On the dynamical structure of the midshelf water column off northwest Africa

ContinentalShelfResearch,Vol. 5, No. 6, pp. 629 to 644. 1986. Printed in Great Britain.

0278-4343/86$3.00 + 0.00 ~) 1986PergamonPress Ltd.

O n the d y n a m i c a l structure o f the m i d s h e l f w a t e r c o l u m n o f f n o r t h w e s t Africa ANTOINE BADAN-DANGON,* KENNETH H . BRINK~" a n d ROBERT L.

SMITH:~

(Received 11 February 1985; accepted 29 March 1985) Abstract--KuNDu (1977, Bottom turbulence, pp. 187-207) showed that the upwelling system off northwest Africa is dominated by turbulent friction and suggested that over such broad and shallow continental shelves, the surface and bottom frictional boundary layers overlap in the water column. Different estimates for the thickness of the boundary layers have been proposed more recently, which take into account, amongst other things, the effects of stratification. The application of these various estimates and the direct computation of the transports within the resulting layers provide a qualitatively consistent picture of the time-dependent structure of the water column on the northwest African continental shelf, with the observed cross-shelf transports in reasonable agreement with the expected Ekman transports. The only exceptions are two instances when the passage of upwelling fronts by the mooring appear to introduce an appreciable difference between the observed and the expected transports. Our results confirm those of KUNDU(1977), hut only for times when the wind is strongly upwelling favourable. For periods of weak winds, our calculations suggest that a non-turbulent interior region develops. Thus, the structure of the water column is dynamically non-stationary, fluctuating between non-turbulent and frictionally don:inated regimes, as a function of the intensity of the wind. This implies that the study of currents thr~:~,h a stationary time-series approach at individual depths may not be applicable in these regions.

1.

INTRODUCTION

CERTAINcoastal regions present consistently favourable conditions for the upweiling of cool water. Often, the upwelled water is nutrient-rich and promotes areas of high productivity and abundant fisheries, thus generating considerable interest in this phenomenon. Traditional models have assumed the process of upwelling to be two-dimensional, in a direction normal to the coast. But the intense research effort developed during the 1970s on upweUing systems has provided abundant evidence of the three dimensionality of upwelling which, we now know, is instead closely associated with a more complex and physically interesting coastal circulation system (ALLEN,1980; WINANT, 1980). It is the purpose of this communication to present some simple estimates of the timedependent dynamic structure of the midshelf water column off northwest Africa, where upwelling favourable winds predominate during most of the year (WOOSTERet al., 1976). This region is particularly interesting from a physical point of view because its broad and shallow shelf makes turbulent bottom friction especially relevant dynamically (KuNDU, 1977).

* C1CESE, Apdo. Postal 2732, Ensenada, B.C., Mexico. t Woods Hole Oceanographic Institution, Woods Hole, MA 02543, U.S.A. ~t College of Oceanography, Oregon State University, Corvallis, OR 97331, U.S.A. 629

630

A. BADAN-DANGONet al.

2.

THE EXPERIMENT

This paper is based on some of the current meter measurements made during the Coastal Upwelling Ecosystems Analysis JOINT I experiment, on a line at 21°40'N off the coast of northwest Africa during February to April 1974. We will here use exclusively those moorings that were deployed at midshelf (Fig. 1) because that was the only location where near-surface measurements were made. The data used in our calculations were obtained with three vector averaging current meters (VACM's) in a surface array, LISA, at depths of 1, 10 and 12 m (HALPERN, 1977), and three Aanderaa recording current meters deployed in a subsurface array, URBINIA, at depths of 25, 45 and 66 m. All instruments were equipped with temperature sensors (PILLSBURYet al., 1975). The total water depth was nominally 73 m and the two moorings were within 2 km of each other. Standard shipboard hydrographic measurements made during the experiment are reported by BARTONet al. (1975). Wind measurements were obtained with sensors mounted on the surface buoy at mooring LISA (HALPERN, 1977). All the time series used here, representing data originally taken at 10 min intervals, were run twice through Cosine-Lanczos filters. The first run was made through a filter with a half power point at 12 cpd (2 h) and subsampled every hour. These time series were then refiltered with a half power point at 0.6 cpd (40 h) to eliminate inertial and higher frequency oscillations (MooERS et al., 1968), and subsampled every 6 h. We shall refer to these as the hourly and six hourly series, respectively, and we shall also occasionally refer to the latter as the low passed series. The region where the JOINT I experiment took place is characterized by a broad, shallow continental shelf, with a sharp break that leads onto a steep continental slope (Fig. 1). The basic flow field, described by MITTELSTAEDTet al. (1975), consists of an equatorward coastal jet over the shelf, which may extend somewhat beyond the break if the wind is strong. Farther offshore, but still inshore of the Canary Current, the surface flow is

22"00'N

18"00'

Fig. 1.

