gis in water resources review for midterm exam. latitude and longitude in north america 90 w 120 w...
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![Page 1: GIS in Water Resources Review for Midterm Exam. Latitude and Longitude in North America 90 W 120 W 60 W 30 N 0 N 60 N Austin: (30°N, 98°W) Logan: (42°N,](https://reader036.vdocuments.us/reader036/viewer/2022062407/56649f475503460f94c68ea2/html5/thumbnails/1.jpg)
GIS in Water Resources
Review for Midterm Exam
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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)
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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
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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
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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
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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
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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
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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
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UTM Zone 14
Equator-120° -90 ° -60 °
-102° -96°
-99°
Origin
6°
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ArcInfo 8 Reference Frames
• Defined for a feature dataset in ArcCatalog
• Coordinate System– Projected
– Geographic
• X/Y Domain• Z Domain• M Domain
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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
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Network Definition
• A network is a set of edges and junctions that
are topologically connected to each other.
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Flow to a sink
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32
16
8
64
4
128
1
2
Eight Direction Pour Point Model
Water flows in the direction of steepest descent
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Flow Direction Grid
32
16
8
64
4
128
1
2
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Cell to Cell Grid NetworkThrough the Landscape
Stream cell
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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
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Delineation of Streams and Watersheds on a DEM
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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
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A Mesh of Triangles
Triangle is the onlypolygon that is always
planar in 3-D
Points Lines Surfaces
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Tin Triangles in 3-D
(x3, y3, z3)
(x1, y1, z1) (x2, y2, z2)
x
y
z
Projection in (x,y) plane
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Delauney TriangulationMaximize the minimum interior angle of trianglesNo point lies within the circumcircle of a triangle
Yes No
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Flow On a Triangle
2.0
13.0
9.0
10.0
5.0
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Flow On a TIN
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