Effect of Equatorial Long Waves on the North Equatorial Countercurrent

An analytical, reduced-gravity, equatorial long wave model is employed to study the effect of equatorial long waves on the North Equatorial Countercurrent (NECC). This model is first forced by an abruptly switched-on-off zonal wind stress which is distributed uniformly in the zonal direction. As the wind is turned on, an eastward current with a maximum speed at 5 ° N and a trough of thermocline at 3 ° N are generated in the western basin. These features coincide with the observed distribution of NECC. The initial intensification of this eastward current is due to the forced first meridional mode Rossby wave. The duration of intensification is related to the wind fetch and Rossby wave speed. After the forced Rossby wave has passed, the eastward current is decelerated or accelerated by a series of reflected Rossby waves generated at the eastern boundary. As the steady state is reached, the easterly wind is then turned off. The forced first meridional mode Rossby wave, now generated by wind relaxation, decelerates the eastward current and even turns the current westward, due to overshooting. · Replacing the uniform wind with a linear wind, we find that the general features remain unchanged but the NECC now has larger amplitude and smaller zonal domain. The present linear wind has similar zonal distribution to the trade wind on the tropical Atlantic Ocean.

amount of water, heat, and salt are transported from the western to the eastern tropical ocean by the NECC.The transport amount is quite comparable with the Gulf Stream (Richardson and Reverdin, 1987).The NECC undergoes a very distinguished seasonal variation; it builds up abruptly as the trade wind intensifies in the boreal spring and abruptly collapses as the trade wind relaxes in the early winter.The dynamics of this seasonal variation have been discussed by Richardson and Reverdin (1987).The curl of the local wind stress (Garzoli, and Katz 1983) and the equatorial Rossby wave (Delcroix et al. 199 1) are the most likely mechanisms for controlling the NECC variation.In this paper, a simple equatorial analytical model forced by an easterly wind stress is applied to investigate the effect of equatorial long waves on the NECC.Since the model is analytical, the variation of NECC related with any individual wave can be traced.
The paper is organized into 4 sections.Previous studies of the seasonal variation of the NECC are reviewed in Section 2. The temporal and spatial variation of the wind stress and the NECC on the equatorial Atlantic Ocean are described.In Section 3, the results from an analytical equatorial Jong wave model, forced by various types of wind, are used to study the effect of equatorial long waves on the NECC.The domain of the analytical model is similar to the basin of the equatorial Atlantic Ocean.A switched-on-off zonal wind stress is first applied to force the model.The model responses with no boundary, western boundary only and western and eastern boundaries are examined.Finally, the model is forced by a zonal wind stress which is more complicated but realistic.The result is studied and compared to the observed velocity and at 6°N, 28°W.Section 4 provides the discussion and conclusion.

