U.S. State Survey Maps
Reading Working With Public Land Survey Coordinates
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A Customer Case Study
The 'ALL TOPO MAPS:' Application Developer Received A Call With The Following 'All Topo Maps: GPS' Tool Accuracy Complaint:
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Customer's Question:
"The All Topo Maps: GPS
Tool does not work! I physically occupied
a NGS
horizontal control point (see
http://www.ngs.noaa.gov/datasheet.html)
at our local airport, set my GPS (a
Garmin 35LP) on top of the X scribed on the
stainless steel cap. The All Topo Maps:
GPS reported position is:
N 33 17
20.7 W 95 53 53.1
The enumerated NGS
position is:
N 33 17
21.0593 W 95 53 54.2151
Another mapping program,
using the same GPS at the same position, much
more accurately reports the 'true' position.
All Topo Maps obviously do not work! When
will you fix the GPS tool?"
Answer: Datum
Shift
This Is A Classic
Datum Shift
Question. The 'All Topo Maps: GPS'
Tool Is Not Broken, The User Has Mixed
Coordinates From Multiple
Datums.
The NGS Reported Position
Is Expressed In NAD83 Datumed Coordinates. 'All
Topo Maps: Texas' expresses coordinates in
NAD27 datums (Every Texas Quadrangle Is NAD27
Datumed And We Want Our Bombsight Cursor To
Report The Same Coordinates That Are Printed On
The Maps.)
The 'All Topo Maps: GPS'
Tool Receives The GPS Position In WGS84 Datum
Over The Serial Interface Connection From The
GPS Receiver. 'All Topo Maps:' (And
The GPS) Use The 'Molodensky Datum
Transformation' To Convert The Received WGS84
Coordinate To A NAD27 Coordinate And Report A
NAD27 Position (see
http://www.colorado.edu/geography/gcraft/notes/datum/datum_f.html
for further information).
It is worth mentioning
that the Molodensky Datum Transformation is an
approximation, but it does quickly generate
conversions that are close enough for consumer
GPS work. A more accurate conversion
is provided by the CORPSCON program (download
from
http://crunch.tec.army.mil/software/corpscon/corpscon.html
).
A Closer Look
Let's closely look at the
original NGS coordinate, the transformations and
the observed GPS position for this coordinate
set:
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NGS
NAD83 coordinate
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N
33 17 21.0593 W 95 53 54.2151
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NAD27
converted by Molodensky
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N
33 17 20.5500 W 95 53 53.27000
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NAD27
converted by Corpscon
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N
33 17 20.6587 W 95 53 53.33877
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Observed
GPS coordinate
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N
33 17 20.7 W 95 53 53.1
The difference between the
NAD83 coordinate and the Corpscon-converted
NAD27 coordinate is 84.7 feet.
The difference between the
Molodensky-converted NAD27 coordinate and the
Corpscon NAD27 coordinate is 12.4 feet.
The GPS reading reported
by 'All Topo Maps: Texas' is within 20.93
feet of the Molodensky NAD27 value and 20.7 feet
of the Corpscon NAD27 coordinate.
20 feet (6.1 meters) is
about 1.6 pixels in the 'All Topo Maps'
image database!
The Following Image Displays The Relationship
Of These Points:
This Example From
'All Topo Maps' Was Generated With The Following
Annotation Set:
<P 3>
N 33 17 21.0593 W 95 53 54.21510; WGS84 <P N> <F
Red> <S Red>
N 33 17 20.65867 W 95 53 53.33877; <P W> NAD27
Corpscon <F Blue> <S Blue>
N 33 17 20.5500 W 95 53 53.27000; NAD 27
Molodensky <P SW> <F Green> <S Green>
N 33 17 20.7 W 95 53 53.1; GPS Reading <P E> <F
Black> <S Black>
Additional
Inaccuracies
In the case above,
we are lucky to have a very accurate horizontal
coordinate point available from the NGS
database. (The point was used as a survey
base for a public airport.) Typically 'All
Topo Map' users are marking locations from
features found on the topographic maps.
How accurately might we expect to recover these
points?
The base USGS
Quadrangles are produced in accordance with the
'National Map Accuracy Standards'. From these
standards (see
http://rockyweb.cr.usgs.gov/nmpstds/acrodocs/nmas/NMAS647.PDF
) we find:
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1.
Horizontal accuracy.
For maps
on publication scales larger than
1:20,000, not more than 10 percent
of the points tested shall be in
error by more than 1/30 inch,
measured on the publication scale;
for maps on publication scales of
1:20,000 or smaller, 1/50 inch.
These limits of accuracy shall apply
in all cases to positions of
well-defined points only.
Well-defined points are those that
are easily visible or recoverable on
the ground, such as the following:
monuments or markers, such as bench
marks, property boundary monuments;
intersections of roads, railroads,
etc.; corners of large buildings or
structures (or center points of
small buildings); etc. In general
what is well defined will be
determined by what is plottable on
the scale of the map within 1/100
inch. Thus while the intersection of
two road or property lines meeting
at right angles would come within a
sensible interpretation,
identification of the intersection
of such lines meeting at an acute
angle would obviously not be
practicable within 1/100 inch.
Similarly, features not identifiable
upon the ground within close limits
are not to be considered as test
points within the limits quoted,
even though their positions may be
scaled closely upon the map. In this
class would come timber lines, soil
boundaries, etc. |
At 1:24,000
Scale, 1 Inch Equals 2,000 Feet; Therefore:
1/30 inch =
66.6 feet
1/50 inch =
40.0 feet
1/100 inch =
20.0 feet
Depending upon
how you interpret the official statement, we
expect map coordinates to be within 40-67
feet 90% of the time! (No indication
of standard deviation is implied, so 10% of
the points could be, ?)
In addition to
the base map inaccuracy, the
DRG (Digital Raster
Graphics) that 'All Topo Maps' are
based upon, are rubber-sheet transformed to
UTM
projection. This mathematical transformation
is based upon control points manually
snapped onto the map surface. Additional
errors are introduced with each step.
To the mapping
errors, datum conversion errors, cursor
positioning errors, map georeferencing
errors, we also must add the GPS 'Estimated
Position Error' (see
EPE,
commonly displayed on the Satellite
Constellation display page) which is based
upon the 'Dilution
of Precision' (DOP
is a measure of the number of satellites and
quality of satellite positions.)
Summary
Hopefully, the realities of geodetic
coordinates and GPS accuracy will not
shatter your expectations of consumer GPS
receivers and their applications. A
consumer GPS System's ability to accurately
pinpoint your location, on the face of the
planet or in the sky, is one of the most
amazing feats of technology contrived during
the 21st
century.
The Above Article Was
Provided By Mark Silver, iGage Mapping Corp.
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