topic Re: Scale bar inaccurate on a projected geo-referenced map image, why? in Coordinate Reference Systems Questions

Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Wed, 27 Jul 2016 17:07:17 GMT

I want to geo-reference a series of map, digitize features using polygons, and calculate accurate area measurements. I encountered the following issue:

After georeferencing a map image (.png) using the lat-long posted on the four corners of the map and projecting it using an appropriate UTM projection (WGS_1984_UTM_Zone_29N), I noticed that the scale bar is not accurate (the 50 km scale bar measures 34.4 km on the projected map). However, using the Measure Tool to find the length (in km) of 1 degree of latitde and lengths of 3.5 degrees longitude along both 46 deg. & 47.5 deg. latitude; the measurement results and corresponding errors are listed in the table below:

Note the large error from the scale bar (>30% error) and relatively insignificant error on the latitude and longitude measurements (<0.1% error).

Questions:

1. Why would the scale bar length be inaccurate (especially when the image lat-long appear to be projected correctly and can be measured accurately in ArcMap)?

2. Is this an error in my geo-referencing? If so, is there a better method for geo-referencing this type of map image?

3. Am I using an incorrect projection? I believe a projected UTM is appropriate for area calculations and should provide accurate length measurement for features located within the UTM zone.

Any assistance is appreciated. Thanks!

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

AbdullahAnter — Wed, 27 Jul 2016 18:22:16 GMT

What is the projection for maps images?

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Wed, 27 Jul 2016 18:46:43 GMT

The map image in question was originally drafted in a geographic coordinate system, but after I geo-referenced it appeared to project correctly in a data frame using a projected UTM coordinate system.

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

DarrenWiens2 — Wed, 27 Jul 2016 18:52:51 GMT

Just some quick clarification:

- you're talking about the scale bar that came through on the original map, not an ArcMap layout scale bar, correct?

- I assume you've overlaid your georeferenced map over some known correct data to confirm that your georeferencing matches reality.

- Have you checked the map for fine print regarding scale (e.g. "scale only applies to such-and-such a latitude") or does it have a variable scale bar?

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Wed, 27 Jul 2016 19:09:35 GMT

I will address your questions in order:

- The scale bar in question is on the original map.

- Yes, I have checked and the georeferenced map with known data (a lat-long grid) and it matches up very well.

- The original map does not have a variable scale. It only ranges from 46 to 47.6 degrees latitude; as a result, a 50 km (non-variable) scale bar should only have an inaccuracy of about 1.5 km within the map area. However, I am observing an error of over 15 km.

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Wed, 27 Jul 2016 19:55:47 GMT

The first image is the corner of the original map projected using a geographic coordinate system (WGS_1984), which shows how well the map lines up with the lat-long grid. The top "50 km" scale bar (from the original map) matches the lower "50 km" scale bar (created in ArcMap layout view). When I measure them with the Measure Tool they are 34.4 km long. Why would the scale bar (even the one created in ArcMap) not be correct length according to the Measure Tool?

The second image is the same map in a projected coordinate system (UGS_1984_UTM_Zone_29N). Now the scale bars are not aligned. Using the Measure Tool the original "50 km" scale bar again measures 34.4 km, while the ArcMap derived "50 km" scale measures 50 km

What do I need to do to find an accurate / trustworthy length measurement? And after that what settings can be used to calculate areas?

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

AbdullahAnter — Wed, 27 Jul 2016 20:10:10 GMT

Do you have 2 data frame in layout?

perhaps the scale bar for another data frame.

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Wed, 27 Jul 2016 20:14:01 GMT

No, there is only one data frame.

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

DarrenWiens2 — Wed, 27 Jul 2016 20:45:23 GMT

What do I need to do to find an accurate / trustworthy length measurement? And after that what settings can be used to calculate areas?

You should only start measuring length/area once everything (data and data frame) are in a projected coordinate system. As a compromise projection, UTM distorts both distance and area, so technically you should measure distances using an appropriate equidistant CRS, and areas using an appropriate equal area CRS, but most people use UTM for convenience.

This doesn't answer why this is happening for you, but if you always do your measurements on projected data, you should be fine.

edit: I'll just call over Melita Kennedy, because she can explain this better than anyone I know.

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Wed, 27 Jul 2016 21:53:47 GMT

First, I agree with your point that UTM will distort distance and area. Based on the fact that I will not be measuring areas that extend beyond a single UTM zone (often much smaller and up to a few 100 km), I was considering using a projected UTM for measuring distance and area. Will this method introduce significant error?

