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?