In a conversation I had with Loyal Olson a couple of years ago, researching for an article I have never gotten around to writing about Local, Low Distortion Projections, Loyal started me thinking on an idea.
I love industrial-age technology and the State Plane Coordinate System is no exception. Considering the value the system added to surveyors in the ability to calculate geographic coordinates from chain and transit surveys conducted from a known geographic point is pretty slick, especially with limited computing power. However, with modern computing power being what it is, custom projections can be developed and implemented as easily as SPC's with the added benefits of less scale distortion and North being very nearly North.
Thanks to a nifty program developed by a friend several years ago, my HP-49G calculator can develop custom projections and reproject to any other projection (SPC, UTM or custom, as well as Lat/Long). This got me really started in local projections, since then, we've acquired a data collector that works with custom projections and more recently CAD software that will as well. Our GPS post processing software has facilitated custom projections forever. So the implementation has become very easy. Third party applications, like Global Mapper also have this feature for a pretty low price.
With the latest adjustment of NAD83, I'm wondering just how much longer it will be until we drop NAD83 and make the step into ITRF at a defined epoch. One of the concerns with this is that ITRF is a 4D system, comprised of time (and thereby velocities). So our points are in constant motion, which seems unruly to manage. How do you do a survey today, that borders a survey you did five years ago, with all of the coordinates now moved several centimeters in space?
I would submit that a LDP (Low Distortion Projection) would be a viable solution to this problem. Depending on the control source, a particular epoch could be used for several years. Only once a new epoch was used for the control, would the movement of the coordinates become an issue. How often this might need to be done would be up to the surveyor or whomever might have jurisdictional control over his work. Once a new epoch was implemented, a new LDP could be designed. But in this new LDP, the only modification to be made would be the false Northing and Easting values. The LDP name could be date tagged to correspond with the ITRF epoch. The result would be that the plane coordinates of the job from five years ago could be unchanged from the coordinates of this year's job, even though the underlying geographic coordinates might be entirely different.
For instance. This year I perform a survey of the Baker Estate, which encompasses 500 acres. I start of with a GPS control survey tied to NAD83(2011) by ties to CORS. I develop a custom projection, which I name Baker2012, with scale factors so insignificant they can be ignored with no adverse effect to the survey. With my LDP loaded in the GPS software, any additional GPS control can be worked in to my real world coordinate system without any Grid vs Ground issues. My total station turns angles and distances that directly compute to coordinates on the LDP grid. When I inverse between coordinates, 100 feet is really and truly 100 feet. North is very nearly North through out my project because I'm very near the design central meridian. My CAD file and coordinate file is left in my local system.
In 2014, a developer purchases the Baker Estate, and wants to divide half of it into large tracts. Returning, I continue to use the same GPS control as before, using RTK to mark corners, I place the base on a control and begin work without any localization (because it isn't necessary) my projection, entered in the data collector, automatically puts me on local coordinates.
In 2020, we are called back to survey the remaining tract for a city water treatment facility. NAD83(2011) is obsolete. The modern technical procedure is to place surveys on ITRF, epoch XXXX. Using the modern equivalent to HTDP, I determine that the translation from NAD83 to ITRF is 2.5 feet in Northing and 2.8 feet in Easting. I apply these values to the false Northing and false Easting of my Baker2012 projection and name it Baker2020. I use the network RTK service, which is based on ITRF, epoch XXXX, in my area to survey the tract for the city. Because I handled the translation in my new projection, I am still able to survey on the same coordinates I used back in 2012, even though the underlying geographic coordinates are several feet different. I continue to work on the same system, adding coordinates to the work I've done over the course of several years with no need to translate from one system to the other.
The State Plane Coordinate System benefits from universality in its codified parameters. It's easy for Trimble, Leica, Carlson, MicroSurvey to include predefined projections, like SPC, because they are written in stone. However, SPCS's lack the agility to move with their user's needs. We'll continue to publish SPC's on our surveys, but it isn't difficult to see the end for them coming into view.
In agreement and hLow Distortion Projections and ITRF (long)
In agreement and have seen the problem from the day the movement of the Earths crust was first able to be measured by GPS. I didn't expect that the light would dawn during my lifetime. Large projections have their uses, but they serve local surveyor poorly because we live on a live planet. Looking forward to more of your writings.
jud
I proposed a similar concept a few years ago, with a twist.
I do deformation surveys on 39 dams around here. All of the monitored points (anywhere from 5 to 120 points on each damn) have NSRS2007 coordinates. I cannot have coordinates changing, or it would not be possible to detect actual movements (at the millimeter level).
