- Email: [email protected]
Physical oceanography of upwelling
Geoforum
11172
Physical Oceanography of ~pwetting Physikatische Ozeanographie des Auftriebsprozesses L’oc~anograp~e
Koji HIDAKA,
physique de I’upwelting
Tokyo*
Abstract: Upwelling - the ascending motion of water in the ocean - is a very important phenomenon as it brings, with the ascending water, the nutrients from the deeper layers where consumption is only small, into the surface layers. For this reason, upwelling increases the fertility of the surface and subsurface layers, which results in the establishment of rich fishing grounds. Upwelling is classified into three categories according to the place of occurrence, origin and to the mechanism: (1) coastal upwelling (2) mid-ocean upweliing and (3) equatorial upwelling. The physical explanation of the nature and occurrence of each of these three is given, including examples of upwelling occurring at different areas of the world’s oceans. No particular description is made on the downwelling or sinking which exists in the ocean as the result of continuity of the incompressible fluid. Zusammenfassung: Als ein Prozess, bei dem aufsteigendes Wasser die NXhrstoffe der tieferen Schichten des Ozeans, deren NBhrstoffzehrung nur gering ist, in die oberfi&chennahen Schichten bring& ist Auftrieb-von groger Bedeutung. Auftrieb erhoht die Fruchtbarkeit der obe~l~chennahen Schichten, die die Grundlage fdr reiche Fischgriinde bildet. Auftrieb wird in drei Gruppen unterschleden, eingeteilt nach dem Ort des Auftretens, der Unache und dem physikalischen Prozess: (1) Kbstennaher Auftrieb, (2) Auftrieb im offenen Ozean und (3) Xquatorialer Auftrieb. Form und Vorkommen der drei Gruppen werden physikalisch erklgrt, und Beispiele aus verschiedenen Gebieten des Weltozeans werden dargestellt. Eine besondere Beschreibung des Absinkens des OberflBchenwassers, das infolge der Kontinuitit des inkompressible Mediums aus dem Auftrieb im Dzean resultiert, wird nicht gegeben. R&urn& L’ ~upwelling~ le mouvement vertical des eaux ocianiques vers la surface - est un phenom&ne trds impo~ant, entrainant un transport des nutrients des couches d’eau s’itendant i grande profondeur 02 la consomption des nutrients est insignificante, aux couches suprrficielles. Par consiquant l’upwelling augmente la fertilite’ des eaux superficielles et sub-superficielles causant I’existance des rigions de p&che tris poissonneux. L’upweiling est divide entre trois types selon la region d’occurrence, I’origine et le mechanisme: (1) upwelling &tier, (2) upwelling de pleine mer et (3) upwelling equatorial. La nature et I’occurrence de chacun des trois w sont expliquees par rapport au mdchanisme physique, et des exemples d’upwelling de diffirentes regions de I’ocian mondial sont present& On s’abstient d’une description du tdownwelling% ou de la descente des eaux en particulier qui i cause de la continuite’ des fluides incompressibles, doit exister dans I’ocdan.
1. Introduction The physical interpretation of the phenomenon of upwelling is not very old. We can go back to 1909 when Hermann THORADE the California chapter:
prepared
current
Wirkung~n
a very elaborate
dissertation
and discussed the upwelling
on
in a
und Ursachen des kalten Auftriebwas-
sers (Teil I I). He showed how the temperature cycle of San Francisco differedfrom that off the estuary of the Columbia, and ascribed the cold water temperature during the period from July to September to the upwelling of cold water by NNW monsoon from beneath the surface and subsurface fayers. George F. MCEWEN could estimate *
Prof. Dr. Koji HIDAKA, Ocean Research institute, Tokyo University, Nakano, Tokyo 164, lapan.
the velocity of upwelling by finding out the theoretical relation between the monthly changes of temperature and the vertical velocity off the Californian coast (1912, 1918). Afterwards, several physical oceanographers tackled this problem. We can mention, among others, Albert DEFANT (1936)
and H. u. SVERDRUP
(1938,1941)
who have de-
veioped the theoretical explanation of this phenomenon. Recent development is due to Koji HIDAKA, HIDA,
Henry
STOMMEL,
Kozo YOS-
and others.
The phenomenon of upwelling is mostly correlated with the divergence on the sea surface produced by the prevailing winds. It can occur in an open sea far from the coast on all sides. According to E. C. La FOND (1966), localized upwelling deveiops in: (1) the iees of islands; (2) the lees of major land promontories projecting into a current; (3)
10
Geoforum 11/72
over shoais or sea-mounts; (4) in counterclockwise (clock-
phenomenon is correlated with surface convergence and
wise) eddies in the northern (southern) hemisphere; (5) at
the divergence at a lower layer where the descending
water mass boundaries; and (6) in thermal domes or ridges
motion terminates.
in the open sea. However, it develops quite strongly when there is wind approximately parallel to a coast which lies
The upwelling is very important from the biological points of view, as it brings a lot of water from intermediate
to the left (right) of an observer looking leeward in the northern (southern) hemisphere. Because the water is up-
depths, supplies a great deal of nutrients to the surface water, and thus gives rise to the development of large and
welled from the intermediate depths to the surface and
rich fishing grounds.
subsurface layers, the surface water temperature in the upwelled areas is considerably lower than the surrounding surface water. This difference often amounts to 7 “C
2. Classification
(SCHUMACHER, 1933) off the north-western coast of
R. I_. SMITH (1968) classified the upwelling into two patterns: (1) the coastal upwelling, which is the rising motion of water produced by interaction with coastal barriers, and
Africa (Fig. 7). Generally speaking, the upwelling velocity is estimated from low5 to 10e2 cm/set, and it is so small that during the past no instrument was sensitive enough to directly measure this ascending velocity. Thus the speed of upwelling is almost exclusively calculated from the equations of motion, continuity,
advection, etc.
(2) the open ocean upwelling, or mid-ocean upwelling, which occurs in a much larger scale and produces vertical motions as those driven by wind stress curl, the main oceanic thermocline, and equatorial oceanic currents. The intensity of coastal upwelling is typically much larger than that of open ocean upwelling. Vertical velocity of an or-
Descending motion of water, which is the reverse of the upwelling, is called “sinking” or “downwelling.”
of upwelling
This
der of low3 cm/set are quite common in coastal upwelling, while Henry STOMMEL (1956) considers 10T4 cmlsec to be characteristic of the mid-ocean upwelling. In addition. to the two patterns mentioned above, the present author wants to stress the importance of a third type of upwelling, i. e., (3) the equatorial upwelling. However, the equator, where the Coriolis force changes sign from plus to minus as we cross it from the northern to the southern hemisphere, can be treated as a kind of dynamical barrier. As a matter of fact, the upwelling along the equator is characterised by its greater vertical velocities, which sometimes amount to 10 to 100 times as large a value as usual mid-ocean upwelling. This fact was pointed out by the present author in 1965 from much evidence, and was recently supported by H. ROTSCHI (1968) from the result of actual observations. Equatorial upwelling has been described as a special class of upwelling process by j. t.. REID (1967).
3. Coastal upwelling Coastal upwelling is common to the areas where there Source: DEFANT 1961 Fig. 1
0 Mean anomalyof the seasurfacetemperatureoff the north-west coast of Africa for April in ‘C.
0 Mittlere Abweichungder Oberfkhentemperatur von der ozeanischen Verteilung entlang der NW-afrikanischen Kiiste im April P3. l Anomalie moyenne de la temphrature superficielle le long de la
c&e de I’Afrique du Nordauest pendant I’Avril (“C).
blows a wind parallel to a coast which lies to the left (right) of an observer looking leeward in the northern (southern) hemisphere. To this category belongs the upwelling off the Pacific coasts of North America, and South America, the Atlantic coasts of Africa, and northwestern coast of Australia and off Somaliiand, East Africa. The most common and well-studied upwelling takes place off the North American Pacific coast between about 46 “N and 25 ON, especially off California. It starts usually in March and reaches its maximum during the summer months, July and August, coinciding with the m~imum frequency of the northwest winds parallel to the coast. No upweliing is seen in the fall and winter.
Geoforum 11172
11
onomdy ,
OC
Fig. 2 0 Schematic cross-section normal to the coastof south-west Africa, showing the lines of constant density, the axis of the current vortex (wavy line), the zonal and vertical velocity components (arrows) and the meridional flow parallel to the coast (N towards north, S towards south). l Schematischer Schnitt senkrecht zur SW-afrikanischen
Kiiste, mit Darstellung der tinien gleicher Dichte, der Achse der Stromvortex (Schlangenlinie), der zonalen und vertikalen Striimungskomponente (Pfeile) und der meridionalen Komponente der Strijmung entlang der Kiiste (N nach Norden, S nach Men).
Source: DEFANT
1961
0 Coupe schtmatique perpendiculaire i la c&e de I’Afrique du Sud-Ouest, prdsentante les lignes de den&C constante, I’axe de la ctvortex, du courant (ligne ondulie), les composantes du courant zonales et verticales (flbches), et la composante du courant meridionale le long de la c&e (N vers le Nord, S vers le Sud).
The cold upwelted water in February and March off the
offshore and banked up at a distance about 100 km from
South American Pacific coast is remarkable and has been studied by GUNTHER (1936). There is some upwelling
the coast.
along the west coast of Australia as described by Gerhard SCHOTT (1935).
A somewhat different picture is obtained by a detailed analysis of the data. From the vertical displacement of the temperature, salinity and oxygen curves, the average
comes to the surface after flowing in the lower part of the
vertical velocities during the 41.day interval were computed. Knowing the vertical velocities, the equation of continuity gave the horizontal flow. The final result is
top layer, in the thermocline and beneath it towards the
shown in Fig. 3.
coast and gradually rises just off the coast. The upwelling
The lines with arrows represent the average streamlines
is largely confined to the narrow strip between the diver-
in the 4l-day interval. The horizontal velocities are indicated by curves. The average outward velocity of the
The first model of coastal upwelling (Fig. 2) was given by DEFANT (1936). It consisted of a divergent stream which
gence line and the coast. The water is brought to the sea surface from only a depth of 100 to 200 m.
boundary region between the upwelled water and the offshore surface water in the same period was computed
A necessary consequence of this type of circulation is the destruction of the thermocline in the upwelling region off
to be 3 cm/set. The distance of this outer boundary from the coast was about 90 km. At a distance of 75 km from
the coast. The gradual breakdown of the thermocline,
the coast, the outward transport above a depth of 40
which at times also strongly develops in the area closest to the coast, is a result of internal tidal waves which be-
meters, as computed from the equation of continuity,
is
26 x lo3 cm3 Isec, whereas a value of 25 x lo3 cm3 jsec
come gradually unstable as was shown by a series of ob-
is obtained from the average tangential stress of the wind
servations.
in the 41.day interval. The thickness of the upper homo-
For the mechanism of coastal upwelting, SVERDRUP (1938) gave a detailed analysis and interpre~tion of this
geneous layer is 41 meters.
phenomenon, which took place along the California coast, from the data of three cruises of the “Bluefin,” the vessel of California State Fish and Game Commission off Port San Luis in the earlier part of 1937. It is necessary, in order that the upwelling takes place most favourably, that a north-west monsoon blows continuously for a sufficient-
a cellular circulation extends to about 80 meters from the surface within which the water flows away from the coast above 40 meters, and towards the coast below 40 meters. Near the coast the motion is ascending, near the offshore boundary it is descending. The offshore boundary is, however, moving slowly away from the coast and the inner cell is, therefore, being fed from below by water which flows towards the coast. This inflow appears to take place at depths not exceeding 200 meters.
ly long duration. And this occurs on the California coast throughout April, May, and june. According to SVERDRUP’S analysis, the light water along the coast is driven
Between the coast and the banked-up light surface water,
12
Geoforum 11/72
Fig. 3 0 Computed vertical circulation in the time interval between two successivecruises. l Ve~ikalzirkuiation,
berechnet fiir den Zeitraum zwischen zwei aufeinanderfolgenden Beobachtungsfahrten.
l Circulation verticale, calculCe
pour I’interval entre deux campagnes successives.