30'

17°00 ' W

Location of the midshelf moorings during JOINT-I.

631

Water column at midshelf

generally directed poleward against the wind, due to the large scale oceanographic conditions of the region (MITTELSTAEDT, 1983). Beneath, closely hugging the continental slope between 200 to 300 m, is a well defined undercurrent that flows poleward at typical speeds of 10 cm s-1. Fluctuations in the velocity field over the shelf and slope are well correlated with the wind, which is dominated by events whose duration is of a week or more. The flow over the shelf responds within a day to these wind fluctuations ( B A D A N DANGON,1982). During a typical upwelling event, the cool water initially reaches the surface close to shore but, as the high wind speed persists, the location of the coldest water migrates offshore towards the shelf break (BARTONe t al., 1977). A comparison study of the northwest Africa and Oregon upwelling systems (HUYER,1976), indicates that these have similar basic kinematical configurations. Major differences between the two are due to the weaker stratification and the more defined, shallower, continental shelf off northwest Africa, whereby the undercurrent is generally confined to the slope region. As a result, the near-bottom, cross-shelf flow over the shelf is almost always directed onshore in this region and provides a frictionally driven mechanism to bring the cool upwelled water to shore. This is consistent with the results of Ktmou (1977), who showed that it is the importance of turbulent friction that mostly distinguishes these two regions from a dynamical point of view. The cross-shelf structure of flow was analyzed by HALPERNet al. (1977) and by SMITH (1981), who showed that a two-dimensional mass balance in the local geographical coordinates does not generally exist in the region. Later, in a study of the mean heat and momentum budgets off northwest Africa, RICHMANand BADAN-DANGON(1982) showed that a 6° rotation, counterclockwise from the local geographical coordinate system, was sufficient to force a local mean two-dimensional mass balance, but did not affect the three dimensionality of the corresponding mean heat and momentum balances. The same is true for the depth-integrated time-dependent heat and momentum balances (BADAN-DANGON, 1981; ALLEN and SMITH, 1981). For completeness, we have made all the calculations presented in this paper both in the local geographical system of coordinates and in the mass balancing system. Results were found to be qualitatively equivalent in both systems and we give preference to the local geographical reference system throughout, in which we take (u,v) to be the horizontal velocity components in the (x,y), or cross-shelf and alongshore directions, respectively, positive to the east and to the north. 3.

TIME DEPENDENCE

OF THE THERMAL

AND VELOCITY

STRUCTURE

The response of the water column on an event time scale is evident in Fig. 2, which shows the time evolution of the thermal and velocity fields as a function of depth, measured at the midshelf moorings. During the strong upwelling favourable wind events as, for example, from 12 to 16 March, 18 to 23 March, and 29 March to 6 April, the surface layer is well mixed and its thickness increases, but stratification is maintained at the top of the bottom layer by the cool water that is brought onto the shelf. These events, where cool water predominates over the shelf, are associated with a clearly developed two-layer structure in the cross-shelf flow, with strong onshore flow of approximately 0.15 to 0.20 m s-t at about 10 m off the bottom, and a somewhat weaker offshore flow near the surface. Concurrently, the southward alongshore flow intensifies to about 0.5 m s-1, showing at times a separation between a near-surface velocity maximum and a second maximum somewhat deeper in the water column. Although it cannot be ruled out that this configuration of the

632

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Fig. 2. The alongshore component o f the wind and time-depth variations o f temperatures and velocity c o m p o n e n t s at midshelf during J O I N T - I . Shaded areas represent, respectively, portions of the water c o l u m n that are colder than 16°C, where offshore flow occurs, and of s o u t h w a r d flow > 20 cm s-~.

flow reflects possible effects from the different instruments and mooring techniques used in the upper and lower portions of the water column, it is in agreement with the concept that a coastal jet is not directly driven by the wind, but results instead from the coupling between the cross-shelf and alongshore dynamical balances through a developing geostrophic balance ( A L L E N , 1980). Between the strong northerly events the wind weakened considerably but reversed to southerlies only twice for very short periods, once at the beginning of the experiment and once again during 7 to 10 April. This simplifies the description of the dynamics of this region, for some of the complexities that result from the irreversibility of upwelling (DE SZOEr.Eand RICHMAN,1981) can be ignored. During weak winds, for example, from 24 to 29 March and from 7 to 10 April, the surface layer is occupied by water up to 2 or 3° warmer and the water column tends to a more uniform stratification, due to the strong solar heating at the surface and the absence of an onshore flow of cool water near the bottom. The

Water column at midsheif

633

velocity field is substantially modified, lacking the clear organization manifested during periods of strong winds. With these measurements it is now possible to examine the evolution of the water column structure, by following some simple models that have been proposed for the surface and bottom boundary layers. It will then be straightforward to estimate the boundary layer transports and make some conclusions about the processes in the boundary layers. 4.

