84 INTRODUCTORY DYNAMICAL OCEANOGRA

84 INTRODUCTORY DYNAMICAL OCEANOGRAPHY
absolute value of either Vx or V2 we will know the absolute value of the other.
There are several possibilities:
(1) assume that there is a level or depth of no motion (reference level) e.g. that
V2 = 0 in deep water, and then calculate Vx for various levels above this
(the classical method);
(2) when there are stations available across the full width of a strait or ocean,
calculate the velocities and then apply the equation of continuity to see if
the resulting flow is reasonable, i.e. complies with all facts already known
about the flow and also satisfies conservation of heat and salt;
(3) use a "level of known motion", e.g. if surface currents are known or if the
currents have been measured at some depth(s) by current meters or
neutrally buoyant floats (preferably while the density measurements for
the geostrophic calculations were being made). In the future, it is
possible that satellite measurements of the surface slope may enable the
surface currents to be calculated, at least in regions of strong currents.
Note that the above techniques are the "classical" ones for obtaining
absolute velocities; a more recent technique, the "beta-spiral" approach, is
described in Section 8.9.
Since surface velocities are important and can be inferred quickly from the
slope of the sea surface (which is assumed to be isobaric) it is common to plot
the geopotential (or "dynamic") topography of the sea surface relative to some
deeper surface, if a sufficient grid of station data is available. The relative
current directions will be parallel to lines of constant geopotential and relative
speeds will be inversely proportional to the spacing of the lines (i.e. close
spacing = steep slope = large speed, e.g. Figs. 8.8 or 11.4(b)). It is also possible
to plot the geopotential topography of subsurface isobaric surfaces to deduce
the motion there.
Remember that these geopotential topography plots are usually based on
some assumed level of no motion, generally in the deep water, unless adequate
direct current measurements are available which is rarely the case. If the
average upper-layer currents are much larger than the average deep currents,
which is often the case, we may get quite good values for them even if the deep
currents are not exactly zero. Note, however, that although a small current
which is neglected (or not known) in the deep water may not affect the
calculated velocities in the upper layer very much, it may make a substantial
contribution to the total volume transport when integrated over the full depth.
For instance, an average current of 10cms"1 in the upper 1000 m based on
zero current assumed at (and below) 1000 m would give a volume transport
from surface to 4000 m of 100 m3 s "* for each metre width of the current. If the
actual current from 1000 to 4000 m were 2 cms~* in the same direction as that
in the upper layer, this would give rise to a 20% error for the upper layer



 
GAMBAR 96BOLA DUNIA


 
velocity but the total volume transport from surface to 4000 mm would be
180 m 3 s - 1 or 80% more than that assuming zero current below 1000 m.
Notice that there is one known velocity region which cannot be used as a
level of no motion—the sea bottom. The reason why this level cannot be used is
that the velocity tends to zero there because of the action of friction, a force
which was deliberately assumed to be negligible when deriving the geostrophic
equation. Remember then that the geostrophic equation does not apply in
regions where friction is important.
8.6 Relations between isobaric and level surfaces
Classically the basis for the assumption of a level of no motion was the belief
that velocities are small in deep water. Observations in recent years with
86 INTRODUCTORY DYNAMICAL OCEANOGRAPHY
Swallow floats* have indicated that this belief may not always be correct, and
ripple marks on sand bottoms recorded in photographs in deep water suggest
that bottom currents of 0.5 m s~1 or more may occur. However, it is possible
that these indicate only local and/or transient currents and in many regions
there are indications from distributions of water properties that speeds
averaged over several months or more, or over tens or hundreds of kilometres,
are probably small in deep water, and the selection of a level of no motion at
about 1000 m depth may give quite good results for geostrophic calculations.
In the Pacific, the uniformity of properties in the deep water suggests that
assuming a level of no motion at 1000 m or so is reasonable, with very slow
motion below this. In the Atlantic, there is evidence of a level of no motion at
1000-2000 m (between the upper waters and the North Atlantic Deep Water)
with significant currents above and below this depth. A selection of relations
between isobaric and constant geopotential or level surfaces is shown in Fig.
8.9. Figure 8.9(a) is typical of the west Pacific and Fig. 8.9(b) of the west Atlantic
(Gulf Stream region) with the characteristics described above. Figure 8.9(c)
would indicate little motion at the surface but increasing speed into the deep
water, which is unlikely in the real ocean. Figure 8.9(d) shows a situation where
all the isobaric surfaces are parallel and equally inclined to level surfaces—the
so-called "slope current" situation. In this case, the application of the
geostrophic calculation would yield zero relative velocity at all depths which
would be correct although the absolute velocity would not be zero. This