Source:SVERDRUP 1938
Finally the crosses (+) show a zone with a stronger flow parallel to the coast and directed into the picture. in a study of a large amount of data of Californian upweliing collected at the Scripps Institution of Oceanography, DEFANT (1950, 1951) pointed out that the piling-up and upwelling processes are associated with characteristic displacements of the sea surface and of the internal boundary layer which gradually develop under wind influence and adjust itself with the circulations simultaneousiy formed and normal to the coasts. They finally tend tb a stationary state. During the first cruise, February 28 to March IS, 1944, the wind component towords the coast predominated over the entire region with a maximum of S m/set, which caused considerable piling-up of water along the coast. During the second cruise, April 27 to May 15, in contrast
surface in the direction of the coastline, the equations of motion and the equation of continuity are:
a2u A, a=u -.--f_.+Zwsinrpv -g -xax = 0 p az2 p a2
A,
A,4,+A, P
a2v G--2wsinqu=O,
-. P
3x2
&+aw=, ax
az
1
where { is the elevation of the surface of the sea varying in the direction perpendicular to the coast. If the wind blows in a positive direction ofy in the belt between the coast, then x = 0 and x = L. The conditions to be satisfied on the surface of the sea are
to the first case, the water was driven uwuy from the coast where as a consequence upwelling took place. Thus the first cruise gave a typical example of water accumulation along the coast, while the second furnished a typical example of coastal upwelling. The result can be seen in the topographic representations of the sea surface off this
; z
-A,$=0
=o:
(3) -A,g=r
forO
i =OforL
coast quite dearly. In 1922, Harold JEFFREYS investigated the effect of a steady wind on the surface of a homogeneous ocean near the coast. In 1952, DEFANT gave a similar theoretical explanation on the assumption of a sea composed of two layers with different densities. Even by these simple models it was possible to explain the behaviour of upwelling rather satisfactorily, A theory of stationary upwelling produced by a wind parallel to a coast has been given by Koji HIDAKA (1954), whereby the effect of the Earth’s rotation and the frictional forces due to both vertical and lateral mixing have been taken into account. He deals with the steady state only. Because there is no slope of the sea
where r is the stress of the wind and may be either a constant or a function of x. On the bottom z = h, the boundary conditions are z=h:u=~=O,
(4)
because of vertical friction. Along the coast which is considered to consist of vertical cliffs, x=o:lJ=v=o, because of horizontal friction. In the region very far from both the coast and wind region, x= m:U=“=%O
ax
*
(51
Geoforum 11/72
13
60 8-
a)
Source: TOMCZAK 1970
4
Fig. 4 Computed vertical circulation in an ocean with turbulent diffusion: a) homogeneous (identical to Hidaka’s solution), b) weakly stratified, c) strongly stratified. Berechnete Vertikalzirkulation c) starker geschichtet.
in einem Ozean mit turbulenter Diffusion: a) Homogen (identisch mit Hidakas Losung), b) schwach geschichtet
Circulation verticale, calculQe pour un ocean avec diffusion turbulante: a) Homogane (identique avec la solution de Hklaka), b) avec une faible stratification, c) avec une stratifaction plus forte. L’ = z/D,,, Lo = L/D,.
(A,/Al)t’2,
x0 = x/DV. (A,/Al)“‘.
The solution is rather complicated and numerical calculation of the magnitude of the offshore currents and the up-
HIDAKA also investigated the case arising when a wind
welling velocity allows the results to be compared with
the direction of the wind is perpendicular to the coast, the induced circulation has a rather complicated structure
values estimated correctly from observations. Figure 4a gives the solution in the form of streamlines in a vertical section perpendicular to the coast. Upwelling develops close to the coast, and there is no offshore movement of the water in the upper layers of the sea directly beneath
blows at a certain angle to the direction of the coast. If
with two vortices with horizontal axes in the upper layers, one of which is situated close to the coast and the other is near the outer boundary of the wind belt. The upwelling due to a longshore wind is far more effective in lowering
the surface swept by the wind. The upwelling is confined
the temperature of the coastal region than that induced
to the strip within i Dh (Oh = ndm)
by a wind perpendicular to the coast since the former
from the
coast, and the downwelling process occurs outside the wind zone. If the vertical mixing coefficient A, is estimated at 1,000 c. g. s., the vertical Ekman’s depth Dv will be 162 m at 30 ON. For a horizontal mixing coefficient, Ar = 10’ was chosen because the ratio Al/A,
- 3.14 x 10e3 cm/set or 2.7 m/day or 80 m/month, for the wind stress r = 1 c. g. s.
favourable wind direction for upwelling is 21O.5 cum sole with the coastline for a person looking leeward.
= lo6 ap-
pears to be reasonable. For this value of A,, the horizontal frictional depth D,, will be 162 km. Estimation gives the width of the wind zone to be 2.0944. Dh = 339 km. The average horizontal velocity between the surface and 0.2 Dv was calculated as 3.35 cm/set offshore. The maximum upwelling velocity can be estimated to be
brings a larger amount of cold subsurface water to the surface from deeper levels than the latter. The most
Extension of HIDAKA’S
theory to the transition stage was
worked out by Yasukazu SAITO (1956) who calculated the development of the upwelling process after the sudden occurrence of a wind. In the case of a circulatory wind like a typhoon or a heavy cyclone, the wind blows approximately parallel to the isobars or towards the centre. Intuitively it may be imagined that upwelling will not occur when there is a wind stress component towards the centre. However, the upwelling will still take place when the wind has, like in
14
Geoforum I 1I72
a typhoon or a cyclone, the components by some angle
As is shown by observations, the process of upwell~ng is
towards the centre of the circular wind system. in a
not a steady phenomenon. If the duration of the wind is
paper of 1955, HIDAKA and AKIBA assumed a circular wind system:
as short as a few hours, the offshore component of surface water transport will not be very large because drift currents will not fully develop. If the winds are more or less steady for several hours up to as much as a day, the drift
current may develop but it will not be accompanied by considerable upwelling due to the oscillations of the thermocline. However, the process will be different if the where r,,, is the maximum wind stress, while r,
is the
distance of the maximum wind stress from the centre (P = 0) of the wind system. First they treated the case when the wind blows contru so/em tangential to the isobars. In this case, the upwelling occurs mainly within the distance r = &
where i& = II x_!-
and AI is the
coefficient of lateral eddy viscosity. The upwelling is most intense approximately
at r = 0.6 Oh, and the maxi-
mum vertical velocity is w = 2.4 * 10m3cm/set or 2.1 m/day for T = 1 c.g.s. (Fig. 5). In the second place, the case was treated where the wind stress is directed 45 degrees in an inward direction from the isobars, which is
wind continues for several days up to a week. If the wind blows continuously for a longer duration than a week, the surface currents will reach a steady state with an intermediate stage for a wind lasting for a few days up to a week during which geostrophic equilibrium is approached. Kozo YOSHIDA (1955) treated this latter section of the process, relying on a case of Californian upwelling. In his model the x-axis is directed eastwards, they-axis northwards, the latter representing the coast. The z-axis is taken positive downwards with z = 0 being placed on the mean sea level. The process was assumed to be independent of the north-south direction so that only the variables x and z were considered. YOSHIDA considered only a
welling taking place at r = 0.6 Dh and the upward velocity
small-scale process extending over a period of several days and over a distance of up to 10 km. The equations of
being 1.5 * 10m3cmlsec or 1.3 m/day for the same wind
motion are then
less effective in producing upwelling, the maximum up
stress 1 c. g. s. -fv=gwithf=Zwsing
I
2Oh
&
;i-;'f!l'G
a
(A$)-%.
A, is the vertical coefficient of eddy viscosity, T,, is the northward component of wind stress. H is the average thickness of the upper mixed layer. The corresponding vorticity and divergence equations are a$ fwh V--mat H
curi, 7
(8)
H
where wh is the vertical velocity at the depth of thermodine z = h. The equation of continuity and condition for the quasi-isostatic adjustment with g* = g 9 give Source: HIDAKA
and AKIBA
1
1955
wh----. g*
ax
The mutual adjustment between the pressure and the current seems to be completed within a day or two, so that
Fig. 5 @ Upwelling as induced by a circular wind parallel to the isobars. & Durch einen j~baren~ar2llelen, vorgerufener Auftrieb.
aP
rin~~rmjg
wehendtn Wind hep
0 Upwelling due a un vent soufflant circulairement le long des isobares.
the above equation is reasonable for up to about a week after this first stage of adjustment is over. From Equations (8), (9), and {lo}, equation k= a*W -_-k*W=-.. axz f
a7 ax
(11)
Geoforum 11/72
15
is obtained where k = f/ &%.
The boundary condition
The second half of YOSHIDA’s
paper deals with the
changes in surface conditions derived from the above model which represents a transient state of upwelling. He
u = 0 along the coast requires
found that the variations in surface characteristics were largely confined to within a narrow coastal region. The with the condition w = 0 when x = -m. (1 ‘I ) then witI be
The solution of
coastal upwelling is associated with considerable changes in surface conditions within the coastal water of width L, while upwetling or downwelling outside of this strip will not give rise to such signi~cant changes during a period of only a week or two. In the succeeding stage of the upwell-
-0
0
0
If Ikxl%
(12)
ing process, in which the isostatic ~jus~ent now can be considered as complete, the lateral mixing process in the inshore regions stands out as the most important factor. The dynamic equations are now
1, it follows
(36)
1 a?,
W=-f&, _-
where AI is the coefficient of laterai mixing. The upward and
03)
movement of the thermocline, due to the ascending motion, will produce a sharp horizontal density gradient, and
rye” dx
when conditions are variable in an oscillatory way, as is usually the case, internal waves will be produced and
-m
along the coastline. A uniform northerly wind over offshore water will give rise to a coastal upwelling of the amount W.
cause intense mixing across the ~~er~~/jRe.
The equa-
tion for the conservation of mass now becomes aP =A$
a&.
ax= ’
“az 04)
The upwelling velocity wilt be proportional to the intensi-
or approximately
w=_&i?
ax=*
ty of the northerfy wind but is not directly dependent on the latitude. When g* = g $$ = 2.5,~=~m=4x103cm,
The boundary condition at the coast gives v = 0, so that
and rY,O = - 0.5, w follows
finally it follows
W%=O = - 5 x 10m3 cm/set. In five days this upwelling will give an upward displacement of the thermocfine of 22 meters. This upward movement of the thermociine off the coast will continue until an equilibrium is reached in about a week. This state seems then to be maintained for about one month or two. This coastal upwelling is almost entirely confined to a narrow strip close to the coast. With the numerical values introduced above, w will be reduced to 6 % of that of the coast and to 3 % of the coast w-value at 50 km only, the-process being practically Jimited to a distance of 40 to 50 km from the coast. The effective width of coastal upwelling is given by a characteristic length n
7r&Y?