BACKGROUND
Richardson and Reverdin (1987), using data gathered by surface drifters, current meters, and ship drifts, gave a general description of the seasonal variation of the NECC in the tropical Atlantic Ocean.They concluded that the seasonal cycle of the NECC is very regular from year to year.Each year the NECC starts up west of 18°Win May-June and disappears or reverses from about January-February.The origin of the NECC is the North Brazil Current which carries heat from the south to the north, crossing the equator.It fl ows northwest, with a speed of up to 143 cm sec -1 , along the western boundary.Figure 1 shows the average speed of the NECC along 28°W in July.The meridional distribution of NECC is not symmetrical.The maximum eastward current occurs at 5 ° N. The zonal velocity gradient is larger south of this latitude than north.Similar results were obtained by analyzing historical data (Garzoli and Katz, 1983) and ship drifts (Richardson and Walsh, 1986).Henin and Hisard (1987} analyzed data from nine cruises, collected during the Programme Franr;ais Ocean et Climat dans I' Atlantique Equatorial (FOCAL) experi ment.They found that the NECC underwent a distinguished seasonal cycle, but that the cycle could be signifi cantly modified by interannual variation.Using a three dimensional numerical model, Philander and Pacanowski (1986) de scribed the transport of NECC in detail.They found that the eastward transport of the NECC decreases in a downstream direction primarily because of downwelling.This downwelling water flows along the thermocline and then injects into the Equatorial Un dercurrent (EUC).The eastward transport between 2. 5 ° N and 10 ° N in the upper 317 m is greatly reduced from west to east.The variation of transport is related with the variation of thermocline.No explicit explanation was offered by them to account for the dynamics of the NECC.
By analyzing historical data, Garzoli and Katz (1983) concluded that the variation of NECC is controlled by the curl of wind stress.This conclusion somewhat �isagrees with the finding by Kessler (1990), who found that the wind stress curl has very little variability over the annual period in the north tropical Pacifi c, whereas the NECC has large annual variation.By examining the annual fluctuation of 20°C isotherm depth, he found a west-ward propagating Rossby wave near 5 ° N. A similar feature was found by Meyers (1979) in the Pacific Ocean and by Steger and Carton (1991) in the Atlantic Ocean.Using Geosat data, Delcroix et al. (1991) discovered more evidence that the NECC is strongly influ enced by the equatorial Rossby long wave.
A time series current data at 6°N, 28°W, collected during the Seasonal Response of the Equatorial Atlantic (SEQUAL) Experiment, was used by Richardson and Reverdin (1987) to describe the temporal variation of NECC.Their data is shown in Figure 2. The NECC was similar in both 1983 and 1984 except that the latter showed greater velocity.It onset rapidly in May and flowed swiftly eastward until December.The mean flow was low from January to May.
The zonal wind stress on the equator is a major external force for generating the equatorial wave, which has significant impact on the NECC.Its variation is crucial for studying the NECC. Figure 3 shows the zonal wind stress, which was measured at St. Peter and St. Paul Rocks (SPPR), located at I 0N, 29°W The length of time series is 2.7 years, from February 1983 to November 1985.Its variation has been described by Colin and Garzoli (1987).A comparison of zonal wind stress with current measurement (Figure 2) shows an abrupt intensification of easterly wind in April 1983, followed by the rapid onset of NECC.The time lag between the easterly wind and NECC was nearly one month.After an initial build up, both wind stress and NECC maintained their strength, with a large fluctuation in amplitude until the trade wind collapsed in December 1983.Both the easterly wind and the NECC regained their strength in May 1984.In spite of the shorter time lag between the easterly wind and NECC, the relation between the easterly wind and NECC was similar to the previous year.
The relation between the easterly wind on the equator and the NECC on the off equator might be due to the equatorial long waves.An analytical equatorial long waves model is applied to explore this relationship.The effect of the equatorial waves on the NECC is examined.

