Anticipated problems for determining ocean dynamics signals from sea surface topography are discussed. The needs for repeated tracks are listed if oceanic tides or ocean turbulence are to be determined

Whitehead, J. A., Jr.

English

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N79 21492
Problems in Determining Sea Surface Topography
John A. Whitehead, Jr.
Woods Hole Oceanographic Institution
Woods Hole, Massachusetts 02543
Abstract. Anticipated problems for determining
ocean dynamics signals from sea surface topography
are discussed. The needs for repeated tracks are
listed if oceanic tides or ocean turbulence are to
be determined.
People want to observe sea surface topography
for many reasons and I would like to discuss the
ocean dynamics aspects/ in contrast to the geo-
dynamics aspects which I feel have been presented
by others.
Geodesists and geophysists are interested in
things that are shown in Figure 1, which I will
call oceanographic noise. This is presented as
a function of typical wavelength. Approximate
amplitudes are also given. In the middle we see
the footprint size of SEASAT represented as a
footprint. Features smaller than the footprint
lie outside our interests. A big signal of ampli-
tude 40 meters or so comes from trenches. The var-
ious global highs and lows are not particularly
related to surface tectonics in any clearly under-
stood way that I know of. They are up to 100
meters in amplitude. Ridge systems give a very
small signal but they do apparently affect the
second derivatives very strongly.
I'm not really concerned with the geophysical
signal here, what I'm interested in telling you
about is shown in Figure 2, entitled Geodesists
and Geophysists noise.
In this figure we present the deviation of the
ocean surface from the geoid as a function of
length scale. The span of such wavelengths is
represented by a horizontal line and I caution
you that this is meant to be very crude. Equally
crude estimates of amplitudes are included.
Starting on the left we see capillary waves,
spray, foam, and seaweed in the millimeter to
centimeter range. Next come wind waves in the
10" to 103 meter range and as we know, these
are very variable both spatially and temporally.
Amplitudes vary from a tenth of a meter to ten
meters. We believe there is a fairly good sized
minimum (we're not really sure) in the wavelength
range from about a kilometer to roughly 50 km.
In this range lies the footprint size of SEASAT,
represented as a footprint. Above 50 km or so
we get a strong contribution from oceanic eddies.
These are low frequency events with periods of
weeks or longer and with amplitudes from 20 cm to
one meter. There are stationary counterparts to
these in various frontal zones near the Gulf
Stream, the current that goes around Antarctica,
and so forth. From 1000 to 5000 km lie tides,
which are really shallow water gravity waves, in-
fluenced by rotation of the earth, and with eas-
ily identified, sharp frequencies of various
sorts. Equatorial currents and the non-frontal
aspects of the big ocean currents appear to be at
most a few thousand km. Little is known of any
structures of 10,000 km, but there may be some
long basin modes (periods up to about 30 hours).
First, let us note that the wind-driven waves
contribute the most height and lie below the
footprint size. This causes me as much worry as
anything, although I've been assured that empir-
ical corrections can be made down to the 10 cm
level of SEASAT. One additional feature is that
OCEANOGRAPHER'S
NOISE DRAG
FREE
MUD HUNTER
COUNTRY
1M
40 M
TRENCH
GEMS
5M
SEAMOUNTS
RIDGES
100 M
GLOBAL
HIGHS 8 LOWS
Iog10\ (METERS)
Fig. 1. Oceanographer's noise.
Proc. of the 9th GEOP Conference. An International Symposium on the Applications of
Geodesy to Gtodynamics. October 2-5.1978. Dept. of Geodetic Science Rept. No. 280, The
Ohio Stale Univ.. Columbus. Ohio 43210.
233
https://ntrs.nasa.gov/search.jsp?R=19790013321 2020-03-21T23:59:32+00:00Z
i
t.
GEODESIST'S AND GEOPHYSICIST'S NOISE
FOAM SPRAY
1CM
SARGASSUM
1CM
CAPILLARY
WAVES
1-10 M
WAVES
50 CM
O A M EQUATORIALSTREAM CURRENTS
20-90 CM
fioTs
OCEAN
EDDIES
LONG
GRAVMODES
- 3 - 2 - 1 0 1 2 3 4 5 €
logloX (METERS)
Fig. 2. Geodesists' and Geophysicists' noise.
patches of waves (under storms) are from 100 km
to 1000 km in size generally, and thus overalp
ocean eddies.
Ocean eddies, of the size 100 km or so, have
been observed by standard oceanographic methods
for the past ten years. Figure 3 (from MODE
Atlas (1977)) shows estimated pressure at 150
meters depth from float and hydrographic data, in
units of equivalent centimeters of head. The re-
gion encompasses a 300 x 300 km region and the
eddies are of order 100 km. The amplitude peak
to peak is about 25 centimeters. To see how this
signal stands up against the geoidal deflection,
Figure 4 shows a sketch of the GEOS altimeter out-
put for the region. There is change in depth of
the geoid of about 2 to 3 meters. It is obvious
from this that the oceanic turbulence is going to
be a small relative signal indeed and we would
really need to take continuous tracks for inter-
vals of well over a month in order to get the
signal.
