Improving Geoid Undulations and Ocean Dynamic Topography
Through Altimetry and a Modified Kalman Filter
Dru A Smith (NOAA/National Geodetic Survey, Silver Spring, MD 20910; 301-713-3202;
This study has investigated a method for combining gravimetric and oceanographic data with
satellite altimetry to estimate geoid undulations and oceanographic dynamic topography. The
method chosen was a modified Kalman filter algorithm used to correct pre-calculated grids of
undulations and dynamic topography. Approximations to the transition matrix of the dynamic
topography required that a stabilization of the Kalman filter be developed to prevent divergence.
Data needed were TOPEX altimetry, pre-calculated gravimetric geoid undulations and
pre-calculated oceanographic dynamic topography (Semtner, 1993). Evaluation of this global
dynamic topography data in the localized area of the Gulf Stream showed a consistent
disagreement with the TOPEX/geoid implied dynamic topography. This disagreement was seen
in differences of Gulf Stream location (RMS Diff 150 km) velocity (RMS Diff 100 cm/s), width
(RMS Diff 80 km), and height jump (RMS Diff 40 cm). An investigation of these systematic
discrepencies concluded that the magnitude of these local feature differences from the
TOPEX/geoid values necessitated replacing the dynamic topography model with a synthetic
model before proceeding with the modified Kalman Filter.
To run the Kalman filter, an estimate of the transition matrix governing the dynamic topography
was calculated by assuming a one-layer quasi-geostrophic approximation to the Navier-Stokes'
equations. Divergence due to the errors in the transition matrix were removed through a
down-weight scheme, based on a-priori standard deviations of the geoid undulations and dynamic
topography. Results of the modified Kalman filter with stabilization showed that filter stability,
with realistic results was obtainable, even with the simplified transition matrix approximation. It
is concluded that this method will be useful for future applications of combining existing grids of
undulations and dynamic topography which are generally calculated from different sources.
Semtner, A.J., Very High-resolution Estimates of Global Ocean Circulation Suitable for Carbon-cycle Modeling, Proc.Of the 1993 OIES Global Change Institute, 1993.