Gravity, Geoids, and Other Vertical Datums

in the Puerto Rico/Virgin Islands

Region

Dr. Daniel R. Roman

and Dr. Yan Ming Wang

Significant Concepts & TermsGeodetic• Ellipsoidal Height and/or

Datum (h)• Geodetic or Orthometric

Height and/or Datum (H)• Geoid Height (N)• h = H + N• The geoid and gravity

anomalies are related mathematically:

Oceanographic• Global Mean Sea Level

(MSL)• Local MSL (LMSL) or

Local Mean Tide• Mean Dynamic

Topography (MDT)• MSL + MDT = LMSL• MSL => Geodetic Datum• LMSL => Local Vertical

Datum

T

N R

T

r

Tg

2

OCEAN Earth

’s

Surfa

ce

“Ellipsoid”

Geopotential Surface

Geopotential Surface

Geopotential Surface

“Geoid”

“P”

“Q”

h

N

h = H + NΔg = gP - γQ

“P”0

H

Normal to geoid

Normal toellipsoid

Deflection of Vertical

MSL

LMSL

MDT

ellipsoid

geoid

tide station/datum point

MSL + MDT = LMSL

N local geodetic datum

predicted storm surge reachactual storm

surge reach

unexpected area of storm surge

bias

From the National Geospatial-Intelligence Agency Website at:http://cddis.gsfc.nasa.gov/926/egm96/egm96.html

Statistical Comparison Between Available Geoid Height Models and 13-Point GPS on BM Profile Along NW Puerto Rico Shoreline

Geoid Height Model

Average (m) St. Dev. (m)

GEOID99 2.34 0.04

CARIB97 2.53 0.04

EGM96 2.07 0.73

No Biases Removed from GEOID99, CARIB97, or EGM96 Differences with GPSBM's

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

1 2 3 4 5 6 7 8 9 10 11 12 13

GPS on BM station

Res

idu

al G

eoid

Hei

gh

t (m

)

GEOID99 CARIB97 EGM96

Biases Removed for GEOID99 (2.34 m), CARIB97 (2.53 m), and EGM96 (2.07 m)

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1 2 3 4 5 6 7 8 9 10 11 12 13

GPS on BM station

(Rel

ativ

e) R

esid

ual

Geo

id H

eig

ht

(m)

GEOID99 CARIB97 EGM96

SRTM 30 m SRTM 90 m NED 1 arcsecond

Available Elevation Data Sets

Conclusions

• Tidal and Geodetic datums are related

• Additional gravity data are required

• Geoid modeling is best constrained with additional oceanic gravity observations

• Some limited terrestrial observations will help fill in gapped regions but also help to eliminate any datum problems

Outlook

• Improved terrain models already exist to help model the shortest wavelengths

• Simultaneous lidar observations would help to model the local sea surface and any implied datum shifts

• Impending satellite gravity missions aid in resolving global mean sea level

• A future gravimetric geoid can be generated that will cover CONUS & PR/VI