L=k=f’ whose value varies from 10 km to 340 km for different values of gH& and different latitudes.
fB wh=--'--_ g*
av ax
07)
The expression for w will become the same as in the earlier stage and the vertical velocity distribution will therefore remain unchanged throughout the entire period of the process as long as the wind is kept steady. During this period, the ascending water movement will be subject to mixing with the su~ounding waters, and the thermocline will not be elevated to any large extent. From Equation (17), it follows that at this stage the vorticity in the surface layer will be proportional to the vertical velocity. Thus upwelling will be associated with cyclonic vorticity in contrast to the initial inshore increase in negative vorticity produced by the coastal upwelling. YOSHIDA and Mizuki TSUCH~YA (1957) noticed something like a “vertical divergence of isotherms” at certain intermediate depths, say, between 200 and 500 meters. In some sections normal to the California coast, it is often
observed that the isotherms or isopycnals above 100 to
76
Geoforum 11172
200 meters conspicuously rise towards the coast, while those in the lower layers beiow 200 to 500 meters fall towards the coast. These two authors explained it as the
The upwelling phenomenon taking place at a spot in the
northward current in deeper layers correlated with-the up-
ocean far apart from the coast may be classified in this
welling in surface and subsurface layers above from 20C1-
category. Kozo YOSHIDA and Han-tee MAO were the first to discuss the theory of this problem. They used the
500 m, and developed a theory thereof.
4.
Mid-ocean upwelling or Open-ocean upwelling
There appeared recently several improved theories on coastal upwelling. First of ah, there can be mentioned that of Matthias TOMCZAK, Jr. (1970) which is an im-
approximate vorticity equation derived by eliminating the
provement of HIDAKA’S
they obtained
theory of coastal upwelling ap-
plied to a stratified sea instead of the homogeneous ocean. An addition of the equation
horizontal pressure gradients from the equations of motion. After disregarding the terms which are less important,
i&!=@,+U!_ az f f ar cur&r
df
with p = -
4’
.
(18)
Substituting from the equation of motion
(19)
where r is the coefficient of vertical diffusion, enabled TOMCZAK
to solve various inter~ting cases which could
not be solved in HIDAKA’S result was that TOMCZAK
theory. The most remarkable
welled from shallower layers than when simply the homogeneous water is assumed. Figures 4a, 4b, and 4c give the streamlines generated by the same wind field as that had been used by HIDAKA,
where p is pressure, it follows at the surface layer
could show that water is up-
k
wizo=-P P
I’
$dz-+
(TV + f cur!, 7) P
but with different degrees of strati-
fication represented by a parameter US. Figure 4a is identical with HIDAKA*S there is no water stratification
result, that is, when
(OS = 0), while Figs. 4b and
4c show the streamlines when the stratification is specified by US = 0.002 and US = 0.02 respectively, the latter being stratified more strongfy. This result shows that the water upwells to the surface layer directly even at strong stratification from very deep layers. This conclusion may be visualized from actual observations. Moreover, the density distribution strongly depends on diffusion even for the same pattern of circulation and on wind speed. These results show that it is not possible to obtain a definite conclusion as to the depth of upwelling and to the pattern of
where z = z. is the sea surface and r is the wind stress at the sea surface with its components rX and rY. After several simplifications, the verticai velocity at a level z = H where stability is great, say 150 m, is obtained:
WH=-- :f$dz H
(21) =-.-P
More recently Richard W. GARVINE
(1971) pointed out
that HIDAKA eliminated the chief mechanism whereby fluid is returned beneath the wind friction layer to supply mass for the upwelling motion by omitting the longshore pressure gradient at the outset. GARVINE argues that the return flow supplying the upwelling motion in HIDAKA’s problem must have been intimately related not only to the intermediate layer but to a strong Ekman layer at the
vdz,
f
circulation from observed density distributions.
H
after substitution from (19). Equations (20) and (27) represent the vertical component of flow across the horizontal plane. If h is the thickness of the mixed layer, (20) the vertical flow across the plane z = h is
(22)
bottom. In the same year, HSUEH and Q’BRIEN f1971) discussed a possibility for an upwelling to be induced on a continental shelf by the existence of a large-scale ocean current. Their theory does not necessitate winds blowing over the sea surface. They explain this vertical motion in relation to the actually existing ocean currents off the Oregon, Peruvian, and West Florida coasts. This means that the California and Peruvian upwelling can exist all year round as the effects of the California and Peru currents.
wk m-! curl, 7
f
(23)
very closely. Equation (21) shows a close relationship between the vertical velocity at z = H and meridional mass transport
Geoforum 11/72
17
ap
in the layers deeper than the layer z = H. Thus a subsur-
Now a~ can be known by occupying two hydrographic
face poleward component of the current must be associated with an ascending motion in both hemispheres. In ac-
stations on the same latitude circle, while F(z) is to be
cordance with the theory, we may anticipate the following
regarded as a more or less undeterminable function of z. It differs from zero only in a thin upper layer extended
facts which are confirmed in reality: Off California ascending motion exists in the inshore areas with a north-
from z = 0 to z = - D, where D is the depth of frictional
bound current in lower layers, while a descending motion occurs offshore with a southbound current in lower layers. On this principle, they could calculate
influence. Of course F(0)
is known explicitly in terms of
the distribution of wind stress on the sea surface in the neighbourhood of the pair of hydrographic stations. Integrating Equation (26), it follows
wh = 7 x 10s4 cm/set
(28)
16 meters/month taking H = 150 m and cp= 30”. They could show that the distribution of calculated ascending velocity at the 150 m
where we define
level is in good agreement with the areas where the density changed in equal amount between April and June 1949. These two authors also stressed that their method is ap plicable satisfactorily to coastal upwelling, not only off California, Peru, and West Africa but also to the western boundary of the oceans where the Kuroshio and Gulf Stream flow. On discussing the abyssal circulation of the oceans, it was
-B
And C is a constant of integration. Now the meaning of the function a(z) is familiar, for it follows from the first equations
pv = 9(z) + c
necessary for Henry STOMMEL (1958) to investigate the behaviour of the oceanic thermocline. Allan ROBINSON and STOMMEL (1959) have derived an upwelling velocity
which is the equation of pure geostrophic flow, and C is the undetermined reference velocity. Thus determination
3 x lo-’
of the constant C is equivalent to determining the depth
cm/set as the most probable value in lower lati-
tudes. The vertical velocity 1 - 5 x 10m5 cm/set obtained by Klaus WYRTKI also is in good agreement. In his paper on determination of the depths of no meridional motion,
at which v vanishes. Here it is seen that the level of no meridional motion coincides with that of the maximum vertical motion, and that the level of no zonal motion
Henry STOMMEL (1956) derived an expression to compute the vertical velocity in the open ocean from observed
does not necessarily coincide with either.
distributions of mass and of wind stress on the sea surface.
Integrating Equation (28) once more, it follows
He starts with the equations of motion
aP -2wsirnp*pv=--+-
ax
2wsincp.pu=-G+;,
a% a2
(24)
ap a5
pw=K
z
P IS
cP(z)dz+ C . (z + B)
-B
I
- F(z),
(29)
if pw vanishes at the surface I = 0 or is fixed by some small
aP 9P = z
known mean evaporation-precipitation
correction. The con-
stant C can be determined as
and the equation of continuity
& (PU)+ $ (PV)+$ (PW) =0.
(25)
c=-j1 2wsinq F(O)
6 (PW) = -
(2
wtinp)2 .$ - $
Although STOMMEL
F(z)
(26)
can be obtained, where F(z)
=
a -.-k-
ax 2wsincp
---
a ay
7x 2wsinlp
and (27)
/3 = a (2wsinp). ay
(30) --B
From these equations, -&j
_
I(
could determine the depth of no
motion only for meridional flow, his method was successful in determining the velocity of vertical motion. Although his method can only determine pw + F(z), the function will vanish below Ekman’s depth of frictional influence, so that it will be applicable to the depths below 100 m level except at or very close to the equator. Some of his results were extracted from Table 1 of his paper.
18
Geoforum 1 l/72
Table
1
in Honolulu occupied on board the “M/S Hugh M. Smith”
0 Geschwindigkeit 0 Velocity
Depth
des Vertikalstroms
of Vertical
(m)
10-5
0 so 100 tso 200 250 300 350 400 450 500 600 700
Flow
cm/set
-
(STOMMEL,
(sTOMMEL,
1956)
are all located at approximately
1956)
Depth
fm)
800
9 - 6 - 4 1 1 3 5 7 9 11 13 16 19
on her Cruise No. 30, July-August
900 1,000 1,200 1,400 1,600
r
&J In the computation, it is assumed that ;i;; and ap practicalay ly vanish at and below the 1,000 m level. The result shows
1 O-5 cmjsec
1,800 2,000 2,500 3,000 3,500 4,000 4,500 s ,000
l_
that there is weak upwelling in most depths.
21 22 22 23 24 24 23 23 20 17 13 9 5 0
Thus the maximum vertical velocity was 24 x 10’
Table 2 0 Geschwindigkeit zusammengesteiit
des Auftriebs f-) und Absinkens (+) in cmfsec, nach POFI NorPac-Daten (HIDAKA, 1961)
0 Velocities of Upwelling (-) and Sinking (+) (cm&c), from POFI NorPac Data (HIDAKA, 1961)
T Depth
cm/set
at about 1,500 meters. Another method was given by HIDAKA
1955. These stations
the same latitude 50 “N.
in 1961 for calcu-
lating mid-ocean upwelling. He started again from Equations (24) and (25) but expressed the pressure by density differences explicitly. The resulting equation for the vertical velocity in terms of the density field is
0 2oR (sin* 9/cos 9) . p(z),
(m)
0 10 50 100 200 300 400 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000
Computed
Stations 81-83 (cmjsec)
-
0 0.028 0.121 0.199 0.309 0.346 0.434 0.432 0.464 0.778 0.623 0.467 0.311 0.156 0
83-84
-I-
84-86 (cm/secf
t
0 0.00s 0.009 - 0.009 -0.118 - 0.257 - 0.332 - 0.450 - 0.676 - 0.522 - 0.417 - 0.313 - 0.209 - 0.104 0
(cm/=) x IO”
(31)
-
0 0.062 x lO”l 0.306 0.568 1 *OS4 1.498 1.942 2.283 3.050 3.492 2.793 2.09s 1.397 0.698 0
x IOJ
A-.
The velocity of mid-ocean upwelling is mostly of an order of IO-’ to 10T5 cm/set. This is consistent with the result
where
by STOMMEL.
5. Equatorial
ri-
Even if there are no land barriers, the equator is a kind of
f-172 hi + 20R
upwelling
(32)
(sin’cplcosg)
i * (ph wh - p. wo).