So, I suggested picking one of the reference points (usually a pedestal) at each project, and creating a simple tangent system with origin at that particular point. So, the system would be created by assigning say 1000/5000 coordinate to that particular NSRS2007 lat/long. If the coordinates change (as happened with the 2011 adjustment, or if they decide to go to ITRF), I would just change the definition of the system such that the same origin point would still be 1000/5000, but the lat/long would change in the definition. Since any rotation is likely to be extremely small, and the systems cover a limited area (up to 1 mile), the local coordinates would not change. And it would be easy to go from grid to geodetic and back.
I would use a very simple tangent system raised to the surface rather than a more complex LDP, Lambert, or TM system. Since the areal extent is small, scale factors would not be an issue.
The same concept could apply to a county-wide system, but a more complex LDP system could be created.
Here is a real world example that I worked with:
City of Pittsburgh origin is at 40°26'N, 80°00'W on NAD (predecessor to NAD27). The coordinates at that point are 100,000N/100,000E.
Next they went to NAD27, then NAD83, then NAD83 1992, then NAD83 (NSRS2007), and now NAD83 (2011). Each time the latitude and longitude of the origin changed:
NAD: 40°26'00"N/80°00'00"W
NAD27: 40°25'59.60277N/79°59'58.89709
NAD83 (86): 40°25'59.852057N/79°59'58.08817
etc.
But the grid coordinates never change. The software has to be setup so that the origin coordinates can be changed. By specifying which system (and therefore which origin coordinates to use) the transformation from grid to geodetic can be easily made.
Not being expert on these matters, I nonetheless wonder why resort to a 2D system when trying to understand real-world 3D changes. Why not use geodetic coordinates (latitude, longitude and ellipsoid height) for sites then work in ECEF Cartesian and LGH (DX,DY,DZ and DE, DN, DU)?
I can do anything with geodetic coordinates and still retain 3D coordinates.
LDP's are standard for me and have become very simple (small ones). I'd take the approach of fixing the Origin to a monument on the ground. This origin has the false northing and easting and I decide on an elevation to calc the scale factor. I use OPUS to get the lat and long. So assuming that the project is not so large as the earths crust can be assumed to be stable in your LDP area then your LDP grid coordinates are fixed and won't change. Then the only thing that would need an update for time would be the geodetic coordinates of your origin. So as time passes you just measure the hard origin point and update the lat and long of your LDP origin and you are good to go. Probably should have a few hard points in case your origin monument gets destroyed. If your whole LDP area rotates then in the future you would need to apply the rotation or use an LDP you can rotate to keep everything straight.
So it appears I'm doing the same as John.
> The State Plane Coordinate System benefits from universality in its codified parameters. It's easy for Trimble, Leica, Carlson, MicroSurvey to include predefined projections, like SPC, because they are written in stone. However, SPCS's lack the agility to move with their user's needs. We'll continue to publish SPC's on our surveys, but it isn't difficult to see the end for them coming into view.
I think you're glossing over the power of standard projections. When you get a chance, post examples of the metadata for the custom projection you're using that you'll have to attach to every map and every written description that you prepare unless you want to simply pretend you have no idea what the geodetic coordinates of the project are, but have used a local coordinate system just like the old days.
Presently, the LDP's we've been using are in-house only. I still put SPC's on all of our boundary work. (Converting between and LDP and SPC is very simple with many software programs available today). On our plats, bearings and distances are geodetic-ish and horizontal surface just like we've always done. The only exception was a couple of topographic surveys for the nearby city a few months ago. One was fairly long, the second was not so big, but a couple of miles away from the first. I left the CAD work in the LDP I designed for the city, and labeled LDP coordinates and SPC's for several primary points and gave the projection parameters in the metadata. Ultimately, I think a surveyor could work in her LDP system and publish Lat/Long. She would then only need to give metadata for the coordinate basis (ie NAD83,2011 tied to NGS CORS...), bearing relation, and units for distances.
Businesses, including surveying businesses, data collector manufacturers, and software vendors, are generally quite a bit more fragile and subject to change than the earth's crust. (This might even be true in Iceland; tough to tell which will fall apart first, the ground or the economy.) The consumer of a survey would be foolish to assume that the surveyor, the data collector, or any proprietary software data format will still be around in 2020. In the absence of a land transfer, the only way to publicly record a boundary survey in my state is to submit a mylar to the town clerk. So don't tell me about your wonderful software, tell me about the test you've run on your plotter ink to be sure it will still be adhering to the mylar in 2020. And reassure me you bought your mylar from a reputable manufacturer and not from some country with a reputation for lead paint on baby toys. Did you ever run a test to see if it is practical to accurately transcribe all the data necessary to reestablish the low distortion projection from a mylar?
