# Origin of Geographic Coordinates

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```					GIS in Water Resources

Review for Midterm Exam
Latitude and Longitude
in North America

Austin:
(30°N, 98°W)

Logan:
(42°N, 112°W)
90 W
Length on Meridians and Parallels
(Lat, Long) = (f, l)

Length on a Meridian:
AB = Re Df                             R
(same for all latitudes)        R Dl       D
C
Re    Df B
Re
Length on a Parallel:
A
CD = R Dl = Re Dl Cos f
(varies with latitude)
Example: What is the length of a 1º increment along
on a meridian and on a parallel at 30N, 90W?
Radius of the earth = 6370 km.

Solution:
• A 1º angle has first to be converted to radians
p radians = 180 º, so 1º = p/180 = 3.1416/180 = 0.0175 radians

• For the meridian, DL = Re Df = 6370 * 0.0175 = 111 km

• For the parallel, DL = Re Dl Cos f
                      = 6370 * 0.0175 * Cos 30
                      = 96.5 km
• Parallels converge as poles are approached
Horizontal Earth Datums
• An earth datum is defined by an ellipse and
an axis of rotation
• NAD27 (North American Datum of 1927)
uses the Clarke (1866) ellipsoid on a non
geocentric axis of rotation
ellipsoid on a geocentric axis of rotation
• WGS84 (World Geodetic System of 1984)
uses GRS80, almost the same as NAD83
Vertical Earth Datums
• A vertical datum defines elevation, z
• NGVD29 (National Geodetic Vertical
Datum of 1929)
• NAVD88 (North American Vertical Datum
of 1988)
• takes into account a map of gravity
anomalies between the ellipsoid and the
geoid
Coordinate System
A planar coordinate system is defined by a pair
of orthogonal (x,y) axes drawn through an origin

Y

Origin                             X

(xo,yo)
(fo,lo)
Universal Transverse
Mercator
• Uses the Transverse Mercator projection
• Each zone has a Central Meridian (lo),
zones are 6° wide, and go from pole to pole
• 60 zones cover the earth from East to West
• Reference Latitude (fo), is the equator
• (Xshift, Yshift) = (xo,yo) = (500000, 0) in
the Northern Hemisphere, units are meters
UTM Zone 14
-99°
-102°   -96°

6°

Origin
Equator
-120°          -90 °   -60 °
ArcInfo 8 Reference Frames
• Defined for a feature
dataset in ArcCatalog
• Coordinate System
– Projected
– Geographic
• X/Y Domain
• Z Domain
• M Domain
X/Y Domain
(Max X, Max Y)     Long integer max value
of 231 = 2,147,483,645

(Min X, Min Y)

Maximum resolution of a point = Map Units / Precision
e.g. map units = meters, precision = 1000, then
maximum resolution = 1 meter/1000 = 1 mm on the ground
Network Definition
• A network is a set of edges and junctions
that are topologically connected to each
other.
Edges and Junctions
• Simple feature classes: points and lines
• Network feature classes: junctions and edges
• Edges can be
– Simple: one attribute record for a single edge
– Complex: one attribute record for several edges in a
linear sequence

• A single edge cannot be branched

No!!
Polylines and Edges
Junctions
• Junctions exist at all points where edges
join
– If necessary they are added during network
building (generic junctions)
• Junctions can be placed on the interior of an
edge e.g. stream gage
• Any number of point feature classes can be
built into junctions on a single network
Connectivity Table
p. 132 of Modeling our World
J125
J123    J124, E1
E2
J124
J124    J123, E1 J125, E2 J126, E3
E1     E3
J125    J124, E2
J123
J126    J124, E3                                            J126

This is the “Logical Network”
Flow to a sink
Eight Direction Pour Point Model

32     64     128

16             1

8       4      2

Water flows in the direction of steepest descent
Flow Direction Grid

32 64 128

16       1

8    4   2
Cell to Cell Grid Network
Through the Landscape

Stream cell
Contributing Area Grid
1    1   1    1    1   1   1       1             1   1

1   4    3    3    1   1       4        3        3   1

1   1    12   1    2                             1
1   1                         2
12
1   1    2    16   1   1                2            1
1                 16
1   3    6    25   2   1       3        6
2
25

Drainage area threshold > 5 Cells
Delineation of Streams and
Watersheds on a DEM
Stream Segments
0   0       0            0    0

0       3       2        2    0

0
0   0                         1
11
0             1               0
0
15
0       2       5
1
24
Stream Segments in a Cell Network

1
1           2
1   2
5
3                 5
3         5
4 4 4           3 5
4 4
6 6
6
Watershed Outlet
Watershed Draining to This Outlet
Watershed and Drainage Paths
Delineated from 30m DEM

Automated method is more consistent than hand delineation
1000 Cell Threshold Exceeded at Stream Junction

510    989
1504 (>1000)
Subwatersheds for Stream Segments

Same Cell Value
Grid Code to Cell Equivalents

Vector
Streams
Grid
Streams
Delineated Subwatersheds and Stream Networks
A Mesh of Triangles

Triangle is the only
polygon that is always
planar in 3-D

Points   Lines      Surfaces
Tin Triangles in 3-D
(x3, y3, z3)

(x1, y1, z1)
(x2, y2, z2)

z

y                           Projection in (x,y) plane

x
Delauney Triangulation
Maximize the minimum interior angle of triangles
No point lies within the circumcircle of a triangle

Yes                           No
Flow On a Triangle
13.0

10.0
9.0

5.0

2.0
Flow On a TIN

120
110
100
90
80
70

60

50

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