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Texas Centric Albers Equal Area projection

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john-hamilton
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I was requested by a client to convert a file with NAD83 (2011) lat/longs to Texas Centric coordinate system, which is an Albers Equal Area projection that covers the entire state.

I found the parameters online for the system:
Latitude of Origin: 18å¡00'00"
Longitude of Origin: 100å¡00'00"
Latitude of 1st standard parallel: 27å¡30'00"
Latitude of 2nd standard parallel: 35å¡00'00"
False easting: 1,500,000 m
False northing: 6,000,000 m

I don't have any software (that I know of) that will do this, so I wrote a routine using the formulas in "Map Projections Used by the U.S. Geological Survey" (Chapter 12) to convert from lat/long to N/E. The formulas are a bit complicated (one of them is, for q, the rest are fairly straightforward).

My problem is that I have no way to check my program. If anyone has access to software that will do this, could you compute the N and E of a test position in Texas (TXFR CORS):
latitude = 30 14 45.49667 N
longitude = 098 50 48.42806 W

Thanks in advance.


 
Posted : March 27, 2017 1:15 pm
Gene Kooper
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John,

I get 7,347,878.430, 1,610,774.776 (N,E in meters) using an Albers Equal Area Conic projection (assumes fact not in evidence that I didn't fat finger one or more parameters).

The scale factor is 1.00027873 and convergence is 0.59699258 degrees.

However, I found online a source listing this, "Texas Centric Mapping System Lambert". Using the Lambert Conformal Conic projection with two standard parallels and using the same parameters you provided I get the following.

For the Lambert case, I get 7,366,869.719, 1,610,773.128 (N,E in meters)

The scale factor is 0.99802872 and convergence is 0.59869317 degees.

Quite the difference in the northings!

On another note, I found this on the following Univ. of Texas web site.
http://www.geo.utexas.edu/courses/371c/Labs/lab2.htm#Texas%20in%20the%20Texas%20Centric&apos ;"> http://www.geo.utexas.edu/courses/371c/Labs/lab2.htm#Texas in the Texas Centric

I have no idea why they show two values for the latitude origin (boldfaced and underlined). One is 31 15' N and the other used in the exercise is 18.

GEO327G/386G: GIS & GPS Applications in Earth Sciences
Lab 2: Map Projections and Coordinate Systems in ArcGIS v.10
2.433 Texas in the Texas Centric Mapping System - setting a custom projection

In order to present a pleasing map of Texas, and to minimize distortion of distance in state-wide maps, the Texas State GIS Committee has approved a standard projection of Texas called the Texas Centric Mapping System. There are two variations on this projection, one is a Lambert Conformal Conic projection, the other is an Albers Equal Area. We'll use the Albers Equal Area Conic. The definition of this projection is:

Datum: North American Datum of 1983 (NAD83)
Ellipsoid: Geodetic Reference System of 1980 (GRS80)
Map units: meters
Central Meridian: 100å¡W (-100.0000)
Latitude of Origin: 31å¡ 15' N (31.25; we will use 18.0 for the exercise below)
Standard Parallel 1: 27å¡ 30å« N (27.5000)
Standard Parallel 2: 35å¡ N (35.0000)
False Easting: 1,500,000
False Northing: 6,000,000

This means that the standard parallels (where the cone penetrates earth's surface) are located at about 1/6 of the distance from the top and bottom of the state, respectively, and that the origin of the coordinate system (at the intersection of the central meridian and the reference latitude) is south of Texas in the Gulf of Mexico, to which the coordinates (x, y) = (1500000, 6000000) meters is assigned so that the coordinates of all locations in the state will be positive.


 
Posted : March 27, 2017 2:46 pm
mkennedy
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I wish you'd given your results. Here's what I get (with extra precision):

E = 1610774.776440 m
N = 7347878.430257 m

EPSG:6579


 
Posted : March 27, 2017 2:47 pm
mkennedy
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Gene,

The Lambert case should be even farther off--EPSG lists the false northing value as 5 million rather then the 6 million used for Albers. So when I check the same coordinates in EPSG:6580:

E = 1610773.127531204 m
N = 6366869.718453525 m


 
Posted : March 27, 2017 2:54 pm
lee-d
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John - FYI - Trimble Business Center supports Albers equal area projections, I'm keying it in now.


 
Posted : March 27, 2017 2:56 pm

john-hamilton
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exactly what I get, to the millimeter (I only output to three decimals), thanks for the verification Gene and Melita!

John


 
Posted : March 27, 2017 2:57 pm
john-hamilton
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Lee D, post: 420497, member: 7971 wrote: John - FYI - Trimble Business Center supports Albers equal area projections, I'm keying it in now.

Lee: didn't think to look in there, I checked star*net and Geolab. But I need to convert a csv file with lat/long/name. I guess I could import it into TBC and then export it back out. But my program works fine, I get the same coordinate as Gene and Melita

Thanks


 
Posted : March 27, 2017 3:00 pm
Gene Kooper
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Melita,

Glad to see that we got the same results with both projections (after I subtract 1000000 from the northing for the Lambert projection). I created two custom projections with an old copy of Geographic Calculator.


 
Posted : March 27, 2017 3:00 pm
lee-d
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Here's what TBC spit out in meters:

Point ID Easting Northing Elevation Feature Code
1 1610774.776 7347878.430 22.391

The elevation is just based on a 0 ellipsoid height using Geoid 12B.


 
Posted : March 27, 2017 3:04 pm
lee-d
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I see that TBC agrees with Gene and Melita as well. Good to know that's in there.


 
Posted : March 27, 2017 3:05 pm

Gene Kooper
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I see that 31 15' N is halfway between the two standard parallels in the UoT lab exercise. I guess they were trying to keep the students on their toes.


 
Posted : March 27, 2017 3:13 pm
mathteacher
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This online calculator gets the same answer: http://tool-online.com/en/coordinate-converter.php


 
Posted : March 27, 2017 3:21 pm
john-hamilton
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Thanks for the great link, MathTeacher. Another good tool to have.


 
Posted : March 27, 2017 3:29 pm