Map Projections (1/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources...
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Transcript of Map Projections (1/2) Francisco Olivera, Ph.D., P.E. Center for Research in Water Resources...
Map Projections (1/2)
Francisco Olivera, Ph.D., P.E.Center for Research in Water Resources
University of Texas at Austin
Definition
A geodetic datum defines the size and shape of the earth, and the origin and orientation of the axis used to define the location of points.
Over time, geodetic data have evolved from simple flat surfaces and spheres to complex ellipsoids.
Flat earth models can be accurate over short distances (i.e., less than 10 Km), spherical earth models for approximate global distance calculations, and ellipsoidal earth models for accurate global distance calculations.
Shape of the Earth
We think of the earth as a sphere ...
... when it is actually an ellipsoid, slightly larger in
radius at the equator than at the poles.
P
O a
b
X
Ellipse
Z
An ellipse is defined by:•Focal length = •Flattening ratio: f = (a-b)/a
•Distance F1-P-F2 is constant for all
points P on ellipse•When = 0 then ellipse = circle
For the earth:•Major axis: a = 6378 km•Minor axis: b = 6357 km•Flattening ratio: f = 1/300
F1F2
P
Standard Ellipsoids
Ellipsoid Majoraxis, a (m)
Minoraxis, b (m)
Flatteningratio, f
Clarke(1866)
6,378,206 6,356,584 1/294.98
GRS80 6,378,137 6,356,752 1/298.57
Ref: Snyder, Map Projections, A working manual, USGS Professional Paper 1395, p.12
Standard Horizontal Geodetic Data
NAD27 (North American Datum of 1927) uses the Clarke (1866) ellipsoid.
NAD83 (North American Datum of 1983) uses the GRS80 ellipsoid.
WGS84 (World Geodetic System of 1984) uses GRS80.
Earth Surfaces
Geoid is a surface of constant gravity.
Topographic surface
EllipsoidSea surface
Geoid
Elevation
P z = zp
z = 0
Mean Sea level = Geoid
Topographic Surface
Elevation is measured from the Geoid
Standard Vertical Geodetic Datum
A vertical datum defines elevation z, taking into account a map of gravity anomalies between the ellipsoid and the geoid.
NGVD29 (National Geodetic Vertical Datum of 1929).
NAVD88 (North American Vertical Datum of 1988).
Map Projections
A map projection is a mathematical algorithm to transform locations defined on the curved surface of the earth into locations defined on the flat surface of a map.
Map Projection
Representative Fraction
Globe distanceEarth distance
Scale Projection
(e.g. 1:24,000) (e.g. 0.9996)
Scale Fraction
Map distanceGlobe distance
Types of Projections
Conic: Screen is a conic surface. Lamp at the center of the earth. Examples: Albers Equal Area, Lambert Conformal Conic. Good for East-West land areas.
Cylindrical: Screen is a cylindrical surface. Lamp at the center of the earth. Examples: (Transverse Mercator). Good for North-South land areas.
Azimuthal: Screen is a flat surface tangent to the earth. Lamp at the center of the earth (gnomonic), at the other side of the earth (stereographic), or far from the earth (orthographic). Examples: Lambert Azimuthal Equal Area. Good for global views.
Distortion Projected Maps
In the process of transforming a curved surface into a flat surface, some geometric properties are modified.
The geometric properties that are modified are:
Area (important for mass balances)
Shape
Direction
Length
The difference between map projections has to do with which geometric properties are modified.
Depending on the type of analysis, preserving one geometric property might be more important that preserving other.