MDT is the offset between the LMSL (the likely vertical datum point) and the global geoid (MSL) datum. MDT can vary significantly over small regions, particularly from one side of an island to another. MDT derives from temperature/density (salinity) differences and cause the ocean currents. This discussion will center first on the geodetic concepts and models, then will be followed by the relationship of those models to the oceanographic features.

-an ellipsoid is a first order approximation of the Earth’s shape (oblate spheroid) -it is used because of it’s mathematical simplicity and because such a gravity field adequately describes the path of the orbiting GPS satellites -the geoid is one of an infinite number of geopotential surfaces that surround the Earth, which decrease with elevation -the difference is about -30 to -50 meters in PR/VI region (i.e., the geoid is below the ellipsoid as shown above) -note that the equation is only a first order approximation, too (the orthometric and ellipsoidal normals are not coincident) – this is OK for most height applications -difference between the normals if called the deflection of the vertical (DoV) => DEFLEC99

The selected local geodetic datum is a geopotential surface separated from the global geoid by a bias. In this context, LMSL on the opposite side of the island would be higher than the local geodetic datum. Implication is that a storm surge from that side would run up higher on land than the orthometric heights might imply. LMSL is very well defined at tide stations but shoreline observations are necessary to fill in along other shorelines. Also, lidar observations are necessary to develop a more complete model of MDT (thereby deriving LMSL) over the transition from near shore to deeper offshore. You would get similar problems if a datum point is established on one island and used for all of them.

This is a widely used global geoid height model that provides the reference field for all current NGS models including GEOID99 and CARIB97. This very significant in the vicinity of extreme geophysical features such as a plate boundary/trench system. It is a “gravimetric” geoid in that it is determined by gravity values instead of GPSBM’s.

Hence, it also is a “gravimetric” geoid in that it is determined by gravity values instead of GPSBM’s.

Hence, it also is a “gravimetric” geoid in that it is determined by gravity values instead of GPSBM’s. This model differs from CARIB97 in that it uses a smaller selection of data (creating a difference in bias) and has a higher density of information (one versus two arcminute data spacing).

Very smooth contours imply little short wavelength feature.

Some features associated with the Virgin Islands can now be seen.

Similar results as before with a different bias.

Note that they are scattered in the lowlands along the coast away from challenging terrain. They do provide excellent control over the trench-related gravity features to the North though.

While EGM96 has a lower bias, the scatter of the residual geoid height signal is much larger. Both CARIB97 and GEOID99 provide similar results – differing only by a bias value. Also note that the usual fitting technique involves more than removing a bias. It takes local trends into account. As insufficient data exists in Puerto Rico, no such model has yet been developed. Expansion of the existing set of stations will likely create an opportunity for a hybrid geoid model similar to the mainland model (i.e., a “hybrid” geoid).

Note the extreme depths in the vicinity of Puerto Rico and the Virgin Islands, particularly between St. Croix and the other Virgin Islands. These steep bathymetric features have a significant impact on the geoid and oceanic datums. Insufficient gravity coverage over these ocean areas will contribute to a poorer results in PR/VI due to extrapolation.

Lack of coverage impacts all solutions because the signal is interpolated across the gaps.

There is generally some good data in the near shore environment, but not much only 20 km offshore for PR. VI are better but lack of data still impacts the islands as lack of data occurs about 50 km away.

Fairly good coverage in between islands in NS direction (about 5 km line spacing). This is particularly problematic for islands bordering the trenches where gravity gradient is greatest.