1. Wind Stress and Ekman Mass Transport along CalCOFI lines: 67,70 and 77 by Lora Egley

2. Scientific Objective Analyze shipboard wind data for Leg1
Compute Surface wind stress and Ekman Mass Transport.
Ekman had hypothesized a momentum balance in the ocean surface layer between wind stress and Coriolis acceleration and a velocity spiral he had never directly observed.

3. Forcing Total Current: Geostrophic flow:
Frictional, wind driven (Ekman) Flow
Within the oceanic Ekman layer the wind stress is balanced by the Coriolis force and frictional forces. .
Boundary Conditions:

4. FORCING
Transport
Wind Stress
Coriolis Force

5. The theory:
This is a review of what we have had from class. Steady winds blowing on the sea surface produce a thin, horizontal boundary layer called the Ekman Layer. This layer may be 10 m, 50 m, or at most 100 m thick. Each layer of the ocean affects the layer beneath it through its movement. The surface water is directed at an angle of 45º to the wind, to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
With increasing depth in the boundary layer, the current speed is reduced, and the direction rotates farther away from the wind direction following a “Ekman”spiral.

6. Indirect and repeated confirmation of Ekman layers in the open ocean
Has only occurred recently
1981: Davis et. al. showed a mixed layer response to the winds in the northeastern Pacific which was “Ekman like”
1987: Price et. al. demonstrated the spiral Ekman layer structure in the subtropical North Atlantic
1995: Chereskin found direct evidence for Ekman balance in the California Current

7. Ekman’s assumptions Assumptions: Steady State
Closure assumption (Eddy Viscosity constant)
Vertical Homogeneous ocean
Away from horizontal boundaries
Difficult to meet wind direction is highly variable.
Closure express reynolds stresses as mean quantities because we can’t measure the fluctuations directly.

8. Data consisted of:
The SAIL data: Wind Direction, Wind Speed, Position, Time, Air Temperature, Relative humidity, Sea surface temperature, Pressure
Measurements taken from 2-5 AUG 2001

9. Methods Utilized Bulk Formulas
Most difficult part was to get spatially oriented so that I could calculate the pertinent component along each leg
Stress calculations based on every data point
Time averaged stress x and y components hourly (30min average at corners of the box)
Then solved for the hourly mass transport
Determined distance traveled each hour
Then solved for the Volume transport

10. Calculated Mass Transport using Bulk Formulas: Reference Smith(1988)
Base equations
to begin
indirect
calculations

11. Transport relation predicts a net westward transport for our southward wind stress

12. 2AUG01 1945-2045 taux~.03km/ms^2 My=0.26m^2/s Hourly average
(CalCOFI Line: 67)

13. Data showing a
transport out of
box.

14. Data showing a
transport out of
box.

19. Net Volume out of the box CalCOFI line 70: -0.16214Sv.
Net Volume into the box
CalCOFI line 67: Sv.
Net Volume out of the box
CalCOFI line 70:
Sv.
CalCOFI line 77:
Sv.
Total
Sv.

20. Southwest
Transport

21. Central Coast of California: Northwest Pacific
Eastern Boundary Current: California Current
Coastal box: ~225km x 170km
Taux
Mass Transport y Sv
Meeting the assumption away from horizontal boundaries. Sv
Sv.

22. Concerns Biggest concern was the time and spatial variability
Wind Direction is highly variable. (Fortunate enough to have steady winds towards the Southeast for the 4 days)

23. Time Series Hanning Window Filtfilt
From an autocorrelation function: Calculated integral time scale: ~20 hours
Velocity aliasing results from undersampling the high frequency components of a signal. Nyquist frequency fn-1/2deltat

24. Summary of Results
Net mass transport predominately to the Southwest supporting the Ekman theory.
Net loss out of the box. (Indicating Upwelling)
Magnitude agreed within 3%; phase within 4%/
Also her spirals were slightly flatter compared to the more circular theory