Accuracy Of Topographic Maps And Of Topozone

[Papa-Bear-NYC]

I'm posting this here rather than on the other forum in hopes of getting some NGS or other professional opinions.

 

I often use USGS topographic maps to help find a mark. Assume for the moment that we are talking about horizontal control points which I believe are accurate to less than a foot.

 

My question is how accurate is the map. Of course the map is originally based on the (some of the) same horizontal control points laid down, together with aerial photos.

 

Case in point: I went looking for a mark yesterday (KU2178) which is a surveyors PK driven into a concrete pad. The description contains elements such as engineering trailers and chain link fences which are 20 years out of date. But the location is specified to 5 decimal digits of the seconds. I plugged these into Topozone (which may in turn introduce rounding or truncation errors for this level of accuracy) and got this: Topozon map for KU2178.

 

From studying this I know I should look just south of the extend line of the south side of East 91st Street. This line is quite visible since the buildings are all built out to the building line and you can clearly see when they all line up.

 

So the questions are:

 

Can I trust the USGS quads to this level of accuracy?

Does Topozone introduce any errors at this level of accuracy (I know the Topozone guy reads these forums)?

 

Thanks

[+Renegade Knight]

5 Decimals? No.

 

Topo's are made from ortho rectified (I think that's the term) arial photo's. There is a loss of accuracy for the arial photo being warped to correct, and you can only be so acurate to begin wtih because of the limitations of the resolution of the photo.

 

I would trust topo to be accurate to within a few fet for features as they relate to each other. However not 5 decimals.

[Papa-Bear-NYC]

Thanks RK

 

I would trust topo to be accurate to within a few fet for features as they relate to each other. However not 5 decimals.

 

I would guess the 5 decimal places on the datasheets are an artifact of converting from NAD27 to NAD88 since no surveyor instrumentation is that accurate.

 

But a few feet is all Iwas hoping for in this case.

 

Pb

[+PFF]

I have found the TopoZone product to be very accurate. However, it works best in the decimal degree mode. Here's an example from earlier this week:

 

The target was FY0176, with scaled coordinates, listed in the wrong county, and no recovery since 1934. References included a road which probably had moved, farm buildings no longer standing, and an abandoned railway line. (And if it was abandoned when the 1932 description was written, one can speculate what remains, seventy years later!)

 

As preparation for the hunt, I decided to print the map from TopoZone. I noticed an "X" near the cursor; i.e., where the scaled coordinates plotted.

 

Holograph recently gave an example of a benchmark where the map's "X" was pretty far west of the actual mark. I suspect this is unusual. My experience has been that the "X" on a topo map is fairly accurate. In this case, it put me within 25 feet of the benchmark.

 

Here's how the numbers played out:

 

N36.43278 SCALED COORDINATES FROM DATA SHEET

N36.4325- COORDINATES OF TOPOZONE "X"

N36.43258 HANDHELD GPS READING (PLUS/MINUS 13.1 FEET)

 

Longitude calculations:

W78.29611 SCALED COORDINATES FROM DATA SHEET

W78.2960- COORDINATES OF TOPOZONE "X"

W78.29614 HANDHELD GPS READING

 

The Topozone coordinates were determined by using the scale 1:10,000, and then trying my best to center the cursor over the crossed lines of the "X". Highly accurate? No. But it makes a good "second opinion", rather than depending entirely upon SCALED ccordinates to guide you to the spot.

 

So, I'd answer your question by saying the TopoZone map is excellent. I've got no stake in TopoZone, other than the annual subscription fee for some premium features. But the product is so valuable that even if it were not tax deductible for my business, I'd still pay for it.

 

I hope that sheds some light on your question.

 

Best regards,

Paul

[holograph]

In principle, the scanned USGS quads (DRGs) that are displayed in Topozone retain the accuracy of the source map. National mapping standards specified that fewer than 10% of the points on the original USGS map should exceed about 1/30 of an inch error on the map. For USGS quads at a scale of 1:24000, that means that 90% of the points on the original printed map would be within 67 feet of their true positions.

