much smaller than the observational errors committed when coordinates are scaled from maps.





Moritz, Helmut, 1984: "Geodetic Reference System 1980." Bulletin Geodesique, vol. 54, No. 3 (also republished in vol. 58, No. 3). International Association of Geodesy, Paris.


National Geodetic Survey, 1986: Geodetic Glossary. National Geodetic Information Branch, NOAA, Rockville, MD 20852, 274 pp.


Defense Mapping Agency, 1987: "Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems." DMA Technical Report 8350.2. Defense Mapping Agency, Hydrographic/Topographic Center, Washington, DC 20315.


Edited by elcamino
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Thanks To El Camino for pasting the Datum Info, that was cool! I know this thread is a little cold but here is some further food for thought. Some things we may know, or not.


Another way of looking at datums is like this, as simple as it can be, and in truth it really isn't simple.


Obviously we have the Earth. For horizontal and vertical measurements made on the Earth we have developed a reference standard surface level we call a Geoid. The Geoid is a hypothetical surface of the earth that coincides everywhere with mean sea level. This is not an average of peaks and valleys, this is as if everywhere on the globe, both under Mt. Everest and over Death Valley, Mean Sea Level is known. Think of it as having Mean Sea Level known in Oklahoma, even though there are no seas anywhere near.


How we know where Mean Sea Level (MSL) is, is a matter of which Datum you choose. If you page through your GPS you will see there are many choices. For this discussion let's stick to three.


NAD 27, NAD 83 and WGS84.


Now a Datum is a set of parameters that is used to describe where Mean Sea Level is. Inherent in the problem is that the Earth is not a perfect sphere, it is ellipsoidal and it has bumps and undulations in it that change over time. So since the geoid is not spherical nor perfectly elipsical, the Datum can't be either. The geoid does not make it easy on the datum to describe it.


If we could picture it in our heads we could imagine 3 one foot diameter globes meant to represent the earth as it actually is, but they each, in their attempt to be an exact replica, they fail just a little in their own ways, yet some offer more accuracy than others. All three a representation of Earth's Geoid. Each globe represents a Datum of the Geoid, such as NAD 83...


From the Mathematical reference standard Geoid (the datum) we measure both distances from point to point on the geoid (MSL) with Lattitude and Longitude, distances which represent elevations as depth below or heights above the Datum. The total surface Mean Sea Level allows us to have a reference to measure from, it is where the world wide zero point is.


The main things we need to know in a basic way are as follows.


Test the Datums for yourself. Take your GPS and go to a point about a mile or so from where you are, make that spot a waypoint and come back. Maybe you can use a waypoint you already have. Now, check which Datum your GPS is set to and then set a Go To with your GPS to that waypoint and write down the bearing and distance. Then change to several other Datums and compare your bearing and distance to that place across the datums. The further the distance from you the waypoint is, the larger the error. You are where you are as far as the sattelite is concerned, but the datums are handling where that waypoint is in reference to you differently. You will see it makes a difference.


Geocaching is a world wide activity. WGS 84 is usually the default Datum on most GPS and it is a Datum that works well anywhere in the world. You can take it from country to country and it works well, keeps things simple. I cannot reccomend using it for finding Benchmarks and it is unsuitable for reporting them.


The NOAA/NGS, by way of being the C&GS, NOS NGS etc, Have developed their models of the Geoid as time has gone by. They did a good bit of the early body of work in NAD 27 and The Latter in NAD 83. This is what they prefer to use. NAD 83 is the Datum required when looking for and reporting Bench Marks to NGS


Old Measurements are well, Old. It does not mean they are bad or cannot serve a purpose, But here is the problem. Not all earth is stable earth. Sometimes Earth moves via Tectonic activity, Disimilar soil type shifting, Hydrologic Forces, Earthquakes, Erosion, and Tampering, both intentional and unintentional. At the same time, The total database is very large. Yet many Bench Marks are missing or destroyed. How many old company watertanks and chimneys are now gone since the ending of the old industrial age? How has progress destoyed or buried some of the discs we have attempted to find? Buildings get remodeled. Did a road need repaved or a law that requred a wheelchair ramp in a sidewalk interfere with a Bench Mark? Many of those super tall Bench Mark/Landmarks (which were used for triangulation) are no longer with us, or are replaced with something new which is not the Bench Mark. Has anyone not noticed for many years until we noticed? Did the USPSQD not notice this Bench Mark change or discrepency from the window of their car as they drove by at 30mph? Then verified the the Mark "Good as Described" or "Not Found" after doing so? I know we all have found that Bench Mark before. (enough fun at their expense there) Of those that remain, they were monumented and that was likely the last time they may have had their position verified. They may have been found and had their condition and description reported but not measured. In addition, many of them have seem many things used to describe how to find them change, making some (as we well know) difficult to locate.