D E F I N I T I O N OF B O U N D A R Y L A Y E R T H I C K N E S S E S

In an earlier study, KUNDU (1977) used observations from the JOINT I midshelf moorings to estimate the thickness of the bottom boundary layer (BBL) during selected periods of strong winds. He concluded that turbulent frictional boundary layers occupied the entire water column at those times. A difficulty with his study, however, is that he used the traditional estimate of the bottom boundary layer thickness (WIMBUSH and MUNK, 1960), hmb --

0.4u,

f

,

(4.1)

which neglects the stabilizing effect of stratification. Here fis the Coriolis parameter and u, is the friction velocity defined in terms of the stress at the boundary x0 and of the water density P0 as __

u,

k~o,] .

(4.2)

More recently, WEATnERLYand MARTIN(1978) have proposed a BBL thickness estimate that includes the effect of stratification: 1.3u, hb

f[1 + (N~/f2)l ~-"

0.3)

We will take advantage of the improved formula to obtain more realistic estimates of the BBL thickness throughout the duration of the experiment. In it, N 2 is the ambient BruntV~iis/il/i frequency squared, and u, can be estimated when z0, in turn, is defined by the quadratic drag law (LUMLEYand PANOFSKY,1964): "1[0 = DO CDlUlU"

(4.4)

The drag coefficient C o can be defined by knowing that within a distance

2u2, 5log- f G '

(4.5)

the velocity is given by the well known logarithmic law: U.

Z

u--~ln~. Ko Zo

(4.6)

634

A. BADAN'DANOON et al.

In these formulae, G is the midwater 'geostrophic' velocity (measured at 28 m above the bottom in our case), Ko is von K~irm~in'sconstant, Z0 is a roughness scale height and z is the height of the velocity sensor above the bottom. From these we get

[

CD ---- Ko2 In

.

(4.7)

Since Z0 is not known, we must instead make a reasonable guess at Co. One approach is to assume the r.m.s, bottom roughness to be d ~ 1 cm, from which Z0 = d/30 (WEATHERLY, 1972). This yields Co = 1.6 x 10-'3. Varying Zo within a factor of 10 causes no more than 70% change in Cn, corroborating the well known robustness of its numerical value. On the other hand, it should be noted that this method ignores the effect of gravity waves (GRA~rr and MADSEN, 1979), and probably underestimates somewhat the bottom stress. One means of verifying this estimate is to do a calculation similar to that of WlNA~rr and BEARDSLEY(1979), where Co is chosen essentially as a regression coefficient between xo and the alongshore componentpolu(v, which assumes a shallow water limit. This approach yields values of Co that range from 1.3 to 2.3 x 10-3, depending on whether the calculation was made with hourly or low pass filtered data, and on which of the midshelf velocity sensors was used. This is in reasonable agreement with our earlier calculation and we shall therefore retain Co -- 1.6 x 10.3 as an estimate. For these considerations to be valid, the deepest sensor at a height z above the bottom should find itself most of the time within the bottom logarithmic layer, given by (4.5). To verify this we have computed an hourly time series of 8~ogwhich is shown in Fig. 3 after being low pass filtered. It shows the bottom logarithmic layer to be quite well developed, particularly when the wind is strong, thus lending further support to our estimate of Co. The current meter at 66 m depth is usually within the logarithmic layer, or right on its edge (Table 1). Finally it should be noted that the effect of the bottom slope, while often important, will be ignored here, since it has not been parameterized in general. This omission could be disastrous in a region where the cross-shelf flow close to the bottom is predominantly

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Fig. 3. Low pass filtered time series of the thickness of the various layers in the water column, as defined in the text. Units are in meters. Also shown are the time series of alongshore surface wind and bottom stresses in Pascals.

Water column at midshelf

635

Table 1. Basic statistics o f the thickness o f the principal layers in the water column. ~ = o(T/2T0) is the r.m.s. error in the estimation o f the mean (KuNDU and ALLEN, 1976). Units are meters

Layer

Mean

e

S.D.