Practically qfz] can be disregarded if either or both of w. and wh is or are smaller than 10e3 cmfsec, so that the upwelling velocity -w(z) is given by Equation (31) with
dynamical boundary as long as the motion of sea water is concerned. Therefore, close to the equator the upwelling phenomenon may be considered greatly different from the usual open-ocean upwelling. The most remarkable feature of the equatorial upwelling is that the upwelling velocity is so intense that a velocity of theeorder of 1Oa2 cmjsec is quite common. This means that the vertical
q(z)= 0. Of course, this formula fails to be valid at the equator and poles because the denominator of it vanishes
flows along or close to the equators are 10 to 100 times as large as those occurring in the open ocean of higher latitudes.
there. The following table is extracted from a computation of vertical water flows by Equation (31), use being made of the density data at four NorPac stations 81,83, 84, and 86 of the Pacific Oceanic Fishery Investigations
In 1960, HIDAKA gave a simple theory on the equatorial upwelling. He did not evaluate the resulting equation or the vertical velocity numerically; however, he published a paper in 1965 in which he pointed out several evidences
Geoforum 11172
Source: HIDAKA
19
1955
Fig. 6 0 Distribution of divergence (shaded) and convergence areas in the Pacific Ocean, mg/m’/sec. l
Verteilung der Divergenz- (schraffiert) und Konvergenzgebiete im Pazifischen Ozean, mg/m3/sec.
l
Distribution des r&ions de divergence (hachures) et de convergence dans I’Oc6an Pacifique, mg/m3/sec.
of an intense upwelling at the equator. He gave some results of the estimation of upwelling velocity for some
ern Pacific has reinforced the upwelling of the subsurface
simple cases and checked the magnitude of the equatorial upwelling.
phosphate concentration in the upper 60 meters had practically doubled and the surface water was heavier.
The formula for the estimation did not give a vertical
The observed distributions of nitrate and density imply
velocity less than 1O-’ cm/set unless AY > 1O4 c. g. s.
a vertical speed (of upwelling) much higher than that
There is other evidence of unexpectedly intense upwelling velocity at the equator. Recently Henri ROTSCHI and
which has been evaluated in a steady state circulation.” They derived from the change of concentration of nitrates,
F. JARRIGE (1968) published a paper indicating the intense upwelling produced by the intensification of the east component of the trade wind at the equator. They state, “in October 1966 an intensification of the east component of the trade wind at the equator in the west-
waters. After the wind had blown for three days, the
- w = -w= -w=
9 3 2 - w = 0.3
x x x x
1B2 cm/set low2 cm/set 10d2 cm/set 1OS2 cm/set
at at at at
10 20 30 50
meters meters meters meters,
20
Geoforum 11/72
and they obtained -w=2x
DEFANT,
A. (1951):
10V2 cm/set
out several other examples for the intense upwelling at the equator.
DEFANT,
A. (1952):
des Windstaus hydrogr. DEFANT,
A glance at the atlas of the Pacific (Fig. 7) reveals an
cold because of the intense upwelling in the area of the Peru/Chile current which extends to the north broadening in the westward direction and merges in the narrow equatorial tongue just mentioned. It must be the object
prevailing easterlies along the equator. Part of this water
dynamics.
Kiisten;
Dt.
Oceanography,
Vol.
1.
J. Phys. Oceanogr.,
1, 169-179.
A report on oceanographical ‘Discovery”
investiga-
Rep.,
13, 107-
276. K. (1954):
Contribution
coastal currents; Amer. HIDAKA,
K. (1955):
to the theory
Geophys.
Divergence
Union
of upwelling
of surface drift currents
in terms
to the location
upwelling
1, 47-56.
and sinking;/ap.
K. (1960):
HIDAKA,
K. (1961):
Wks /apan,
J. Geophys.,
On the equatorial
Kobe Mar. Observatory,
14, 12-l
Calculation
6, 1 l-l
upwelling;
of
Memorie
of
4.
of upwelling; Rec. oceanogr.
5.
K. (1965):
Evidences of an intense upwelling
equator; Bull. Sot. franco-jap. K. and Y. AKIBA
Oceanogr.,
(1955):
Y. and J. J. O’BRIEN
induced by along-shore
induced
Wkslapan,
(1971):
current;/.
at the
3, l-8.
Upwelling
circular wind system; Rec. oceanogr. HSUEH,
and
Trans., 35,431-444.
of wind stresses, with special application
HIDAKA,
ing at the equator as far west as 170 “E or more.
zum Phanomen
an ozeanischen
A simple model of coastal upwelling
E. R. (1936):
HIDAKA,
far apart from the west coast of South America show
JARRIGE
an ozeanischen
W/en, 4, Ser. A,
Uberlegungen
tions in the Peru coastal current;
HIDAKA,
quite high nutrient concentration, and high productivity
Physica/
R. W. (1971):
GUNTHER,
may be ascribed to this action of advection. However, the fact that the equatorial waters located in the mid-Pacific
along the equator suggests the evidence of intense upwell-
Theoretische
und des Auftriebs
A. (1961):
HIDAKA,
of discussions that this cold water might be the cold water upwelled, but not entirely the water transported by
and
Bioklim.,
Z., 5,69-80.
GARVINE,
elongated cold water mass exactly at the equator, extending from the Ecuador coast westward to as far west as Polynesia. This suggests a possible occurrence of intense upwelling at the equator. According to the temperature charts, we can realize that the water off the west coast is
ROTSCHI
und Auftrieb
206-308.
as an average value for the layer 0 - 60, m. They pointed
As
Windstau
Kiisten; Arch. Met. Geophys.
by a
2,7-18.
Steady coastal upwelling Phys. Oceanogr.
1,180-
186.
pointed out, the equatorial up-
JEFFREYS,
H. (1923):
The effect of a steady wind on the sea-
level near a straight shore; Phil. Mag. 46, 115-125.
welling is highly sensitive to the variation of the trade winds. In the western part of the equatorial Pacific, there sometimes appear strong westerlies, choking the upwelling for some time. The result is that the swelling upward of the thermocline at and around the equator vanishes, and the water temperature becomes uniform from the
LaFOND,
E. C. (1966):
Fairbridge, McEWEN,
Upwelling.
G. F. (1912): of upwelling.
. . . Int.
of Oceanography.
New York.
The distribution
along the west coast of North theory
Encyclopedia
R. W., ed., 957-959,
of ocean temperatures
America
deduced from
Revue ges. Hydrobiol.
Ekman’s
Hydrogr.,
5,243-286.
surface to thermocline. Thus, the density distribution
McEWEN,
might suggest from time to time that upwelling in the sur-
G. F. (1918):
solar radiation
Ocean temperatures,
and oceanic circulation.
their relation
to
Bull. Scripps lnstn
biol. Res., 335-421.
face and subsurface layers does not exist at and around
REID,
the equator.
J. L. (1967):
physics.
Upwelling.
Runcorn,
ROBINSON,
international
S. K., ed., 1638-1640,
A. and H. STOMMEL
of Geo-
Oxford.
(1959):
cline and the associated thermohaline
Dictionary
The ocean thermocirculation;
Tel/us,
11,
295-308. ROTSCHI,
H. and F. JARRIGE
Upwelling
Equatorial;
Oceanogr.,
6,87-90.
SAITO,
Y. (195 1): On the velocity
J. Inst. Polytech. ARTHUR,
R. S. (1965):
eastern boundary
On the calculation
motion; J. geophys. DAWSON,
of vertical motion
currents from determinations Res., 70, 2799-2803.
E. Y. (1951):
sociated vegitation
in
of horizontal
A further
SAITO,
(1968):
Y. (1956):
Sur le Renforcement
Cah. 0. R. S. T, 0. M. Noumea,
d’un
ser.
of vertical flow in the ocean;
Osaka Cy Univ., 2, ser. B l-4. Theory
of the transient
welling and coastal currents; Amer.
state concerning
Geophys,
Union
up-
Trans.,
37, 38-42.
study of upwelling
along Pacific Baja California,
and as-
Mexico; /.
SCHOTT,
G. (1935):
Hamburg,
l-41
Geographie
des lndischen
und Stillen
Oceans.
3.
mar. Res., 10, 39-58. DEFANT,
A. (1936):
Siidwest Afrikas, Nobert
Das Kaltwasserauftriebsgebiet Landerkundiiche
Krebs zur Vollendung
Forschung,
vor der Kiiste Festschrift
des 60 Lebensjahres
dargebracht,
pp. 52-66. DEFANT,
A. (1950):
SCHUMACHER,
SHELL, Memorandum
concerning
the work of the
marine life research program; Bull. Scripps Inst. Oceanogr.
A. (1933):
Nordwest-Afiikanische 333. I. I. (1970):
Current
Variability
and upwelling
75,5225-5241.
Zwei Oberflachenschnitte Auftriebwasser;
Ann. Hydr.
and persistence
off southwest
Africa;/.
durch das Mar. Met.,
in the Benguely geophys.
Res.,
Geoforum I 1172
21
$MITH, F. G. W. (1951): Distribution of vertical water movement. Calculated from surface drift vectors; Bull, mur. Sci. Gulf Cwii&, 1, 187-195. SMITH, R. L. (1968): 11-46.
Upwelling;A.
Rev. Oceanogr. hr.
Bid.,
WY RTKI, K. (1961): The thermohaline circulation in relation to the general circulation in the oceans; Deep Sea Res., 8,39-64. WY RTKI, K. (1964): Bull., 63,355-372.
Upwelling in the Costa Rica Dome; Fishery
STOMMEL, H. (1956): On the determination of the depth of no meridional motion; Deep Sea Res., 3,273-278.
WYRTKI, K. and E. 3. BENNETT (3963): Vertical eddy viscosity in the Pacific equatorial undercurrent; Deep Se0 Res., 10, 449-4.55.
STOMMEL, 80-82.
YOSHIDA, K. (195): Coastal upweiling off the California coast; Rec. oceono@r. Wks /apen, 2,f -15.
H, (1958): The abyssal circufation; Deep Seu Res., 5,
SUERDROP, H. U. (7933): OR vertical circulation in the ocean due to the action of the wind with application to conditions within the Antarctic Circumpolar Current; “Discovery” Rep., 7, +39-170. SVERDRUP, H. U. (1938): On the process of upwelling;/. Res., I, 155-164.
mar.
SVERDRUP, H. U. and R. H. FLEMING (1941): The waters of the coast of southern California, March to July 1937;Buli~ Scripps &I.@? OcerJffogr.., 4, No. 10. THORADE, H. (1909): Die Kel~for~j5cken ~eere~~r~rn~~eff. I-32, Gottingen. TOMCZAK, M. Jr_ (1970): EIne lineare Theorie des stationEren Auftriebs im stetig geschichteten Meer; DP. hydrogr. Z., 23, 214-234.
YOSHIDA, K. (1967): Circutation in the eastern tropical oceans with special references to upwelling and undercurrents;/up. /. Geophys., 4,1-75. YOSHIDA, K. and H.-L. MAO (1957): A theory of upwelling of large horizontal extent;/. mur. Res., 16,40-54. YOSHIDA, K. and H.-L. MAO, and P. L. HORRER (1953): Circulation in the upper mixed layer of the equatorial North Pacific;j. mur. Res., 12, QQ-t20. YOSHIDA, K. and M. TSUCHIYA (1957): Northward flow in lower tayers as an indicator of coastal upwelling; Rec. oceonogr. Wks lawn, 4 (new series), 14-22.
