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Home , Cape Palmas, Gulf of Guinea, Wind fetch

99

UPWELLING IN THE OF

Results of a mathematical model 2 2 6 5 0

A. BAH Mécanique des Fluides géophysiques, Université de Liège, Liège (Belgium)

ABSTRACT A numerical simulation of the oceanic response of an x-y-t two-layer model on the 3-plane to an increase of the stress is discussed in the case of the tro­ pical Atlantic . It is shown first that the method of mass transport is more suitable for the present study than the method of mean velocity, especially in the case of non-linearity. The results indicate that in the oceanic equatorial is due to the eastward propagating equatorially trapped , and that in the coastal region upwelling is due to the westward propagating reflected Rossby waves and to the poleward propagating Kelvin wave. The amplification due to non- linearity can be about 25 % in a month. The role of the non-rectilinear is clearly shown by the coastal upwelling which is more intense east than west of the three main capes of the ; furthermore, by day 90 after the wind's onset, the maximum of upwelling is located east of Three Points, in good agree­ ment with observations.

INTRODUCTION When they cross over the Gulf of Guinea, monsoonal take up humidity and subsequently discharge it over the African in the form of precipitation (Fig. 1). The upwelling observed during the summer along the coast of the Gulf of Guinea can reduce oceanic evaporation, and thereby affect the rainfall pattern in the region. Years of intense upwelling could be very dry and years of reduced upwelling should result in periods of relatively high rainfall. Clearly, a better understanding of the upwelling regime might contribute significantly to improved land-use. Many investigators have attempted to explain the generation and evolution of up­ welling in the Gulf of Guinea. It was soon apparent that localJwinds could not provide an adequate forcing mechanism (Houghton, 1976). Philander (197$) concluded that the 100

Fig. 1. Sketch of the monsoon wind pattern over the Gulf of Guinea (after Dhonneur, 1974). upwelling is not due to local oceanic circulation, but rather is part of the large scale oceanic circulation system. This explanation seems reasonable since Adamec and O'Brien (1978) have already shown that variation of the trade winds regime in the western tropical could excite an equatorially trapped Kelvin wave which would induce upwelling on its way eastwards (see also Moore, 1968; Moore and Philander, 1977; Moore et al., 1978). But their study does not explain the irregular intensification of upwelling locally along the northern coast of the Gulf of Guinea. Some previous workers have tried to demonstrate the effects of zonal and meridio­ nal on equatorial waves (Philander, 1979; Weisberg et al., 1979). Recently, the study of Clarke (1979) dealt with local longshore variations in the wind stress and the resulting long trapped waves travelling along the northern coast of the Gulf of Guinea. Yoshida (1967) and Arthur (1965) have described enhanced upwelling near a cape. Their results suggest that the role played by the irregular geometry of the northern coast of the Gulf of Guinea should be examined. This is the object of the present paper. r

101

1. THE NUMERICAL MODEL 1.1. Model geometry In contrast with the model developed by Adamec and O'Brien (1978), our model deals with a non-rectilinear coastline. The numerical simulation concerns the oceanic res­ ponse of an x-y-t two-layer model on the 3-plane to an increase in the wind stress X and y increase eastwards and northwards, respectively. The bottom of the Ocean is assumed flat, and the depth of the upper layer is constant. Fig. 2 shows the geometry of the basin, where horizontal dimensions Lx and L are respectively 3000 and 5000 km .

1000 km

Fig. 2. The model geometry with the irregular coastline.

1.2. Model formulation The quasi-hydrostatic and Boussinesq approximations are made. The layer densities Pi and p2 are constant. The effects of atmospheric pressure, and thermohaline mixing are neglected. If there is no pressure gradient in the second layer (i.e. Vp2 = 0), the linea­ rized equations for a two-layer viscous flow reduce to :

5u (1) at PH0

gyu - g ^ (2) at 102 &♦«<&* g" °

The equations governing the mass transport are, on the other hand,

= ßyV - g'H + — + A V2U (4) 3t 3x p f - (5) f * s * § - » where A and A h are the horizontal viscosities (assumed constant), Ho the undisturbed depth of the upper layer, h the perturbation of the upper layer thick­ ness, H the total (disturbed) depth and

