## Class Update ## Read Chapter 10 of text. ## Deadline for Reading Assignments (2) is 16 April 2009. ## Good set of definitions are available at: - http://www.geod.nrcan.gc.ca/hm/gloss_e.php#qg
## Good article on latest U.S. geoid model - http://www.ngs.noaa.gov/GEOID/USGG2009/tech.html
## Geoid ## The equipotential surface of the Earth's gravity field which best fits, in a least squares sense, global mean sea level. ## Dependent upon the irregular distribution of masses of the Earth. ## It is the surface to which heights refer. ## There are two “implementations” of geoid modeling: gravimetric and hybrid.
## Geoid Model and Horizontal Datum ## NAD 83 - Earth-centered (geocentric) ellipsoid. GRS-80.
- Heights determined by GPS are computed with respect to it.
## NAD 27 - Fitted to the reference ellipsoid.
- NOT geocentric.
**No geoid model associated with NAD 27. **
## NAVD 88 ## Based on a minimum-constraint adjustment of Canadian-Mexican-U.S. leveling observations. ## The height of the primary tidal benchmark at Father Point/Rimouski, Quebec, Canada, was held fixed as the constraint. ## This constraint satisfies the requirements of shifting the datum vertically to minimize the impact of NAVD 88 on U.S. Geological Survey (USGS) mapping products
## NAVD 88 datum + global geopotential ## A “recent” study by Rapp (1996) compares ITRF93 GPS positions and a global geopotential model against the NAVD 88 vertical datum. ## Rapp found a mean offset for the NAVD88 datum of -27 cm when computed with a set of 397 GPS points. - In sense that NAVD 88 is beneath global geoid model.
## Marine Geoid ## Height of the sea surface caused by both gravity and the active ocean circulation. ## Topex/Poseidon launched 1992.
## SST Equations ## a = c*(delta_t / 2) - “a” distance from satellite to sea surface
- “C” is speed of light (electromagnetic energy)
- “delta_t” is roundtrip time of signal
## h = N + Hbar + a - “h” ellipsoid height
- “N” is geoid height
- “Hbar” is difference between mean instantaneous sea level and geoid
- “a” height observation from satellite
## Sea Surface Topography SST ## SST: Deviation of the mean sea surface from the geoid. - Salinity difference
- Large-scale differences in atmospheric pressure
- Strong ocean currents
## Use of SST yields precision of ~ 2 meters.
## Gravity Datums ## Potsdam Gravity Reference System 1909 - Standard until IGSN adopted (60 years)
- +/- 3 milliGals
## International Gravity Standardization Net 1971 - Worldwide network: 24,000 gravimeter, 1,200 pendulum and 10 absolute measurements.
- Collected over twenty years.
- Adjusted by a small Working Group of the International Association of Geodesy.
- Datum is determined not by an adopted value at a single station, but by the gravity values for 1854 stations obtained from a single least squares adjustment of absolute, pendulum and gravimeter data.
- Standard error +/- 50 microGals
## Surface Gravity measurements ## Absolute - Formerly pendulum now falling mass
## Relative - Each meter has own calibration value.
- Observations made at a number of points with the differences the measurement.
- Require observations be made in loops that start and end on same point to account for drift in instrument.
**Gravity anomaly** is the difference between the actual acceleration of gravity at a point on the surface of the earth and the computed normal acceleration of gravity of the same point on the level ellipsoid.
**Free-air** - Only accounts for the elevation of the station not mass between the station and the geoid.
**Bouguer** – Accounts for the variations of gravity due to differences in the density and mass of underlying materials.
## Geoid Height ## Distance from the ellipsoid to the geoid measured along the normal to the ellipsoid. - Geoid height, geoid separation or geoid undulation
## Stokes function
## U.S. Geoid models ## Gravimetric geocentric geoid - based on Earth Gravity Model, DEM data, and gravity measurements.
- Current model USGG 03 (beta version USGG 09 is posted to NGS site)
## Hybrid - based on Gravimetric Model with datum transformations plus GPS on benchmarks
- Current model is Geoid 03 (beta version Geoid 09 is posted to NGS site)
## Gravimetric geoid data used ## 2.6 million terrestrial, ship, and altimetry-derived gravity measurements ## 30 arc-second Digital Elevation Data ## A1-arcsecond DEM for the Northwest USA (NGSDEM99) ## The **EGM96** global geopotential model
## Geoid 03
## USGG 09 Characteristics ## One arc-minute model (2 km by 2 km nodal spacing) ## Based on the EGM08 reference model. - Model is complete to spherical harmonic degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159.
## Improved surface gravity and terrain data.
## USGG 09 evaluation ## Has significantly reduced long wavelength errors EGM 09. ## More accurate than previous models: ## In comparison with GPSBM implied geoid undulations, the improvement goes from 9.1 cm to 7.3 cm for USGG2003 and USGG2009, respectively.
## Geoid 09 ## Builds on gravimetric model. ## Incorporates National Readjustment of 2007 - modified most GPS-derived coordinates (including heights) at the cm- to dm-level.
- Changes in vertical component mostly around 2 cm, with few changes exceeding 10 cm.
## Produced by tailoring USGG2009 to fit the 12,715 points where both GPS-derived ellipsoid height and NAVD 88 differentially-determined heights were available.
## GPS-derived heights ## Differential leveling is too expensive. ## Accurate GPS height determinations can only be achieved using differential methods. - GPS baselines result from the combination of data observed simultaneously at at least two sites. Common errors cancel.
## GPS observations only yield ellipsoid heights. ## We must apply a geoid model to approximate NAVD 88 heights.
## http://www.ngs.noaa.gov/PUBS_LIB/NGS59%20-%202008%2006%209-FINAL-2.pdf
## Note on hybrid geoid modeling ## Regional gravimetric geoids and quasi-geoid models are now commonly fitted to GPS leveling data which simultaneously absorbs leveling, GPS and quasi-geoid errors due to their inseparability.
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