ANALYTICAL MODEL AND RESULTS
A linear, reduced gravity, equatorial J3-plane model fashioned after Cane and Sarachik (1976,1977,1981) and as applied by Weisberg and Tang (1983, 1985, 1987, 1990) and Tang and Weisberg (1984) is applied here to study the effect of the equatorial long waves (2) ah au Jv -+ -+-= -Eh at ax ay (3) where u and v are the velocity components in both x (east) andy (north) directions, his the upper layer thickness perturbation, t is time, 't is the zonal component of wind stress, and E is a damping parameter.The equations have been nondimensionalized using time and length scales T = (c/3)-v.and L = (cl{J)v.,where c = (g'H)v.is the reduced-gravity wave speed corresponding to the reduced-gravity g' and the undistributed upper layer water depth H, and f3 is the gradient in planetary vorticity.The length sc�e, the time scale and the baroclinic Kelvin wave speed are 267 km, 1.92 days, and 1.6 m sec-1, respectively.
The analytical solution of these equations is discussed by Cane andSarachik (1976, 1977) for the undamping case and by Weisberg and Tang (1987) for the damping case.The procedure is to Fourier transform the equations of motion, project the forcing function onto the appropriate equatorial wave modes of the homogeneous equations that form a complete set over the interval -oo<y<oo, integrate these projections in time, and then invert the Fourier transforms using.along wave approximation.The result of the foregoing operations yields the directly forced part of the solution.These forced waves then refl ect off of the meridional boundaries to yield the additional long equatorial waves that together comprise the total solution.
The provided damping, Rayleigh friction and Newtonian cooling, is necessary once the integration time of the model becomes long compared to the propagation time for the waves comprising the solution to traverse the basin.Although it provides for damping, it does not distort' the form of the undamped equatorial wave solutions that can then be traced analytically through their evolution.In a real sense, dissipative losses in a forced response can occur for a variety of reasons, including eddy exchanges of momentum and heat both laterally and vertically, vertical propagation into the deep ocean, nonlinear inter actions with the background currents, and imperfect reflections from meridional bounda ries.Weisberg and Tang (1987) studied the model responses for various damping coeffi cients and suggested that the damping coefficient, 0.01 (thee-folding time is 192 days), is more realistic.This value is applied here.
The model domain relative to the equatorial Atlantic Ocean and the meridional distri bution of zonal wind stress are shown in Figure 4. Uniform and linear distributed zonal wind stress are also shown in Figure 4.The former one is simple so that its induced ocean response is easily interpreted.The later one has similar distribution with the trade wind on the equatorial Atlantic (Weisberg and Tang, 1987).Dimensionally, the model basin ex tends from 46 ° W to 8. 6 ° E for a total width of 6000 km.The nondimensional force func tion has the form Yi r(x,y,t) = ye-2 X(x) F(t) and for a uniformly distributed wind stress, or ( 7 ) for a linearly distributed wind stress, where H represents step function.The parameters of the wind stress are y and S, specifying the magnitude of the variations, Ti specifying the duration of these variations, and L1 and L2 specifying the fetches.Dimensionally, the origins of the wind stress distributions are set at S0Wwith L1 and L2 equal 4500 and lSOO km, respectively.The amplitude of the easterly wind stress is O.S dyn cm-2 for the uni formly distributed wind stress and 0.67 dyn cm-2 for the linearly distributed wind stress at the western boundary.
In order to study the variation of NECC induced by the equatorial long waves in detail, the simplest force function will be applied first.A switched-on-off uniformly dis Figure 6 shows the zonal velocity and the upper layer thickness perturbations as a function of x and y on Day 80.The ocean response on this day nearly reaches a steady state.In the western basin, a positive meridional gradient of zonal velocity is located between the equator and 5SO km north of the equator.This strong velocity gradient, especially south of y=300 km, is a mechanism generating the 2S-day equatorial instability wave (Philander, 1978, Cox, 1980, and Weisberg, 1984).The maximum eastward veloc ity is found at around S0N, SSO km north of the equator.The zero crossing of zonal velocity is at around 3 ° N, where the upper layer thickness perturbation has largest value.
These features, a maximum eastward velocity at 5 ° N and a ridge of upper layer thickness located at 3 °N, is in agreement with the observation (Richardson and Reverdin, 1987) and numerical model result (Chang and Philander, 1989).
In summarizing the above results, the NECC is accelerated immediately by the equa torial forced first meridional mode Rossby wave after the easterly wind is switched-on.
Since the Ross by wave is propagating westward, the duration of acceleration of NECC is a function of location, wind fetch, and the Rossby wave speed.It has larger amplitude further west due .to the integrated response.The meridional location of the maximum NECC is related with the length scale of the equatorial wave.This length scale is deter mined by the stratification of the equatorial ocean.

