Low Distortion Projections

[DWoolley]

I have read most everything I can find on Low Distortion Projections (LDP). Shaun Billingsley wrote a two part series in American Surveyor circa 2012 - at that time I concluded the LDP was gimmicky and figured the idea to be short lived. There are lots of smart folks signed onto the idea of creating LDPs. I am thinking I may have a blind spot. To my knowledge, I have not had any issues working with state plane coordinates on large or small projects.

I have a few questions:

1. Is the only purpose of an LDP to make grid and "ground" distances the same?

If the answer to 1 is yes, then:

2. What problem is being fixed? Years ago, I keep a log of how many times I measured with a total station over 1000'. It was less than a handful of times annually. Longer distance were measured using static GPS. I am completing a large project now. The difference between grid and ground is 0.15 feet in 5280' feet - 0.01' per 300'. This means I am beginning to exceed the instrument specifications of 0.02' in 600'. We limit our setting of construction stakes at 500' - grid and ground are the same at 500'.

3. Why distort good grid measurements? Grid is always grid is always grid. Besides subdivision mapping and final monuments - which are set with an instrument at distances less than 300' from known control - how does an LDP i.e. distorted coordinates benefit a project?

4. Has anyone looked at the 38 zones in Oregon? California has six in comparison. Oregon has layered their zones by overlapping zones. In fact, some zones have a boundary that overlaps two existing zones. This means a small project could be in three different zones.

If the surveyor is using RTN GPS grid and ground do not matter in most instances due to the golf ball accuracy of RTN.

I appreciate any thoughts that might help me better understand an LDP. Thank you in advance.

DWoolley

[Robert Martin]

Not speaking directly to LDP but when I worked at a firm in Oregon most of the projects were put on a "Local Projection" one benefit being ground dist.=grid dist. but the larger benefit was no convergence! The rotation of the Local Projection was based on a record bearing, so there was no rotating back and forth from record ground bearing to field grid bearings for mapping verses staking, or mapping verses field ties.

Right now I’ll bet 99% of my projects are on SPC. The only bugger about it is rotating and scaling back to a record bearing and ground distance for mapping the project. But still, that is a minor inconvenience compared to the major benefit of having 99% of my projects on SPC.

[Jim Frame]

Shaun Billingsley wrote a two part series in American Surveyor circa 2012

I don't have the articles in front of me, but I'll bet the author was Shawn Billings. He often advocated in favor of LDPs (and probably still does).

I have yet to encounter a job that justifies the development of an LDP, but I mostly work in an area where the combined factor is around 0.99996. My understanding is that the folks who work thousands of feet above sea level find the concept more appealing.

[CBarrett]

I read the articles, and it sounds like they want to make state plane coordinates more usable to non-surveyors in the field, with surveyors controlling how the datums fit together.
I can't foresee what kind of consequences this would have overall. If these are done right, and transparent to the end user, like a utility locator, they can reduce errors due to datums, but if the end user has to tinker with datums, then it could be a disaster. I guess a lot would depend on implementation.

As far as managing a multitude of low distortion projections, we already do that on each project in a little less formalized environment, with localized projections and coordinate systems on every single project, and on occasion when there are sister projects next door, they will share a projection. (I think most of that goes without saying really)

If we want to put the world on one coordinate system, or at least large areas, why not do away with plane rectangular coordinate systems all together and go with 3 dimensional earth centric system? Plane coordinate systems are simplifications anyway created to simplify calculations. With 99% of the work already done in 3D and digitally, the simplification step could potentially be omitted. (However the road to get there is probably long)

[DWoolley]

After adequate time for comments, nobody has volunteered information indicating I have a blind spot for the benefits of a low distortion projections (LDP). Thank you to the people that posted.

I believe there are a few driving factors in developing an LDP. A couple of which are as follows:

1. Those folks that were performing GPS in the early years, circa 1990-94, have a great appreciation for the knowledge and skill that was required to perform the work. It was no easy task. These GPS folks were an elite class of land surveyor in the industry - they were the best and brightest the industry had to offer. GPS allowed land surveyors to perform accurate measurements that were previously unimaginable. The early static GPS work, subsequent control networks, GIS base mapping, writing the California Public Resource Code, coordinating with the folks at NGS, creating and funding CSRC, the establishment of the first CORS network, refining the geoid models, establishing epochs – was a unique and incredible period in the timeline of land surveying. The few industry thought leaders were in demand to perform the work, to establish the reference frames and to educate the masses. A heady time even for the humblest of practitioners.

