1. by ENS William C. Blodgett, Jr. 22MAR02
Rotary Cross Spectral Analysis of Low Frequency Currents With Co-located Wind Measurements in the Southern Monterey Bay
by ENS William C. Blodgett, Jr.
22MAR02

2. Introduction Purpose Rapid Environmental Assessment Laboratory (REAL)
“Using complex rotary cross spectra, determine the coupling of low frequency currents at two specific heights in the water column with collocated winds in the southern Monterey Bay”
Rapid Environmental Assessment Laboratory (REAL)
Monterey Inner Shelf Observatory (MISO)
Broadband Acoustic Doppler Current Profiler (BADCP)
Paro-scientific pressure sensor
Scanning acoustic altimeter
Under-water video camera and laser light
Bistatic Coherent Doppler Velocity and Sediment Profiler (BCDVSP)
Shoreline Meteorological Station
10m height wind speed and direction
air temperature and dew point
short and long wave incident radiation
barometric pressure
rain fall rates

3. Data Acquisition
BADCP Data
Wind Data

4. Cross-Shore Normal Coordinate System
Data Orientation
MISO Site
Cross-Shore Normal Coordinate System
Alongshore (AS)
Cross-shore (CS)
Beach

5. Data Preparation and Processing
+3 
- 3 
Deglitching 60
120
Current Velocity Data (s)
Current Velocity Data (2 min) Wind Velocity Data (2min) 2
Data Averaging
Data Time-Series Selection
Gap Removal
Data Averaging – Averaged BADCP data to 2 minute intervals to coincide with temporal spacing of wind data. Used a 1 min window around each 2 min spacing.
Data Time-Series Selection – wind data initiated on day , so constrained to year for testing. Created a timeline of gaps in data (due to equipment failure / maintenance, etc.). Chose 100 days of relatively gapless data: (roughly June,2000). There were only 5 short gaps in this time series (4 hr on average).
Deglitching -

6. Complex Rotary Cross Spectral Analysis
Goal
characterize the degree of coupling between wind and surface / bottom current measurements
Method
statistical measure of the coherence, phase, and power spectral density versus frequency
Standard Spectral Analysis
Limitations
Rotary Cross Spectral Analysis
Advantages
Requirements

7. Complex Rotary Cross Spectral Analysis Products
Fourier Transform of Time Series =
Inner Cross Spectrum
Inner Autospectra
Inner Coherence Squared
Inner Phase
Input: Wind and Current Complex Time Series
Significant Coherence
&

8. Complex Rotary Cross Spectral Analysis Products
Outer Phase
Significant Coherence
Outer Cross Spectrum
Outer Autospectra
Outer Coherence Squared

9. Complex Rotary Cross Spectral Analysis (Example)=

10. Complex Rotary Cross Spectral Analysis (Example Continued)

11. Complex Rotary Cross Spectral Analysis of a Current and Wind Time-Series in Monterey Bay, CA

12. Wind (anticlockwise) & Diurnal Current (anticlockwise)
Wind (clockwise) & Semidiurnal Current (clockwise)

13. Significant Coherence @ 1 cycle/day for negative frequencies
~90 Phase Lead

14. Clockwise Wind & Current Energy Dominates

15. Once again, but to a lesser extent…..
Wind (anticlockwise) & Diurnal Current (anticlockwise)
Wind (clockwise) & Semidiurnal Current (clockwise)
Once again, but to a lesser extent…..
Near-Surface
A decrease in coupling near the bottom could indicate a deep log layer in unstratified (well-mixed) conditions, or the presence of stratification with a slippery surface layer.

16. Near-bottom coherence levels lower and less significant than near-surface
>90 Phase differential / substantial error

17. Increased Diurnal Anticlockwise Energy, Less Clockwise
Near-Surface

18. Summary Surface and bottom coupling between wind and currents exists.
Decrease in energy between surface and bottom could be due to the formation of a deep log layer in unstratified conditions, OR due to decoupling in a stratified water column.
Upon inspection of the coherence levels, however, one can conclude that the surface current and wind velocities are coupled, while the bottom current and wind velocities are less coupled over the 100 day time-series.
The surface phase angles around 90 reflect Eckman coupling at the surface boundary layer, though the limited time-series results in a large phase error.
The bottom phase relationship are not robust due to the reduced coherence, reflecting de-coupling of bottom current with the wind.

19. Questions