~im~ h,,~ h, hr~b hb 61o~

15.7 30.9 30.8 58.0 17.5 8.8

2.6 6.0 2.6 5.1 1.5 0.8

7.8 21.1 9.5 17.5 5.3 2.8

offshore, for then the BBL destabilizes rapidly (WEATHERLYand VAN LEER,1977). In the present case, however, the BBL is generally associated with an onshore flow of cool water (HALPERNet al., 1977), and we do not expect this to introduce an appreciable qualitative error. Pursuing the estimation of (4.3), we calculated the buoyancy frequency squared, N 2, as a function of time using the temperature measurements obtained with the current meter records, a plausible computation because an excellent correlation has been found between temperature and salinity throughout the water column in this region (BADAN-DANGON, 1981). The instantaneous values of N 2 ranged typically from I x 10-4 S-2 t o I x 10-6 s-2, depending on the vertical separation of the sensors used in the calculation and on the degree of thermal stratification of the water column. As the value N 2 that should be used in (4.3) is that immediately above the boundary layer (CALDWELL, 1983), we made several runs in computing the time series of hb, using different depth levels to calculate N 2 each time. The results were qualitatively similar for all of them, although the stratification does play an important role in reducing the variance of the boundary layer thickness. The scheme that was finally retained was that of computing N 2 from the sensors at 45 and 66 m depth when hb is closer to the bottom than the 45 m sensor, and from the sensors at 25 and 45 m depth when h b includes the 45 m sensor. In the very few instances when a temperature inversion was encountered and N2obecame smaller than 1 x 10-6, stratification was considered to play a negligible role and h b made to coincide with the WIMBUSHand MuNK (1960) estimate of the bottom boundary layer hmb (4.1). The resulting hourly time series was then low pass filtered and decimated at six hourly intervals (Fig. 3). The inclusion of stratification reduces the estimated BBL thickness by more than a factor of three throughout (Table 1). We now focus our attention on the near-surface processes. Whereas there are several available means to estimate the depth of the surface boundary layer (BRINK, 1983), all ultimately require that the surface mixed layer and the surface Ekman layer be considered congruent, which is consistent with, for example, the slab model of NIILER (1977). AS a first case we can use the Monin-Obukhov length as an estimate for the quasi-steady limit of the surface boundary layer depth (DE SZOEKEand RICHMAN, 1981): pomou3, hms -

~(agQo/pCp)

"

(4.8)

Here the parameterization results from an estimate of a potential energy evolution equation that balances the effects of the rate of work of the wind on the ocean, u 3 (KRAUS

636

A. BADAN-DANGONel al.

and TURNER, 1967), with that of the surface heat input Qo. In it, we have taken the constant mo -- 0.5, as estimated empirically by DAVISet al. (1981a), and the solar radiation input was also taken as a constant Qo = 150 W m -2, after the results of RICHMANand BADANDANGON(1982). As a means for comparison we can use the estimate proposed by POLLARDet al. (1973), which is based on considerations of the shear generated turbulence. This equation is

hs

1.7u, (fNo)~ ,

(4.9)

which is consistent in form with the estimate of the BBL (4.3). Here, the friction velocity is given by (4.4) in terms of the surface wind stress and of the water density. The estimation of the buoyancy frequency N 2 in (4.9) was made from vertical temperature differences in a manner analogous to that of (4.3) and, after several attempts, we have retained the hourly estimates made with N 2 values from the 25 and 45 m depth temperature records when hs is shallower than 45 m, and from 45 and 66 m depth when it exceeds 45 m depth. In the exceptional cases where temperature inversions were encountered and N02 became imaginary, hs was made equal to h,,,s, given by (4.1). The depth given by (4.9) should be attained one half of an inertial period after the imposition of a steady impulse of wind, or 16.3 h for the present case. Finally, a third, more direct alternative method is to use the relatively dense nearsurface temperature sampling to define the surface mixed layer depth, 8,,~, as the level at which the temperature is at least 0. I°C less than at 1 m depth, the level of the sensor closest to the surface. The temperature difference criterion used here, although arbitrary, agrees with that used by DAVlSet al. (1981b) and was preferred over others because it maximizes the variance of the surface mixed layer's thickness, while still reducing its depth to zero when the wind was calm. In the estimation of 8,,,x by this method, the irregular vertical sampling of temperature biases the values of the surface mixed layer thickness towards those of the sampling levels. To correct for this effect we have fitted a cubic spline to the instantaneous hourly vertical temperature profiles and sampled these at 1 m increments. A time series of the hourly surface mixed layer depth was then computed from this data. The low pass filtered estimates of the various layer depths and of the surface and bottom stresses are shown in Fig. 3, where the high correlation amongst layers is evident. In this figure, and in the transport calculations of the following section, the series for hs, hms, and hb have been lagged by 12 h to account for the spin up times of the boundary layers, which are discussed below. The WIMBUSHand MUNK (1960) estimate of the BBL, h,,,b, is not shown because it is often much larger than the local water depth (Table 1). These series show a clear relation between both the surface and bottom boundary layer variations and the fluctuations of the local wind stress. The surface boundary layer depth increases in response to an intensification of the wind stress with about a 12 h lag, whereas the bottom boundary layer depth, which is dependent upon the local alongshore velocity, lags the wind by about a day. This is, of course, consistent with the observation that the subsurface alongshore velocity component lags the local wind by about 12 h (BADANDANGON, 1981). There is a tendency for both frictional boundary layers to expand and occupy jointly most of the water column during the strong wind events. The general behaviour of the surface boundary layers is reflected by the surface mixed layer computed from temperature differences, 8rex. The Monin-Obukhov criterion, hm~,

