Historical Introduction
7
not be coined for another thirteen years (Gold, 1963), it is still puzzling why they took
such a roundabout route when the geostrophic approximation falls so readily out of
the momentum equations. [When he reworked some of the material from The Oceans
for meteorologists, Sverdrup (1942, pp. 97–98) made that approximation explicitly,
and identified the equations with those of the “geostrophic” wind in the atmosphere.
This is the earliest use of the term in an oceanographic context that I have found—and
it is borderline.]
Unlike meteorologists, before satellite altimetry oceanographers were never
able to measure horizontal pressure gradients directly at even a single level with
sufficient accuracy for geostrophic-velocity determinations. In effect, they integrated
the thermal-wind equation, with some assumption instead about the velocity at some
reference surface. A common practice, for example, was to assume zero velocity at
1000 or 2000 m, which were convenient depths for terminating hydrographic casts
if one weren’t interested in the deep water. Since current speeds generally increase
sharply upward through the thermocline, one could calculate reasonable near-surface
speeds on that basis, and it did not much matter where in the deep water one placed
his “level of motion.” On the other hand, for calculating the full volume transport of
a current, and, especially, for treating deep currents at all, the choice of integration
constants was (and is) a much more delicate matter.
W¨ ust’s (1924) comparison of dynamically calculated and directly measured
velocities in the Florida Current was justly celebrated for demonstrating the utility
of the dynamic method. Given modern strictness about significance of results, it is
perhaps worthwhile, however, to recall what W¨ ust actually did. He used Pillsbury’s
current measurements which, on the classic section III across the Straits of Florida
(Fowey Rocks to Gun Cay, occupied in 1885 and 1886), consisted of values at six
depths between the surface and 130 fathoms on five anchor-stations, and at 200 fathoms as well on a sixth. Each measurement took one-half hour but was, in fact, an
instantaneous reading; many repetitions were made and averaged, so the total time per
station ranged from 38 to 555 hours. Pillsbury plotted vertical curves of the averaged
speeds at each station, extrapolated the curves to the bottom (maximum depth about
900 m), and found a line of zero velocity running a little above the bottom. W¨ ust
thought this was consistent with a temperature inversion reported near the bottom
(now known to be spurious), and did his dynamic calculations with Pillsbury’s nullline as the reference. For local hydrographic data he found three temperature–salinity
stations from 1914, and eight temperature-only stations from 1878 for which he used
the 1914 temperature–salinity correlation to get density values; from these he developed four velocity–depth curves. While there was thus a good deal of flexibility in
contouring both the “calculated” and “observed” velocity sections (illustrated with
the observation points deleted as Fig. 184 in The Oceans), the agreement was impressive. Indeed, his estimated volume transport through Section III, 26 × 10
6 m
3 s
−1 ,
is only some 20% less than the present-day measurement. Nevertheless, as much as
one admires W¨ ust’s ingenuity in finding and combining meager material to make a
7
not be coined for another thirteen years (Gold, 1963), it is still puzzling why they took
such a roundabout route when the geostrophic approximation falls so readily out of
the momentum equations. [When he reworked some of the material from The Oceans
for meteorologists, Sverdrup (1942, pp. 97–98) made that approximation explicitly,
and identified the equations with those of the “geostrophic” wind in the atmosphere.
This is the earliest use of the term in an oceanographic context that I have found—and
it is borderline.]
Unlike meteorologists, before satellite altimetry oceanographers were never
able to measure horizontal pressure gradients directly at even a single level with
sufficient accuracy for geostrophic-velocity determinations. In effect, they integrated
the thermal-wind equation, with some assumption instead about the velocity at some
reference surface. A common practice, for example, was to assume zero velocity at
1000 or 2000 m, which were convenient depths for terminating hydrographic casts
if one weren’t interested in the deep water. Since current speeds generally increase
sharply upward through the thermocline, one could calculate reasonable near-surface
speeds on that basis, and it did not much matter where in the deep water one placed
his “level of motion.” On the other hand, for calculating the full volume transport of
a current, and, especially, for treating deep currents at all, the choice of integration
constants was (and is) a much more delicate matter.
W¨ ust’s (1924) comparison of dynamically calculated and directly measured
velocities in the Florida Current was justly celebrated for demonstrating the utility
of the dynamic method. Given modern strictness about significance of results, it is
perhaps worthwhile, however, to recall what W¨ ust actually did. He used Pillsbury’s
current measurements which, on the classic section III across the Straits of Florida
(Fowey Rocks to Gun Cay, occupied in 1885 and 1886), consisted of values at six
depths between the surface and 130 fathoms on five anchor-stations, and at 200 fathoms as well on a sixth. Each measurement took one-half hour but was, in fact, an
instantaneous reading; many repetitions were made and averaged, so the total time per
station ranged from 38 to 555 hours. Pillsbury plotted vertical curves of the averaged
speeds at each station, extrapolated the curves to the bottom (maximum depth about
900 m), and found a line of zero velocity running a little above the bottom. W¨ ust
thought this was consistent with a temperature inversion reported near the bottom
(now known to be spurious), and did his dynamic calculations with Pillsbury’s nullline as the reference. For local hydrographic data he found three temperature–salinity
stations from 1914, and eight temperature-only stations from 1878 for which he used
the 1914 temperature–salinity correlation to get density values; from these he developed four velocity–depth curves. While there was thus a good deal of flexibility in
contouring both the “calculated” and “observed” velocity sections (illustrated with
the observation points deleted as Fig. 184 in The Oceans), the agreement was impressive. Indeed, his estimated volume transport through Section III, 26 × 10
6 m
3 s
−1 ,
is only some 20% less than the present-day measurement. Nevertheless, as much as
one admires W¨ ust’s ingenuity in finding and combining meager material to make a