The scaled and adjusted coordinates we see on the datasheets for older Bench Marks were often originally derived from NAD 27, were originally scaled with rules on a Map, and are often not good enough to walk us right to an older Bench Mark with a GPS. That is what the description was always for. When we find them and report them with a GPS fix and report that fix by noting what the gps says when we place the GPS directly on top of the bench mark and write that coordinate down, we enable the future Scientists, Engineers and all the other professionals who use them an update that allows them to use their GPS to walk right to that Bench Mark and Go right to work.


When you use a map to help you locate a location, if it lists a Datum, Set your GPS to match the datum, then where you are on the ground will match the map. It helps! (really!) Many USGS Quadrangle Maps use the NAD 29 Datum, so when you find the Bench Mark, remember to switch back to NAD 83 for the Mark Position.


And Finally, remember that the Map is not the territory, the GPS is not the territory, the description is not the territory, and well, the territory is not what you might have expected. But do be impressed and enjoy! Happy Bench Marking!

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Old Measurements are well, Old.  It does not mean they are bad or cannot serve a purpose, But here is the problem. Not all earth is stable earth. Sometimes Earth moves via Tectonic activity, Disimilar soil type shifting, Hydrologic Forces, Earthquakes, Erosion, and Tampering, both intentional and unintentional.


That is something I have wondered about, especially here in California. The land around here is always moving in different directions with faults everywhere. How accurate are stations that were placed 50 or 60 years ago? What about ones that were placed 1800s?


With the number of faults running across LA and Orange counties in particular, it would be pretty easy to shoot a location across a fault line.


For example, the world's best known fault, the San Andreas, moves about 35mm/year. Over 50 years, this would be a difference of 6'. If a mark was placed in 1890, today, it would displaced over 13' from a location on the other side of the fault.


While the San Andreas is well known and is probably accounted for by surveyors, there are a lot of faults that aren't well known and are sometimes only dicovered when they rupture (i.e. earthquake).


How are these accounted for in surveying? Or are they accounted for at all because the movement is relatively small (i.e. 5 or 6 " over 50 years)?

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  How are these accounted for in surveying? Or are they accounted for at all because the movement is relatively small (i.e. 5 or 6 " over 50 years)?


Well there are several answers to this, and it depends on what you are trying to do.


First off, for many years, these little discs and the measurements made with them were how we knew the faults, such as the San Andreus and any others moved and how much. Getting back to which are geologicallly more stable than the others is a mater of simply retrangulating them to get a new fix on position and elevation, and then updating the data. Bench Marks in high movement areas are as a matter of course, updated much more frequently.


Some discs which are in high movent areas got a lot of updating through re-leveling and triangulation, and some still do, as any benchmark can be used to do it, but some are used more than others due to location, ease of use etc. Much of the work that monitors geodedic stability is monitored through CORS stations for the NGS and other agencies too as we have learned. Then there is the work of monitoring the movement of shorelines as well.


In the case of a local surveyor using a 50 to 75 year old Bench Mark that has not been checked in a while, well things are not so bad as you think. The Criteria for seting a Bench Mark is pretty stringent, the book on how to do it is available from the NGS as a pdf file here: http://www.ngs.noaa.gov/PUBS_LIB/GeodeticBMs.pdf So we know that the attempt to be as stable and accurate as possible was made when it was monumented, and unless it looks disturbed, and from the recovery notes, we have to trust that it will be good enough for our purposes.


It is rather like an order of relativity for the Local Surveyor. He is not using the station to Trangulate for geodetic reasons. Rather he is likely to use it as an elevation reference to traverse from, and he may use it and another to perform a triangulation for local civil work, but getting back to the relativity part, it is a local area survey, and so if the benchmark has moved by 2 hundreds of a foot in 75 years, it is good to know, but that wont hurt you when you are solving for the rise over run for a sewer line, A storm drain, Grading a road or setting the site elevation for a building pad. Besides, the likelyhood that the benchmark is what it is supposed to be is very high.


So the answer is, Some stations are checked more often than others, and the stations that are not are still in many ways pretty accurate when where they are located and the local conditions taken under consideration. In the end, it can depend on what is being attempted on the survey, and who the survey is for.

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