A Measured Energy Transformation Application
(META) For Long Beach Harbor, Site 2 Using A
James P. McKinney and William D. Corson
U.S. Army Corps of Engineers Engineering Research & Development Center
Vicksburg, MS, 39180
August 28, 2003
This discussion compares prototype and computed spectral results for gages located
at Long Beach Harbor, CA. Comparisons are made by examining the differences in the
prototype and computed harbor total energy, Et, very long period energy between 200
and 30 seconds, E200-30, and energy spectrums. Spectral analysis allows the energy of
the total wave record to be broken down into discrete frequency bands. Spectral results
from an incident gage, LB8, located at Queens Gate and Long Beach Site 2, LB2, were
used to calculate an energy transfer spectrum for LB2.
Wave records were collected every 4 hours using subsurface pressure sensors. The
sample rate for these sensors was 0.5 Hz and the burst length was 8096 seconds.
The analysis utilized the Welch, , spectral analysis method with 50% overlapping
segments. Since the raw time series were obtained using sub-surface systems, a depth
determined high frequency cutoff was applied. The averaged co-and quad-spectra from
each analyzed record were used to calculate Et, E200-30, and energy spectrums.
To provide a direct comparison of incident and transferred energy, a transfer coeffi-
cient spectrum, Sx, was calculated by dividing the transferred energy at each frequency
by the corresponding incident energy, eqn.1.
where Etf is the energy per frequency transferred at LB2 and Eif is the incident
energy per frequency from LB8. For this simple analysis, concurrent records when the
LB8 E200-30> 5.0 cm2 were selected to compute Sx.
Plots of the yearly Sx spectrums for 1998 - 2002 are provided. See figures 1 thru 5.
An estimated energy spectrum, Sest at LB2 was calculated for each incident spec-
trum, Si, using equation, eqn.2.