1. 1 JongJin Park Woods Hole Oceanographic Institution Decay Time Scale of Mixed Layer Inertial Motions in the World Ocean (Observations from Satellite Tracked Drifters) Internal Wave Workshop, 3-4 October 2008, Applied Physics Laboratory-University of Washington, Seattle

2. 2 Inertial energy budget in the mixed layer Mixed Layer Inertial kinetic energy( ) Global Inertial Kinetic Energy ( E I ) Park et al. [2005]: Mixed layer KE Alford and Whitmont [2007]: Depth integrated Previous Studies Inertial energy flux from wind ( ) Alford [2001; 2003] Watanabe and Hibiya [2001] Jiang et al. [2005] ~ based on a slab ocean model Plueddemann and Farrar [2007] wind  Long-Term Goal : Global inertial energy budget in the oceanic mixed layer Global distribution of decay time scale Inertial energy efflux out of the mixed layer

3. 3 What is Inertial Decay Timescale ? Wind Mixed Layer Pollard and Millard [1970]’s slab ocean model : decay time-scale ( ) Parameterization of decaying inertial motion in the mixed layer  Inertial motion decays exponentially Q: How is the decay time scale distributed in the global ocean ?

4. Dynamics of inertial motion decay 4 Two ways of decaying inertial motion in the mixed layer - Propagation of inertial-internal wave (Non-Turbulent process) : [Gill, 1984; D’Asaro, 1989; Zervakis and Levine, 1995; Meurs, 1999; etc…] - Turbulent mixing at the base of the mixed layer (Turbulent process) : [D’Asaro, 1995; Eriksen, 1991; Hebert and Moum, 1994] Most of the previous studies focused on the wave propagation as a major decaying process. The wave propagation may be primarily responsible for the fast decay of mixed layer inertial energy [Balmforth and Young, 1999; Moehlis and Smith, 2001]. - Buoyancy Frequency - Forcing scale : Gill [1984], D’Asaro [1995] - Wave number change by Beta effect : D’Asaro [1989] - Mixed layer depth : Zervakis and Levine [1995] - Flow convergence : Weller [1982] - Relative vorticity : Kunze [1985], Balmforth and Young [1999] - Relative vorticity gradient : Van Meurs [1999] - Etc : Advection by background flow Vertical shear of the flow Without background flowWith background flow Q: Which factor can play more important role to control the global distribution of inertial decay timescale?

5. Method to estimate inertial amplitude from Satellite Tracked Drifter Weighted Function Fitting Method m : cycle number (Park et al., 2004) Inertial Recti- linear Trajectory segment length : > 0.7 * local inertial period Number of fixes : > 5 Data latitude : 60 o S~60 o N except 29 o ~31 o Rectilinear velocity : < 50 cm/s Data Criteria Inertial amplitude Distribution of inertial amplitudes (U) estimated from Satellite tracked drifters (1990~2004)

6. Global distribution of inertial amplitude (U) 6 Mean Inertial amplitude (2 o x2 o ) 1990~2004 (cm/s) Drifter measurement of U Inertial energy flux estimated by a slab model and NCEP wind

7. 7 Assumption : Homogeneous amplitude within (Uncorrelated observation error, homogeneity of error, homogeneity of variance) Freeland et al. [1975] Separation Time (day) Correlation e-folding (δ) = 4.9 (4.1- 6.1) (95% confidence interval) North Pacific (Winter) U I (t j ) U I (t i ) Lag - 1day Corrcoef. = 0.84 U I (t j ) U I (t i ) Lag - 5day Corrcoef. = 0.44 Estimating decay time scale of inertial amplitude (U)

8. 8 Concept of estimating decay time scale Preset Decay Function Auto- Correlation Random Pair Sampling Inertial amplitudes from a short-term trajectory segment Independent dataset for 15 years Temporal correlation function in the basin average sense Utilizing the whole data in a certain area by the pair-sampling method

9. Examples of Correlation Function (Bootstrap resampling) 9 (%) Temporal correlation function of inertial amplitudes from the Drifter Observation δ=12.9 (9.2-16.6) North Pacific (50 o N~60 o N) δ= 3.7 (3.0-4.4) North Pacific (20 o N~30 o N) δ= 4.0 (3.4-4.5) North Atlantic (20 o N~30 o N) δ= 4.8 (4.2-5.5) North Atlantic (50 o N~60 o N) Exponential shape Basin wide difference Meridional difference