71°W 70° 69° 68°
Fig. 3. Pressure in units of equivalent cent-
imeters of head, as deduced from float and den-
'sity data. Contour interval is 1 cm. Source:
/MODE Atlas, p. 131.
Not all eddies have such a small amplitude.
Figure 5 shows some typical sections of isotherms
in relatively quiet regions of the ocean. The
undulations in the isotherms are due to such tur-
bulence as we saw on the previous slide with est-
imated surface deflections of 10 cm. However,
Figure 6 shows a section further north, where
there is evidence of very much stronger eddy act-
ivity. These may get up to 50 or 60 centimeters
surface deflection.
One should be able to take advantage of the
time dependence of these eddies to filter out
some of their contributions to "geodesists noise."
Steady counterparts to these eddies such as the
edge of the Gulf Stream or the Antarctic circum-
polar front won't be so easily isolated except
that, fortunately, they tend to wiggle about. .
There will be no way to determine the gravity
field to 10 centimeters in the 100 km wavelength
region in my opinion short of extensive ship sur-
veys, and handling this "wiggle of streams" prob-
lem is essential if those currents are to be
resolved.
Tides are another feature whose time depend-
ence may aid in their analysis, especially since
Fig. 4. Geoidal variation as seen from the
GEOS-3 satellite of the MODE area. Contour
interval 1 meter.
234
0200
400
600
800
28°S7'N 27°43'N 26°22'N 25°24'N 25°47'N
0
200
400
600
800
0 200 400 600 800 1000 1100 KM
XBT 555 560 565 570 575 580 585 59O 595 6OO
Fig. 5. Section of isotherms of Atlantic Ocean
at approximately 30° north.
60°W
i i i i i i i i i i i i i i i n 111 i i i i ill
Fig. 6. Section of isotherms of Atlantic Ocean
at approximately 50° north. There is evidence
of much stronger eddy activity.
20° S 10° 0° 10° 20° N
j100
i
150
200
Fig. 7. Hypothesized north-south section of the
equatorial ocean. The surface deflection has
never been measured.
their frequencies are so sharp, it would appear
that there are some interesting spatial-temporal
biasing problems connected with the tides since
the basic coarse grid for SEASAT takes three
days to get established. The problem of observ-
ing the tides is old and fascinating, but accord-
ing to the most recent survey (Hendershott (1977))
deep ocean tides all over the world are not known.
There has been a lot of debate over whether it
is necessary to subtract out a geoid which is ac-
curate to ten centimeters. The present planning
is for SEASAT to cover the entire earth oceans
twice in the first year, hence the geoid plus the
steady oceanic currents could be reasonably well
determined. My view is that, although it would
be desirable to know the orbit of SEASAT to an
accuracy of 10 cm, it does not appear to be
crucial, since the orbit is extremely smooth for
short wavelengths. Although the orbit may bump
around at long'wavelengths (over 1000 km) we
have good spherical harmonic gravity models such
as the GEM series to determine this orbit correc-
tion. By an appropriate least squares fitting,
slow changes of the orbit, which I understand
will be less than 10 cm per orbit, will contrib-
.ute to only the lowest orders of the apparent
gravity field, and can therefore be easily
subtracted.
Lastly I would like to tell of possible long
wavelength features such as long basin-filling
sloshing modes with periods up to 30 hours or so.
We know little about them and they should be rel-
atively easy to pick out with the assistance of
a good gravity model. They might be less than
ten centimeters in amplitude, and if so the basic
problem will be the usual one of separating a
weak signal from the noise.
In terms of stationary long modes, Figure 7
shows an oceanographer's view of the tropics from
the famous Sverdrup, Johnson, and Fleming (1942)
textbook. The anticipated surface deflection is
schematically sketched in and spectral compon-
235
ents of the geoid should be known to sufficient
accuracy to aid in observing such a surface. To
assist .in such'an endeavor, however, one could
look'for a banded structure in an east-west di-
rection. This is absent in the gravitational
field as far as we' know.
There are many more ocean surface features
which haven't been mentioned, many possessing
their own particular challenges. Some examples
are the sea level adjustment on shelf areas,
level changes across straits such as Gibraltar,
sea level changes between Pacific and Atlantic,
and the response of an oceanic surface during an .
earthquake event.
References
Hendershott, Myrl C., in The Sea, Vol. 6, E. D.
Goldberg, I. N. McCave, J. J. O'Brien, and
J. A. steele, Eds., John Wiley and Sons, New
York, 1048 p, 1977.
MODE Atlas, Valery Lee and Carl Wunsch, Eds.
Atlas of the Mid-Ocean Dynamics Experiment.
POLYMODE Office 54-1417, Massachusetts In-
stitute of Technology, Cambridge, MA 02139,
274 p, 1977.
Sverdrup, H. V., Martin W. Johnson, and Richard
H. Fleming, The Oceans. Prentice Hall, Inc.
Englewood Cliffs, NJ, 1087 p, 1942.
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Problems in determining sea surface topography

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