637

Water column at midshelf

agrees well with the mixed layer depth during times of weak winds, but suggests a surface boundary layer thickness that is more than twice the surface mixed layer depth when the wind is strong. As a result, both its mean and its standard deviation are larger than those of ~,,,x (Table 1). On the other hand, the POLLARDet al. (1973) estimate, hs, mirrors the behaviour of fi,,,xrather well, whence their standard deviations are very similar, but with an additive constant close to 10 m throughout. This provides the impression that hms is more satisfactory than hs in weak wind conditions but that hs is closer to reality when the wind is strong. One must conclude that the Monin-Obukhov estimate becomes ineffective when stratification close to the bottom intensifies because of the intrusion of cool water due to upwelling. It would be probably more exact in the absence of lateral advection, although the results of the MILE experiment also suggested the h,,,s surface boundary layer estimates were too large by about a factor of t w o (NI1LER, personal communication). It appears, then, that neither estimate is entirely satisfactory by itself in this region, and that a better estimate for application in coastal waters should include considerations of both principles implicit in the formulae (4.8) and (4.9) above. The linear correlations amongst the various layer thicknesses and the surface and bottom stresses are given in Table 2, generally showing good correlations between the different estimates. The development of the surface layers tends to lead that of the bottom layers by 12 to 24 h, as might be expected. In particular, we find that the two estimates of the surface boundary layer (4.8) and (4.9) are well correlated with the surface mixed layer, with the latter lagging the former two by about 12 h. This supports the notion that the

Table 2. Lagged linear correlations amongst the time evolution of the different layers in the water column. Shown beneath each correlation value is its statistical significance estimated as in SCmEt,4AMMANO(1979), with an equivalence to significance levels such that 1.7 = 90%, 2,0 = 95%, 2.6 = 99%, 3.0 = 99.9%. The right upper half of the matrix gives the correlations at zero lag; the left lower half shows the maximum correlations with the lag, in days, shown in parentheses. A positive lag indicates the column leads the row

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085 259

060 196

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049

060

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-066

0.95 ~

0.89 ~

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-0.87

0.89 2.87

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638

A. BADAN-DANGONet al.

changes in the surface Ekman layer should lag changes in the wind by about half of a pendulum day, as suggested by POLLARDet al. (1973). To be consistent, the bottom EKMAN layer depth (4.3) has been lagged by 12 h as well. WEArrmRLVand MARTIN(1978) did not specify any spin up time for the boundary layers, but the 12 h appear to be a reasonable lag. Altogether, the conclusion of KUNDU (1977) that the water column is dominated by turbulent frictional dynamics when the wind is strong, is verified in Fig. 3, if hs is taken to be the true surface boundary layer thickness. If 8,,~ were the true thickness, there is a tendency for Kundu's conclusion to hold, but never entirely. These calculations show, on the other hand, that when the wind weakens, an interior layer develops, which is presumably dominated by inviscid dynamics. This agrees with results that show this to be the case in the m e a n (RICHMAN and BADAN-DANGON, 1982) and in the fluctuating component of the dynamical balances (BADAN-DANGON,1981; ALLENand SMITH, 1981). 5.

THE C R O S S - S H E L F T R A N S P O R T S

The depths of the surface and bottom boundary layers can now serve as time-dependent bounds of integration for computing the cross-shelf component of Ekman transports. We define the transports for the surface layer as

Ms(t)= f~

(5.1)

u(t) dz, D(t)

where D(t) is the thickness of the surface Ekman layer, defined alternatively by h,,,s (4.8), by hs (4.9), or taken to be equal to the mixed layer depth ~i,,~. The transport in the interior is -D(t)

Mi(t)=J_n+hb(t)U(t) dz,

(5.2)

and the transport in the bottom layer is ;-H+hb(t)

Mb(t) = ~

u(t) dz,

(5.3)

3 -H

Table 3. Basic statistics o f the cross-shelf transports, integrated through the different layers shown in Fig. 3, and o f those expected from Ekman dynamics. The values are shown both in Iocal geographical coordinates and in the rotated system o f reference that forces a two-dimensional mass balance in the mean. Units are m 2 s-~ Geographical

Ms(fi,,x) Ms(h,,~) Ms(hs) Mi

Mb x~9 x~'~

Rotated

Mean

c

S.D.

Mean

e

S.D.

