map projections (2/2) francisco olivera, ph.d., p.e. center for research in water resources...
Post on 19-Dec-2015
222 views
TRANSCRIPT
![Page 1: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/1.jpg)
Map Projections (2/2)
Francisco Olivera, Ph.D., P.E.Center for Research in Water Resources
University of Texas at Austin
![Page 2: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/2.jpg)
Overview
Geodetic Datum
Map Projections
Coordinate systems
Global Positioning System
![Page 3: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/3.jpg)
Coordinate Systems
A coordinate system is used to locate a point of the surface of the earth.
![Page 4: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/4.jpg)
Coordinate Systems
Global Cartesian coordinates (x,y,z) for the whole earth.
Geographic coordinates (,, z) for the whole earth.
Projected coordinates (x, y, z) on a local area of the earth’s surface.
The z-coordinate in Global Cartesian and Projected coordinates is defined geometrically; and in Geographic coordinates gravitationally.
![Page 5: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/5.jpg)
Global Cartesian Coordinates
O
X
Z
Y
GreenwichMeridian
Equator
•
![Page 6: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/6.jpg)
Geographic Coordinates
P
Meridian
Equator
plane
Prime Meridian
![Page 7: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/7.jpg)
Geographic Coordinates
Longitude line (Meridian)
N
S
W E
Range: 180ºW - 0º - 180ºE
Latitude line (Parallel)
Range: 90ºS - 0º - 90ºN
N
S
W E
(0ºN, 0ºE) Equator, Prime Meridian
![Page 8: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/8.jpg)
Geographic Coordinates
90 W120 W 60 W
30 N
0 N
60 N
![Page 9: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/9.jpg)
Geographic Coordinates
Meridian of longitude
Parallel of latitude
X
Y
ZN
EW
=0-90
°S
P
OR
=0-180°E
=0-90°N
•
Greenwich meridian = 0°
•
Equator = 0°
•
•=0-180°W
- Geographic longitude
- Geographic latitude
R - Earth radius
O - Geocenter
![Page 10: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/10.jpg)
Geographic Coordinates
Earth datum defines the standard values of the ellipsoid and geoid.
Latitude () and longitude () are defined using an ellipsoid (i.e., an ellipse rotated about an axis).
Elevation (z) is defined using a geoid (i.e, a surface of constant gravitational potential).
![Page 11: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/11.jpg)
Latitude
•Take a point S on the surface of the ellipsoid and define there the tangent plane mn.
•Define the line pq through S and normal to the tangent plane.
•Angle pqr is the latitude , of point S
Sm
n
q
p
r
![Page 12: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/12.jpg)
Longitude
0°E, W
90°W(-90 °)
180°E, W
90°E(+90 °)
-120°
-30°
-60°
-150°
30°
-60°
120°
150°
= the angle between a cutting plane on the prime meridian and the cutting plane on the meridian through the point, P
P
![Page 13: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/13.jpg)
If Earth were a Sphere ...
0 N R
rr
A
BC
Length on a Meridian:AB = R (same for all latitudes)
Length on a Parallel:CD = r = R Cos(varies with latitude)
D
![Page 14: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/14.jpg)
Example:What is the length of a 1º increment on a meridian and on a parallel at 30N, 90W? Radius of the earth R = 6370 km.
Solution: • A 1º angle has first to be converted to radians: radians = 180°, so 1º = /180° = 3.1416/180° = 0.0175 radians
• For the meridian: L = R = 6370 Km * 0.0175 = 111 km
• For the parallel: L = R Cos= 6370 * Cos30° * 0.0175 = 96.5 km
• Meridians converge as poles are approached
If Earth were a Sphere ...
![Page 15: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/15.jpg)
Cartesian Coordinates
(o, o)
(xo,yo)
X
Y
Origin
A planar cartesian coordinate system is defined by a pair of orthogonal (x,y) axes drawn through an origin.
![Page 16: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/16.jpg)
Coordinate Systems
Universal Transverse Mercator (UTM) - a global system developed by the US Military Services.
State Plane - civilian system for defining legal boundaries.
![Page 17: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/17.jpg)
Universal Transverse Mercator
Uses the Transverse Mercator projection.
60 six-degree-wide zones cover the earth from East to West starting at 180° West.
Each zone has a Central Meridian (o).
Reference Latitude (o) is the equator.
(Xshift, Yshift) = (xo,yo) = (500,000, 0) in the Northern Hemisphere.
Units are meters
![Page 18: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/18.jpg)
UTM Zone 14
Equator
-120° -90 ° -60 °
-102° -96°
-99°
Origin
6°
![Page 19: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/19.jpg)
State Plane
Defined for each State in the United States.
East-West States (e.g. Texas) use Lambert Conformal Conic, North-South States (e.g. California) use Transverse Mercator.
Texas has five zones (North, North Central, Central, South Central, South) to give accurate representation.
Greatest accuracy for local measurements
![Page 20: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/20.jpg)
Overview
Geodetic Datum
Map Projections
Coordinate systems
Global Positioning System
![Page 21: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/21.jpg)
Global Positioning System (GPS)
24 satellites in orbit around the earth.
Each satellite is continuously radiating a signal at speed of light.
GPS receiver measures time lapse t since signal left the satellite, and calculates the distance to it r = c t.
Position obtained by intersection of radial distances r from each satellite.
Differential correction improves accuracy.
![Page 22: Map Projections (2/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources University of Texas at Austin](https://reader036.vdocument.in/reader036/viewer/2022062300/56649d2b5503460f94a00ffa/html5/thumbnails/22.jpg)
Global Positioning System (GPS)
r1
r3r2
r4
Numberof Satellites
1234
Object Defined
SphereCircle
Two PointsSingle Point