 

There is also the ambiguity of the pixel size in the DRG image. Most of the quads are represented with a resolution of 250 pixels per inch, which means that a pixel represents roughly an 8 foot by 8 foot square on the ground.

 

You should note that the 8 foot pixel is the pixel size on the DRG image, not on the image that you see on your screen. Topozone and your browser will display the DRG pixels at varying sizes. If you look at the size of the jagged lines in the zoomed image, each step would be one pixel in the original DRG image, and 8 feet on the ground.

 

In summary, anything you locate using Topozone should have an error of less than about 70 feet. That translates to about 0.0002 degree.

Edited October 7, 2005 by holograph

[edmcnierney]

Papa-Bear-NYC -

 

You may also get quicker answers if you ask us at TopoZone about TopoZone questions, rather than posting them someplace we have to hunt for them! I've never quite understood why some TopoZone users seem to ask everyone BUT us about TopoZone questions...

 

holograph did a very good job of summarizing the issues. Many users expect USGS topographic maps to be MUCH more accurate than they really are. Remember that you're starting with a printed map at a scale of 2,000 feet per inch. Any symbol that is off by 1/100th of an inch is off by 20 feet. Even if the original plates were perfect, it is very difficult to keep the printing process perfect, and paper is not entirely dimensionally stable, and can stretch.

 

Then the USGS scans the printed map, adding one more source of potential error. Again, even if everything is perfect, one pixel is 2.4384 meters on a side, and you therefore cannot have a coordinate resolution smaller than that. At 40 degrees North latitude, one second of arc is roughly 27 meters (the average of the length of one second of latitude and one second of longitude at that latitude). Five decimal places would be one one-hundred-thousandth of a meter, or 10 micrometers (microns). So your datasheet is reporting coordinates to a precision of less than the width of a human hair. That's not likely to be an appropriate level of precision to be using......

 

Back to TopoZone - so one pixel is roughly 0.1 seconds of latitude/longitude in most of the US. We deliberately try to AVOID displaying bogus precision in coordinates, so we round that up to one second (whole seconds). However, we're not perfectly consistent about that and round different display formats to slightly different amounts. UTM coordinates are displayed in integer meters, and that's the most precise coordinate format we display.

 

In theory, however, the coordinates on TopoZone are perfectly accurate. It's the maps that are the problem! Image a clear glass sheet with coordinates etched on it with perfect precision. That's what we're using for TopoZone coordinates. Then you slide a map sheet under that glass. There are two possible sources of error in reading coordinates from that map sheet: (1) the symbols on the map sheet are not in the correct location, and/or (2) the map sheet was not positioned properly/is distorted. These correspond to the error sources described above, in the production and in the georeferencing of the map.

 

In general, (2) errors are minor. These maps were georeferenced by the USGS and they're pretty good. There are some errors, but these affect individual maps, and they're big errors, not small ones. The most common is that the USGS incorrectly reports the datum used for the scanned image; the less common is that the map was incorrectly georeferenced. We've seen a few hundred of the former (out of almost 60,000 maps) and correct the ones we find. We've seen only three or four of the latter.

 

By far the largest source of error is the simple fact that the symbols aren't in the right place, and has nothing to do with TopoZone or any other mapping service. The most accurately-placed symbols on a topo map are third-order or better horizontal benchmarks, and those are supposed to be shown within 40 feet of their true location (remember, that's only 1/50th of an inch on the mylar sheet that is the source "dataset").

 

So to answer your first question, no, you can't trust USGS quads to 10 microns of precision, and they are not as accurate as you seem to think they are!

 

Ed, the aforementioned "TopoZone Guy"

[mloser]

But they are still fun to look at!

 

And great sources of information, as long as you realize there are limitations!

[Papa-Bear-NYC]

Thanks Ed

 

Actually when I wrote my initial query, I added the Topozone question as an afterthought. It's good to know that Topozone doesn't introduce any additional "meaningful" uncertainties.