P 2 “ Pi g ' _ g ------P 2 the reduced gravity. Definitions of the other terms are obvious. This model repre­ sents the simplest formulation of the first baroclinie response. In non-dimensional form, the system of equations (1-3) can be rewritten (Bah, 1979;

Bah et al., 1979) :

9u 9h T 92u 92u — = yv - a! — + a2 — + a 3 — - + ai+ - . (7) 9t 9x p 3X2 9y

9v 9h t 92v 92v ^ = - yu - ^ + a2 - + a3 + a, ^ (8)

|h + ai |¡L + |v = 0 {9) at 9x 9y where ai = ; a2 = ß-^g'-374 hÔ 7/4 ; a , = A 4 B1 g'■ H.' 3/4 ; a, = Aß* (g ' H0 )' 3/4 X Ly /g'Ho ßLx

Lx and L y are the zonal and the meridional length scales respectively. Working with the system of equations (4-6) one gets from the equation of conti­ nuity

9h 9u , 9v 9u 9h , 9v 9h . im — + a] — + — + aih — + a lU — + h -5- + v — = 0 (10) 9t 9x 9y 9x 9x 9y 9y 103

Thus, working with equations (1-3) relative to the mean velocity results in ne­

glecting the last four terms of equation (10), which is equivalent to neglecting contributions at least of the same order of magnitude as the respective second terms of the right side of eqs (7) and (8). The values for , a 2 , a 3 and a^ for the case of a 50 m depth are respec­ tively 2.24 , 4.47 X 1CT 2.24 X 10 3 and 4.47 x 10"* (Bah, 1979).

1.3. Numerical scheme The numerical model uses the numerical scheme developed by Ronday (1976) u and

V are computed according to the following spatial grid.

I I I I I I I I 2 1+2 9-- -©- 0 - for I i i for I i i for I i I i 2 I i ' “ t

□ - - - AY I i 2 1 - 2 0 ----- — © - i ! I 2 J 2 J 2 J + 2 ■ AX

Fig. 3. Spatial grid used for the computations.

We have for the temporal grid, in the unidimensional case for example

u n + 1 = a u n + , b , h , n

n +1 n +1 n h = c u + d h

u , V and h are computed at the same moment, but in the computation of h , esti­ mated values of u and v are used. All the boundaries are walls, and the normal velocity is assumed equal to zero at the coast. All calculations are done with a constant grid resolution of 50 km in both x and y directions. The stability condition

At At < 1 Ax Ay

requires At to be < 18 248 s (about 5 h) . The chosen temporal step was At = 3 h 104

(1/8 day). Other constants are : H 0 = 50 m ; A = IO2 m2s -1 ; g' = 2 x IO-2 m s -1 ; 3 = 2 x io'11 nf 1s“ 1 .

Since we are interested in studying the probable effect of the irregular coastline geometry on the upwelling generation, evolution and intensification, we have chosen to study two major aspects : - the first one with prominent coastline features such as , Cape Three Points, Cape Formoso and ; - the second, for comparison, with a linear coastline for the west african coast. For both cases, two situations are investigated :

1.3.1. a standard linear situation with an increase of respectively 0.025 Nm and 0.0125 N m 2 in the westward wind stress over the western 1 500 km of the basin (fig. 4) and without any meridional wind;

0 1 2 3 4 5

Distance km x 10 3

0 - 1 5

- 20 -

Fig. 4. Spatial variation of the zonal wind stress.

1.3.2. a second situation, non linear, similar to the first but including advec- tive effects, local depth in the stress term, non-linearities in the continuity equa­ tion and an increase of 0.0125 N m -2 of the westward wind stress.

In each situation, integrations are performed at least over 90 days, starting from rest (u = v = 0 at t = 0), with a sudden increase of wind stress (fig. 5) remaining constant throughout the following period of integration. To allow an easy comparison of the results, we have used the same denomination fo boundaries as did Adamec and O'Brien (1978) : the eastern boundary extending 500 km north of the and 1500 km south is the south-eastern (S-eastern) boundary; the eastern boundary extending 500 km north of the Equator to 1500 km is the north­ eastern (N-eastern) boundary; the northern boundary is then the northern boundary of the Gulf of Guinea, extending approximately from Cape Palmas to Cape Formoso, i.e. r 105 ■i f

0 0 10 20 30 40 50 60 70 80 90 Days

Fig. 5. Temporal variation of the wind stress.

from 3 000 to 5 000 km east of the western boundary; the north-northern (N-northern) boundary is the northern boundary of the basin extending 3 000 km from the western boundary (fig. 2).

