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

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

Data Acquisition BADCP Data Wind Data

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

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 2000117, so constrained to year 2000-2001 for testing. Created a timeline of gaps in data (due to equipment failure / maintenance, etc.). Chose 100 days of relatively gapless data: 2000175-2000275 (roughly June,2000). There were only 5 short gaps in this time series (4 hr on average). Deglitching -

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

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 &

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

Complex Rotary Cross Spectral Analysis (Example) =

Complex Rotary Cross Spectral Analysis (Example Continued)

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

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

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

Clockwise Wind & Current Energy Dominates

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.

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

Increased Diurnal Anticlockwise Energy, Less Clockwise Near-Surface

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.

Questions