11172
Physical Oceanography of ~pwetting Physikatische Ozeanographie des Auftriebsprozesses L’oc~anograp~e
Koji HIDAKA,
physique de I’upwelting
Tokyo*
Abstract: Upwelling - the ascending motion of water in the ocean - is a very important phenomenon as it brings, with the ascending water, the nutrients from the deeper layers where consumption is only small, into the surface layers. For this reason, upwelling increases the fertility of the surface and subsurface layers, which results in the establishment of rich fishing grounds. Upwelling is classified into three categories according to the place of occurrence, origin and to the mechanism: (1) coastal upwelling (2) mid-ocean upweliing and (3) equatorial upwelling. The physical explanation of the nature and occurrence of each of these three is given, including examples of upwelling occurring at different areas of the world’s oceans. No particular description is made on the downwelling or sinking which exists in the ocean as the result of continuity of the incompressible fluid. Zusammenfassung: Als ein Prozess, bei dem aufsteigendes Wasser die NXhrstoffe der tieferen Schichten des Ozeans, deren NBhrstoffzehrung nur gering ist, in die oberfi&chennahen Schichten bring& ist Auftrieb-von groger Bedeutung. Auftrieb erhoht die Fruchtbarkeit der obe~l~chennahen Schichten, die die Grundlage fdr reiche Fischgriinde bildet. Auftrieb wird in drei Gruppen unterschleden, eingeteilt nach dem Ort des Auftretens, der Unache und dem physikalischen Prozess: (1) Kbstennaher Auftrieb, (2) Auftrieb im offenen Ozean und (3) Xquatorialer Auftrieb. Form und Vorkommen der drei Gruppen werden physikalisch erklgrt, und Beispiele aus verschiedenen Gebieten des Weltozeans werden dargestellt. Eine besondere Beschreibung des Absinkens des OberflBchenwassers, das infolge der Kontinuitit des inkompressible Mediums aus dem Auftrieb im Dzean resultiert, wird nicht gegeben. R&urn& L’ ~upwelling~ le mouvement vertical des eaux ocianiques vers la surface - est un phenom&ne trds impo~ant, entrainant un transport des nutrients des couches d’eau s’itendant i grande profondeur 02 la consomption des nutrients est insignificante, aux couches suprrficielles. Par consiquant l’upwelling augmente la fertilite’ des eaux superficielles et sub-superficielles causant I’existance des rigions de p&che tris poissonneux. L’upweiling est divide entre trois types selon la region d’occurrence, I’origine et le mechanisme: (1) upwelling &tier, (2) upwelling de pleine mer et (3) upwelling equatorial. La nature et I’occurrence de chacun des trois w sont expliquees par rapport au mdchanisme physique, et des exemples d’upwelling de diffirentes regions de I’ocian mondial sont present& On s’abstient d’une description du tdownwelling% ou de la descente des eaux en particulier qui i cause de la continuite’ des fluides incompressibles, doit exister dans I’ocdan.
1. Introduction The physical interpretation of the phenomenon of upwelling is not very old. We can go back to 1909 when Hermann THORADE the California chapter:
prepared
current
Wirkung~n
a very elaborate
dissertation
and discussed the upwelling
on
in a
und Ursachen des kalten Auftriebwas-
sers (Teil I I). He showed how the temperature cycle of San Francisco differedfrom that off the estuary of the Columbia, and ascribed the cold water temperature during the period from July to September to the upwelling of cold water by NNW monsoon from beneath the surface and subsurface fayers. George F. MCEWEN could estimate *
Prof. Dr. Koji HIDAKA, Ocean Research institute, Tokyo University, Nakano, Tokyo 164, lapan.
the velocity of upwelling by finding out the theoretical relation between the monthly changes of temperature and the vertical velocity off the Californian coast (1912, 1918). Afterwards, several physical oceanographers tackled this problem. We can mention, among others, Albert DEFANT (1936)
and H. u. SVERDRUP
(1938,1941)
who have de-
veioped the theoretical explanation of this phenomenon. Recent development is due to Koji HIDAKA, HIDA,
Henry
STOMMEL,
Kozo YOS-
and others.
The phenomenon of upwelling is mostly correlated with the divergence on the sea surface produced by the prevailing winds. It can occur in an open sea far from the coast on all sides. According to E. C. La FOND (1966), localized upwelling deveiops in: (1) the iees of islands; (2) the lees of major land promontories projecting into a current; (3)
10
Geoforum 11/72
over shoais or sea-mounts; (4) in counterclockwise (clock-
phenomenon is correlated with surface convergence and
wise) eddies in the northern (southern) hemisphere; (5) at
the divergence at a lower layer where the descending
water mass boundaries; and (6) in thermal domes or ridges
motion terminates.
in the open sea. However, it develops quite strongly when there is wind approximately parallel to a coast which lies
The upwelling is very important from the biological points of view, as it brings a lot of water from intermediate
to the left (right) of an observer looking leeward in the northern (southern) hemisphere. Because the water is up-
depths, supplies a great deal of nutrients to the surface water, and thus gives rise to the development of large and
welled from the intermediate depths to the surface and
rich fishing grounds.
subsurface layers, the surface water temperature in the upwelled areas is considerably lower than the surrounding surface water. This difference often amounts to 7 “C
2. Classification
(SCHUMACHER, 1933) off the north-western coast of
R. I_. SMITH (1968) classified the upwelling into two patterns: (1) the coastal upwelling, which is the rising motion of water produced by interaction with coastal barriers, and
Africa (Fig. 7). Generally speaking, the upwelling velocity is estimated from low5 to 10e2 cm/set, and it is so small that during the past no instrument was sensitive enough to directly measure this ascending velocity. Thus the speed of upwelling is almost exclusively calculated from the equations of motion, continuity,
advection, etc.
(2) the open ocean upwelling, or mid-ocean upwelling, which occurs in a much larger scale and produces vertical motions as those driven by wind stress curl, the main oceanic thermocline, and equatorial oceanic currents. The intensity of coastal upwelling is typically much larger than that of open ocean upwelling. Vertical velocity of an or-
Descending motion of water, which is the reverse of the upwelling, is called “sinking” or “downwelling.”
of upwelling
This
der of low3 cm/set are quite common in coastal upwelling, while Henry STOMMEL (1956) considers 10T4 cmlsec to be characteristic of the mid-ocean upwelling. In addition. to the two patterns mentioned above, the present author wants to stress the importance of a third type of upwelling, i. e., (3) the equatorial upwelling. However, the equator, where the Coriolis force changes sign from plus to minus as we cross it from the northern to the southern hemisphere, can be treated as a kind of dynamical barrier. As a matter of fact, the upwelling along the equator is characterised by its greater vertical velocities, which sometimes amount to 10 to 100 times as large a value as usual mid-ocean upwelling. This fact was pointed out by the present author in 1965 from much evidence, and was recently supported by H. ROTSCHI (1968) from the result of actual observations. Equatorial upwelling has been described as a special class of upwelling process by j. t.. REID (1967).
3. Coastal upwelling Coastal upwelling is common to the areas where there Source: DEFANT 1961 Fig. 1
0 Mean anomalyof the seasurfacetemperatureoff the north-west coast of Africa for April in ‘C.
0 Mittlere Abweichungder Oberfkhentemperatur von der ozeanischen Verteilung entlang der NW-afrikanischen Kiiste im April P3. l Anomalie moyenne de la temphrature superficielle le long de la
c&e de I’Afrique du Nordauest pendant I’Avril (“C).
blows a wind parallel to a coast which lies to the left (right) of an observer looking leeward in the northern (southern) hemisphere. To this category belongs the upwelling off the Pacific coasts of North America, and South America, the Atlantic coasts of Africa, and northwestern coast of Australia and off Somaliiand, East Africa. The most common and well-studied upwelling takes place off the North American Pacific coast between about 46 “N and 25 ON, especially off California. It starts usually in March and reaches its maximum during the summer months, July and August, coinciding with the m~imum frequency of the northwest winds parallel to the coast. No upweliing is seen in the fall and winter.
Geoforum 11172
11
onomdy ,
OC
Fig. 2 0 Schematic cross-section normal to the coastof south-west Africa, showing the lines of constant density, the axis of the current vortex (wavy line), the zonal and vertical velocity components (arrows) and the meridional flow parallel to the coast (N towards north, S towards south). l Schematischer Schnitt senkrecht zur SW-afrikanischen
Kiiste, mit Darstellung der tinien gleicher Dichte, der Achse der Stromvortex (Schlangenlinie), der zonalen und vertikalen Striimungskomponente (Pfeile) und der meridionalen Komponente der Strijmung entlang der Kiiste (N nach Norden, S nach Men).
Source: DEFANT
1961
0 Coupe schtmatique perpendiculaire i la c&e de I’Afrique du Sud-Ouest, prdsentante les lignes de den&C constante, I’axe de la ctvortex, du courant (ligne ondulie), les composantes du courant zonales et verticales (flbches), et la composante du courant meridionale le long de la c&e (N vers le Nord, S vers le Sud).
The cold upwelted water in February and March off the
offshore and banked up at a distance about 100 km from
South American Pacific coast is remarkable and has been studied by GUNTHER (1936). There is some upwelling
the coast.
along the west coast of Australia as described by Gerhard SCHOTT (1935).
A somewhat different picture is obtained by a detailed analysis of the data. From the vertical displacement of the temperature, salinity and oxygen curves, the average
comes to the surface after flowing in the lower part of the
vertical velocities during the 41.day interval were computed. Knowing the vertical velocities, the equation of continuity gave the horizontal flow. The final result is
top layer, in the thermocline and beneath it towards the
shown in Fig. 3.
coast and gradually rises just off the coast. The upwelling
The lines with arrows represent the average streamlines
is largely confined to the narrow strip between the diver-
in the 4l-day interval. The horizontal velocities are indicated by curves. The average outward velocity of the
The first model of coastal upwelling (Fig. 2) was given by DEFANT (1936). It consisted of a divergent stream which
gence line and the coast. The water is brought to the sea surface from only a depth of 100 to 200 m.
boundary region between the upwelled water and the offshore surface water in the same period was computed
A necessary consequence of this type of circulation is the destruction of the thermocline in the upwelling region off
to be 3 cm/set. The distance of this outer boundary from the coast was about 90 km. At a distance of 75 km from
the coast. The gradual breakdown of the thermocline,
the coast, the outward transport above a depth of 40
which at times also strongly develops in the area closest to the coast, is a result of internal tidal waves which be-
meters, as computed from the equation of continuity,
is
26 x lo3 cm3 Isec, whereas a value of 25 x lo3 cm3 jsec
come gradually unstable as was shown by a series of ob-
is obtained from the average tangential stress of the wind
servations.
in the 41.day interval. The thickness of the upper homo-
For the mechanism of coastal upwelting, SVERDRUP (1938) gave a detailed analysis and interpre~tion of this
geneous layer is 41 meters.
phenomenon, which took place along the California coast, from the data of three cruises of the “Bluefin,” the vessel of California State Fish and Game Commission off Port San Luis in the earlier part of 1937. It is necessary, in order that the upwelling takes place most favourably, that a north-west monsoon blows continuously for a sufficient-
a cellular circulation extends to about 80 meters from the surface within which the water flows away from the coast above 40 meters, and towards the coast below 40 meters. Near the coast the motion is ascending, near the offshore boundary it is descending. The offshore boundary is, however, moving slowly away from the coast and the inner cell is, therefore, being fed from below by water which flows towards the coast. This inflow appears to take place at depths not exceeding 200 meters.
ly long duration. And this occurs on the California coast throughout April, May, and june. According to SVERDRUP’S analysis, the light water along the coast is driven
Between the coast and the banked-up light surface water,
12
Geoforum 11/72
Fig. 3 0 Computed vertical circulation in the time interval between two successivecruises. l Ve~ikalzirkuiation,
berechnet fiir den Zeitraum zwischen zwei aufeinanderfolgenden Beobachtungsfahrten.
l Circulation verticale, calculCe
pour I’interval entre deux campagnes successives.