2. THE ANALYTICAL MODEL

For a better understanding and in order to interpret the numerical results, ana­ lytical expressions are considered. They are derived from linear theory and will be used as a guide.

Because of the peculiarity of the wind stress (which is firstly uniform over the entire period of integration, and secondly zonally variable), the solutions will in­ clude the longitudinally unbounded interior response, the excitation of equatorially trapped waves and the reflections of these waves at the boundaries. Moreover, with the irregular coastline, the existence of capes and bights should cause local intensification of upwelling along the northern boundary.

2.1. Equatorial waves

Kindle (1979) has reviewed some aspects of dynamics. It is useful to examine here the procedure he used to describe the nature of waves generated in a model such as ours. Consider the linear, inviscid, hydrostatic, non-divergent system of equations on the equatorial ß-plane :

at

3v di) at

gp where is the mean density gradient in the vertical direction. dz According to the formulation of Gili and Clarke (1974) by expanding in series of the vertical modes of the system, a resulting equation can be written in terms of the meridional velocity, i.e.

Vttt + e V v t - x2n(ßvn + v2vt) = - hi (12) where forcing terms have been added. Note that À is the speed, and is expressed as

An = (g'H)*

i(kx - (x)t) Now, if we assume a waveform dependance in the zonal direction i.e. e , then, equation (12) reduces to :

4 . 3k _ k a _ 3! | i \ v = (13) *n “ / whose solution if bounded as y ->• ± °° can be written

V = e ^ ^m(y) • m > 0 (14) where (y) is a Hermite function. So long as

[ (2m + l)Xn]5

the solution is oscillatory, but as soon as

[ (2m + l)An] J ,y) > ----

it becomes "monotonie" i.e. it decays exponentially after it has changed its nature at the point

[ (2m + 1) A n] y = ------

(Kindle, 1979). The corresponding relation of (13) is 107 where k = k(m,to) . This relation includes four types of waves : inertia-gravity waves with high frequencies, mixed Rossby-gravity waves with low frequencies, Rossby waves, Kelvin waves [set v E 0 and solve equations (1-3) ; for details, see Moore and Philander (1977) or Adamec and O'Brien (1978)]. Solving equation (15), we get

kl = - ¿ V S + 4 - - (is) 2 2 w V A n 4üJ A n

Special cases When m = 0 ,

, m p k i = -— - — and k2 = - X

However, the solution with k2 is not acceptable because of the exponential growth of U and P with y (Moore and Philander, 1977); with k = ki , the so­ lution is

i [(-y- - -~j)x - o j í] *■> V = e (y) and corresponds to a Yanai wave or mixed Rossby-gravity wave. For this wave, the group velocity is eastwards, but the phase velocity is either eastwards or westwards. When m > 1 , and so long as

[2m + 1 + 2 /m (m + 1) ] j waves are gravity waves ; as soon as

( (3À I * I to I < j - [ 2 m + 1 - 2 /m (m + 1 ) ] [ , they are planetary waves. For to2 > (2m+l)3An , Kindle (1979) has shown that inertia-gravity waves may exist, so that at the Equator, and for a given mode, the inertial oscillations period is m 2 7T [ (2m + 1) $A ] : where m > 1 . In our case, ^ is slightly more than 9 days. 108

Fig. 6a. Variation of the interface in the linear case 20 days after the wind's onset: dashed lines denote upwelling and full ones with values in meters (from O'Brien et al., 1978).

UJ

0 10 20 30 HO

Fig. 6b, Variation of the interface 40 days after the wind's onset (from O'Brien et al., 1978), 109

DRY •¿S r.

•'•k

d o

n XL

W'Jv .>92

3 l ¿

30 40

Fig. 6c. Upwelling in the Gulf of Guinea 60 days after the wind's onset (from O'Brien et al, 1978).

