GIS in Water Resources. Review for Midterm Exam. Latitude and Longitude in North America. Austin:

### GIS in Water Resources

Review for Midterm Exam

Latitude and Longitude in North America

Austin:

(30°N, 98°W)

Logan:

(42°N, 112°W)

60 N

30 N

60 W

120 W

90 W

0 N

Length on Meridians and Parallels

(Lat, Long) = (f, l)

Length on a Meridian:

AB = ReDf

(same for all latitudes)

R

Dl

D

R

30 N

C

B

Re

Df

0 N

Re

Length on a Parallel:

CD = R Dl = ReDl Cos f

(varies with latitude)

A

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 = ReDf = 6370 * 0.0175 = 111 km
• For the parallel, DL = ReDl 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
• NAD83 (NAD,1983) uses the GRS80 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

X

Origin

(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°

Origin

Equator

-90 °

-120°

-60 °

Defined for a feature dataset in ArcCatalog

Coordinate System

Projected

Geographic

X/Y Domain

Z Domain

M Domain

ArcInfo 8 Reference FramesX/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.
Flow to a sink

32

64

128

16

1

8

4

2

Eight Direction Pour Point Model

Water flows in the direction of steepest descent

32

64

128

16

1

8

4

2

Flow Direction Grid

Stream cell

Cell to Cell Grid Network

Through the Landscape

1

1

1

1

1

1

1

1

1

1

1

4

3

3

1

4

3

1

1

3

1

1

2

1

1

12

1

2

1

12

1

1

1

2

16

1

1

2

1

16

2

1

3

6

25

3

6

1

2

25

Contributing Area Grid

Drainage area threshold > 5 Cells

Delineation ofStreams and Watersheds on a DEM Hortons Laws: Strahler system for stream ordering

1

3

• most upstream is order 1
• when two streams of a order i join, a stream of order i+1 is created
• when a stream of order i joins a stream of order i+1, stream order is unaltered

1

2

1

2

1

1

1

1

1

2

1

2

1

1

1

1

1

1

A Mesh of Triangles

Triangle is the only

polygon that is always

planar in 3-D

Lines

Surfaces

Points

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

13.0

10.0

9.0

5.0

2.0

Flow On a TriangleFlow On a TIN