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Cited 48 times Keywords: ENSO, Phase locking

Cited 48 times Keywords: ENSO, Phase locking. 1. Introduction. El Nino events happen irregularly which makes their prediction difficult. In spite of its irregularity, El Nino tend to peak near the end of the calendar year. Two-year segments of the observed

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Cited 48 times Keywords: ENSO, Phase locking

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  1. Cited 48 times Keywords: ENSO, Phase locking

  2. 1. Introduction El Nino events happen irregularly which makes their prediction difficult In spite of its irregularity, El Nino tend to peak near the end of the calendar year Two-year segments of the observed NINO3 index during several El Nino events Phase Locking http://www.deas.harvard.edu/climate/eli/Level2/research-elnino.html

  3. 2. The Mixed-mode Regime Ocean dynamics model + Thermodynamics model + wind coupling to SST Model equation – ocean dynamics • Assumptions • Shallow water anomaly equation • Equatorial beta plane • Neglect meridional damping & wind stress • Neglect Advection, Density change by SST, … : Thermocline depth from its mean state (1a) : Mean thermocline depth (1b) : Oceanic damping coefficient (1c) u from (1b) and v from (1a) and eliminating u and v with (1c) (2)

  4. Ocean Dynamics Two-strip approximation : to evaluate solution at the equator (y=0) and zonal band off the equator (y=yn) : Represent equatorial Kelvin wave and off-equatorial long Rossby wave Kelvin wave solution form (3) (3) -> (2) at y=0 (4) : wind stress at equator Integrating (4) from western boundary at time to eastern boundary at basin length (Kelvin wave crossing time) Assumptions : The wave is excited by wind stress from to : The wind stress is evaluated at , Then we can derive (5)

  5. Ocean Dynamics (2) Solve (2) at the off-equatorial band (y=yn) Neglecting 2nd term and applying Rossby wave form into h (6) Integrating along Rossby wave from east boundary at (7) Reflection: Rossby -> Kelvin @ west, Kelvin -> Rossby @ east (8)

  6. Ocean Dynamics Using equator solution (5), off-equator solution (7), and boundary condition (8) Reflected waves Rossby waves (9) Kelvin waves Thermodynamics The equation describing SST changes : mean upwelling : thermal damping coefficient (10) : temperature anomaly at (lower layer temperature?) function of thermocline depth anomaly h advection by mean upwelling damping : parameter relates temperature anomaly entrained to deeper temperature variation

  7. Ocean-Atmosphere Interaction Taking wind stress to be a function of the SST at the Equator ( ) : function relates SST to wind stress (11) : seasonal coupling coefficient oceanic deformation radius atmospheric (9) Replacing wind stress terms in (9) with (11) (12) : Obtained by solving a Gill-type atmospheric model => Linear relation between wind stress and equatorial SST

  8. Ocean-Atmosphere Interaction The function A for the wind stress is assumed to be proportional to the temperature in the eastern Pacific (13) : Annual mean coupling strength Mixed-mode Model (9) (12) Eq (9) can be re-written using (12) and (13)

  9. Mixed-mode Model Expressing as a function of and at previous times Free Rossby and Kelvin waves Excited Rossby waves (14) Excited Kelvin waves The thermodynamic equation (10): Evaluating at the eastern side of the basin (15) (14) and (15) => mixed-mode model Investigating ENSO’s tendency to peak toward the end of the calendar year.

  10. Seasonally Varying Ocean-Atmosphere Coupling Strength Absence of seasonal cycle -> No phase locking Imposing on the model seasonally varying relation between wind stress and SST Seasonal coupling coefficient : Strength of seasonal cycle : Annual frequency : Phase (max. in May, min. in Nov.) - Events are not regular - Peak in Sep. ~ Dec. (about 6 months after maximum coupling) a) Eastern Pacific SST b) Separation period between events c) Number of peak events for each month (black: El Nino, white: La Nina)

  11. Seasonally Varying Upwelling Applying seasonality of upwelling in thermodynamic equation : max. in Jan., min. in Jun. Ocean – atmosphere coupling is set to its annual mean - Events peak in May-Oct. (upwelling minimum) - Less locked to the seasonal cycle a) Eastern Pacific SST b) Separation period between events c) Number of peak events for each month

  12. Combined Effect of Coupling Strength and Upwelling Examine the event locking to seasonal change in coupling and upwelling - Peak time in Sep. – Nov. (Almost same in case of seasonally varying coupling strength only) - Event amplitude is smaller - Upwelling is a secondary importance a) Eastern Pacific SST b) Separation period between events c) Number of peak events for each month <= SST time series for case of seasonally varying coupling strength only Phase locking of La Nina is less robust than that of El Nino (Asymmetry in )

  13. Physical mechanism for phase locking in the mixed-mode regime Linearization of the model -> Separating each process 12 runs with different initial condition All integrations have their peak at the end of the calendar year => Phase locking is not from nonlinearity

  14. Physical mechanism for phase locking in the mixed-mode regime : Thermal damping of the SST : Upwelling depends on the SST : Free Rossby/Kelvin wave : Excitation of Rossby wave due to wind : Excitation of Kelvin wave due to wind 1. EK warms SST : warm SST from central Pacific : Very fast… (almost instantly affects) : Nov: strong wind but weak coupling 2. ER cools SST : Slow… (6months lags) : May: weak wind but strong coupling => They are balanced near Dec…

  15. Thank you!

  16. 3. The fast-SST limit Fast-SST limit: SST adjustment time is much shorter than the ocean dynamics or SST is assumed to respond instantaneously to thermocline depth changes (15) Taking time derivative to be zero from (15) (25) (5) (6) From (5) and (6), (to avoid numerical noise) (26)

  17. 3. The fast-SST limit Clear tendency to lock to Aug. – Oct. ROS: Rossby wave (RK + ER) KEL: Kelvin wave excitation (EK) - Very similar results with mixed-mode regimes case - About 2 months’ difference : 2 months’ delay by upwelling Mixed-mode Fast-SST

  18. 4. The fast-wave limit Fast-wave limit: Rossby/Kelvin wave propagation speeds are assumed infinite Instantaneous adjustment of thermocline depth and velocity Taking time derivatives to be 0 from the governing equation (1) Dividing the Pacific basin into two boxes: east Pacific / central Pacific Then we can get followings (skip the solving process here, see appendix B) (27) (28) DO DU HU DO: Damping due to cooling DU: Damping due to upwelling HU: Effect of the thermocline depth on the upwelling Index c: central Pacific Index e: eastern Pacific

  19. 4. The fast-wave limit - Even in this case, events peak in Aug. – Oct. (Not very robust, but phase locking) DO: Damping due to cooling DU: Damping due to upwelling HU: Effect of the thermocline depth on the upwelling

  20. Summary ENSO’s phase locking to the seasonal cycle - Seasonal variations in ocean-atmosphere coupling strength is important - Effect of upwelling is less important - Not from non-linearity Mechanism of phase locking - Seasonal excitation of the Kelvin and Rossby waves by wind stress - Balance between warming and cooling trends at the peak time due to (downwelling) large amplitude Kelven wave amplified weak coupling and (upwelling) weak Rossby wave amplified strong coupling Fast-SST limits - Similar with Mixed-mode - 2 months difference from adjustment time of SST Fast-Wave limits - SST adjustment time - Interaction between eastern and central Pacific

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