A traditional survey contains a great deal of redundant data, so if a spot on the mylar becomes illegible when a town hall visitor scrapes it across a sharp desk corner, the illegible patch can be reconstructed by calculation. What if the scrape runs right through one of the projection parameters? (OK, that objection might be equally applicable to state plane coordinates if only one or two points have their coordinates stated.)
> Businesses, including surveying businesses, data collector manufacturers, and software vendors, are generally quite a bit more fragile and subject to change than the earth's crust. (This might even be true in Iceland; tough to tell which will fall apart first, the ground or the economy.) The consumer of a survey would be foolish to assume that the surveyor, the data collector, or any proprietary software data format will still be around in 2020. In the absence of a land transfer, the only way to publicly record a boundary survey in my state is to submit a mylar to the town clerk. So don't tell me about your wonderful software, tell me about the test you've run on your plotter ink to be sure it will still be adhering to the mylar in 2020. And reassure me you bought your mylar from a reputable manufacturer and not from some country with a reputation for lead paint on baby toys. Did you ever run a test to see if it is practical to accurately transcribe all the data necessary to reestablish the low distortion projection from a mylar?
>
> A traditional survey contains a great deal of redundant data, so if a spot on the mylar becomes illegible when a town hall visitor scrapes it across a sharp desk corner, the illegible patch can be reconstructed by calculation. What if the scrape runs right through one of the projection parameters? (OK, that objection might be equally applicable to state plane coordinates if only one or two points have their coordinates stated.)
LDP's, fortunately, are often published by states and counties, in pdf. check out some of these, Cochise County AZ, all of Wisconsin, all of Oregon (thanks to shelby and others). At least that would possibly account for any mylar smudges. include your metadata, but you could also reference a publication.
in addition, if a good LDP is submitted to NGS, they will include the parameters and outputs in any given flavor of OPUS (per Loyal Olson). now there are up to two degrees of freedom on your projection data.
NGS & LDPs
Although there is (or was) talk at NGS HQ about creating an LDP database (possibly linked to OPUS), that has not as yet come about as far as I know. When (or even if) this will happen is above my pay grade (which is ZERO).
I do believe however, that this IS the wave of the future in more ways than one.
LDPs have been in use around these parts since [AT LEAST} the late 1970s, and become more widespread every day.
Example of Projection parameters:
Coordinate System : Tooele County (TCCS2011)
Zone : Tooele City Special (t06)
Projection : Transverse Mercator
Datum/Reference Frame: NAD83(2011) Epoch 2010.0000
Linear Unit : U.S. Survey Feet (USSF)
Central Meridian = 112° 14' 5.000000" West
Origin Latitude = 40° 30' 0.000000" North
Scale Factor = 1.000 235 244 (unitless)
False Northing = 20,000.0000 USSF
False Easting = 145,000.0000 USSF
Design Elevation = 5,000 NAVD88_USSF
Loyal
> Presently, the LDP's we've been using are in-house only. I still put SPC's on all of our boundary work. (Converting between and LDP and SPC is very simple with many software programs available today). On our plats, bearings and distances are geodetic-ish and horizontal surface just like we've always done.
That's sort of the worst of all worlds. You provide the coordinates of boundary corners in a completely different system than the one in which you express bearings and distances? If they were in the same system, some other surveyor could digitize your coordinate list and use the bearings and distances in your written description as an easy check.
Basically, it sounds as if you're using the Custom Projection as a workaround for not wanting to deal with scale factors and mapping angles, which seems weird to me since you end up with isolated surveys that each has its own reference North, just like the bad old days. In theory, perhaps some future surveyor can spend some time and figure out where your survey falls on some standard projection, but I see that as being a time wasting exercise when a survey involves many different tracts (either directly or as adjoiners), each with its own custom projection.
I can see that a Custom Projection would be a useful workaround when you are providing CAD products to engineers and architects, since neither are likely to be able to deal well with the SPCS. However, dumbing down the records of boundary surveys just because an engineer was involved doesn't seem like the best choice.
> in addition, if a good LDP is submitted to NGS, they will include the parameters and outputs in any given flavor of OPUS (per Loyal Olson). now there are up to two degrees of freedom on your projection data.
In my opinion, the codification of projection parameters by statute is the superior option. Anything that a DOT or the NGS maintains won't really be permanently archived for the obvious reasons.
