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USGG2003 & GEOID03. Northeast States Geodetic Conference Daniel R. Roman, Ph.D. Research Geodesist. DISCUSSION OUTLINE. Background on Geodetic Datums/Models USGG2003 – Base Model for GEOID03 GPSBM2003 – Control Data Single Gaussian Matrix Model (GEOID99) Multi-Matrix Model (GEOID03) - PowerPoint PPT Presentation
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USGG2003&
GEOID03
Northeast States Geodetic Conference
Daniel R. Roman, Ph.D.Research Geodesist
DISCUSSION OUTLINE
• Background on Geodetic Datums/Models• USGG2003 – Base Model for GEOID03• GPSBM2003 – Control Data• Single Gaussian Matrix Model (GEOID99)• Multi-Matrix Model (GEOID03)• Results from Single Gaussian Model• Results from Multi-Matrix Model• Summary
Background
• Mean Sea Level (MSL) is the best reference for a height datum
• The “geoid” describes the undisturbed equipotential surface of the oceans
• Gravity Anomalies can be related to the geoid through a mathematical relationship
• The U.S. vertical datum, NAVD 88, is a realization of that equipotential surface
OCEAN Earth
’s
Surfa
ce
“Ellipsoid”
Geopotential Surface
Geopotential Surface
Geopotential Surface
“Geoid”
“P”
“Q”
h
N
h = H + N
“P”0
H
Normal to geoid
Normal toellipsoid
Deflection of Vertical
Geoid Processing Flow Chart(Simplified)
Ref. Mdl
Ref. FAGA
Ref. Und.
Obs. FAGA Res. FAGA Stokes Res. Und.
Gravimetric Geoid
Gridded Residuals Between GPSBM2003 and USGG2003
100%
50%
Correlation (L) length
Cor
rela
ted
Si g
nal
Pow
er (
cm2 )
Distance (D) from Reference Point (km)
Elements of a Correlation Curve
0%
signal amplitude (A0)
0
if: Dll = L
then: CL = 0.5 A0
increasing distance =>
sll llC=
if: Dll = L
then: s =
=
0 5 0
0 7 1
0
0
.
.
A
A
it is easier to thinkin terms of cm than cm2, so use standarddeviation instead ofthe variance
C A ell
DLll
=- æèç
öø÷
0
2
k
k = @12 1 2ln .
Least Squares Collocation Using a Single Gaussian Function
Least Squares Collocation Using a Multiple (Two) Gaussian Functions
Modeled Geoid Height Signal Between GPSBM2003 and USGG2003
MMLSC Modeled Geoid Height Signal Between GPSBM2003 and USGG2003
Final Fit Between GPSBM2003 and Single-Matrix Model
Final Fit Between GPSBM2003 and Multi-Matrix Model (GEOID03)
Final Unmodeled Geoid Height Signal Between GPSBM2003 and Single-Matrix Model
Final Unmodeled Geoid Height Signal Between GPSBM2003 and MMLSC Model
Statistics for NE States• State # Points MIN MAX AVE STD• (m) (m) (m) (m)• CT 20 -0.024 0.025 0.000 0.013• DE 33 -0.054 0.041 0.000 0.024• MA 40 -0.048 0.042 -0.000 0.020• MD 400 -0.075 0.071 -0.001 0.020• ME 66 -0.060 0.092 0.000 0.024 • NH 16 -0.062 0.106 0.005 0.038• NJ 275 -0.077 0.051 0.000 0.015• NY 130 -0.052 0.065 -0.000 0.018• PA 98 -0.090 0.117 0.000 0.024• RI 22 -0.026 0.083 -0.001 0.023• VT 327 -0.059 0.086 0.000 0.018• all NE 1427 -0.090 0.117 -0.000 0.019• CONUS 14185 -0.205 0.227 -0.000 0.024
Error Sources
• GPS Obs.• Short/Int. • Statewide
adjustments (HARNs)
• CORS• National re-
adjustment
• Gravimetric Geoid• Faye anomalies• DEM resolution
and accuracy• Remove-and-
Restore (EGM96)• 1D FFT solution• New DEM/gravity• Combined data &
Fourier solution
• Leveling (BM)
• Long/Int. • Quality of
initial gravity
• The effect is greatest in the mountains
• Propagation
• GPS/Leveling
Summary & Outlook
• More complex models of the Gaussian function better emulate GPSBM residuals
• Further near term improvements will derive from readjusting and improving input data
• Long term improvements require revising the entire approach taken to generate the underlying gravimetric geoid
Questions?
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