Today, the work has been done and the remnant of their Coliseum is in the archives, but the early GPS gladiators linger – their heads full of knowledge with no demand. No different than an athlete or B list actor after they hit the wall. These folks, particularly the private practitioners, are trying to churn one more bucket of glory by plying their wares – repackaging their knowledge without honestly considering the usefulness of the work product. The master craftsman meets Ikea.

These early GPS folks mentored some of their best and brightest. The mentees have the knowledge and experience to carry the banner. Unfortunately, they arrived after the GPS revolution was in the last days, they never had their moment. They want to make their mark, follow the footsteps of the GPS gurus, and have something they can call their own, hence, the LDP. Usefulness is not the purpose. It makes them feel good, smart and allows the early folks to relive their glory days. Who doesn’t want that? If someone is willing to pay for it, it must be worth something, right? Snake oil is in the eye of the beholder.

In a world of GPS RTN – especially with long baselines - the error oftentimes exceeds the distortion. In the higher elevations and/or a long project that runs north and south there may be a need to create a LDP, but nothing comes to my mind. Arguably, the California High Speed rail fits that bill – that didn’t happen, probably for good reason. In the event a surveyor needed to measure/layout something precise the relative coordinates for the structure would be accurate within themselves, every time. Another thought, as a professional land surveyor, it is incumbent upon the community to understand and work on the grid.

I will finish this post another time. In the meantime, I ask that our public agency friends not to buy and spread unpublished snake oil on our legislatively defined zones to help someone relive their glory days or to give their mentees something to call their own.

DWoolley

PS Jim Frame, you were correct on the name.

[David Kendall]

Mr Woolley-

I tend to agree with your assertions regarding the value of LDP. I never really thought about it mostly because I never needed to which I feel is a statement in itself.

It seems to me that the late 1990s-early 2000s High Precision Geodetic Network may have solved this distortion problem for most of our California urban areas. The rural areas rarely require the extra precision.

I recall a presentation about ten years ago where Mike McGee described a LDP that he developed (at great expense) for the City of San Francisco. I believe it was primarily to provide harmony in municipal vertical benchmark functions

Beyond that I don't understand any practical application for LDP. I don't entirely understand the concept either. In my mind any local coordinate system would qualify

[hellsangle]

Arguably, the California High Speed rail fits that bill

Wooley,

That brought to mind the Continental Railroad of 1860s. LOL

Start here. End there.

Crazy Phil - Surveyor to Recorder

[Jim Frame]

Start here. End there

.

Of far greater concern for the CA high speed rail project, IMO, is land subsidence. I don't know how they're dealing with it, but I wouldn't want to be riding in a train going 200 mph when it hits a spot that's half a foot lower than it was 6 months ago.

[JKnox]

Dave
One issue which may be of concern to some would come up when running long corridor alignments for construction projects. In the old days at OC, I used to run my alignments until I reached a comfortable distortion in stationing, say 0.15 feet, then break the alignment and start a new one correcting up the stationing. Then I went to CT where we used grid stationing on alignments, which completely eliminated the problem. When I returned to OC a decade + later, we purposely revisited the issue, and with buy-in from all parties started generating grid alignments. Problem solved.

[CBarrett]

What I can't wrap my head around is why there is a need to legislate this into an officially sanctioned, whatever the word is I am looking for, formalize it into a law.
Does anyone out there understand the rationale behind the proposal?

[CBarrett]

I ended up having a chat with Greg Helmer the author of this proposal so I can gain a better understanding of the intent. I'll likely spend some time this weekend digesting all of it.

[DWoolley]

Dave
One issue which may be of concern to some would come up when running long corridor alignments for construction projects. In the old days at OC, I used to run my alignments until I reached a comfortable distortion in stationing, say 0.15 feet, then break the alignment and start a new one correcting up the stationing. Then I went to CT where we used grid stationing on alignments, which completely eliminated the problem. When I returned to OC a decade + later, we purposely revisited the issue, and with buy-in from all parties started generating grid alignments. Problem solved.

John:

As you know, my experience is similar. We used to create station equations on large corridor projects to compensate for distortion. I wouldn't do it today, but like you, today I would keep everything in grid, always.

Nobody has offered a convincing argument - here or in private correspondence - in support of LDPs. When pressed the LDP supporters fallback position is "all of the cool kids are doing it, we just as well sanction it". My translation is...if we can round up enough donkeys we'll have a rodeo. Maybe someone will convince me otherwise. Hope springs eternal.

It is always good to have your input.

