Upload
helena-powell
View
220
Download
1
Embed Size (px)
Citation preview
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
50
60
70
80
90
100
110
120
50
60
70
80
90
100
110
120
50
60
70
80
90
100
110
120
50
60
70
80
90
100
110
120
50
60
70
80
90
100
110
120