 

As for "Meaningless" uncertainties, yes I know (and always knew) that the 5 digits the NGS publishes in the seconds is not meaningful. I'm guessing that the original measurements had probably .1 seconds of accuracy. When the NGS converted from NAD27 to WGS84/NAD83, they probably got those 5 digit numbers.

Can anyone from NGS fill us in on this quesion?

 

The bottom line is what I thought: 1 pixel on topozone approximates the uncertainties in the original maps (that is the uncertainty due to the printing process) and that is a couple of meters. The uncertainty of placing the symbols on the map is up to about 5 or 6 times that. Works for me.

 

So, when my map showed a mark near the side of a street in NY City, I can be justified in looking there and not a block away (about 100 yards), or for that matter, even on the other side of the street (about 75-100 feet) - this for third order or better horizontal control marks.

 

Thanks again for the thorough response.

Pb

Edited October 8, 2005 by Papa-Bear-NYC

[caseyb]

As for "Meaningless" uncertainties, yes I know (and always knew) that the 5 digits the NGS publishes in the seconds is not meaningful. I'm guessing that the original measurements had probably .1 seconds of accuracy. When the NGS converted from NAD27 to WGS84/NAD83, they probably got those 5 digit numbers.

Can anyone from NGS fill us in on this quesion?

I am not the best person to answer this, so hopefully somebody else will jump in here. But as I understand it, NGS's surveys are much more accurate than .1 seconds and have been so for a long time. Keep in mind that 1 arcsecond is about 30 meters, so .1 arcsecond is 3 meters, and I know the surveys were more accurate than that. One person told me that a lot of the original horizontal surveys were accurate to the centimeter, maybe even better.

 

-Casey-

[caseyb]

Dave Doyle just posted this in the other forum.....

 

 

NGS has been publishing the precision of coordinates in arc seconds to 5 decimal places since the early 1970's, many years prior to the adjustment of NAD 83. Users of coordinate data are often cautioned to NEVER look at the number of digits to the right of the decimal point as an indicator of positional accuracy. This data element is always linked on the NGS data sheet with one the 7 horizontal orders of accuracy “HORZ ORDER,” adopted by the Federal Geographic Data Committee:

 

A-Order (1:10,000,000)

B-Order (1:1,000,000)

First-Order (1:100,000)

Second-Order Class I (1:50,000)

Second –Order Class II (1:20,000)

Third-Order Class I (1:10,000)

Third-Order Class II (1:5,000)

 

Many years ago, NGS adopted 5 decimal places in arc seconds to be able to realize the spatial integrity of points with well determined horizontal positions to the millimeter level. This certainly doesn’t imply that all points are known to mm accuracy, but it maintains the relationships between points at mm level. For example, look at the data for stations ELK LICK (JW1482) and ELK LICK 2 (JW1480). Note that the distance between them was measured with a very accurate invar steel tape as 55.146 m and is well known at the mm level. If you compute the distance between them by using the program INVERSE from the NGS Geodetic Tool Kit, you will find that the distance returned is 55.146 m. If however you truncate their respective positions to say three decimal places, which might more closely represent their actual positional accuracy, the distance returned by INVERSE is 55.130 m, or a difference of 1.6 cm. This may not seem like much, but as you add observations across the country these errors would accumulate very quickly to an unacceptable level.

 

Surveyors and other spatial data users are constantly being trained by NGS at workshops and seminars on the intricacies of how to properly use and evaluate the accuracy of geospatial data.

[+Black Dog Trackers]

With reference to Papa-Bear-NYC's question, let me try to assimilate this based on some reading on error propagation and adjustment I did several years ago.

 

1. The process of adjustment is apparently done by the NGS until at least a 5-decimal PRECISION is reached. During adjustment of data, the measured positions of points are adjusted (i.e. moved) to agree to the maximum extent mathematically possible to the measured positions of the rest of the points in the matrix. The resultingly MOVED positions agree with each other to the desired level of PRECISION. If any sources of error (like some positions with badly measured positions, systematic errors, etc. are found and removed as part of the adjustment process, then the MOVED positions are also ACCURATE to a high level. However, that level of ACCURACY cannot be more than the general accuracy of the original measurements. In other words, if a bunch of third order stations were measured to within 0.1 second and then adjusted to within .0000000000001 second of each other's positions, the adjusted net will have .0000000000001 INTERNAL AGREEMENT (precision) between those stations but the real positional ACCURACY of any of them will be only accrurate to about 0.1 second.