DWoolley

[Edward M Reading]

If you are working at a high elevation where the State Plane elevation factor is considerable, an LDP is very useful. You can create one where grid essentially equals ground and never have to worry about it. I did this in the valley (6,000') where I lived in Idaho, and it worked great.

[DWoolley]

If you are working at a high elevation where the State Plane elevation factor is considerable, an LDP is very useful. You can create one where grid essentially equals ground and never have to worry about it. I did this in the valley (6,000') where I lived in Idaho, and it worked great.

Ed M. Reading:

What problem is being solved? Who is the benefactor? I ask in earnest. I am completely sincere when I state I do not understand the problem being solved or for whom. I have worked almost exclusively in grid for the last 25 years. I have had several smart people advocate for LDPs, but cannot answer this question in a way that allows me to understand the need or benefit.

For reader context, I have included an NGS point in Truckee at 6000'
DH6445! - Elev Factor x Scale Factor = Combined Factor
DH6445!SPC CA 2 - 0.99971831 x 0.99991943 = 0.99963777

This combination factor makes 2' between grid and ground in one mile, 5280'.

Thanks again, Ed. I very much appreciate the posts.

Another thought:
I would venture a guess that less than 1-2% of the entire California population of 40M live above 3500'. Do we really want 20, 30, 40 new zones to solve a problem that, in my mind, does not exists? For context, Oregon has 38 "zones" - because grid and ground befuddles them?

As far back as the early 90s I have had software that allowed me to work in grid and enter a combination factor for those few times I wanted to distort my good grid measurements.

DWoolley

[Steve Martin]

Municipal GIS operators prefer a Low Distortion Projection because distances represented by the GIS more closely represent what is on the ground.

[Steve Martin]

From the Oregon DOT web site: https://www.oregon.gov/odot/ETA/Pages/OCRS.aspx

The advantages of a low distortion projection are:

Grid coordinate zone distances closely match the same distance measured on the ground.
Limited distortion and reduced convergence angle.
Easy to transform between other coordinate zone systems.
Maintains a relationship to the National Spatial Reference System.
Can cover entire cities and counties, making them GIS-friendly.

Modern geographic information systems and surveying software now bring the opportunity to create low distortion map projections and coordinate systems that can relate closely to measure distances on the ground.

The function of low distortion projections is to minimize the distortions of angles, azimuths, distances, and areas. These distortions are present as we live on a spheroid.

It is impossible to represent a curved surface on a plane. We must account for that distortion by creating a mathematical model map projection that will allow us to work in a coordinate grid where calculated positions and distances are represented closely by the same positions and distances we measure on the ground.

For GIS professionals, low distortion projections may now demonstrate that "rubber-sheeting" data sets to make things fit is no longer necessary. Both survey and GIS data can co-exist without either dataset being degraded.​

[DWoolley]

From the Oregon DOT web site: https://www.oregon.gov/odot/ETA/Pages/OCRS.aspx

The advantages of a low distortion projection are:

Grid coordinate zone distances closely match the same distance measured on the ground.
Limited distortion and reduced convergence angle.
Easy to transform between other coordinate zone systems.
Maintains a relationship to the National Spatial Reference System.
Can cover entire cities and counties, making them GIS-friendly.

Modern geographic information systems and surveying software now bring the opportunity to create low distortion map projections and coordinate systems that can relate closely to measure distances on the ground.

The function of low distortion projections is to minimize the distortions of angles, azimuths, distances, and areas. These distortions are present as we live on a spheroid.

It is impossible to represent a curved surface on a plane. We must account for that distortion by creating a mathematical model map projection that will allow us to work in a coordinate grid where calculated positions and distances are represented closely by the same positions and distances we measure on the ground.

For GIS professionals, low distortion projections may now demonstrate that "rubber-sheeting" data sets to make things fit is no longer necessary. Both survey and GIS data can co-exist without either dataset being degraded.​

This is precisely the type of vapid snake oil I mentioned in my posts above. For example, the Oregon DOT folks, hat tip Steve Martin, repeat themselves by substituting different words to make one substantive paragraph into several paragraphs i.e. grid and ground differences are minimized. Their own description of the benefits of an LDP makes my point, meaningless words to sell services to the unsuspecting novice. Why sell 1, 2 or 6 zones when you can sell 38 zones in Oregon.

To snap the flimsy neckbone of this unimaginative argument, consider the following in California:

1. Most GPS RTN data is collected on a 2017.50 epoch. Resource grade GPS is collecting real time coordinates, I believe it is 2022.25 epoch. The majority of the GIS base maps are on 1991.35 or the “modern” systems use 2007.00 epoch. This means they have several feet, as much as 6’ floating around between data sets, and they are worried about grid coordinates? Pfft.

