The mean dynamic ocean topography (DOT) is the difference between a time-averaged sea surface, constructed from years of altimetric data, and a geoid. The DOT measures the long term-averaged strength of ocean currents, the 'steady-state' circulation; one example is the Gulf Stream, whose position averaged over any one year now is about the same as in 1786, when Ben Franklin and Timothy Folger charted it (Richardson, 1980). The North-South (meridional) gradient of the DOT is proportional to the East-West (zonal) geostrophic component of ocean surface current velocities (the rest is the wind-driven Ekman current); likewise, the zonal gradient of the DOT is proportional to the meridional velocity.Here we offer one spatially filtered version of the DOT (see below). Others are possible.

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Processing

Our input and processing are:

Mean Sea Surface (MSS):
the GSFC MS 00 (Wang, 2001), which is the same one used in the Jason Geophysical Data Record (see PO.DAAC). It is representative of the ocean during the 1990s, as most of the data used are from TOPEX/POSEIDON, ERS-1 and 2. However, GEOSAT data from 1985-88 were also included.

Geoid (GGM):
it is the GGM02c geoid, released October 29, 2004. It is based on 363 days of GRACE data, spanning April 2002 and December 2003. It is complemented with surface ravity data to degree 360.
(Note: the time variations of the geoid over the ocean are < 10 cm, much less at lower latitudes, and much less when averaged over at least one year. On the other hand, the sea surface height can vary by 50 cm or more, therefore to first approximation it is the time-span of the MSS that controls which time is represented in the DOT).

Filtering:
spatial filtering is crucial because the MSS has energy of the gravity field at all wavelength up 1-2 km (the ocean depth; the gravity signal decreases exponentially with distance, here distance to the ocean floor). On the other hand, GRACE can only recover the gravity signal up to ~400 km wavelength (spherical harmonic degree 100 or so) for the same reason, since the approximate current altitude of the satellites is 400 km (as the mission continues, the satellites will slowly fall towards the Earth; this and the additional data will allow recovery of shorter wavelengths).

As a consequence, MSS-GGM is dominated by energy in the gravity field at wavelength shorter than about 400 km. Since the geoidal energy spectrum is about 2 orders of magnitude above the energy spectrum of the DOT, this residual geoid masks any useful DOT signal, unless it is filtered out.

The computational steps are somewhat peculiar, and they are based on using a succession of filters:

The computational steps are somewhat peculiar, and they are based on using a succession of filters: 

1. DOT0 = MSS-GGM, unfiltered  (FIG 1)

2. DOT2 = DOT1 + Filter (DOT0-DOT2, wavelenghts >444 km) (FIG 5 )

3. DOT = DOT2 + Filter(DOT0-DOT2, wavelenghts > 400km) (Fig 8)