When we list a call for a bearing, we prefer that bearing to be relatively close to referencing North, not some abstraction of North. And when we give a call for a distance, we prefer that distance to very nearly represent the actual distance here at Earth surface where we live, again not along some abstract plane somewhere below or above us. We give the convergence angle and the scale factor. If a savvy user of SPC's wants to calculate around, he can easily apply the convergence angle and combined scale factor given in our metes and bounds description or on our plat to the reported bearings and distances and have grid bearings and grid distances. For the uninitiated, North is North and 100 feet is 100 feet.
As for the use of low distortion projections, I think they are a very suitable intermediary between ECEF coordinates from GPS and angles and distances from a total station. What's more, they also facilitate publishing work in ECEF, Lat/Long, SPC, UTM or any other projection, as well as vectors between points on any of those systems. It's a gateway.
I understand your hesitation. I have a profound respect for the SPCS and the computing power it gave our professional progenitors. And the system still works, same as it always has, but has sadly been abused to the point of impotence. (How many questions come to mind when you see a published State Plane Coordinate? Do you have the same questions when you see a published UTM coordinate?) I can see a beneficial evolution from the SPCS of old to the prowess of custom projections.
Perhaps an affidavit filed at the county clerk's office could alleviate this? Not sure if this would work, just a thought off the top of my head.
NGS & LDPs
Loyal, is the idea to update the origin lat and long as CORS updates?
This would "fix" the coordinates and allow new OPUS/CORS solutions to attach to the coordinate system.
I've been having this exact problem (coordinates moving on points, but more importantly elevations shifting with new Geoids); but in state plane projects. Old state plane jobs from the late 1990's (with high resolution photos already flown), originally located with GPS from HARN points and first order bench marks get an OPUS solution thrown over the top with the new GEOID model: what a mess!
I have at least 3 projects where this has happened.
These are all state plane but the same problem can happen in an LDP, although, I think it would be muted as the surveyor would have to at least look at the parameters before he started.
I notice there is no mention of an elevation system (GEOID model, bench marks) in the projection parameters.
> When we list a call for a bearing, we prefer that bearing to be relatively close to referencing North, not some abstraction of North. And when we give a call for a distance, we prefer that distance to very nearly represent the actual distance here at Earth surface where we live, again not along some abstract plane somewhere below or above us. We give the convergence angle and the scale factor. If a savvy user of SPC's wants to calculate around, he can easily apply the convergence angle and combined scale factor given in our metes and bounds description or on our plat to the reported bearings and distances and have grid bearings and grid distances. For the uninitiated, North is North and 100 feet is 100 feet.
>
> As for the use of low distortion projections, I think they are a very suitable intermediary between ECEF coordinates from GPS and angles and distances from a total station. What's more, they also facilitate publishing work in ECEF, Lat/Long, SPC, UTM or any other projection, as well as vectors between points on any of those systems. It's a gateway.
>
> I understand your hesitation. I have a profound respect for the SPCS and the computing power it gave our professional progenitors. And the system still works, same as it always has, but has sadly been abused to the point of impotence. (How many questions come to mind when you see a published State Plane Coordinate? Do you have the same questions when you see a published UTM coordinate?) I can see a beneficial evolution from the SPCS of old to the prowess of custom projections.
That is possibly the most cogent response and argument to look hard at them. I especially love the "North is North and 100 feet is 100 feet" part. There is so much molestation of the SPC by the "other" end users that is finds the best of both worlds.
Now, that being said, since you're like 40 miles North of me, the scale factor cannot be that bad. That's the benefit of working in the low lands (under 800') and near the zone boundary lines. 🙂 Get down in the Sabine river bottom and in the corner of the zone, and 100' is 100', regardless of the projection you're on. All that is really needed is a convergence angle and you're running! 🙂
To stay on point, good job. I remember when you and your Dad were building this and you two took painstaking process' to make sure that it worked No. 1 and that it was reproducible by others No. 2. Good job buddy!
I work in so many counties, and it's easier to just stay on the grid and report what I'm doing that to set up LDP for every field or large tract. If'n I were working in the Davis Mountains or the middle of a zone where the factor makes more than say, 1.0' per mile, then I might look really hard at it. For the 4 mile pipeline I just did in Van, Texas, 4 miles was 21,120' surface and my grid distance was like 21,117.70 feet.
