GIS/GPS Chapter 3

Geodesy

shape of the Earth and definition of Earth datums

Map projection

transformation of curved Earth to a flat map

Coordinate system

x, y, z coordinate systems for map data

Spatial reference

datum + projection + coordinate system

Datums

can’t use sea-level/ground-level due to changes, reference/foundation surface against which accurate precision measurements are made, identifies “0” on a measurement scale

What are the foundation for navigation in the US that makes up the NSRS?

2 main datums

History

5,000 yrs ago the Baylonians believed the Earth shape was an oyster, 2,000 yrs later Thales and Homer thought the Earth was a flat disk, time passed various other shapes were proposed like a cube/cylinder, Columbus said Earth was a roundish pair

Earth’s size

multiple people have tried to measure Earth’s size, closest was Posidonius and Eratosthenes were closest, true circumference is 40,096 km/24,901 miles, Issac Newton thought the Earth would be bigger at the equator than compared to the poles

How did Posidonius and Eratosthenes measure the Earth’s size?

measured height in Alexandria and looked at the shadow, same for a well

How was it solved when people thought it would be skinnier at the equator than compared to the poles?

taken at the Arctic pole and the equator in South America

Ellipsoids

sphere based on a circle, based on an ellipse, rotating an ellipse about 1 of its axes, ellipsoid of rotation is created, type of ellipsoid most closely approximated the Earth’s shape, more precise the Earth rotates about its shortest axis/minor axis (oblate ellipsoid)

Ellipsoids when describing the Earth’s shape

semi-major and semi-minor exes are given, spheroid is an ellipsoid that approximates a sphere, 2 common world spheroids used today with their values rounded to the nearest meter

What is the difference between each spheroid?

major axis and minor axis is less than 0.34%

Why need different spheroids?

elliptical deviations, earth’s spheroid deviates slightly for different regions of the Earth

Elliptical deviations

minor axis (S pole) is closer to the major axis (equator) than is the most N point of the minor axis (N pole), Earth’s spheroid deviates slightly for different regions of the Earth

Geoid

equipotential surface of the Earth’s gravity field that best fits global mean sea level

Geoid examples

sea level is a surface of constant gravitational potential, gravity of Earth measured by the GRACE satellite, youngest part is blue adn the geoid height is the lowest, shape of the Earth isn’t an exact perfect circle

Geoid/Gravity Anomaly

elevation difference between a standard shape of the Earth (ellipsoid) and a surface of constant gravitational potential (geoid)

Gravity

changes on a single position over time

Why does gravity shift?

tectonic plates shifting the masses around, at night things start to contract at night, elevation decreases at night, temperature can change gravity day to day, long term is climate change

Equator

expands and contract over time, has to do with the position of the sun and the moon

Sun and the Moon with Seasons

closer to the sun when in winter, further when in summer

Elevation

measured from the geoid, Z = zp, Z = 0

What are the ways to measure elevation?

orthometric, ellipsoidal, tidal

Orthometric heights

land surveys, geoid

Ellipsoidal heights

lidar, GPS

Tidal heights

sea water level

Where is tidal heights used?

off-shore drilling places use this a lot

What happens when the measuring elevation techniques combine?

some uncertainty comes in

How does it fit the geoid using datums?

not just changing exes but also the middle, for vertical data sets use orthometric for big regions, smaller regions use ellipsoidal (Half of PA)

Horizontal Satums

collections of points on the Earth that have been identified according to their precise N/S location (latitude)/ E/W location (longitude)

Identifying Horizontal Satums

mark each position with brass/aluminum disk monument, use GPS to accurately get position of markers in geographic space, create unified connected network of measurements (datum)

Horizontal Satums History

1927 US Coast and Geodetic Survey connected all of the existing horizontal monuments together using terrestrial surveying triangulation to create NAD27, National Geodetic Survery created the NAD83, most used for horizontal control datum in US

Vertical Datums

collection of spatially distributed point on the Earth with known heights either above/below mean sea level, markets used to designate point locations

Vertical Datums History

1929 NGS compiled all existing vertical benchmarks and created NGVD29, adjusted again in 1988 to NAVD88 is most used today

What is the elevation of a geographic location?

height above a fixed reference point geoid/mathematical model of the Earth’s sea level

Digital Elevation Model (DEM)

continuous digital elevation surface in reference to sea level

Digital Surface Model (DSM)

elevation of all features in the terrain above sea level

Example of DSM

bare ground, buildings, trees, powerlines

Digital Terrain Model (DTM)

refers to only elevation of the bare ground above sea level

Bathymetry

study of the underwater depth of lakes, seas, ocean floors

Datums

transformations of datums, point file attributed with elevation difference between NGVD and NAVD 88, NGVD 29 terrain + adjustment = NAVD 88 terrain elevation