Wind Stress and Ekman Mass Transport along CalCOFI lines: 67,70 and 77 by Lora Egley http://www.mlml.calstate.edu/marinops/marinops.htm
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.
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:
FORCING Transport Wind Stress Coriolis Force
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. http://www.sp.uconn.edu/~geo101vc/Lecture20/sld014.htm
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
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.
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
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
Calculated Mass Transport using Bulk Formulas: Reference Smith(1988) Base equations to begin indirect calculations
Transport relation predicts a net westward transport for our southward wind stress
2AUG01 1945-2045 taux~.03km/ms^2 My=0.26m^2/s Hourly average (CalCOFI Line: 67)
Data showing a transport out of box.
Data showing a transport out of box.
Net Volume out of the box CalCOFI line 70: -0.16214Sv. Net Volume into the box CalCOFI line 67:0.0027381Sv. Net Volume out of the box CalCOFI line 70: -0.16214Sv. CalCOFI line 77: -0.03698Sv. Total -0.19912Sv.
Southwest Transport
Central Coast of California: Northwest Pacific Eastern Boundary Current: California Current Coastal box: ~225km x 170km Taux Mass Transport y +0.0027Sv Meeting the assumption away from horizontal boundaries. -0.1621Sv -0.0370Sv.
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)
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
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