Roger Lukas*, Peter Hacker*, Ming Mao*, Eric Firing*,
Adriana Huyer, and P. Michael Kosro

* School of Ocean and Earth Science and Technology,
University of Hawaii, Honolulu, HI 96822

College of Oceanic and Atmospheric Sciences,
Oregon State University, Corvallis, OR 97331


Scientists aboard the R/V Wecoma conducted three survey cruises during the Intensive Observation Period of the TOGA Coupled Ocean-Atmosphere Response Experiment (COARE) within the Intensive Flux Array (IFA; Fig. 1). One purpose of the surveys was to measure the velocity structure on horizontal scales of 1-100 km in order to describe the temporal evolution of the velocity field and to estimate the importance of advection in the heat, salt and momentum budgets.

[Fig. 1]

Figure 1-Map of the TOGA COARE Intensive Flux Array and the locations of various observational systems. The butterfly pattern sampled repeatedly by the R/V WECOMA is shown. Ship movements are indicated by arrows. Moorings are indicated by diamonds. "MW" indicates the position of the R/V MOANA WAVE near the IMET mooring.

Velocity observations were made with a 150 kHz, RD Instruments acoustic Doppler current profiler. Dual GPS receivers were used to determine ship heading and to correct for gyro heading errors. The nominal depth range of observations is 20-300 m. Vertical resolution is 8 m; horizontal resolution is less than 1 km. The velocity observations are accurate to better than 2 cm s¯ ¹ on horizontal scales greater than 10 km. Repeat transport calculations around the closed survey segments indicate that current biases are less than 1 cm s¯ ¹. Observations were made almost continuously along the standard butterfly track within the IFA during the periods 13 Nov. to 2 Dec. 1992 (Leg 1), 18 Dec. 1992 to 9 Jan. 1993 (Leg 2), and 27 Jan. to 15 Feb. 1993 (Leg 3).

Our initial analysis focused on the horizontal and vertical structure of velocity along individual segments of the butterfly surveys, and on the mean spatial structure over the three legs. We early realized that the space-time sampling along individual velocity sections, which took about 6 and 10 hours to complete, convolved the unusually strong internal semidiurnal tidal signals, making estimates of horizontal gradients problematic. In order to remove the effect of tides and other higher frequency and short spatial scale features, we implemented a modification of the Candela et al. (1992) method.

Our purpose in this analysis is to determine the spatial and temporal gradients of the velocity field on time scales longer than a day, in order to evaluate the various velocity terms in the momentum and scalar property budgets. Preliminary results from our analysis are presented here.


Candela et al. (1992) described a method for the separation of tidal and subtidal currents in ship-mounted acoustic Doppler current profiler (ADCP) observations. We have modified the method to allow for linear variations of the horizontal current in time and space and to include simple semidiurnal and diurnal tidal components.

The method consists of representing the observations for each depth and time interval as a sum of terms of the form:


where u(x,y,t) is the observed eastward current component at a given time and position; the omega_i are the frequencies of the ith tidal constituent (we used a single semidiurnal and a single diurnal constituent); ai and bi are constants; c1...c6 are constants; r(x,y,t) is the residual. A similar representation was used for the north velocity component, v(x,y,t).

For each mapping period, the coefficients are determined by imposing a least squares requirement on the residuals. We used a three-day period for each analysis, which is long enough to allow for 2 complete circuits around the survey pattern, allowing us to estimate the temporal change at each point. A longer analysis period would have smoothed the rapid temporal changes observed during the IOP. The three-day analysis window was moved temporally through the data in 12-hour steps, to yield a time­centered velocity field estimate every 12 hours.

The velocity terms in the following figures represent estimates at the center point of the survey pattern. Estimates can be generated at all points within the survey domain.

A measure of the robustness of our estimates can be obtained from the number of velocity samples in each analysis, the condition number of the matrix, and the covariance matrix of the coefficients.