2. Ortho photography shown as the background in large GIS systems is not constrained by ground control, think Google Earth, and varies in quality by several feet depending on the location. Also, pixel sizes vary greater than grid v ground distortion.

3. The cadastral land base varies greatly in quality – much greater than grid to ground distortion. The best quality GIS systems are built by using coordinate geometry to enter in old subdivision maps. The metes and bounds deeds are sandwiched between the old maps (some of which do not close or have less accurate data i.e. pre-1900) and are forced to be closed polygons – again, the inaccuracy far exceeds grid and ground deltas. Keep in mind, many GIS systems are not based on the more accurate cogo land base. If every land base parcel, I believe Orange County has more than 800,00, was surveyed and placed on the same epoch, well, they may have an argument. Alas, that is not the fact set.

4. Of the 450+ cities in California, only 8 cities are more than 100 square miles (although not square, roughly 10x10 miles). As land surveyors, we know there is little distortion in the east-west direction. Few cities are above 3000’, the distortion that is being “corrected” is of no consequence when considering items 1 through 3 above.

The GIS folks will have to get up a little earlier in the morning to sell this land surveyor some LDP snake oil.

DWoolley

[SPMPLS]

Another thought:
I would venture a guess that less than 1-2% of the entire California population of 40M live above 3500'. Do we really want 20, 30, 40 new zones to solve a problem that, in my mind, does not exists? For context, Oregon has 38 "zones" - because grid and ground befuddles them?

Two LDP Zones in California were submitted to NGS for consideration and approval, not 20-40 (or many more to cover all of California with distortions under 50 ppm). Both have been preliminarily approved with some minor modifications and finalization of zone names.

NGS had initially proposed placing the projection surface at the average topographic height across each of our 6 zones in SPC2022. However, the California stakeholders asked that a population weighted algorithm be used to determine the height of the projection surface instead. NGS accepted the request, thus the distortions in then new Zone 5 (for example) will be very similar to what we have now because the majority of the people, and work, reside within 100 miles (or so) of the coast.

[Steve Martin]

...repeat themselves by substituting different words to make one substantive paragraph into several paragraphs i.e. grid and ground differences are minimized.

I did copy the contents of two brief pull-downs into my post, but the purpose of my post was not to argue with Dave, it was to give more information so that fellow surveyors can decide for themselves.

I don't believe that outlawing professionals from using what is essentially mathematical equations with certain criteria that allows us to represent the curved earth on flat maps, and requiring the use of the same equations with slightly different criteria.

"Not every human problem deserves a law" Governor Jerry Brown in his veto of a proposed law to fine parents if their kids went skiing without a helmet.

I do think that practitioners should be encouraged to use the standard projections as established and maintained by NGS.

There is a prevalent practice of "scaling CCS up to ground". It would be better to focus efforts on the fallacy of creating these often undocumented "hybrid" coordinate systems, however outlawing the practice would not necessarily work. Education is the better process. If encouraging the use of officially sanctioned LDPs maintained by NGS (with definitions included in software such as AutoCAD and ArcGIS) keeps people from creating "hybrid" ground coordinate systems, I am all for it.

Attached is a diagram from an early paper by Michael Dennis showing how a LDP performs better than a "scaled to ground" coordinate system. It is in Appendix E of V1.1 of NGS Real Time User Guidelines.

The current Lambert Conformal Conic (LCC) Projections used for CCS83 were developed about 90 years ago without the computation power of today.

For the State Plane Coordinate System of 2022, the same 6 zones are being optimized to reduce the combined scale factor, as Scott points out, considering where the most people live in addition to the topographic surface.

The computation power to do that did not exist in the 1930's. The current LCC projections were developed using a maximum grid scale of 1 part in 20,000 with no consideration for the elevation factor part of the combined factor.

A LDP is optimized for 1 part in 50,0000 maximum distortion relative to the topographic surface.

Scott Martin can probably give a more in depth discussion of the Low Distortion Projections, but I'll leave it there for brevity.

For those interested in the State Plane Coordinate System, see NOAA Special Publication NOS NGS 13 "The State Plane Coordinate System"

[DWoolley]

I do think that practitioners should be encouraged to use the standard projections as established and maintained by NGS.

There is a prevalent practice of "scaling CCS up to ground". It would be better to focus efforts on the fallacy of creating these often undocumented "hybrid" coordinate systems, however outlawing the practice would not necessarily work. Education is the better process.