DRY

iù

d O

E XL

U) HO KM *1 0 2

‘Fig, 6d, Upwelling and downwelling pattern 80 days after the wind's onset (from O'Brien et al, 1978).

i 110

3. RESULTS 3.1. The standard linear case with rectilinear coastline First, to test the method, we consider the case with rectilinear coasts using an increase of 0.025 N m 2 in the westward wind stress over the western 1 500 km of the basin and no meridional wind. The results (fig. 7) are in good agreement with those of O'Brien et al. (1978) [fig. 6]; for instance on day 10, one can recognize the well defined elliptical shape of the upwelling cell, the symmetry about the equa­ tor and equatorial trapping, the maximum value of 13 m for the perturbation h and 30 cms"1 for the associated corresponding maximum u component. The eastward propagation of the perturbation along the Equator is also clearly ­ servable. Note that by day 50, the perturbation has reached the eastern boundary, and then begins to propagate polewards from the Equator along the eastern and the northern boundaries of the Gulf of Guinea. Upwelling is more and more important and its maxi­ mum intensity occurs along nearly all the northern coast (days 80 and 90).

15 10 5______

o ______'v, \ r n \ (5 0° ) 1 i i i i i i i i i i i a i S L r

Fig. 7a. Variation of the interface 10 days after the wind's onset. Ill

¡ p

Fig. 7b. Upwelling and downwelling pattern on day 20.

Fig. 7c. 30 days after the wind's onset, upwelling occurs in the western part of the Gulf of Guinea. 112

Fig. 7d. On day 40, the leading edge of the upwelling cell reaches the Sao Thome .

o >10

Fig. 7e. 50 days after the wind's onset, the upwelling cell has already reached the South-eastern boundary. 113

Fig. 7f. Occurrence of upwelling on day 60 along the northern coast of the Gulf of Guinea.

20

Fig. 7g. By day 70, upwelling is present in the entire Gulf of Guinea.

1 1X4

I IHO

■'''I/ U l

Fig. 7h. Poleward propagation of the upwelling along the north-eastern coast on day 80. The maximum of upwelling occurs along the most part of the northern boundary.

C£

Fig. 7i. Upwelling and downwelling pattern 90 days after the wind's onset. 115

3.2. Standard linear case with irregular coastline

Fig. 8a. Foreward propagation of the perturbation in the case of a non rectilinear coastline 40 days after the onset of the wind stress.

20 .

25

Fig. 8b. Upwelling in the Gulf of Guinea 50 days after the wind's onset. 116

Fig. 8c. North-westward propagation of the perturbation along the African coast, 60 days after the wind's onset.

»B 20

25

in

Fig. 8d. Upwelling is present in the entire Gulf of Guinea (day 70). Fig. 8e. On day 80, the maximum of upwelling occurs in the of .

25

Fig. 8f. The maximum of upwelling is located east of Cape Three Points by day 90, after the wind's onset. 118

Qualitatively, the results (Fig. 8) confirm those already obtained, and the gene­ ration and the evolution of the upwelling in the Gulf of Guinea can be explained as follows. As does the western boundary of the basin, so the eastern edge of the fetch zone of the wind stress (1500 km from the western boundary) excites eastward propagating Kelvin waves, eastward or westward propagating Yanai waves and westward propagating Rossby waves (e.g. Kindle, 1979). Let Ki be the Kelvin wave excited with the onset of the wind stress at the eastern edge of the wind fetch zone, and K2 the respective Kelvin wave at the western boundary of the basin. In the equatorial zone, upwelling should result from the eastward propagating Kelvin waves Ki and K2 (Yanai waves eventually) excited at the edges of the trade wind fetch zone; in the coastal zone (northern coast), it should be "due to the poleward propagating Kelvin wave and the westward propagating Rossby waves excited by the former (e.g. Hulburt and Thompson, 1976; Hulburt et al., 1976; Adamec and O'Brien, 1978). Indeed, in linear theory, the combination of Ap and H gives the phase velocity of the internal Kelvin wave

c Kal = H) 4 = ' g '0)4 = ^ H n) J

10

0 10 20 30 40 50 60 70 80 90 days

Fig. 9. Upwelling at an Equatorial point, 4025 km from the western boundary (standard case).