-0.82 -0.82 -0.90 0.34 1.56 -1.89 1.04

0.18 0.18 0.30 0.23 0.33 0.33 0.28

0.79 0.83 1.30 1.06 1.03 1.12 0.87

-1.24 -1.24 -1.70 0.04 1.19 -1.78 1.09

0.25 0.25 0.39 0.21 0.25 0.28 0.28

0.99 1.04 1.55 1.00 0.79 0.99 0.89

639

Water column at midshelf

where hb is given by (4.3), u(t) is the cross-shelf velocity component and z is positive upwards. The values of the transports Ms, M;, and Mbw e r e computed from the low passed series of current meter data and bounds of integration, by means of a simple trapezoidal rule of integration; these calculations were made in both the local geographical and mass balancing systems of coordinates for comparison. There is a reasonable agreement between the statistics of the calculated transports and those expected from Ekman theory (Table 3). In general, the calculated transports show an excess directed onshore with respect to the expected Ekman transports, suggesting the possibility of a non-Ekman flow component superposed on the transports associated with the Ekman layers. The visual agreement between the computed and expected values is good, especially for the bottom boundary layer (Fig. 4). When the transports are recomputed in the system of coordinates determined by a mean mass balance, the agreement is improved both in the statistics (Table 3) and visually (Fig. 5). The lagged linear correlations amongst the various transports are generally significant, with the exception of those involving the transport in the interior (Table 4). The rotation into the mass balancing system does not modify the correlations substantially, since it mainly affects the measured transports in the mean (Table 5). A regression model between the fluctuations of the transports in the boundary layers and the corresponding stresses yields approximately Ms b -----+0.6 X~')b "

(5.4)

Oof'

for both the surface (+) and the bottom (-) boundary layers. The presence of substantial boundary layer transports, of course, is consistent with the pronounced Ekman veering effects documented in the region (KUr~DU, 1977; BADAN-DANGON, 1981).

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IO

20 APR

Fig. 4. Low pass time series of volume transports within the various layers in the water column. Also shown are the surface and bottom transports predicted by simple Ekman theory. Reference system is of local geographical coordinates.

A. BADAN-DANGON et al.

640

T(y)

2

~o

fudz _A~'

¢.oz A

~"

A

I~z

%-

iii]llllllllllllllllll]lllllllllll]llllllll]lllllllll

E

5F

T(yl

4b

~.b

[111 IJ -" h+hb

.:':

"'\

~

0 I ~ .......... ,....1

............ ..:

'~.;~'"'I

"...""~...-;~

.................

-I I

I0

20

I

I0

MAR

Fig. 5.

20

APR

Same as Fig. 4, but in the mass balancing system of reference, rotated 6° clockwise from local geographical coordinates.

Table 4. Lagged linear correlations amongst the time evolution of the various transports computed in the local geographical frame of reference. The format is identical to that of Table 2 M~(8,,.,.)

M~(h,,,s)

M~(h,)

Mi

Mb

~;! )

~"__._~

of 0.95 4.0----6

M,(8,,,) Ms(h,,,.)

0.95 ~(o)

M,(h~.)

0.92 3(o1

~(o)

Mi

0.39

0.37

0.92 ~

0.39 1.8--'-'0

-0.56 -2.04

0.71 2.70

0.70 2.53

0.90 3.87

0.36 1.68

-0.54 -2.04

0.53 2.04

0.53 1.96

0.53

-0.39 -1.41

0.66 2.5----0

0.60 2.13

-0.17 -0.70

0.38 1.64

0.38 1.49

-0.65 -1.97

-0.85 -2.45

0.56/_

25o~-b

-0.49 "c~!~

0.71

~-~)

o~(~)

o.o1(_~)

-

,~,,

W-

~

0.66, 1~

k2]

0.39t 1~

1.49

-0.78/" 3) -2~.3 ~,•- - 0 . 8 5 / ~ -2.45 t o ]

0.70 2.1-3 0.80 [3~ ~-.-.-.-.-.-.-.-.-.Tg~ 1

Water column

641

at midshelf

Table 5. Same as Table 4• but f•r the transp•rts c•mputed in the r•tated• rnass ba•ancing frame •f reference Ms(&,=)

Ms(&,,x) M,(h,,~)

0.94

M,(h,)

0.95

Mi

0.33

Ms(h,,,~)

Ms(hs)

M,

Mh

x~ )

xg)

0.94

0.95

0.32 ~

-0.63 ~

0.78 ~

0.82 2.69

0.93

0.30 ~

-0.60 ~

0.71 2.49

0.76

0.47

-0.48 -1.-Z"J

0.76 ~7i

0.74 LTT5

0.02 ~

0.29 ~

0.27 1.11

-0.62 ~

-0.80 -2.30

0.50{ lX ~7i'0~- 4)

t T.t'',~

0.79

p-b7

~

(o) t

o.8

-0.55 [.1~ [1~)

0.24/.\ .--.-.~k4) 1

~77T (0)0.76

~0"31(_ 1)

~-0"75( )_1

0.80 (1) 27_.~

0.27 {1]