Wait, what happened to the GIS argument? I understand it wasn't your argument, Steve...but, you posted it. Nobody believes a GIS land base is better than 1:50k.

The counter to the Gov. Jerry Brown quote is "Everything which is not forbidden is allowed".

I would offer, the best "encouragement" would be to not recognize the LDP - especially as being an acceptable CCS.

The prevalent practice of "scaling up to ground" has probably been around since Clark's Spheroid of 1866. We have been on '83 for about 35 years and some folks still "scale to ground". What new twist in education will make the next 35 years any different?

Our community is at a technical nadir - see what I did there - as it relates to SPC. It is an RTN world with 30k baselines. They no longer teach post processing classes, dropped about 12 years ago, because they could not get anyone to attend. Let's not sanction poor practice and ruin the reference frame for those folks that understand and use it properly. Those RTN folks are going to do what they're going to do, let'em, but do not offer any form of legitimacy.

SPMPLS:

I like the idea of the population weighted algorithm rather than averaging the topography. In the low lying populated areas the 1:50k may be achieved without an LDP.

Now that we know the GIS chicanery does not make sense, anyone else have better guesses as to purpose?

DWoolley

[SPMPLS]

Mr. Woolley,

You can't imagine how relieved I am to know that you endorse the concept of a population weighted algorithm being recommended by the California stakeholders. Warms my heart.

That said, I will not get in the mud to wrestle on this forum or anywhere else. I will allow my professional reputation and contributions to stand alone without citing Latin. I will simply close with this quote from someone we would both surely bow down to regarding literary prowess. I know I would.

To quote Mark Twain, “Never argue with a fool; onlookers might not be able to tell the difference."

Scott P. Martin, PLS 5684

[DWoolley]

Mr. Woolley,

You can't imagine how relieved I am to know that you endorse the concept of a population weighted algorithm being recommended by the California stakeholders. Warms my heart.

That said, I will not get in the mud to wrestle on this forum or anywhere else. I will allow my professional reputation and contributions to stand alone without citing Latin. I will simply close with this quote from someone we would both surely bow down to regarding literary prowess. I know I would.

To quote Mark Twain, “Never argue with a fool; onlookers might not be able to tell the difference."

Scott P. Martin, PLS 5684

Mr. Martin:

Yes, I thought the population weighted algorithm was a great idea. Genuinely, it would have never occurred to me - thank dog for the stakeholders and their welcomed ideas. Long live the vaunted holders of the stake.

Like you, I have an appreciation for Mark Twain. I could not chose the better quotes between Lewis Carroll, Mark Twain or Will Rogers.

DWoolley

[Derek_9672]

I have never utilized a custom LDP, but I've been working on a bunch of railroad right of way lately, and the following instance has occurred to me where one might be handy.

Say you are surveying railroad right of way the nominal width of which is 100'. The state plane grid scale factor in the project vicinity produces a half-width of 49.994' through the corridor you are surveying. A LDP would be useful whereby you "fix" the right-of-way width at 100.00' throughout, that being the most important dimension in your survey and one you do not wish to distort. Leaving the scaled width intact would be fine of course, but could lose you some elegance or clarity points in your mapping.

[TTaylor]

Dave,

I've been attending the NGS webinar series on the upcoming change to a new NSRS.

Check out this one by Michael Dennis which has info that may be relevant to your question.

BTW, after the lessons learned from transitioning from 27 to 83 I firmly recommend NOT putting into law NSRS2022.
https://www.ngs.noaa.gov/web/science_ed ... 2022.shtml

[DWoolley]

Dave,

I've been attending the NGS webinar series on the upcoming change to a new NSRS.

Check out this one by Michael Dennis which has info that may be relevant to your question.

BTW, after the lessons learned from transitioning from 27 to 83 I firmly recommend NOT putting into law NSRS2022.
https://www.ngs.noaa.gov/web/science_ed ... 2022.shtml

Tom:

Thank you for the link. Michael Dennis is an engaging presenter. The presentation indicates California will have 9 zones. I believe this would account for the original 6 zones, a state zone and two LDPs (?). I am thankful we are not working in Utah with their 90 zones for a state that has large areas of uninhabited land and only 29 counties. Apparently Arizona wanted in on some of that action with their proposed 63 zones.

Based on the map of California, most of the state is mapped to be less than 50ppm in distortion. I see no better argument against us adopting LDPs - most of us can live with 50ppm, right?

Thanks again.

DWoolley