Fig. 9 shows the development of upwelling at an equatorial point situated 4025 kr from the western boundary. We can see that with such a phase speed c (c = 1 m s *) ^ wave Ki arrives after 29 days. The rate of increase in vertical displacement re­ mains relatively unchanged from day 40 until day 60, except for a slight modificatio: due to the eastward crossing of the wave K 2 on day 47. There is a dramatic change about day 66, however, with the arrival of wave Rj reflected at the south-eastern boundary. As for wave R2 reflected from wave K2 , it reaches the point under con

sidération about the day 84 . m u (D No wind stress ■pcu 20 e

40 50 60 70 90 100 days

co u Q) Ü 20 e No wind stress

10 .

40 50 60 70 80 90 100 days

Fig. 10. Upwelling in the vicinity of Cape Three Points; a) east of the cape, b) west of the cape.

20 No wind stress

10

0 0 40 50 60 70 80 90 100 days

20 No wind stress

10

0 0 40 50 60 70 80 90 100 days

Fig. 11. Upwelling in the vicinity of Cape Palmas; a) east of the cape, b) west of the cape.

Upwelling begins about day 60 with the arrival of the leading edge of the Rj , followed by intensification before reaching a maximum value after day 70. Fig. 10 and 11 show that the onset, intensification and maximum of upwelling west of Cape Three Points are delayed about 10 days relative to the region east of the cape. This delay is the same as that observed in the reversal of the between these two coastal areas, separated by about 300 km (Fig. 12), and it is due to wave R; 120

Fig. 12a. Velocity field 60 days after the onset of the wind stress. The reversal of the current occurs east of Cape Three Points. 121

Fig. 12b. Intensification of the eastward current east of Cape Three Points (day 70) . 122

X S W N N \ s s s \ \ \ \ A V \ \ W \

Fig. 12c. 80 days after the wind's onset, the eastward current is present along the entire Northern coast. 123

whose phase speed should be, from linear theory,

cR)= “ = 0.33 m s 1.

The speed of the westward propagation of this reversal is 300 km day"1 (0.35 m s -1), i.e. nearly c Ri . Indeed, 28 days are required for wave Ki to reach the south-eastern boundary and 36 days for wave Ri to arrive east of Cape Three Points, that is roughly 64 days after the wind stress forcing began. The divergence zone accompanying current reversal is due to the fact that eastward propagating Kelvin waves produce a flow to the west, while westward propagating waves produce a flow to the east. This phenomenon could explain the intensification of the Guinea Current frequently observed near Cape Three Points. Calculations from linear theory indicate the presence of wave Ri near Cape Palmas about day 71, in agreement with the numerical results shown in fig. 11 and table 1.

TABLE 1 Values for h in meters

Days 20 30 40 50 60 70 80 90 100 East 0 0 1 1 2 5 12 17 18 Cape Palmas West 0 2 2 3 2 3 7 12 15

East 0 0 0 n 6 1 9 21 70 1 7 Caoe Three Points West 0 0 1 1 2 7 15 19 18 East 0 0 1 8 19 21 19 14 12 Cape Formoso West 0 0 0 3 10 19 21 18 13

In the same way, wave R 2 is present in the about day 76 where tl reversal of the westward current, the intensification and the maximum of the up­ welling are clearly shown (Fig. 12c and 8e).

If we compare now results from the rectilinear coastline case (Fig. 7) with those from the non rectilinear case (Fig. 8 ), some important features are evident. About day 50, southwards from Cape Formoso along the south-eastern coast, the poleward pro­ pagation is more important when the coast is irregular. This corresponds to an exten­ sion of the upwelling zone and an intensification of the upward movement. The northern edge of the upwelling cell is moved southwards near cape Palmas. Later, the intensi­ fication goes forwards as far as the Gulf of Benin. On the other hand, in the vicini­ ty of Cape Three Points, the upwelling is weaker from day 60 until day 80 than in the rectilinear case when intensification of the upwelling begins with the maximum cente­ red east of this cape. Since upwelling is due to the north-westward propagation of the coastally trapped wave following the arrival of waves Kx and K2 at the south-eastern boundary (see § 3.2), the extension is observed first towards the pole, and then westwards if a zonal boundary is present. In the case of a rectilinear coast, the zonal boundary is 124

reached earlier, so that the westward propagation of the perturbation is initiated earlier than when the coast is irregular (in this case, the tendancy of the propa­ gation is northwards into the bights). This could explain the delay of upwelling in­ tensification east of Cape Three Points. In any case, upwelling is always stronger

east than west of the CAPES, as can be seen from table 1. To understand this fea­ ture, we now estimate the upward displacement rate of the pycnocline in the vicinity of Cape Three Points.