 

2. If the measured accuracy of JW1480 and JW1482 was about the equavalent of 3 decimal places, and 3 decimal places equates to a distance level of accuracy of around 1.6 cm, then any result from INVERSE that agrees more than that to the taped measurement is LUCK, unless they are part of a net of stations with far higher measured accuracy that adjusted their positions to more accurate values.

 

Is this right, DaveD? If not, where is it off?

 

I'm not a mathematician, nor a surveyor, and am trying to understand this stuff.

Edited October 11, 2005 by Black Dog Trackers

[+GEO*Trailblazer 1]

I am no math major either and have seen this chart numerous times.

What is 1 for,or = to ?,and What is 10,000,000 for or = to ?

 

1.A-Order (1:10,000,000)

2.B-Order (1:1,000,000)

3.First-Order (1:100,000)

4.Second-Order Class I (1:50,000)

5.Second –Order Class II (1:20,000)

6.Third-Order Class I (1:10,000)

7.Third-Order Class II (1:5,000)

[+GEO*Trailblazer 1]

double post arhhhhhhhhh!!!!

 

Well I will have to take back my question.

And make up for it.

 

1.

meter, abbr. m,

[French mètre, from Greek metron, measure.]

The basic unit of length in the metric system;

It was originally planned so that the circumference of the Earth would be measured at about forty million meters.

 

The international standard unit of length, approximately equivalent to 39.37 inches. It was redefined in 1983 as the distance traveled by light in a vacuum in 1/299,792,458 of a second.

 

fundamental unit of length in the metric system. The meter was originally defined as (2)1/10,000,000 of the distance between the equator and either pole;

however, the original survey was inaccurate and the meter was later defined simply as the distance between two scratches on a bar made of a platinum-iridium alloy and kept at Sevres, France, near Paris. More recently, it has been defined as the distance light travels through a vacuum in 1/299,792,458 of a second. The meter is now the legal standard of length for most of the world, other standards, such as the yard, being defined in terms of the meter.

 

To convert from meters to:

 

centimeters, multiply by 100.

feet, multiply by 3.281.

inches, multiply by 39.37.

kilometers, multiply by .001.

miles (nautical), multiply by 5.399E-04.

miles (statute), multiply by 6.214E-04.

millimeters, multiply by 1000.

yards, multiply by 1.094.

 

And to go a little bit into the 7's is this coincidence?

 

SI units

 

(Système International d'Unites) A system of standard units of measurement finalized at the 14th General Conference on Weights and Measures in 1971. It is based on seven units of measure, including three from the MKS system (meter-kilogram-second), the ampere for electrical current, the Kelvin for temperature, the candela for luminosity and the mole for molecular weight. See MKS system, amp, Kelvin, candela and mole.

 

BASIC SI UNITS

 

Quantity Unit of Measurement

 

length (l) meter (m)

mass (m) kilogram (kg)

time (t) second (s)

current (I) ampere (A)

temperature kelvin (K)

atomic weight mole (mol)

luminosity candela (cd)

 

The GPS using the MKS,

me·ter-kil·o·gram-sec·ond (mē'tər-kĭl'ə-grăm-sĕk'ənd)

adj. (Abbr. mks)

 

Of or being a system of units for mechanics, using the meter, the kilogram, and the second as basic units of length, mass, and time.

and I am shure more.

To more accurately define the measurements of the circumference of the Earth.

 

OK I have rambled on long enough.

I will get back to studying before I post.

Edited October 12, 2005 by GEO*Trailblazer 1

[+Black Dog Trackers]

Actually, the numbers in the table are unitless.

They can be inches, furlongs, meters, light years, or anything.

