GIS in Water Resources

Review for Midterm Exam

Latitude and Longitude in North America

90 W120 W 60 W

30 N

0 N

60 N

Austin: (30°N, 98°W)

Logan:(42°N, 112°W)

Length on Meridians and Parallels

0 N

30 N

Re

Re

RR

A

BC

(Lat, Long) = (, )

Length on a Meridian:AB = Re (same for all latitudes)

Length on a Parallel:CD = R Re Cos(varies with latitude)

D

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 radians = 180 º, so 1º = /180 = 3.1416/180 = 0.0175 radians

• For the meridian, L = Re km

• For the parallel, L = Re CosCoskm• 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

(o,o)(xo,yo)

X

Y

Origin

A planar coordinate system is defined by a pairof orthogonal (x,y) axes drawn through an origin

Universal Transverse Mercator

• Uses the Transverse Mercator projection

• Each zone has a Central Meridian (o), zones are 6° wide, and go from pole to pole

• 60 zones cover the earth from East to West

• Reference Latitude (o), is the equator

• (Xshift, Yshift) = (xo,yo) = (500000, 0) in the Northern Hemisphere, units are meters

UTM Zone 14

Equator-120° -90 ° -60 °

-102° -96°

-99°

Origin

6°

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

(Min X, Min Y)

(Max X, Max Y)

Maximum resolution of a point = Map Units / Precisione.g. map units = meters, precision = 1000, thenmaximum resolution = 1 meter/1000 = 1 mm on the ground

Long integer max value of 231 = 2,147,483,645

Network Definition

• A network is a set of edges and junctions that

are topologically connected to each other.

Flow to a sink

32

16

8

64

4

128

1

2

Eight Direction Pour Point Model

Water flows in the direction of steepest descent

Flow Direction Grid

32

16

8

64

4

128

1

2

Cell to Cell Grid NetworkThrough the Landscape

Stream cell

Contributing Area Grid

1 1 111

1

1

1

1

1

1

1

1

14 3 3

12 2

2

3 2

16

625

1 1 11 1

1

1

1

1

1

1

1

1

1

4 3 3

12 2

2

23

16

256

Drainage area threshold > 5 Cells

Delineation of Streams and Watersheds on a DEM

Hortons Laws: Strahler system for stream ordering

1

1

1

1

11

1

11

1

1

1

1

1

2

2

2

2

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

A Mesh of Triangles

Triangle is the onlypolygon that is always

planar in 3-D

Points Lines Surfaces

Tin Triangles in 3-D

(x3, y3, z3)

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

x

y

z

Projection in (x,y) plane

Delauney TriangulationMaximize the minimum interior angle of trianglesNo point lies within the circumcircle of a triangle

Yes No

Flow On a Triangle

2.0

13.0

9.0

10.0

5.0

Flow On a TIN

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