Source:SVERDRUP 1938
Finally the crosses (+) show a zone with a stronger flow parallel to the coast and directed into the picture. in a study of a large amount of data of Californian upweliing collected at the Scripps Institution of Oceanography, DEFANT (1950, 1951) pointed out that the piling-up and upwelling processes are associated with characteristic displacements of the sea surface and of the internal boundary layer which gradually develop under wind influence and adjust itself with the circulations simultaneousiy formed and normal to the coasts. They finally tend tb a stationary state. During the first cruise, February 28 to March IS, 1944, the wind component towords the coast predominated over the entire region with a maximum of S m/set, which caused considerable piling-up of water along the coast. During the second cruise, April 27 to May 15, in contrast
surface in the direction of the coastline, the equations of motion and the equation of continuity are:
a2u A, a=u -.--f_.+Zwsinrpv -g -xax = 0 p az2 p a2
A,
A,4,+A, P
a2v G--2wsinqu=O,
-. P
3x2
&+aw=, ax
az
1
where { is the elevation of the surface of the sea varying in the direction perpendicular to the coast. If the wind blows in a positive direction ofy in the belt between the coast, then x = 0 and x = L. The conditions to be satisfied on the surface of the sea are
to the first case, the water was driven uwuy from the coast where as a consequence upwelling took place. Thus the first cruise gave a typical example of water accumulation along the coast, while the second furnished a typical example of coastal upwelling. The result can be seen in the topographic representations of the sea surface off this
; z
-A,$=0
=o:
(3) -A,g=r
forO
i =OforL
coast quite dearly. In 1922, Harold JEFFREYS investigated the effect of a steady wind on the surface of a homogeneous ocean near the coast. In 1952, DEFANT gave a similar theoretical explanation on the assumption of a sea composed of two layers with different densities. Even by these simple models it was possible to explain the behaviour of upwelling rather satisfactorily, A theory of stationary upwelling produced by a wind parallel to a coast has been given by Koji HIDAKA (1954), whereby the effect of the Earth’s rotation and the frictional forces due to both vertical and lateral mixing have been taken into account. He deals with the steady state only. Because there is no slope of the sea
where r is the stress of the wind and may be either a constant or a function of x. On the bottom z = h, the boundary conditions are z=h:u=~=O,
(4)
because of vertical friction. Along the coast which is considered to consist of vertical cliffs, x=o:lJ=v=o, because of horizontal friction. In the region very far from both the coast and wind region, x= m:U=“=%O
ax
*
(51
Geoforum 11/72
13
60 8-
a)
Source: TOMCZAK 1970
4
Fig. 4 Computed vertical circulation in an ocean with turbulent diffusion: a) homogeneous (identical to Hidaka’s solution), b) weakly stratified, c) strongly stratified. Berechnete Vertikalzirkulation c) starker geschichtet.
in einem Ozean mit turbulenter Diffusion: a) Homogen (identisch mit Hidakas Losung), b) schwach geschichtet
Circulation verticale, calculQe pour un ocean avec diffusion turbulante: a) Homogane (identique avec la solution de Hklaka), b) avec une faible stratification, c) avec une stratifaction plus forte. L’ = z/D,,, Lo = L/D,.
(A,/Al)t’2,
x0 = x/DV. (A,/Al)“‘.
The solution is rather complicated and numerical calculation of the magnitude of the offshore currents and the up-
HIDAKA also investigated the case arising when a wind
welling velocity allows the results to be compared with
the direction of the wind is perpendicular to the coast, the induced circulation has a rather complicated structure
values estimated correctly from observations. Figure 4a gives the solution in the form of streamlines in a vertical section perpendicular to the coast. Upwelling develops close to the coast, and there is no offshore movement of the water in the upper layers of the sea directly beneath
blows at a certain angle to the direction of the coast. If
with two vortices with horizontal axes in the upper layers, one of which is situated close to the coast and the other is near the outer boundary of the wind belt. The upwelling due to a longshore wind is far more effective in lowering
the surface swept by the wind. The upwelling is confined
the temperature of the coastal region than that induced
to the strip within i Dh (Oh = ndm)
by a wind perpendicular to the coast since the former
from the
coast, and the downwelling process occurs outside the wind zone. If the vertical mixing coefficient A, is estimated at 1,000 c. g. s., the vertical Ekman’s depth Dv will be 162 m at 30 ON. For a horizontal mixing coefficient, Ar = 10’ was chosen because the ratio Al/A,
- 3.14 x 10e3 cm/set or 2.7 m/day or 80 m/month, for the wind stress r = 1 c. g. s.
favourable wind direction for upwelling is 21O.5 cum sole with the coastline for a person looking leeward.
= lo6 ap-
pears to be reasonable. For this value of A,, the horizontal frictional depth D,, will be 162 km. Estimation gives the width of the wind zone to be 2.0944. Dh = 339 km. The average horizontal velocity between the surface and 0.2 Dv was calculated as 3.35 cm/set offshore. The maximum upwelling velocity can be estimated to be
brings a larger amount of cold subsurface water to the surface from deeper levels than the latter. The most
Extension of HIDAKA’S
theory to the transition stage was
worked out by Yasukazu SAITO (1956) who calculated the development of the upwelling process after the sudden occurrence of a wind. In the case of a circulatory wind like a typhoon or a heavy cyclone, the wind blows approximately parallel to the isobars or towards the centre. Intuitively it may be imagined that upwelling will not occur when there is a wind stress component towards the centre. However, the upwelling will still take place when the wind has, like in
14
Geoforum I 1I72
a typhoon or a cyclone, the components by some angle
As is shown by observations, the process of upwell~ng is
towards the centre of the circular wind system. in a
not a steady phenomenon. If the duration of the wind is
paper of 1955, HIDAKA and AKIBA assumed a circular wind system:
as short as a few hours, the offshore component of surface water transport will not be very large because drift currents will not fully develop. If the winds are more or less steady for several hours up to as much as a day, the drift
current may develop but it will not be accompanied by considerable upwelling due to the oscillations of the thermocline. However, the process will be different if the where r,,, is the maximum wind stress, while r,
is the
distance of the maximum wind stress from the centre (P = 0) of the wind system. First they treated the case when the wind blows contru so/em tangential to the isobars. In this case, the upwelling occurs mainly within the distance r = &
where i& = II x_!-
and AI is the
coefficient of lateral eddy viscosity. The upwelling is most intense approximately
at r = 0.6 Oh, and the maxi-
mum vertical velocity is w = 2.4 * 10m3cm/set or 2.1 m/day for T = 1 c.g.s. (Fig. 5). In the second place, the case was treated where the wind stress is directed 45 degrees in an inward direction from the isobars, which is
wind continues for several days up to a week. If the wind blows continuously for a longer duration than a week, the surface currents will reach a steady state with an intermediate stage for a wind lasting for a few days up to a week during which geostrophic equilibrium is approached. Kozo YOSHIDA (1955) treated this latter section of the process, relying on a case of Californian upwelling. In his model the x-axis is directed eastwards, they-axis northwards, the latter representing the coast. The z-axis is taken positive downwards with z = 0 being placed on the mean sea level. The process was assumed to be independent of the north-south direction so that only the variables x and z were considered. YOSHIDA considered only a
welling taking place at r = 0.6 Dh and the upward velocity
small-scale process extending over a period of several days and over a distance of up to 10 km. The equations of
being 1.5 * 10m3cmlsec or 1.3 m/day for the same wind
motion are then
less effective in producing upwelling, the maximum up
stress 1 c. g. s. -fv=gwithf=Zwsing
I
2Oh
&
;i-;'f!l'G
a
(A$)-%.
A, is the vertical coefficient of eddy viscosity, T,, is the northward component of wind stress. H is the average thickness of the upper mixed layer. The corresponding vorticity and divergence equations are a$ fwh V--mat H
curi, 7
(8)
H
where wh is the vertical velocity at the depth of thermodine z = h. The equation of continuity and condition for the quasi-isostatic adjustment with g* = g 9 give Source: HIDAKA
and AKIBA
1
1955
wh----. g*
ax
The mutual adjustment between the pressure and the current seems to be completed within a day or two, so that
Fig. 5 @ Upwelling as induced by a circular wind parallel to the isobars. & Durch einen j~baren~ar2llelen, vorgerufener Auftrieb.
aP
rin~~rmjg
wehendtn Wind hep
0 Upwelling due a un vent soufflant circulairement le long des isobares.
the above equation is reasonable for up to about a week after this first stage of adjustment is over. From Equations (8), (9), and {lo}, equation k= a*W -_-k*W=-.. axz f
a7 ax
(11)
Geoforum 11/72
15
is obtained where k = f/ &%.
The boundary condition
The second half of YOSHIDA’s
paper deals with the
changes in surface conditions derived from the above model which represents a transient state of upwelling. He
u = 0 along the coast requires
found that the variations in surface characteristics were largely confined to within a narrow coastal region. The with the condition w = 0 when x = -m. (1 ‘I ) then witI be
The solution of
coastal upwelling is associated with considerable changes in surface conditions within the coastal water of width L, while upwetling or downwelling outside of this strip will not give rise to such signi~cant changes during a period of only a week or two. In the succeeding stage of the upwell-
-0
0
0
If Ikxl%
(12)
ing process, in which the isostatic ~jus~ent now can be considered as complete, the lateral mixing process in the inshore regions stands out as the most important factor. The dynamic equations are now
1, it follows
(36)
1 a?,
W=-f&, _-
where AI is the coefficient of laterai mixing. The upward and
03)
movement of the thermocline, due to the ascending motion, will produce a sharp horizontal density gradient, and
rye” dx
when conditions are variable in an oscillatory way, as is usually the case, internal waves will be produced and
-m
along the coastline. A uniform northerly wind over offshore water will give rise to a coastal upwelling of the amount W.
cause intense mixing across the ~~er~~/jRe.
The equa-
tion for the conservation of mass now becomes aP =A$
a&.
ax= ’
“az 04)
The upwelling velocity wilt be proportional to the intensi-
or approximately
w=_&i?
ax=*
ty of the northerfy wind but is not directly dependent on the latitude. When g* = g $$ = 2.5,~=~m=4x103cm,
The boundary condition at the coast gives v = 0, so that
and rY,O = - 0.5, w follows
finally it follows
W%=O = - 5 x 10m3 cm/set. In five days this upwelling will give an upward displacement of the thermocfine of 22 meters. This upward movement of the thermociine off the coast will continue until an equilibrium is reached in about a week. This state seems then to be maintained for about one month or two. This coastal upwelling is almost entirely confined to a narrow strip close to the coast. With the numerical values introduced above, w will be reduced to 6 % of that of the coast and to 3 % of the coast w-value at 50 km only, the-process being practically Jimited to a distance of 40 to 50 km from the coast. The effective width of coastal upwelling is given by a characteristic length n
7r&Y?