-0.80

2.140"69

It is worthy of note that there are two periods, centred on 12 March and 1 April, when the computed surface cross-shelf transport is weaker than the expected Ekman transport (Figs 4 and 5). Both occur about 3 days after the onset of a sustained period of upwelling favourable wind. Both of these anomalies present a weakening of the offshore flow throughout the surface Ekman layer, rather than a shoaling of the same (Fig. 2). Also, coincident with these Ekman transport shortfalls are sudden, strong drops in the surface mixed layer temperature. We believe these temperature drops to be advective, because the total water column heat content obviously diminishes, while the surface heat flux tends to warm the water column (RICHMAN and BADAN-DANGON, 1982). We therefore suggest that the surface mixed layer temperature drops represent the passage of upwelling fronts by the midshelf mooring and that the shortfalls of surface Ekman transports are related to the passage of the fronts, perhaps through an unresolved, transient baroclinic tendency (MOOERS et al., 1976; BRINK, 1983). This conclusion is supported by the hydrographic sections collected on those dates, which show a well developed frontal structure that extends over the midshelf region (Fig. 6). Finally, Fig. 2 clearly shows that the nearsurface equatorward velocity accelerates dramatically after the frontal passages, consistent with the presence of a cross-frontal shear.

6.

DISCUSSION

Our calculations tend to support KUNDU'S(1977) finding that the entire water column off northwest Africa is frictional for times of strong wind and point to the conclusion that the dynamical regime fluctuates considerably at the location of the midshelf moorings. For example (Fig. 3), the instrument located at 45 m depth is found, at different times, within the bottom boundary layer, the 'inviscid' interior or within the surface boundary layer. Thus, only the very shallowest and deepest current meters on the moorings can reasonably

642

A. BADAN-DANGONet al.

21"40' N

TEMPERATURE (*C) 12-13 MAR 1974 40' 30' 20' I

130

151

I 132

133

I 134

I APR 1974 I0' I 135

I'PO0' W I 136 STA

50' I 242

40' I 241

240

z~

30' I 239

t~

I

,

;

I

17-~w I

! ! : .,~-15.75;

I0~ w

20(

~5

~

2'5

75

50

i 25

DISTANCE (kin }

Fig. 6.

Cross-shelf temperature section showing a pronounced front over the outer portion of the shetf on (a) 12 to 13 March 1974, and (b) 1 April 1974.

be expected to be in the same dynamical regime consistently. This, in turn, makes time series analysis approaches, which assume dynamical stationarity, ambiguous for the study of the dynamics at any particular depth. For example, for an instrument located within the surface Ekman layer, a negative alongshore wind stress, which is upwelling favourable, should correlate positively with negative offshore flow. Below the surface Ekman layer, in the region of compensating onshore flow, a negative correlation should result. In some regions, such as off Peru (BRINK et al., 1980), the depths of the various layers are sufficiently stable that a correlation approach yields reasonable results. For the present case we do not feel that an individual depth study is appropriate. This does not, however, preclude the validity of a depth-integrated time-series study (BADAN-DANGON, 1981; ALLENand SMITH, 1981). A second conclusion is that the bottom Ekman layer plays a very substantial role in transporting the upwelling source water onshore over the shelf. This is strikingly at variance with, for example, the upwelling systems off Oregon and off Peru, where the onshore flow occurs at mid-depth and the bottom Ekman flow is directed offshore (SMm~, 1981). This contrast is immediately due to the relatively strong frictional effects and to the absence of a poleward undercurrent over the northwest African shelf. Acknowledgements--We are grateful to Modesto Ortiz for helping with the calculations. Maricela Gonzfilez prepared the manuscript and Nancy Hulbirt did the illustrations. This research was supported by the U.S. National Science Foundation and by the Consejo Nacional de Ciencia y Tecnologia of Mrxico. REFERENCES ALLEN J. S. (1980) Models of wind-driven currents on the continental shelf. Annual Reviews of Fluid Mechanics, 12, 389--433.