Second, is there a simple reason why the relationship between the scale bar from the original map and one created in ArcMap changes when using a projected vs. geographic coordinate system?

Particularly, an explanation for the irregularities when using the "Measure Tool" to check the scales: How can the ArcMap based scale bar be wrong/inconsistent (measuring 34.4 km in the GCS and 50 km in the PCS) and the scale bar from the georeferenced image be consistent in length (34.4 km in both GCS and PCS) but wrong (should be 50 km) (as illistrated in the images in my previous post)?

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

NeilAyres — Thu, 28 Jul 2016 08:09:57 GMT

How do you know that the original image was "IN" GCS?

Was this produced by ArcGIS or something. Because if it was an original printed map or similar, it would actually be in some sort of projected system. Even though it has a GCS graticule marked on it. This is very common.

Thus the corners (like on a standard 50k topo map), might have lat/long coordinates marked, but the map is actually in UTM or whatever system. You can still georeference this, when entering the control point, right click then you will see "Enter XY" and the second option is "Enter DMS". These will be automatically translated into the coordinate system of the data frame, which, of course, should always be the actual coordinate system of the map.

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Thu, 28 Jul 2016 15:12:54 GMT

You are correct in asking about the coordinate systems of original image; the map is from a published journal article and I am NOT sure what coordinate system was used. It is a smaller map (about 1.5 degrees latitude and 3.5 degrees longitude) which has a graticule that make perfect squares and the conversion from degrees latitude (or longitude) to km match the scale bar (at least before it is georeferenced). As a result, I guessed that it used a GCS.

Based on your suggestion, I attempted to georeference the map in a PCS (since I do not know what was used on the original, I used the appropriate UTM zone) using the "Enter DMS" function. This resulted in the same ~30% error in the length of the scale bar with the "Measure" tool.

Is it common for scale bars to have this much error (a 50 km scale bar measures 34.4 km, 30% error) when georeferenced?

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

NeilAyres — Thu, 28 Jul 2016 19:05:51 GMT

I still see that the original image you posted above, doesn't have an actual "corner coordinate" in Lat/Long, unless there is some other text outside of the snapshot you have given us.

How did you know the exact Lat/Long of that corner?

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Thu, 28 Jul 2016 19:25:27 GMT

Neil, I did not use the true corner in this example (since, as you pointed out, it does not have a "corner coordinate"). As an alternative, I used the tick mark closest to corner, which is 74.5 degrees N latitude/14 degrees W longitude. The lower right and left corners had labeled coordinates, but I used a similar approachfo the upper right corner, i.e., georeferencing the nearest known point (using a tick mark at 74.5 degrees N latitude/8 degrees W longitude).

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

NeilAyres — Thu, 28 Jul 2016 19:33:30 GMT

Just curious, in that original image the text looks a little "squashed", yet in the "projected" image it looks more normal.

There is something wrong with the coord sys of the original I think.

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

MelitaKennedy — Thu, 28 Jul 2016 23:55:33 GMT

It's possible whatever software was used to generate the original image calculated the scale bar at the equator (ArcMap used to do this; I don't know if it still does), rather than at 47N. I get 0.68% reduction east-west ( cos(47) ) which ends up being 34 km / 50 km.

If it was a bathymetry chart, it could be using Mercator with a standard parallel set around 47N to reduce distortion. That would also give a rectangular graticule.

Melita

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Fri, 29 Jul 2016 16:09:04 GMT

The prospect of the original map's scale bar being calculated at the equator seems to be a plausible (and likely) cause of the issue. That would explain why:

- The original and ArcMap scale bars lengths matched when I used a geographic projection system, and both were incorrect. The "50 km" scale bars were only 34.4 km long. This amount of error would be expected at 47N if they were both sourced at the equator.

- And, while using a projected coordinate system, the ArcMap derived scale was correct (50 km = 50 km) and the original maps "50 km" scale bar was still incorrect by the same amount ("50 km" = 34.4 km).

On your second comment: Yes, the original image is a bathymetry chart.

I think this is the explanation: The original scale bar was incorrect because, while using a geographic coordinate system, they included a scale bar sourced at the equator.

Thank you, Melita Kennedy, for providing the answer!

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

DanPatterson_Retired — Fri, 29 Jul 2016 16:35:14 GMT

Luke... could you mark Melita's answer correct please

Re: Scale bar inaccurate on a projected geo-referenced map image, why?

LukePettinga — Fri, 29 Jul 2016 16:54:04 GMT

Yes! Thanks, Dan.