Case B: Linear Distributed Easterly Wind Stress
Switched-on at t=O day and switched-off at t=300 day The wind stress distribution applied here is described and shown in Figure 4. Figure 12 shows the resulting zonal velocity perturbations at 38 °W, 28 °W and 5 °W along the 5 ° N for an unbounded, a western bounded and a zonal bounded ocean forced by this type of wind.The basic features here are similar to those in Case A Since a small fetch of westerly wind stress is generated west of 5 °W, the eastward current at 38 °W and 28 °Wis first accelerated and then decelerated slightly.This deceleration is related to the westerly wind stress on the eastern basin.Unlike Case A, the acceleration I deceleration in this case is not a constant and is sharper.The zonal velocity and the upper thickness perturbations as a function of x and y on Day 200 for a zonal bounded ocean are shown in Figure 13.
The NECC is now more confi ned to the west but has larger amplitude than in Case A In the eastern basin, the current is weak.The zonal gradient of both upper layer thickness and zonal velocity is enlarged.The negative value of upper layer thickness perturbation (the upwelling region) is in this case much larger than in Case A The maximum upwelling is on the equator in the vicinity of the nodal point of wind stress.The maximum downwelling is still located 275 km north of the equator at the western boundary.Thus, the location of the trough of thermocline remains nearly the same.As the easterly wind collapses, the oceanic response is reversed, similar to that shown in l 000 ruwr11 JrnttiJ�J!Jl � �t�tt mttt�t� �trttJI�@� 1 • I I I t I l I I I I I I l I I I I I �)(:r•:i:•: .J.:.:. 1� 10°N _ !.): : : : )� � {t� N=== 1000 f.:f.'::::::::::::::::::::::::::::;:::::::;:;:::::;:;:;:::::::::::::::::::::::::::::::::�::;:::::;:::;:;:::::;:::::::::::\While maintaining the same spatial wind stress distribution, Case C considers a temporal variation of wind stress very similar to the actual wind measurement recorded at SPPR.Weisberg and Tang (1990) used the exact same wind stress to study the oceanic response on the equator.The model results agreed very well with the observations.The same wind stress and model are applied here, but our attention is now drawn to the oceanic response on the off-equator, especially in the region of the NECC.
c. Case C: Linear Distributed Easterly Wi nd Stress with Realistic Time Variation The applied time series of easterly wind stress is shown in Figure 14.Before the intensification of easterly wind in early April 1983, the trade wind was relaxed.The westerly wind increased for around 10 days and then remained constant for 5 days.The easterly wind built up in 20 days and then kept its strength until December.After the easterly wind collapsed in December, there were no winds for 5 months, and an annual cycle was thus completed.In 1984, the wind intensified in mid-May and collapsed in mid November.The length of the windless season was nearly the same as before, 5 months.The easterly wind regained its strength in May 1985.
Countercurrent (NECC) is a swift eastward current which is located around 3°N to 10°N.North of the NECC is a westward North Equatorial Current (NEC) and south of the NECC is a westward South Equatorial Current (SEC).A large Institute of Oceanography, National Taiwan University, Taipei, Taiwan, R.O. C. 2 Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan, R.O.C.

Fig. 1
Fig. 1 The average zonal velocity for July in the North Equatorial Countercurrent (NECC), South Equatorial Current (SEC) North Equatorial Current (NEC) near 28 ° W from the historical ship drift.(After Richardson and Reverdin, 1987).
on the NECC.The model is forced from a state of rest by a temporally and spatially vaiying zonal wind stress distribution.The equations of motion are du CJh --yv + -= -EU+ r ()( dx av ah -+ yu+-= -EV dt dy

Fig. 3
Fig. 3 The wind record at St. Peter and St. Paul Rocks (SPPR) from the February I 983 to Decem ber 1985.