 

According to the Standards and Specifications for Geodetic Control Networks (1984 standards), the numbers are

1:denominator

 

where denominator = (the distance between 2 points) / (the standard deviation calculated by the least squares adjustment of those and the other points in the adjusted net)

 

An example they give is:

 

(the distance between 2 points) = 17,107

 

(the standard deviation calculated by the least squares adjustment of those and the other points in the adjusted net) = 0.141

 

so, the "denominator" = 17107/0.141 = 121326

 

That means the Minimum Distance Accuracy of the survey is 1:121,326

This is better than the nominal 1:100,000 level of a "first-order" survey, so it is classified as "first order".

 

The 1989 Standards address the increased accuracy afforded by GPS techniques and present the more stringent standards AA, A, and B.

[+Crystal Sound]

Geotrailblazer:

 

For the sake of discussion: could you also define ACCURACY and PRECISION ?

 

These are two terms that are often misused/interchanged.

Edited October 12, 2005 by Crystal Sound

[Z15]

Accuracy is telling the truth . . . Precision is telling the same story over and over again.

Yiding Wang, yiwang@mtu.edu

 

 

Precision

    the degree of refinement in the performance of an operation, or the degree of perfection in the instruments and methods used to obtain a result. An indication of the uniformity or reproducibility of a result. Precision relates to the quality of an operation by which a result is obtained, and is distinguished from accuracy, which relates to the quality of the result.

Accuracy

    the degree of conformity with a standard (the "truth"). Accuracy relates to the quality of a result, and is distinguished from precision, which relates to the quality of the operation by which the result is obtained.

 

>>>>>The info source is here<<<<<

Edited October 12, 2005 by Z15

[+Black Dog Trackers]

Often in measurement, the true value is unknown, so it's hard to say what the accuracy of a measurement or series of measurements is. However, here is an example where the true value is known.

 

Imagine you're supposed to survey the perimeter of a town. You use a tape measure that has millimeters marked on it and measure distances and angles from one point (station) to the next all around the town until you return to your starting point. You call the starting point station 1 and when you finish you call the same point station 200. You calculate all the positions of your 200 stations (where your tape ended each time) around the perimeter (say about 23 kilimeters overall) and find that (no surprise) the positions of station 1 and station 200, which are the same point, are not the same, but say 1.2 meters off (a "closure error"). The true value of the distance between station 1 and station 200 is known, and is of course zero!

 

Your precision is 1 millimeter (=0.001 meter).

 

Your accuracy is 1.2 meters in 23 kilometers, or 1:19,166 which is about the accuracy level of Second Order, Class II.

[+Harry Dolphin]

Another perspective, which might seem pertinent:

I work for a company that boxes freight for overseas shipment. We measure each box to the nearest inch. Our computer generated packing list lists the volume to two decimal points. If the box were 79x45x83", the packing list would state: 170.76 cf. Delightful precision! But meaningless. The box could be as small as 78.5x44.5x82.5" (166.78 cf) or as large as 79.5x45.5x83.5" (174.79 cf).

The digits after the decimal point are completely meaningless. But, the industry demands them.

Even more fun occurs when an overseas customer looks at the metric dimensions, and converts that back to English measurements!

I've given up banging my head against the wall on this one. Oh, well.

BDT, in my limited experience with title searching, I found the maps closed nicely. But those were mostly late 1800's deeds measured in links and chains. (Thence x degrees, 2 chains, one link to an old stump.)

[DaveD]

The procedure Black Dog laid out is generally correct with the exception that you also need to include the survey error induced by angular measurments. Theodolites and transits which measure angles/directions come in many forms with many different levels of angular precision. The type used by most land survyeors in the past would often times measure only to 20-30 seconds of arc where the type used by geodetic surveyors could easily measure 0.1 - 1 seconds of arc. Today, most electronic total stations used by surveyors measure in the 3-6 second range. The errors caused by instruments not being level or directly plumbed over the mark on the ground are combined with errors in pointing and reading by the observer. These errors can often be modeled and are combined with the potential errors in distance measurments to complete the adjustment of all survey observations as outline by Black Dog Trackers.