Module 4 Flashcards
Map Projections –Preference based on need
Equal areal – Preserves area of land and oceans [Albers Equal-Area]
conformal-preserves direction [conformal Mercator]
Preserved shape [conformal conic]
preserved distances [Azimuthal equidistant]
Shortest navigation path presented as a straight line [gnomonic]
HEIGHT SYSTEMS
- Sea Level Heights are based on a local tide datum system
- Ellipsoid heights are measured from the ellipsoid surface, and are geometric quantities based on the reference ellipsoid (used to determine GPS heights).
- Orthometric Heights are measured from the Geoid surface and based on gravity models.
- Geoid surface and based on gravity models. Geoid heights are the difference between the geoid 0-potential surface and the ellipsoid
Engineers and Surveyors Determine “Height” by:
- Classical Optical leveling (Total Station)
- Digital Leveling
- Trig Leveling
- Various Static& RTK GPS techniques
VERTICAL DATUM
A set of fundamental LOCAL elevations to which other elevations are referred
Vertical Datum Types:
- Tidal – Defined by observation of tidal variations over some period of time (MSL, MLLW, MLW, MHW, MHHW etc.)
- Geodetic – Either directly or loosely based on Mean Sea Level at one or more points at some epoch (NGVD 29, NAVD 88, IGLD85 etc.)
TIDAL DATUMS
- High Water: Maximum height reached by a rising tide.
- Mean High Water: The average of all the high-water heights observed over the National Tidal Datum Epoch.
- Higher High Water: The highest of the high waters (or single high water) of any specified tidal day.
- Mean Higher High Water: The average of the higher high water height of each tidal day observed over the National Tidal Datum Epoch.
- Low Water: The minimum height reached by a falling Nde. Mean Low Water: The average of all the low water heights observed over the National Tidal Datum Epoch. Lower Low Water: The lowest of the low waters (or single low water) of any specified tidal day.
- Mean Lower Low Water: The average of the lower low water height of each tidal day observed over the National Tidal Datum Epoch.
- National Tidal Data Epoch: The specific l9-year period adopted by the National Ocean Service as the official Nme segment over which Nde observaNons are taken and reduced to obtain mean values for tidal datums. The present epoch is 1983 through 2001.
Tidal Dantums Characteristics
• Heights Measured Above Local Mean Sea Level
• National Tidal Datum epoch; 19 year series
• Encompasses all significant tidal periods including 18.6 year period for regression of Lunar nodes
• Averages out nearly all meteorological, hydrological, and oceanographic variability
19 year-period needed to observe all lunar node (tide generating) states
Heighting
• Average out nearly all meteorological, hydrological, and oceanographic variability
• 19 year period to observe all lunar node (tide generatin) states
Ellipsoid heights
Heights determined using GPS are referenced to the WGS 84 Ellipsoid
Ellipsoid Heights are heights above the ellipsoid
World Geodetic System (WGS84)
• The prime orientation (X) is Greenwich Meridian
• Positions and Coordinate differences are obtained in the WGS 84
• Coordinate System
– Latitude, Longitude Ellipsoid height
– Geocentric X,Y,Z coordinates
• Origin coincides with Earth’s center of mass (This is an Equipotential Ellipsoid)
• X and Y axis are perpendicular to each other in the equatorial plane
• Z axis is at right angles to the X,Y plane and coincides with the Earth’s rotational
The Geoid
The geoid is essentially a model of the Earth devoid of topographical features.
It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. and continued under the continental masses.
Geoid Anomalies
Or undulations are differences, in meters, between the geoid reference ellipsoid(=geoid height):
- Excess mass: geoid(ocean surface) goes up(geoid=wqp surface-> must remain perpendicular to the gravity field direction.
- Deficit of mass-> geoid (ocean surface) goes down
Gravitational Force
Newton’s law of universal gravitation states that every point in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Gravitational Potential
- Assume: a particle of unit mass moving freely, a body of mass M
- The particle is attracted by M and moves towards it by a small quantity dr
- This displacement is the result of Work, W, exerted by the gravitational field generated by M.
- W= G* (m/r^2)*dr
- The potential U of mass M is the amount of work necessary to bring the particle from infinity to a given distance r
- U=-GM/r
- At a distance r, the gravitational potential generated by M is U
Gravitation Potential of Earth:
Earth’s gravitational acceleration g exerts a work to move a unit mass particle from U to U+dU (spherical homogenous non-rotating earth)
G=-dU/dr
Equipotential surfaces
- Surfaces on which the potential is constant
- U=constant, dU=-g*dr, g not necessarily constant on equipotential surfaces
- Non-rotating homogenous earth- U=G*Me/r, U=constant, r=constant-> equipotential surfaces=speheres centered on Me
- Practical use of equipotential surfaces:
o definition of vertical=direction of the gravity field = perpendicular to equipotential surface
o Equipotential surface= define the horizontal
The Geoid
- There is an infinity of equipotential surfaces
- There is a particular surface on the earth that is easy to locate: The Mean Sea Level
- The geoid= the particular equipotential surface that coincides with the mean sea level
- This is totally arbitrary
- But it makes sense because the oceans are made of water: the surface of the fluid in equilibrium must follow an equipotential
Let’s be clear
• The Geoid is the equipotential surface of the earth’s gravity field that best fits (in a least square sense) the mean sea level
o Potential is a constant on the geoid
o Gravity is not constant on the geoid
• Reference Ellipsoid is the ellipsoid that besr fits the geoid
• Geoid is the actual figure of the Earth
• Ellipsoid is the theoretical shape of the Earth
Example Earth-Moon System:
o Force vectors (particle motion) can be oblique to gravitational isoforce lines: For this reason gravity, g, alone is not used to define the geoid.
o Water could flow laterally (downstream) alone an isoforce contour due to lateral fluctuations in mass.
o mgΔh is gravitational potential at a given point. Along isocontours of gravitational potential the force vector is orthogonal. Water will not flow along lines of isopotential.
Geoid height=
Geoid-ellipsoid
Hawaiian Islands and seamounts:
force vectors caused by increased mass bend along a plumb line toward the edifice. No lateral flow occurs due to gravity along isopotential lines even though they bow up around the edifice.
Types of Heights:
Ellipsoid- The distance along a perpendicular from the ellipsoid to a point on the Earth’s surface
Orthometric- The distance between the geoid and a point on earth surface measured along the plum line
Geoid- The distance along a perpendicualar from the ellipsoid of reference to the geoid