Our studies indicate that:


The IOP-mean velocity structure within the IFA (Fig. 2) was dominated by reversals of current with depth. Strong vertical shear is seen in layers from 30-70 m, 100-150 m, and in the northern half of the section from about 190-240 m. Note also the alternating layers of meridional divergence and convergence in V. The surface layer extended to an average depth of 60 m, flowing eastward at speeds up to 20 cm s¯ ¹ near the surface. Stronger eastward flow occurred at the northern end of the section. The second layer extends from 60-110 m, flowing westward at up to 10 cm s¯ ¹. The third layer is the southern edge of the Equatorial Undercurrent which flowed eastward at up to 30 cm s¯ ¹ from 110 m to about 250 m. Below that, the eastward-flowing Southern Subsurface Countercurrent is found south of 1.9S, and the westward-flowing Equatorial Intermediate Current is seen to the north, resulting in strong meridional shear. Most of the variations of flow on time scales longer than one day observed during the IOP were modulations of these basic flow features. However, currents near the surface did occasionally reverse.

[Fig. 2 top]

[Fig. 2 bottom]

Figure 2-Latitude-depth structure of the IOP-mean zonal (top) and meridional (bottom) velocity components estimated from the model-based analysis. Westward and southward flows are shaded.
Flow in the upper two layers was strongly variable in time (Fig. 3), forced by local winds and, presumably, also by remote winds. The upper layer flow was briefly towards the west in mid-November 1992, late January 1993, and in mid-February; eastward flows were strongest during westerly wind bursts (WWBs) in late November, late December-early January, and early February, reaching 50 cm s¯ ¹. The upper thermocline westward flow (and the EUC) shoaled with the thermal structure during the IOP. This westward flow disappeared briefly during the February WWB, but during the December WWB, the westward flow accelerated in phase with eastward acceleration of the near-surface flow. Peak speeds in this layer were about 30 cm s¯ ¹. The zonal flow in the EUC varied between 15 and 45 cm s¯ ¹ with the fluctuations both in and out of phase with the surface flow at different times. There was no clear correspondence between meridional flow variations and EUC speed, suggesting more complex dynamics than simple meandering of the EUC were responsible for current variations at this depth.

While the basic structure of the zonal flow did not change markedly during the IOP, the meridional flow varied considerably. During Leg 1, the flow was broadly southward, except at the beginning and end of the cruise. Vertical coherence was high. During Leg 2, meridional flow was energetic and highly variable in time and depth; there is a suggestion of vertical phase delay in alternating bands of southward and northward flow. Leg 3 showed a variable and vertically-layered structure with weak vertical coherence. Distinctly different time-depth structures of velocity gradients were observed among the three cruises.

Time-dependent velocity, and velocity gradient (not shown), vertical profiles derived from the model were combined to estimate the advective terms in the momentum balance. During Leg 1, the nonlinear terms were generally an order of magnitude smaller than the local acceleration, Leg 2 had significant nonlinear terms, and Leg 3 had nonlinear accelerations as large as the local acceleration.

The relative vorticity and divergence were computed from the velocity gradients; continuity was used to also estimate the vertical velocity component from the divergence (Fig. 3). Upwelling dominated during Leg 1, while alternating periods of upwelling and downwelling were characteristic of Legs 2 and 3. The magnitude of the relative vorticity (xi) was often comparable to local f (=-4.7 x 10¯6s¯ ¹), and considerably larger during Leg 3. The vertical structure of xi was similar for Legs 1 and 2, with xi being the same sign as f in the upper 100 m, and in a layer centered near 200 m. xi was positive in the layers centered near 120 and 300 m. During Leg 3, however, the upper 80 m and the layer between 220 and 300 m had positive xi, with the layer between 100-220 m having opposite sign with absolute vorticity between 2*f and 4*f. Nonlinear dynamics were clearly important in the momentum balance within the IFA during the TOGA COARE IOP, but most especially near the end of Leg 2 and during Leg 3.


Although the model-based velocity analysis technique has not been optimized, our present results are encouraging. Velocity gradients can be estimated over the IFA ocean survey domain, and the large-scale velocity structure can be sensibly mapped at about a one day time step. Results suggest that nonlinear advection is important in the mean momentum balance in the COARE IFA during the experiment, and very important during some periods of energetic variability.


Julie Ranada and Sharon DeCarlo provided expert assistance with the computations and presentation of the results. The support of this project by the National Science Foundation (OCE-9113948) and the National Oceanic and Atmospheric Administration under TOGA COARE is gratefully acknowledged.


Candela, J., R.C. Beardsley and R. Limeburner, 1992: Separation of tidal and subtidal currents in ship-mounted acoustic Doppler current profiler observations. J. Geophys. Res., 97, 769-788.

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