This is the in-house data sheet I worked up for the City of Kilgore Projection we created. I've done similar data sheets for some of our other projections as well. Like Loyal showed, really the critical information needed are the name, projection type, and, in this case, the Lat/Long of the origin, the false N and E, and the scale factor. This scale factor would allow me to traverse a mile anywhere in the City and lose a couple of hundredths (at the worst) in accuracy if I ignored it. With GPS, I'm not likely to traverse a mile anymore, so it really isn't an issue, but it gives some perspective. The rest of the report is just showing my work, which wouldn't necessarily need to accompany every plat or description I prepared using the projection.
As for software and formats, as I tried to explain, I'm not using specialized software. I'm using a Carlson data collector and Carlson desktop, I've got several GPS programs that all support custom projections, and I even have my $100 calculator (HP-49G) loaded with a wonderful program from Chuck Rushton that I use to actually create and test my projections. I know Carlson isn't the only one to support this. I also have a least squares program that handles custom projections as well. Personally, I could foresee using the custom projection for the intermediary between GPS and terrestrial work and also to mediate differences in adjustments in our control structure, and simply report lat/long. Even less metadata required there.
thanks for the kudos, Kris. I certainly wouldn't suggest that LDP's are the panacea for every ill. It's just a technology that I think could make a valuable contribution for some applications.
Considering the use of your end product, I probably wouldn't have worried about using anything other than SPC either. It helps to know when to get the robot out of the truck and when to grab the cloth tape, so to speak.
(Glad to see y'all are busy).
> When we list a call for a bearing, we prefer that bearing to be relatively close to referencing North, not some abstraction of North.
Well, North is either North or it isn't. I take it that "North" only means geodetic North on one meridian of longitude in your project. Everywhere else it doesn't. So you don't avoid the mapping angle problem and with the bizarre twist that adjoining tracts will have different bearings on the exact same line between the exact same monuments.
> And when we give a call for a distance, we prefer that distance to very nearly represent the actual distance here at Earth surface where we live, again not along some abstract plane somewhere below or above us.
Well, there's no difficulty in reporting surface distances in the SPCS as long as they are all computed using the same Combined Scale Factor.
> We give the convergence angle and the scale factor. If a savvy user of SPC's wants to calculate around, he can easily apply the convergence angle and combined scale factor given in our metes and bounds description or on our plat to the reported bearings and distances and have grid bearings and grid distances.
It sounds to me as if you have never gone through the exercise of trying to put quite a number of tracts on the same projection. Having to deal with as many different projections is a major waste of time. The rational alternative is to put them all on the same projection. Once a standard county projection is adopted and published, I see no reason not to use it. However, following your desire to keep mapping angles as small as possible (for a reason that doesn't make any surveying sense, particularly), you will still be wanting to create a custom projection for every tract.
> As for the use of low distortion projections, I think they are a very suitable intermediary between ECEF coordinates from GPS and angles and distances from a total station. What's more, they also facilitate publishing work in ECEF, Lat/Long, SPC, UTM or any other projection, as well as vectors between points on any of those systems. It's a gateway.
I'm afraid that doesn't make any sense at all. There is no difficulty at all combining conventional survey measurements with the SPCS.
> I understand your hesitation.
I don't think you probably do if you've never had the experience of being able to lift the coordinates of some distant corner directly from a metes and bounds description or map without basically recomputing the entire survey from which it was taken. This is fundamental to work with large tracts and many original land grants. The custom projection are really more one-off deals for engineering projects and tiny parcels.
Mighty
I have several “projects” in which the PROJECTION PARAMETERS have been updated over the years, INCLUDING several that started out with a NAD27 LDP.
In the case of the 1927-1983 “update,” the change in Longitude made things a little tricky, BUT it still worked just fine.
NAD83(1986)-NAD83(1994)-NAD83(2007/CORS96)-NAD83(2011) are pretty easy because the change in Geodetic Position is rather small (and getting smaller every time).
I don't worry too much about GEOID Models when talking about LDP Projection Parameters, simply because the change from [say] GEOID99 to GEOID12a isn't enough to impact the transformation in the horizontal component (N/E). Changes in the Realization DOES effect the Ellipsoid Height, but that is a different issue all together, and still a trivial consideration in the horizontal. A few centimeters (or even decimeters) in the vertical, doesn't really effect the horizontal component enough to worry about in my opinion. In any case, out in these parts an “average” 'N' value must be used anyway (18.0 meters in the above case), and that value can vary half a meter (or MORE) even within a fairly small “zone.”
I DON'T really trust GPS derived “elevations” all that much, so I generally recite the GEOID Model (& 'N' value) actually USED on a given Station when returning GPS derived NAVD88 heights, and let the chips fall where they may. IF I REALLY CARE about NAVD88 heights, then it's time to break out the LEVEL.
Loyal
