Transcript Geodetic Data and Map Projections

Map Projections (1/2)
Francisco Olivera, Ph.D., P.E.
Center for Research in Water Resources
University of Texas at Austin
Overview
Geodetic Datum
Map Projections
Coordinate systems
Global Positioning System
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.
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
b
F1

For the earth:
•Major axis: a = 6378 km
•Minor axis: b = 6357 km
•Flattening ratio: f = 1/300
P
P
O

a
F2
X
Ellipsoid or Spheroid
Z
b
a O a
Rotate an ellipse
around one of its axis.
X
Rotational axis
Y
Standard Ellipsoids
Ellipsoid
Major
Minor
Flattening
axis, a (m) axis, b (m) ratio, 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
Sea surface
Geoid
Ellipsoid
Topographic
surface
Geoid is a surface of constant gravity.
Earth Surfaces
Topographic surface
Ocean
Geoid
Ellipsoid
Gravity Anomaly
Elevation
P
z = zp
Topographic Surface
z=0
Mean Sea level = Geoid
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).
Overview
Geodetic Datum
Map Projections
Coordinate systems
Global Positioning System
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
Scale
Projection
Representative Fraction
Scale Fraction
Globe distance
Earth distance
Map distance
Globe distance
(e.g. 1:24,000)
(e.g. 0.9996)
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 NorthSouth 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.
Conic Projections
Albers and Lambert
Cylindrical Projections
Mercator
Transverse
Oblique
Tangent
Secant
Azimuthal
Lambert
Albers Equal-Area Conic
Lambert Conformal Conic
Universal Transverse Mercator
Lambert Azimuthal Equal-Area
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.