3.3. Estimation of W50 Consider the system of equations (1) and (2) where advective terms have been added; viscous terms are temporarily neglected.

3u 3u 3u 3h t x M _. — + u — + V — = $yv - g ' — + — (17) dt dx dy J dX PH

3v 3v 3v a , 3h xy M Q . — + U— + V — = - 3yu - g 1 — + — (18) 3t 3x 3y 3y pH

In addition, we have the continuity equation

|2i + + | ü = 0 (19) 3x 3y 9z

Doing — ^ (18) - (17) , and using equation (19), we get

d£ _ 3 ,Ty . 3 ,T* tn \ 3w I /o m -7- + 3v + — (— - — — = y+ç r * (20) dt 3x pH 3y pH 3z

3v 3u where ç = — - — 3x 9y

Introducing characteristic length-scales, we find that b ~ 2 . 10 11 s 2 ; Ç ~ IO'7 s" 1 ; 3y ~ io-5 s' 1 (at 5° N) .

Obviously, the term 3y is preponderant in (e) . Also (c ) - {d) ~ 10 13 s 2 and

â£= AL+uiL+ iL~ io" 11 s" dt 3t 3x 3y

3 w Therefore, if ßy — ~ ßv , then w ~ 10 11 m s 1 . Note that if we take viscous Sz3z terms into account, we get

-i- (A V2v) - — (A V2u) = A V2ç m 10 18 s 2 9x dy

where A is assumed constant. r

125

So the use of equation (20) requires only the terms and Sv in the left member of the equation, and

^ + ßv = gy (21) dt dz

3.3.1. East of Cape Three Points On day 80, the current is eastwards near Cape Three Points (fig. 12c). To estimate , we use the following equation (e.g. Arthur, 1965)

V 3V

ç = i - ta <22)

where V is the velocity of the current, R the radius of curvature of the stream- 3V line near the coast, and —— the velocity gradient normal to the streamline. on For the values of V = 0.03 m s ’1 , R = 15.5 IO3 m , we obtain from equations (21) and (22), W 50 = 0.28 10 5 m s 1 or 2.4 m/10 days. Numerical results (see table 1) give w east ~ 2 m/10 days.

3.3.2. West of Cape Three Points Similar calculations give w west ~ 1-5 m/10 days . Thus wwest < w east as expected from theory, indicating that in the presence of a cape, upwelling is more intense off that cape, downwards in the direction of the flow. Moreover, the value obtained by the analytical calculation is smaller than the corresponding numerical value. This result is understandable since Io) estimation of w west is done with the assumption that only the presence of the cape could influence the creation and the development of the observed upwelling; 2°) upwelling near the cape is related essentially to the westwards propagating Rossby waves Ri and R2 .

3.4. Non-linear case Including non-linear terms for advection and instantaneous depth in the standard case, numerical results are in good agreement with those expected from theory. Since h is negative during upwelling periods, the phase speed c [c = g'(H0 + h)5 ] is reduced so that the propagation of the Kelvin wave is slower (Figs. 13, 14, 15 and 16), The leading edge of the perturbation cell elongates, while its trailing edge flat­ tens because of faster phase propagation away from maximum upwelling values region. For the same reason, even if the poleward propagating Rossby waves and the resul­ ting energy transfer prevents a growth of the wave amplitude as proposed by many authors (Hurburt and Thompson, 1976; Hurburt, Kindle and O ’Brien, 1976; Adamec and O'Brien, 1978), the wave's effects are still amplified. Indeed,

_ X _ X Ip(H0 + h )I < IpHoI p(H0 + h) pH0 1

126

Fig. 13a. Upwelling with a reduced wind stress tx = - 0.0125 N m 2 in the standard linear case with rectilinear coasts on day 30 .

Fig. 13b. The upwelling cell reaches the south-eastern boundary, 50 days after the onset of the wind stress. 127

Fig. 13c. Upwelling is present in the entire Gulf of Guinea on day 70 .

Fig. 13d. Upwelling and downwelling pattern on day 90 128

Fig. 14a. Upwelling pattern in the non-linear case with rectilinear coastline (day 30).

