1. LT O’Neill Operational Oceanography Fall 2008
Wavelet analysis of episodic rip currents in the inner-shelf during RCEX 2007
LT O’Neill
Operational Oceanography
Fall 2008

2. Introduction
Rip Currents: remain poorly understood beyond the surf zone
Little is known of vertical and temporal structure
Lack of observations - difficulties in obtaining complete measurements
Rip Current Experiment (RCEX) conducted APR-MAY 2007 at Sand City, CA
6 Bottom-mounted ADCPs, 11 pressure sensors and 30 GPS-tracking drifters
19 days
3m 5m
Surf zone
RCEX instrument layout

3. Introduction
Rip currents occasionally caused drifters to exit surf zone
Inspection of velocity time series shows episodic rip current pulsations (or squirts/jets) that appear at ADCP 5 and ADCP 6 (out to depth of 5 m, 50 m beyond surf zone)
These pulsations vary in time, intensity, and vertical structure
Surf zone

4. Rip current pulsations
2 groups of pulses: surface- dominated and more uniform in vertical
Group-averaging in vertical shows vertical tilt for offshore pulsations (higher velocity)
consistent with previous laboratory studies of rip currents (Haas, et al.)
Effort of this study was to use wavelet analysis to characterize pulsations and gain insight (temporal and rotational characteristics) into these episodic phenomenon
Used data from ADCP 5 and ADCP 6 that had been corrected for sea surface and rotated to shore-normal
Show raw/VLF data of jets
125.3 (sfc dominated)
Vertical tilt to large off-shore velocity component group averages
~0.3 m/s {

5. Methodology Put data into depth-relative framework
Interpolated to incremented scale (z/H)
Bad data -> zeros
Low-frequency filter (<.004 Hz)
Apply wavelet analysis, cross-wavelet analysis and cross-rotary wavelet analysis
Analogous to Fourier analysis but particularly useful for aperiodic phenomenon
Instead of power as a function of frequency, get periodicity (frequency) as a function of time
Apply normalizing coefficient (Liu et al.)
Input pulse -> get frequency spreading - ok as goal is time-lag and rotational aspects

6. Day 125
} ~equal velocities
} surface greater by .05 m/s
125.36
125.37
- Preceding pulse at ADCP5 (7 min time lag between maximum velocities, overlap exists)
VLF adcp5
VLF adcp6

7. Day 125 (ADCP 5 and 6) ADCP6 ADCP5 Wavelet (cross-shore components)
Near bottom
ADCP6
Near top
Done with reference to near-bottom bin (1st series)
Higher power signature present near bottom in 5 than in 6 – makes sense though larger than expected. Also have larger power signtr near top at ADCP 6.
Does not appear to be correlation between lesser peaks in 5 and 6 -
ADCP5
Pulse time
Wavelet (cross-shore components)
Cross-Wavelet (cross-shore components)

8. Day 125 (ADCP 5 and 6) ADCP 5 ADCP 6
Provides estimate of joint energy between 2 series rotating in same direction
ADCP5: 0 rotation assctd with high power signature – 20 deg rotation asstd with smaller power signature.
ADCP6: near bottom pwer sig asstid with 50 deg CCW rotation – no rot in CW though
No other power sigs have asstd rotation
Corrotating Cross-Wavelet (in vertical)

9. Day 125 (between ADCP5 and 6)
Very small area of high power where 5 leads 6, but not in co-rotation, not local pwer max, and not seen
Cross-Wavelet of surface cross-shore components between 5 and 6
Corrotating Cross-Wavelet of surface velocities between 5 and 6

10. Day 126 126.447 - No preceding pulse at ADCP5 VLF adcp5 VLF adcp6
} surface greater by .08 m/s
- No preceding pulse at ADCP5
VLF adcp5
VLF adcp6

11. Day 126 (5 and 6) ADCP6 ADCP5 Wavelet (cross-shore components)
No significant power maxs at pulse time – a bit later we have a pwer sig (22-44 min) in bottom and spread in top at ADCP 6
ADCP5
Wavelet (cross-shore components)
Cross-Wavelet (cross-shore components)

12. Day 129 – uniform ex. 129.732 129.778 - No data available at ADCP5
- No data available at ADCP5
VLF adcp6

13. Day 129 ADCP6 Wavelet (cross-shore components)
Appears to have more power in near-sfc (works for 2nd but not 1st), but also has perplexing power sig in low bin
Has good uniform examples but see primarily sfc domination in WT
Wavelet (cross-shore components)
Cross-Wavelet (cross-shore components)

14. Day 129 Corrotating Cross-Wavelet (in vertical)
Interesting CCW phase ‘ears’ on times of pulses – show CCW rotation from bottom but phase changes and goes negative – doesn’t exatly correlate with power sigs
Corrotating Cross-Wavelet (in vertical)

15. Synthetic pulses to see how this works – 5 min lag between pulses of 15 min duration
2nd - V
1st - U
11 min
22 min
Note – the WTC came out uniformly valued at 1
Pulse – sinusoidal pulse over random (normal) noise of lower intensity
Wavelet
Cross-Wavelet 18

16. Cross-rotary - 5 min lag in pulse (rotated 30°)
2nd – U & V
1st - U 21

17. Results and Recommendations
RCEX pulses – significant events on result plots are confusing, no observable link between near-surface and near-bottom velocities and between instruments
Synthetic pulse – cannot differentiate between time lag and rotation, non-usable results
Wavelet analysis not recommended for analyzing pulses – gain no advantage over direct inspection of time series
Can try different wavelet kernel (Harr vs. Morlet window) – what advantage?

18. References
Grinsted, A., Moore, J. C., & Jevrejeva, S. (2004). Application of the Cross Wavelet Transform and Wavelet Coherence to Geophysical Time Series. Nonlinear Processes in Geophysics, 11,
Haas, K. A., & Svendsen, I. A. (2002). Laboratory Measurements of the Vertical Structure of Rip Currents. Journal of Geophysical Research, 107 (C5), doi: /2001JC000911, 1-19.
Hormazabal, S., Shaffer, G., & Leth, O. (2004). Coastal Transition Zone off Chile. Journal of Geophysical Research, 109 (C0), doi: /2003JC001956, 1-13.
Inman, D. L., Tait, R. J., & Nordstrom, C. E. (1971). Mixing in the Surf Zone. Journal of Geophysical Research, 76,
Liu, Y., San Liang, X., & Weisberg, R. H. (2007). Rectification of the Bias in the Wavelet Power Spectrum. Journal of Atmospheric and Oceanic Technology, 24,
MacMahan, J., Thorton, E. B., Stanton, T. P., & Reniers, J.H.M. (2005). RIPEX: Observations of a Rip Current System. Marine Geology, 218,
Smith, J. A., & Largier, J. L. (1995). Observations of Nearshore Circulation: Rip Currents. Journal of Geophysical Research, 100,
Torrence, C., & Compo, G. P. (1998). A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society, 79,

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