Water column at midshelf

643

ALLENJ. S. and R. L. SMITH(1981) On the dynamics of wind-driven shelf currents. Philosophical Transactions of the Royal Society of London, A302, 617--634. BADAN-DANC,ON A. (1981) On the dynamics of subinertial currents off northwest Africa. PhD dissertation, Oregon State University, Corvallis, 167 pp. BADAN-DANGONA. (1982) Principal components of the velocity field off NW Africa. Rapports et ProcdsVerbaux, CIEM, 180, 78--82. BARTONE. D., M. R. STEVENSONand W. E. GILBERT(1975) CTD/STD measurements off the NW African coast near Cabo Corveiro during JOINT-1. R/V Gilliss cruise GS 7401, February-April 1974. Data Report 63, ref. 75--3. BARTONE. D., A. HUYERand R. L. SMITH(1977) Temporal variation observed in the hydrographic regime near Cabo Corveiro in the Northwest African upwelling region, February to April 1974. Deep-Sea Research, 24, %23. BRINKK. H. (1983) The near-surface dynamics of coastal upwelling. Progress in Oceanography, 12, 223-257. BRINK K. H., D. HALPERNand R. L. SMITH(1980) Circulation in the peruvian upwelling system near 15°5. Journal of Geophysical Research, 85, 4036-4048. CALDWELL D. R. (1983) Oceanic turbulence: big bangs or continuous creation? Journal of Geophysical Research, ~$--C12, 7543-7550. DAVIS R. E., R. DE SZOEKE,D. HALPERNand P. NIILER (1981a) Variability in the upper ocean during MILE. Part I: the heat and momentum balances. Deep-Sea Research, 28, 1427-1451. DAVIS R. E., R. DE SZOEKE and P. NIILER (1981b) Variability in the upper ocean during MILE. Part II: Modelling the mixed layer response. Deep-Sea Research, 28, 1453-1475. GRANTW. D. and O. S. MADSEN(1979) Combined wave and current interaction with a rough bottom. Journal of Geophysical Research, 84-C4, 1797-1808. HALPERN D. (1977) Description of wind and of upper ocean current and temperature variations on the Continental Shelf off Northwest Africa during March and April 1974. Journal of Physical Oceanography, 7, 422-430. HALPERND., R. L. SMITHand E. MITrELSTAEDT(1977) Cross-shelf circulation on the Continental Shelf off Northwest Africa during upwelling. Journal of Marine Research, 35, 78%796. HUYERA. (1976) A comparison of upwelling events in two locations: Oregon and Northwest Africa. Journal of

Marine Research, 34,531-546. KRAUSE. B. and J. S. TURNER(1967) A one-dimensional model of the seasonal thermocline: II, the general theory and its consequences. Tellus, 19, 98-106. KUNDU P. (1977) On the importance of friction in the typical continental waters: off Oregon and off Spanish Sahara. In: J. C. J. NIHOUL,editor, Bottom turbulence, 8th Liege Colloquium in Ocean Hydrodynamics, 1976, Elsevier, New York, pp. 18%207. KUNDU P. K. and J. S. ALLEN (1976) Some three-dimensional characteristics of low-frequency current fluctuations near the Oregon coast. Journal of Physical Oceanography, 6, 181-199. LUMLEYJ. L. and H. A. PANOFSKY(1964) The structure of atmospheric turbulence. Interscience, New York, 239 PP. MITTELSTAEDTg. (1983) The upwelling area off Northwest Africa. A description of phenomena related to coastal upwelling. Progress in Oceanography, 12,307-331. MI'ITELSTAEDTE., R. D. PILLSBURYand R. L. SMITH(1975) Flow patterns in the Northwest African upwelling area. Deutsche Hydrographische Zeitschrift, 28, 145-167. MOOERSC. N. K., L. M. BOGERT, R. L. SMITHand J. G. PATULLO(1968) A compilation of observations from moored current meters and thermographs (and of complementary oceanographic and atmospheric data). Department of Oceanography, Oregon State University, Data Report 30, ref. 68-5. MOOERSC. N. K., C. A. COLLINSand R. L. SMITH(1976)The dynamic structure of the frontal zone in the coastal upwelling region off Oregon. Journal of Physical Oceanography, 6, 3-21. NI1LERP. P. (1977) One-dimensional models of the seasonal thermocline. In: The sea, ideas and observations on progress in the study of the sea, Vol. 6, E. D. GOLDBERG,I. N. MCCAVE,J. J. O'BRIEN and J. H. STEELE, editors, John Wiley, New York, pp. 9%115. PILLSBURYR. D., J. S. BOTTERO, R. E. STILLand MITTELSTAEDT(1975) A compilation of observations from moored current meters, Vol. 8. Wind, currents and temperature off Northwest Africa along 21°40'N during JOINT I, February-April. School of Oceanography, Oregon State University, Data Report 62. Ref. 75-3. POLLARD R. T., P. B. RHINESand R. O. R. Y. THOMPSON(1973) The deepening of the wind-mixed layer. Geophysical Fluid Dynamics, 3, 381-404. RICHMANJ. G. and A. BADAN-DANC~ON(1982) Mean heat and momentum budgets during upwelling for coastal waters off Northwest Africa. Journal of Geophysical Research, 88-C4, 2626-2632. SCIREMAMMANOF. (1979) A suggestion for the presentation of correlations and their significance levels. Journal of Physical Oceanography, 9, 1273-1276. SMITH R. L. (1981) A comparison of the structure and variability of the flow field in three coastal upwelling regions: Oregon, Northwest Africa, and Peru. In: Coastal upwellmg, F. A. RICHARDS,editor, American Geophysical Union, pp. 10%118.

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