Fig. 14b. On day 50 , the upwelling cell reaches the Sao Thome Island. 129

Fig. 14c. Upwelling in the Gulf of Guinea, 70 days after the onset of the wind stress.

Fig. 14d. The maximum of upwelling is extending almost along all the northern boundary (day 90). 130

Fig. 15a. Upwelling with a reduced wind stress tx = - 0.0125 N m 2 in the standard linear case with non-rectilinear coasts, 50 days after the onset of the wind.

Fig. 15b. Poleward propagation of the perturbation along the African coasts (day 70). 131

Fig. 15c. 80 days after the onset of the wind stress, the maximum of upwelling occurs in the Bight of Benin.

Fig. 15d. By day 90, the maximum of upwelling is confined east of Cape Three Points. Fig. 16a. Upwelling pattern in the non-linear case. 50 days after the onset of the wind stress, the upwelling cell is reaching the Sao Thome Island.

Fig. 16b. 70 days after the wind's onset, upwelling is still absent in the vicinity of Cape Three Points. 133

Fig. 16c. Westward propagation of the perturbation along the northern coast of the Gulf of Guinea (day 80).

o

Fig. 16d. By day 90, the maximum of upwelling is located east of Cape Three Points, in the Gulf of Benin. 134

This amplification can be about 25 % during one month (from day 20 to day 50), as demonstrated in table 2.

TABLE 2 Maximum upwelling values at the Equator with a westward wind stress

Days 10 20 30 40 50 60 70 linear case 6 10 9 9 10 10 10 h max non-linear case 7 13 13 12 11 10 11

CONCLUSIONS Our investigations suggest that :

1. The sudden onset of the wind stress in the western Atlantic Ocean can excite wind induced equatorially trapped Kelvin waves which generate upwelling in the Equatorial region on their way eastwards.

2. The poleward propagating trapped Kelvin wave and the westward propagating reflec­ ted Rossby waves induce upwelling along the northern coast of the Gulf of Guinea. Previously, some investigators concluded from measurements of temperature and ve­ locity at the Equator, that there was no evidence of the propagation of a seasonal upwelling along the Equator from the western Atlantic (e.g. Clarke, 1979; Weisberg et al, 1979).

The monthly maps of Surface Temperature (SST) anomalies*" (Fig. 17) clearly show the appearance and the intensification of the negative equatorial anomalies from West to East (look at line - 1°C) with a speed of 980 km per month, i.e. cK = 0.38 m s 1 . Moreover the meandering of the equatorial negative anomalies front suggest an half-sinusoid so that the eastward wave number component k computed = 3^5 km~1 * This should be compared with the observed value at the coast k observed = ^q- km”1 (Clarke, 1979). Looking at line - 1 °C , in the coastal region for August and September, one can see the westward displacement with a speed of 332.5 km month-1 (0.13 m s -1), 1 that i'S — c^ . This result is in very good agreement with the linear theory.

3. The coastal upwelling is more intense east than west of Cape Three Points and Cape Palmas, and thus the presence of a non-rectilinear coastline influences the location and the intensification of coastal upwelling. About 90 days after the wind's onset in the western Atlantic Ocean, equatorial and coastal are present in the Gulf of Guinea. The maximum is located east of Cape Three Points, in good agreement with observations (e.g. Bakun, 1978).

*" Computed for the period, 1946-1972. 135

2 . 5 C?

O

'1>5_

Fig. 17a. SST anomalies in the Gulf of Guinea in May. Only warm waters are present (continuous lines).

o 0

Pig. 17b. The appearance in June of equatorial oceanic cold waters, i.e. equatorial upwelling (dashed lines) . 136

/ -o*"' í / .0.3 /M

Fig. 17c. In July, the equatorial cold waters have moved northwards.

. 0 * 5 -

-1.5

Fig. 17d. Occurrence of coastal cold waters in the vicinity of Cape Three Points and Cape Palmas in August. 137

-9,5-

-Ó - 5 .2.5

Fig. 17e. In September, the coldest coastal waters have moved westwards.

,0.5.

Fig. 17f. SST anomalies pattern in the Gulf of Guinea in October. 138

-0.5 Q x !

Fig. 17g. Southward displacement of oceanic cold waters and disparition of coastal upwelling near Cape Three Points and Cape Palmas (November).