L=k=f’ whose value varies from 10 km to 340 km for different values of gH& and different latitudes.
fB wh=--'--_ g*
av ax
07)
The expression for w will become the same as in the earlier stage and the vertical velocity distribution will therefore remain unchanged throughout the entire period of the process as long as the wind is kept steady. During this period, the ascending water movement will be subject to mixing with the su~ounding waters, and the thermocline will not be elevated to any large extent. From Equation (17), it follows that at this stage the vorticity in the surface layer will be proportional to the vertical velocity. Thus upwelling will be associated with cyclonic vorticity in contrast to the initial inshore increase in negative vorticity produced by the coastal upwelling. YOSHIDA and Mizuki TSUCH~YA (1957) noticed something like a “vertical divergence of isotherms” at certain intermediate depths, say, between 200 and 500 meters. In some sections normal to the California coast, it is often
observed that the isotherms or isopycnals above 100 to
76
Geoforum 11172
200 meters conspicuously rise towards the coast, while those in the lower layers beiow 200 to 500 meters fall towards the coast. These two authors explained it as the
The upwelling phenomenon taking place at a spot in the
northward current in deeper layers correlated with-the up-
ocean far apart from the coast may be classified in this
welling in surface and subsurface layers above from 20C1-
category. Kozo YOSHIDA and Han-tee MAO were the first to discuss the theory of this problem. They used the
500 m, and developed a theory thereof.
4.
Mid-ocean upwelling or Open-ocean upwelling
There appeared recently several improved theories on coastal upwelling. First of ah, there can be mentioned that of Matthias TOMCZAK, Jr. (1970) which is an im-
approximate vorticity equation derived by eliminating the
provement of HIDAKA’S
they obtained
theory of coastal upwelling ap-
plied to a stratified sea instead of the homogeneous ocean. An addition of the equation
horizontal pressure gradients from the equations of motion. After disregarding the terms which are less important,
i&!=@,+U!_ az f f ar cur&r
df
with p = -
4’
.
(18)
Substituting from the equation of motion
(19)
where r is the coefficient of vertical diffusion, enabled TOMCZAK
to solve various inter~ting cases which could
not be solved in HIDAKA’S result was that TOMCZAK
theory. The most remarkable
welled from shallower layers than when simply the homogeneous water is assumed. Figures 4a, 4b, and 4c give the streamlines generated by the same wind field as that had been used by HIDAKA,
where p is pressure, it follows at the surface layer
could show that water is up-
k
wizo=-P P
I’
$dz-+
(TV + f cur!, 7) P
but with different degrees of strati-
fication represented by a parameter US. Figure 4a is identical with HIDAKA*S there is no water stratification
result, that is, when
(OS = 0), while Figs. 4b and
4c show the streamlines when the stratification is specified by US = 0.002 and US = 0.02 respectively, the latter being stratified more strongfy. This result shows that the water upwells to the surface layer directly even at strong stratification from very deep layers. This conclusion may be visualized from actual observations. Moreover, the density distribution strongly depends on diffusion even for the same pattern of circulation and on wind speed. These results show that it is not possible to obtain a definite conclusion as to the depth of upwelling and to the pattern of
where z = z. is the sea surface and r is the wind stress at the sea surface with its components rX and rY. After several simplifications, the verticai velocity at a level z = H where stability is great, say 150 m, is obtained:
WH=-- :f$dz H
(21) =-.-P
More recently Richard W. GARVINE
(1971) pointed out
that HIDAKA eliminated the chief mechanism whereby fluid is returned beneath the wind friction layer to supply mass for the upwelling motion by omitting the longshore pressure gradient at the outset. GARVINE argues that the return flow supplying the upwelling motion in HIDAKA’s problem must have been intimately related not only to the intermediate layer but to a strong Ekman layer at the
vdz,
f
circulation from observed density distributions.
H
after substitution from (19). Equations (20) and (27) represent the vertical component of flow across the horizontal plane. If h is the thickness of the mixed layer, (20) the vertical flow across the plane z = h is
(22)
bottom. In the same year, HSUEH and Q’BRIEN f1971) discussed a possibility for an upwelling to be induced on a continental shelf by the existence of a large-scale ocean current. Their theory does not necessitate winds blowing over the sea surface. They explain this vertical motion in relation to the actually existing ocean currents off the Oregon, Peruvian, and West Florida coasts. This means that the California and Peruvian upwelling can exist all year round as the effects of the California and Peru currents.
wk m-! curl, 7
f
(23)
very closely. Equation (21) shows a close relationship between the vertical velocity at z = H and meridional mass transport
Geoforum 11/72
17
ap
in the layers deeper than the layer z = H. Thus a subsur-
Now a~ can be known by occupying two hydrographic
face poleward component of the current must be associated with an ascending motion in both hemispheres. In ac-
stations on the same latitude circle, while F(z) is to be
cordance with the theory, we may anticipate the following
regarded as a more or less undeterminable function of z. It differs from zero only in a thin upper layer extended
facts which are confirmed in reality: Off California ascending motion exists in the inshore areas with a north-
from z = 0 to z = - D, where D is the depth of frictional
bound current in lower layers, while a descending motion occurs offshore with a southbound current in lower layers. On this principle, they could calculate
influence. Of course F(0)
is known explicitly in terms of
the distribution of wind stress on the sea surface in the neighbourhood of the pair of hydrographic stations. Integrating Equation (26), it follows
wh = 7 x 10s4 cm/set
(28)
16 meters/month taking H = 150 m and cp= 30”. They could show that the distribution of calculated ascending velocity at the 150 m
where we define
level is in good agreement with the areas where the density changed in equal amount between April and June 1949. These two authors also stressed that their method is ap plicable satisfactorily to coastal upwelling, not only off California, Peru, and West Africa but also to the western boundary of the oceans where the Kuroshio and Gulf Stream flow. On discussing the abyssal circulation of the oceans, it was
-B
And C is a constant of integration. Now the meaning of the function a(z) is familiar, for it follows from the first equations
pv = 9(z) + c
necessary for Henry STOMMEL (1958) to investigate the behaviour of the oceanic thermocline. Allan ROBINSON and STOMMEL (1959) have derived an upwelling velocity
which is the equation of pure geostrophic flow, and C is the undetermined reference velocity. Thus determination
3 x lo-’
of the constant C is equivalent to determining the depth
cm/set as the most probable value in lower lati-
tudes. The vertical velocity 1 - 5 x 10m5 cm/set obtained by Klaus WYRTKI also is in good agreement. In his paper on determination of the depths of no meridional motion,
at which v vanishes. Here it is seen that the level of no meridional motion coincides with that of the maximum vertical motion, and that the level of no zonal motion
Henry STOMMEL (1956) derived an expression to compute the vertical velocity in the open ocean from observed
does not necessarily coincide with either.
distributions of mass and of wind stress on the sea surface.
Integrating Equation (28) once more, it follows
He starts with the equations of motion
aP -2wsirnp*pv=--+-
ax
2wsincp.pu=-G+;,
a% a2
(24)
ap a5
pw=K
z
P IS
cP(z)dz+ C . (z + B)
-B
I
- F(z),
(29)
if pw vanishes at the surface I = 0 or is fixed by some small
aP 9P = z
known mean evaporation-precipitation
correction. The con-
stant C can be determined as
and the equation of continuity
& (PU)+ $ (PV)+$ (PW) =0.
(25)
c=-j1 2wsinq F(O)
6 (PW) = -
(2
wtinp)2 .$ - $
Although STOMMEL
F(z)
(26)
can be obtained, where F(z)
=
a -.-k-
ax 2wsincp
---
a ay
7x 2wsinlp
and (27)
/3 = a (2wsinp). ay
(30) --B
From these equations, -&j
_
I(
could determine the depth of no
motion only for meridional flow, his method was successful in determining the velocity of vertical motion. Although his method can only determine pw + F(z), the function will vanish below Ekman’s depth of frictional influence, so that it will be applicable to the depths below 100 m level except at or very close to the equator. Some of his results were extracted from Table 1 of his paper.
18
Geoforum 1 l/72
Table
1
in Honolulu occupied on board the “M/S Hugh M. Smith”
0 Geschwindigkeit 0 Velocity
Depth
des Vertikalstroms
of Vertical
(m)
10-5
0 so 100 tso 200 250 300 350 400 450 500 600 700
Flow
cm/set
-
(STOMMEL,
(sTOMMEL,
1956)
are all located at approximately
1956)
Depth
fm)
800
9 - 6 - 4 1 1 3 5 7 9 11 13 16 19
on her Cruise No. 30, July-August
900 1,000 1,200 1,400 1,600
r
&J In the computation, it is assumed that ;i;; and ap practicalay ly vanish at and below the 1,000 m level. The result shows
1 O-5 cmjsec
1,800 2,000 2,500 3,000 3,500 4,000 4,500 s ,000
l_
that there is weak upwelling in most depths.
21 22 22 23 24 24 23 23 20 17 13 9 5 0
Thus the maximum vertical velocity was 24 x 10’
Table 2 0 Geschwindigkeit zusammengesteiit
des Auftriebs f-) und Absinkens (+) in cmfsec, nach POFI NorPac-Daten (HIDAKA, 1961)
0 Velocities of Upwelling (-) and Sinking (+) (cm&c), from POFI NorPac Data (HIDAKA, 1961)
T Depth
cm/set
at about 1,500 meters. Another method was given by HIDAKA
1955. These stations
the same latitude 50 “N.
in 1961 for calcu-
lating mid-ocean upwelling. He started again from Equations (24) and (25) but expressed the pressure by density differences explicitly. The resulting equation for the vertical velocity in terms of the density field is
0 2oR (sin* 9/cos 9) . p(z),
(m)
0 10 50 100 200 300 400 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000
Computed
Stations 81-83 (cmjsec)
-
0 0.028 0.121 0.199 0.309 0.346 0.434 0.432 0.464 0.778 0.623 0.467 0.311 0.156 0
83-84
-I-
84-86 (cm/secf
t
0 0.00s 0.009 - 0.009 -0.118 - 0.257 - 0.332 - 0.450 - 0.676 - 0.522 - 0.417 - 0.313 - 0.209 - 0.104 0
(cm/=) x IO”
(31)
-
0 0.062 x lO”l 0.306 0.568 1 *OS4 1.498 1.942 2.283 3.050 3.492 2.793 2.09s 1.397 0.698 0
x IOJ
A-.
The velocity of mid-ocean upwelling is mostly of an order of IO-’ to 10T5 cm/set. This is consistent with the result
where
by STOMMEL.
5. Equatorial
ri-
Even if there are no land barriers, the equator is a kind of
f-172 hi + 20R
upwelling
(32)
(sin’cplcosg)
i * (ph wh - p. wo).
