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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. Decay Time Scale of Mixed Layer Inertial Motions in the World Ocean (Observations from Satellite Tracked Drifters) . JongJin Park Woods Hole Oceanographic Institution. P. wind.

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Decay Time Scale of Mixed Layer Inertial Motions in the World Ocean (Observations from Satellite Tracked Drifters)

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

  2. P wind Global Inertial Kinetic Energy ( EI ) Park et al. [2005]: Mixed layer KE Alford and Whitmont [2007]: Depth integrated Inertial kinetic energy( ) Inertial energy budget in the mixed layer Previous Studies Inertial energy flux from wind ( ) 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] Mixed Layer Global distribution of decay time scale Long-Term Goal : Global inertial energy budget in the oceanic mixed layer Inertial energy efflux out of the mixed layer

  3. Wind Mixed Layer What is Inertial Decay Timescale ? • 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 • 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] - 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 • 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] • 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]. Without background flow With background flow Q: Which factor can play more important role to control the global distribution of inertial decay timescale?

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

  6. Global distribution of inertial amplitude (U) Drifter measurement of U (cm/s) Mean Inertial amplitude (2ox2o)1990~2004 Inertial energy flux estimated by a slab model and NCEP wind

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

  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) Temporal correlation function of inertial amplitudes from the Drifter Observation (%) (%) North Pacific (50oN~60oN) North Atlantic (50oN~60oN) δ=12.9 (9.2-16.6) δ= 4.8 (4.2-5.5) (%) (%) North Pacific (20oN~30oN) North Atlantic (20oN~30oN) δ= 3.7 (3.0-4.4) δ= 4.0 (3.4-4.5) • Exponential shape • Basin wide difference • Meridional difference

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

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

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

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

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

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

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

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

  18. Buoyancy structure longer δ • N and Hm seem to be canceled out in terms of spatial distribution. • Shallow Hm 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

  19. Understanding Dynamics From Kunze [1985]’s dispersion relation Group velocity of inertial-internal wave ignoring vertical shear of low frequency background current assuming Stratification and Local inertial frequency fo N2 or Beta Effect and Forcing Scale [D’Asaro, 1989]

  20. [Zervakis and Levine, 1995] High Mode Shallow MLD Low Mode Deep MLD Understanding Dynamics : MLD Mixed Layer Depth 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]

  21. Summary & Conclusion • Temporal correlation function • Theoretical solution Acceptable Rayleigh damping Shape of exponential function • 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. • The decay time scale distribution shown in this study suggested that the mixed layer inertial energy budget may have basin-dependency.

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

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

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