-if1.5

,0-5

Fig. 17h. Reduction of oceanic upwelling in December. 139

4. The upwelling persists for approximately two months.

5. The coastal upwelling is not due to local advection, nor to the monsoonal. winds

(e.g. Adamec and O'Brien, 1978; Bah, 1979).

6.’ The amplification due to non-linearities can be about 25 % during one month.

ACKNOWLEDGEMENTS

The author gratefully acknowledges the help of Prof. J.J. O'Brien of the Florida State University, who suggested the problem, and of Prof. J.C.J. Nihoul who encouraged its realization and presentation at the "12^ International Liège Colloquium on Ocean Hydrodynamics". Discussions with Dr. Ronday have been of immense value. Computer assistance given by P. Closset, J. Ozer and Y. Runfola is highly appreciated. The

.supports of the "Centre Belge d'Océanographie" and the "Ministère de la Politique Scientifique de Belgique" to acquire the SST data are gratefully acknowledged. I am indebted to Prof. J.C.J. Nihoul, Prof. O'Brien, Prof. Parker and Dr. Ronday for their advises in the redaction of the manuscript.

REFERENCES Adamec, D. and O'Brien, J.J., 1978. The seasonal upwelling in the Gulf of Guinea due to remote forcing. J. Phys. Oceanogr., 8:1050-1060. Arthur, R.S., 1965. On the calculation of vertical motion in eastern boundary currents from determinations of horizontal motion. J. Geophys. Res., 70:2799-2803. Bah, A., 1979. Interactions air-mer et problèmes de la sécheresse en zone sahélienne. Rapport, Fondation Roi Baudoin, 90 pp. Bah, A., Loffet, A. and Schayes, G., 1979. Air-Sea Interactions. ICES Committee CM 1979/c:48. Bakun, A., 1978. Guinea Current upwelling. Nature, 271:147-150. Clarke, A.J., 1979. On the generation of the Seasonal Coastal upwelling in the Gulf of Guinea. J. Geophys. Res., 84:3743-3751. Gili, A.E. and Clarke, A.E., 1974. Wind-induced upwelling, coastal currents and sea- level changes. Deep-Sea Res., 21:325-345. Houghton, R.W., 1976. Circulation and hydrographic structure over the Continen­ tal shelf during the 1974 upwelling. J. Phys. Oceanogr., 6:910-924. Hulburt, H.E., Kindle, J.C. and O'Brien, J.J., 1976. A numerical simulation of the onset of El Nino. J. Phys. Oceanogr., 6:621-631. Hulburt, H.E. and Thompson, J.D., 1976. A numerical model of the Somali Current. J. Phys. Oceanogr., 6:646-664. Kindle, J.C., 1979. Equatorial Variability-Seasonal and El Nino time scales. Mesoscale Air-Sea Interaction Group. Technical Report, 134 pp. Moore, D.W., 1968. Planetary-gravity waves in an equatorial Ocean. Ph. D. Thesis, Harvard University. Moore, D.W. and Philander, S.G.H., 1977. Modelling of the tropical oceanic circula­ tion. In: E.D. Goldberg, I.N, Me Cave, J.J. O'Brien and J.E. Steele (Editors), The Sea, VI. John Wiley and Sons, New York, 319-362. Moore, D.W., Hisard, P., Me Creary, J . , Merle, J . , O'Brien, J.J . , Picaut, J. , Verstraete, J.M. and Wunsch, C., 1978. Equatorial adjustment in the Eastern Atlantic. Geophys. Res. Let., 5:637-640. O'Brien, J.J., Adamec, D. and Moore, D.W., 1978. A simple model of upwelling in the Gulf of Guinea. Geophys, Res. Let., 5:641-644. Philander, S.G.H., 1979. Upwelling in the Gulf of Guinea. J. Mar. Res., 37:23-33. 140

Ronday, F.C., 1976. Modèles hydrodynamiques. In: J.C.J. Nihoul and F.C. Ronday (Editors), Projet Mer, 3:270 pp. Weisberg, R.H., Horigan, A. and Colin, C., 1979. Equatorially trapped Rossby-gravity wave propagation in the Gulf of Guinea. J. Mar. Res., 37:67-86. Yoshida, K., 1967. Circulation in the Eastern Tropical with special references to upwelling and undercurrents. Japan J. Geophys., 4:1-75.

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