Practically qfz] can be disregarded if either or both of w. and wh is or are smaller than 10e3 cmfsec, so that the upwelling velocity -w(z) is given by Equation (31) with
dynamical boundary as long as the motion of sea water is concerned. Therefore, close to the equator the upwelling phenomenon may be considered greatly different from the usual open-ocean upwelling. The most remarkable feature of the equatorial upwelling is that the upwelling velocity is so intense that a velocity of theeorder of 1Oa2 cmjsec is quite common. This means that the vertical
q(z)= 0. Of course, this formula fails to be valid at the equator and poles because the denominator of it vanishes
flows along or close to the equators are 10 to 100 times as large as those occurring in the open ocean of higher latitudes.
there. The following table is extracted from a computation of vertical water flows by Equation (31), use being made of the density data at four NorPac stations 81,83, 84, and 86 of the Pacific Oceanic Fishery Investigations
In 1960, HIDAKA gave a simple theory on the equatorial upwelling. He did not evaluate the resulting equation or the vertical velocity numerically; however, he published a paper in 1965 in which he pointed out several evidences
Geoforum 11172
Source: HIDAKA
19
1955
Fig. 6 0 Distribution of divergence (shaded) and convergence areas in the Pacific Ocean, mg/m’/sec. l
Verteilung der Divergenz- (schraffiert) und Konvergenzgebiete im Pazifischen Ozean, mg/m3/sec.
l
Distribution des r&ions de divergence (hachures) et de convergence dans I’Oc6an Pacifique, mg/m3/sec.
of an intense upwelling at the equator. He gave some results of the estimation of upwelling velocity for some
ern Pacific has reinforced the upwelling of the subsurface
simple cases and checked the magnitude of the equatorial upwelling.
phosphate concentration in the upper 60 meters had practically doubled and the surface water was heavier.
The formula for the estimation did not give a vertical
The observed distributions of nitrate and density imply
velocity less than 1O-’ cm/set unless AY > 1O4 c. g. s.
a vertical speed (of upwelling) much higher than that
There is other evidence of unexpectedly intense upwelling velocity at the equator. Recently Henri ROTSCHI and
which has been evaluated in a steady state circulation.” They derived from the change of concentration of nitrates,
F. JARRIGE (1968) published a paper indicating the intense upwelling produced by the intensification of the east component of the trade wind at the equator. They state, “in October 1966 an intensification of the east component of the trade wind at the equator in the west-
waters. After the wind had blown for three days, the
- w = -w= -w=
9 3 2 - w = 0.3
x x x x
1B2 cm/set low2 cm/set 10d2 cm/set 1OS2 cm/set
at at at at
10 20 30 50
meters meters meters meters,
20
Geoforum 11/72
and they obtained -w=2x
DEFANT,
A. (1951):
10V2 cm/set
out several other examples for the intense upwelling at the equator.
DEFANT,
A. (1952):
des Windstaus hydrogr. DEFANT,
A glance at the atlas of the Pacific (Fig. 7) reveals an
cold because of the intense upwelling in the area of the Peru/Chile current which extends to the north broadening in the westward direction and merges in the narrow equatorial tongue just mentioned. It must be the object
prevailing easterlies along the equator. Part of this water
dynamics.
Kiisten;
Dt.
Oceanography,
Vol.
1.
J. Phys. Oceanogr.,
1, 169-179.
A report on oceanographical ‘Discovery”
investiga-
Rep.,
13, 107-
276. K. (1954):
Contribution
coastal currents; Amer. HIDAKA,
K. (1955):
to the theory
Geophys.
Divergence
Union
of upwelling
of surface drift currents
in terms
to the location
upwelling
1, 47-56.
and sinking;/ap.
K. (1960):
HIDAKA,
K. (1961):
Wks /apan,
J. Geophys.,
On the equatorial
Kobe Mar. Observatory,
14, 12-l
Calculation
6, 1 l-l
upwelling;
of
Memorie
of
4.
of upwelling; Rec. oceanogr.
5.
K. (1965):
Evidences of an intense upwelling
equator; Bull. Sot. franco-jap. K. and Y. AKIBA
Oceanogr.,
(1955):
Y. and J. J. O’BRIEN
induced by along-shore
induced
Wkslapan,
(1971):
current;/.
at the
3, l-8.
Upwelling
circular wind system; Rec. oceanogr. HSUEH,
and
Trans., 35,431-444.
of wind stresses, with special application
HIDAKA,
ing at the equator as far west as 170 “E or more.
zum Phanomen
an ozeanischen
A simple model of coastal upwelling
E. R. (1936):
HIDAKA,
far apart from the west coast of South America show
JARRIGE
an ozeanischen
W/en, 4, Ser. A,
Uberlegungen
tions in the Peru coastal current;
HIDAKA,
quite high nutrient concentration, and high productivity
Physica/
R. W. (1971):
GUNTHER,
may be ascribed to this action of advection. However, the fact that the equatorial waters located in the mid-Pacific
along the equator suggests the evidence of intense upwell-
Theoretische
und des Auftriebs
A. (1961):
HIDAKA,
of discussions that this cold water might be the cold water upwelled, but not entirely the water transported by
and
Bioklim.,
Z., 5,69-80.
GARVINE,
elongated cold water mass exactly at the equator, extending from the Ecuador coast westward to as far west as Polynesia. This suggests a possible occurrence of intense upwelling at the equator. According to the temperature charts, we can realize that the water off the west coast is
ROTSCHI
und Auftrieb
206-308.
as an average value for the layer 0 - 60, m. They pointed
As
Windstau
Kiisten; Arch. Met. Geophys.
by a
2,7-18.
Steady coastal upwelling Phys. Oceanogr.
1,180-
186.
pointed out, the equatorial up-
JEFFREYS,
H. (1923):
The effect of a steady wind on the sea-
level near a straight shore; Phil. Mag. 46, 115-125.
welling is highly sensitive to the variation of the trade winds. In the western part of the equatorial Pacific, there sometimes appear strong westerlies, choking the upwelling for some time. The result is that the swelling upward of the thermocline at and around the equator vanishes, and the water temperature becomes uniform from the
LaFOND,
E. C. (1966):
Fairbridge, McEWEN,
Upwelling.
G. F. (1912): of upwelling.
. . . Int.
of Oceanography.
New York.
The distribution
along the west coast of North theory
Encyclopedia
R. W., ed., 957-959,
of ocean temperatures
America
deduced from
Revue ges. Hydrobiol.
Ekman’s
Hydrogr.,
5,243-286.
surface to thermocline. Thus, the density distribution
McEWEN,
might suggest from time to time that upwelling in the sur-
G. F. (1918):
solar radiation
Ocean temperatures,
and oceanic circulation.
their relation
to
Bull. Scripps lnstn
biol. Res., 335-421.
face and subsurface layers does not exist at and around
REID,
the equator.
J. L. (1967):
physics.
Upwelling.
Runcorn,
ROBINSON,
international
S. K., ed., 1638-1640,
A. and H. STOMMEL
of Geo-
Oxford.
(1959):
cline and the associated thermohaline
Dictionary
The ocean thermocirculation;
Tel/us,
11,
295-308. ROTSCHI,
H. and F. JARRIGE
Upwelling
Equatorial;
Oceanogr.,
6,87-90.
SAITO,
Y. (195 1): On the velocity
J. Inst. Polytech. ARTHUR,
R. S. (1965):
eastern boundary
On the calculation
motion; J. geophys. DAWSON,
of vertical motion
currents from determinations Res., 70, 2799-2803.
E. Y. (1951):
sociated vegitation
in
of horizontal
A further
SAITO,
(1968):
Y. (1956):
Sur le Renforcement
Cah. 0. R. S. T, 0. M. Noumea,
d’un
ser.
of vertical flow in the ocean;
Osaka Cy Univ., 2, ser. B l-4. Theory
of the transient
welling and coastal currents; Amer.
state concerning
Geophys,
Union
up-
Trans.,
37, 38-42.
study of upwelling
along Pacific Baja California,
and as-
Mexico; /.
SCHOTT,
G. (1935):
Hamburg,
l-41
Geographie
des lndischen
und Stillen
Oceans.
3.
mar. Res., 10, 39-58. DEFANT,
A. (1936):
Siidwest Afrikas, Nobert
Das Kaltwasserauftriebsgebiet Landerkundiiche
Krebs zur Vollendung
Forschung,
vor der Kiiste Festschrift
des 60 Lebensjahres
dargebracht,
pp. 52-66. DEFANT,
A. (1950):
SCHUMACHER,
SHELL, Memorandum
concerning
the work of the
marine life research program; Bull. Scripps Inst. Oceanogr.
A. (1933):
Nordwest-Afiikanische 333. I. I. (1970):
Current
Variability
and upwelling
75,5225-5241.
Zwei Oberflachenschnitte Auftriebwasser;
Ann. Hydr.
and persistence
off southwest
Africa;/.
durch das Mar. Met.,
in the Benguely geophys.
Res.,
Geoforum I 1172
21
$MITH, F. G. W. (1951): Distribution of vertical water movement. Calculated from surface drift vectors; Bull, mur. Sci. Gulf Cwii&, 1, 187-195. SMITH, R. L. (1968): 11-46.
Upwelling;A.
Rev. Oceanogr. hr.
Bid.,
WY RTKI, K. (1961): The thermohaline circulation in relation to the general circulation in the oceans; Deep Sea Res., 8,39-64. WY RTKI, K. (1964): Bull., 63,355-372.
Upwelling in the Costa Rica Dome; Fishery
STOMMEL, H. (1956): On the determination of the depth of no meridional motion; Deep Sea Res., 3,273-278.
WYRTKI, K. and E. 3. BENNETT (3963): Vertical eddy viscosity in the Pacific equatorial undercurrent; Deep Se0 Res., 10, 449-4.55.
STOMMEL, 80-82.
YOSHIDA, K. (195): Coastal upweiling off the California coast; Rec. oceono@r. Wks /apen, 2,f -15.
H, (1958): The abyssal circufation; Deep Seu Res., 5,
SUERDROP, H. U. (7933): OR vertical circulation in the ocean due to the action of the wind with application to conditions within the Antarctic Circumpolar Current; “Discovery” Rep., 7, +39-170. SVERDRUP, H. U. (1938): On the process of upwelling;/. Res., I, 155-164.
mar.
SVERDRUP, H. U. and R. H. FLEMING (1941): The waters of the coast of southern California, March to July 1937;Buli~ Scripps &I.@? OcerJffogr.., 4, No. 10. THORADE, H. (1909): Die Kel~for~j5cken ~eere~~r~rn~~eff. I-32, Gottingen. TOMCZAK, M. Jr_ (1970): EIne lineare Theorie des stationEren Auftriebs im stetig geschichteten Meer; DP. hydrogr. Z., 23, 214-234.
YOSHIDA, K. (1967): Circutation in the eastern tropical oceans with special references to upwelling and undercurrents;/up. /. Geophys., 4,1-75. YOSHIDA, K. and H.-L. MAO (1957): A theory of upwelling of large horizontal extent;/. mur. Res., 16,40-54. YOSHIDA, K. and H.-L. MAO, and P. L. HORRER (1953): Circulation in the upper mixed layer of the equatorial North Pacific;j. mur. Res., 12, QQ-t20. YOSHIDA, K. and M. TSUCHIYA (1957): Northward flow in lower tayers as an indicator of coastal upwelling; Rec. oceonogr. Wks lawn, 4 (new series), 14-22.