10. 10 Decay time scale of inertial amplitude (U) LOW MID HIGH LOW MID HIGH North AtlanticNorth Pacific Winter (D-A) Summer (J-O) 95% confidence interval Low = 15N~30N, Mid = 30N~45N, High = 45N-60N ★ ★ Winter Summer Previous Moored Obs. North Pacific : Slow decay in high latitude North Pacific : Slow decay in summer North Atlantic : No significant meridional distribution E-folding timescale of observed correlation function ★ ★ ★ ★ ★ ★ ★ ★ ★

11. Meridional distribution of decay time scale Drifter Observation North Atlantic (60W~0) South Pacific (150E~80W) North Pacific (140E~100W) South Atlantic + Indian Ocean (80W~150E) Decay time scale increases with latitude Decay time scale hardly varies from 20 o to 40 o and rapidly increases with latitude higher than 45 o No significant meridional variation in the North Atlantic Q: How is the decay time scale distributed in the global ocean ?  What makes the time scale so different in space?

12. 12 Understanding spatial variation of observed decay time scale [Young and Ben Jelloul, 1997; Balmforth and Young, 1999] [Local change] [Wave advection] [Wave dispersion] [Wave refraction] Propagation equation of Near-Inertial Wave No zonal variation of and A: Small relative vorticity : Linear density profile with mixed layer (H m ) Assumptions [Moehlis and Smith, 2001]

13. 13 Non-dimensionalize Initial condition Simplified Analytical Model (Discussed with Stefan L. Smith at Scripps) U* Solution for amplitude evolution in the mixed layer

14. Initial Scale, MLD, and N from QuikSCAT and Argo floats (2000~2007) λ U ~Meridional scale of correlation (R) (km) Forcing scale (λ U ) With 72 hours high pass filtered QuikSCAT wind (U w ) MLD (H m ) Density based method of Kara et al. [2000] (m) N max (N) (s -1 )

15. Decay timescale based on simplified analytical model (day) 95% Confidence Level estimated by Bootstrap method Decay timescale simulated by theoretical model (day)

16. Comparison of observation and analytical model Theoretical Model Drifter Observation Q: Which factor can play an important role to control the global distribution of inertial decay timescale?

17. Control Factors for decay time scale : Basin-averaged value of the North Pacific Forcing Scale Beta Effect Bouyancy Effect Decay Time Scale North Pacific North Atlantic South Pacific South Atlantic Why are the meridional structures of the buoyancy effect so different?

18. Buoyancy structure N and H m seem to be canceled out in terms of spatial distribution. Shallow H m in the high latitude of the North Pacific is responsible for the longer decay time scale. Weaker stratification in the Southern Ocean makes the time scale longer. In the North Atlantic, deep mixed layer and yet strong buoyancy may be the major cause of the shortest decay time scale in the high latitudes. longer δ longer δ longer δ

19. 19 Understanding Dynamics From Kunze [1985]’s dispersion relation Group velocity of inertial-internal wave ignoring vertical shear of low frequency background current N2N2 fofo or assuming [D’Asaro, 1989] Stratification and Local inertial frequency Beta Effect and Forcing Scale

20. 20 Understanding Dynamics : MLD With a continuously varying density structure, a perturbation is separated into several modes (normal modes). Large MLD induces lower modes to have larger energy [Zervakis and Levine, 1995] [Zervakis and Levine, 1995] Deep MLD Shallow MLD Low Mode High Mode Mixed Layer Depth

21. 21 Summary & Conclusion Global distribution of inertial decay timescale from the drifter observation : Increasing with latitudes in all the basins except in the North Atlantic The analytical model with beta dispersion dynamics reproduces global distribution of the decay timescale fairly comparable to the observation. Dephasing process by beta effect is primarily responsible for the meridional variation of the decay timescale in the North Pacific and the Southern Ocean. In the North Atlantic, buoyancy effect seems to compensate the beta effect which leads to a lack of meridional variation. Temporal correlation function Theoretical solution Shape of exponential function Acceptable Rayleigh damping The decay time scale distribution shown in this study suggested that the mixed layer inertial energy budget may have basin-dependency.

22. 22 Special thanks : Ray Schmitt, Young-Oh Kwon, Chris Garrett, Stefan Smith, Kurt Polzin, Tom Farrar, Julie Deshayes

23. 23 Special thanks : Ray Schmitt, Young-Oh Kwon, Chris Garrett, Stefan Smith, Kurt Polzin, Tom Farrar, Julie Deshayes