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Problem: Significance of XSHIFT/YSHIFT and FALSE EASTING/NORTHING

Solution or Workaround

What is the significance of XSHIFT and YSHIFT in projections? Are they identical to FALSE EASTINGS/NORTHINGS?

Answer:

1. XSHIFT and YSHIFT are used to make X and Y input values smaller BEFORE projecting them to another projection if the data set has been manipulated (for example, four million subtracted from all Y coordinates). They appear in the input section of the projection file.

2. XSHIFT and YSHIFT are always specified in the data units (either feet, meters, or units per meter).

3. FALSE EASTING and NORTHING are used to deliberately change the origin of the projection after the coordinates have been projected. They usually appear in the output section of a projection file. They are used to make all coordinates positive or to increase significant digits.

4. FALSE EASTING and NORTHING are always specified in METERS even though the data may be in feet.

The following examples show how these projection parameters are used.

Example 1: Using XSHIFT/YSHIFT

Begin with the four corners of a 7.5 minute quadsheet in geographic coordinates.

Longitude Latitude
X Y

LR -99.875 40.000
UR -99.875 40.125
LL -100.000 40.000
UL -100.000 40.125

Notice that the lower left corner is 100-degrees West, 40-degrees North.

Generate a coverage (named 'g') to represent these four points at the four corners of a square. Do the following at the ARC prompt.

cw test
w test

generate g
grid
-100,40
-100,41
.125,.125
1,1
q
clean g
list g.tic

g.tic
-----------------------------------------------
Record IDTIC XTIC YTIC
1 1 -99.875 40.000
2 4 -99.875 40.125
3 2 -100.000 40.000
4 3 -100.000 40.125

A projection file named 'p' must be created to project our GEOGRAPHIC coverage to UTM zone 14.

vi p

p
-----------------------------------------------
input
proj geog
units dd
parameters
output
proj utm
units meters
zone 14
parameters
end

project cover g u p /* Our output UTM coverage is called "u"

clean u
list u.tic

u.tic
-----------------------------------------------
Record IDTIC XTIC YTIC
1 1 425307.781 4427914.000
2 4 425444.156 4441788.000
3 2 414637.281 4428026.000
4 3 414793.156 4441900.000
All the YTIC values begin with a 4. The number 4 adds an extra digit to the already large UTM value in meters, it does not add any accuracy. Subtract 4000000 from all the Y values to make the numbers more manageable. This is often done to UTM coordinates.

We can TRANSFORM this UTM cover into another UTM cover (name 't') by subtracting 4000000 from all the Y values:

create t u
tables
SEL T.TIC
LIST
CALC YTIC = YTIC - 4000000
LIST
Q STOP
transform u t
list t.tic

t.tic
-----------------------------------------------
Record IDTIC XTIC YTIC
1 1 425307.781 427914.000
2 4 425444.156 441788.000
3 2 414637.281 428026.000
4 3 414793.156 441900.000

Note that the first 4's in front of all Y values have now been eliminated.

There are still leading 4's for all X and Y coordinates. This is because the study area is very small (.125 deg x .125 deg). The full extent of a UTM zone (6 degrees across) will have different coordinate values.

Assume coverage 't' came from another source. The data provider states that the data are in UTM zone 14. It also tell you that a YSHIFT of -4000000 meters has been applied.

This is where the XSHIFT and/or YSHIFT come into play. In this case, since all Y values are reduced by 4000000, add a YSHIFT of 4 million to all input coordinates to normalize them before projecting them.

Create a new projection file named 'p2'

vi p2

p2
-----------------------------------------------
input
proj utm
units meters
yshift 4000000
zone 14
parameters
output
proj geog
units dd
parameters
end

project cover t g2 p2
list g2.tic

g2.tic
-----------------------------------------------
Record IDTIC XTIC YTIC
1 1 -99.875 40.000
2 4 -99.875 40.125
3 2 -100.000 40.000
4 3 -100.000 40.125
These are the original geographic coordinates.

Example 2: Using FALSE EASTING/NORTHING

The objective is to project the UTM coverage t to a Mercator coverage (name "m").

To minimize distortion, the central meridian should bisect the study area (-99 56 15 DMS). The latitude of true scale should be about midway through the study area (40 03 45 DMS).

Create a projection file named 'p3'

p3.tic
-----------------------------------------------
input
proj utm
units meters
yshift 4000000
zone 14
parameters
output
proj mercator
units meters
parameters
-99 56 15
40 03 45
0.0
0.0
end

project cover t m p3
list m.tic

m.tic
-----------------------------------------------
Record IDTIC XTIC YTIC
1 1 5332.376 3708098.500
2 4 5332.371 3721977.750
3 2 -5332.401 3708098.250
4 3 -5332.394 3721977.500

Note the negative X values. Since it is much easier to deal with positive values, make all X values positive by adding 100000 meters; the FALSE EASTING value would be 100000.

The first digit of the Y values are redundant; subtract 3000000 meters from the Y coordinates. The FALSE NORTHING would be -3000000.

Create another projection file and call it 'p4'

p4
-----------------------------------------------
input
proj utm
units meters
yshift 4000000
zone 14
parameters
output
proj mercator
units meters
parameters
-99 56 15
40 03 45
100000
-3000000
end

project cover t m2 p4
list m2.tic

m2.tic
-----------------------------------------------
Record IDTIC XTIC YTIC
1 1 105332.375 708098.562
2 4 105332.367 721977.812
3 2 94667.602 708098.312
4 3 94667.609 721977.500

The origin has been shifted. This does not change the shape or size of the projection. The same goal could have been achieved by doing a TRANSFORM as in the first example.