Fig. 4
Fig.4The model domain and the spatial zonal wind stress distributions.The cross denotes the wind station at SPPR.The asterisk denotes the current measurement at 6 ° N, 28 ° W.
tributed easterly wind stress (Eqn.6) is considered in Case A. Case B considers a switched-on-off linearly distributed easterly wind.This linear distribution of zonal wind stress is in agreement with both the climatology and the synoptic observations, including the limited Seasat mission(Halpern, personal communication, 1986).In Case C, the linear wind distribution associated with a time series which represents the daily average easterly wind stress values obtained from SPPR is considered.Except for Case C, the oceanic responses for no zonal boundary, western boundary only and eastern and western bounda ries are considered to examine the effect of forced and reflected equatorial long waves on the NECC.a. Case A: Uniform Easterly Wind Stress Switched-on at t =0 day and switched-off at t ,;300 day An unbounded ocean is considered first.Its zonal velocity and upper layer thickness perturbations at 38°W, 28°W and S0W along the S0N are shown in Figure S.As the �nd is switched-on, the downwelling forced first meridional mode Rossby wave is generated immediately.It increases the upper layer thickness and accelerates the velocity eastward at 38°W and 28°W.As the forced Rossby wave passes, the steady state is reached, the downwelling and eastward acceleration cease.The duration of downwelling and accelera tion are longer further west, because the response is integrated.The upwelling forced Kelvin wave has only a small influence on the off-equatorial ocean since it decays exponentially with latitude.The variation of velocity and upper layer thickness at the S0W is small because it is only affected by the forced Kelvin wave.A reverse process occurs as the easterly wind is switched-off on Day 300.The Rossby and Kelvin waves now generate the upwelling and downwelling, respectively, to bring the ocean to a state of rest.

Fig. 5
Fig. 5 The zonal velocity and the upper layer ocean thickness perturbations at 3 8 ° W, 28 ° W and 5°W on the 5°N for an unbounded ocean.The unifonn distributed easterly wind stress i s switched-on on Da y 0 and switched-off on Day 300.

.Fig. 6
Fig.6The zonal velocity and the upper layer thickness perturbations for an unbounded ocean as a function of x and y on Day 80 after the uniform distributed wind stress switched-on.

Fig. 7
Fig. 7 The zonal velocity and the upper ocean thickness perturbations at 38 ° W, 28 ° Wand 5 °W on the S 0N for a west ern bounded ocean.The uniform distribut ed easterly wind stress is swit ched-on on Day 0 and switched-off on Da y 300.

Fig. 8 Fig. 9
Fig.8The zonal velocity and the upper layer thickness perturbations for a western bounded ocean as a function of x and y on Day 80 after the uniform distributed easterly wind stress switched-on.

500
mrnrn��ft}11� tr�t� �rtrtrtt��ttf11 ffi�ttt t±:f:Hi4 tilif it�tn� .-J 5°N Q I" I I I [ I I t :.I.I I I I I I I I [o-t--t.I � I I I I I I "'r-4._I •1� C:.I � l • I I I I I I II I I I I I I I I 1 I J II EQ 0

.
Fig. JO The zonal velocity and the upper layer thickness perturbations for a zonal bounded ocean as a function of x and y on Day 200 after the uniform distributed easterly wind stress switched-on.
Fig. II The zonal velocity and the upper layer thickness perturbations for a zonal bounded ocean as a function of x and yon Day 400, 100 days after the uniform distributed easterly wind stress switched-off.

Fig. 12 5°N0
Fig.12The zonal velocity perturbations at 3 8 ° W, 28 ° W and 5 ° W on t he 5 ° N for an unbounded, western bounded only, and zonal bounded oceans.The li near distribut ed easterly wind stress is switched-on on Da y 0 and switched -off on Da y 300.

Fig. 13
Fig.13The zonal vel ocity distributi on and t he upper layer thickness perturbati ons for a zo nal bound ed ocean as a functi on •of x and y on Da y 200 after the linear distributed easterly wind stress switched •on.
Figure16shows the velocity perturbation as a function of time and longitude at 5 ° N.The NECC immediately built up as the easterly wind abruptly intensified.The NECC is confined to the west of x=3000 km (near 18.5 °W).Although the westward propagating Fig.15The zonal velocity and the upper ocean thickness perturbations at 3 8 ° W, 28 ° Wand 5 ° W on the 5 °N for a zonal bounded ocean in Case C.

Fig.
Fig. The contour of zonal velocity perturbation along the 5 ° N as a function of time and longitude.The contour interval is 5 cm sec -1 • The total length of the wind time series in this case is 950 days, from March 27, 1983 to October 31, 1985.The relaxation of easterly wind in 1985 is not included in this time frame.All of the intensification and