Coupled Moist Kelvin-Rossby Equatorial Wave

Coupled Moist Kelvin-Rossby Equatorial Wave PowerPoint PPT Presentation

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History of MJO theories. MJO documented ? 1972?Holy Grail" of Tropical Meteorology (Raymond, 2001)Madden and Julian (1972) discussion:May be associated with Tides!!Some sort of SST feedbackLarge scale waves due to stationary heatingSimilarity to Kelvin wavesMadden and Julian (1993) review:Wave response to slowly moving heat sourcePropagation faster than Kelvin wavesMoist processes (Kelvin-CISK) can slow down the speedCoupled Kelvin-Rossby model ? adequate first order model.

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Coupled Moist Kelvin-Rossby Equatorial Wave

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1. Coupled Moist Kelvin-Rossby Equatorial Wave Atul Kapur RSMAS, Univ of Miami

2. History of MJO theories MJO documented – 1972 “Holy Grail” of Tropical Meteorology (Raymond, 2001) Madden and Julian (1972) discussion: May be associated with Tides!! Some sort of SST feedback Large scale waves due to stationary heating Similarity to Kelvin waves Madden and Julian (1993) review: Wave response to slowly moving heat source Propagation faster than Kelvin waves Moist processes (Kelvin-CISK) can slow down the speed Coupled Kelvin-Rossby model – adequate first order model

3. Wave theories of the MJO Common Problems Kelvin wave – “only” eastwards propagating equatorial mode Phase speed of Kelvin waves ~ 40 ms-1 (MJO phase speed ~ 5 ms-1) Viscous damping of Kelvin wave (insufficient to slow down) Convectively coupled Kelvin wave theory e.g. Wang (1988) Convective heating interacts with low level convergence Unstable mode arises in Kelvin wave - CISK theory Phase speed ~ 15 ms-1 2-d equatorial zonal plane

4. Coupled Kelvin-Rossby wave Why include Rossby waves? Observed with MJO! Some questions were left unanswered in moist Kelvin wave analysis: Reason for unstable mode selection? Analysis confined to 2-d motion Unrealistic phase speed from No seasonal variation in model

5. Basic model attributes Includes meridional component of motion Rossby and Kelvin waves Semigeostrophic model Zonal wind component in geostrophic balance High frequency waves get filtered out Non linear advection terms neglected Boundary layer moisture convergence

6. More details Absolute humidity falls off exponentially with height Humidity at the surface linearly correlated with SST SST assumed to be an idealized function of y

7. 2½ Layer Model

8. Divergence Equations Vertical motion caused by boundary layer friction Boundary conditions: Free surface condition Barotropic part non divergent We can study the baroclinic part independent of barotropic Lateral boundary condition at

9. Moist mode analysis Inviscid case I and B represent ratio of latent heating rate to adiabatic cooling I and B are related to moisture content Recall moisture content is related to SST Inviscid case – Phase speed becomes purely imaginary for I > 0 No equatorially trapped unstable modes possible necessary for Kelvin–Rossby wave–CISK

10. Viscous case

11. Unstable mode selection Viscous case Rate of generation of perturbation available potential energy is is found to be positive when SST > 20.2°C and increases with rising SST. Equatorial warm water region + positively correlation between and Most favourable for generation of wave energy Sufficiently high moisture concentration Latent heat induced due to frictional convergence can exceed dissipation ? wave growth.

12. Dry Kelvin and first Rossby modes

13. Phase speed and growth rate Comparison with viscous Kelvin wave – CISK model (Wang, 1988)

14. Phase speed and growth rate Wavelength and SST dependence

15. Seasonality Observations: MJO strongest in boreal winter In boreal summer maximum SST moves away from the equator Decrease in moist static energy at the equator Decrease in growth rate of unstable waves

16. Parting Remarks Dry atmosphere is stable: dissipative effects dominate If moisture concentration increases Induced latent heat increases (frictional convergence) May overcome dissipative effects Kelvin mode progressively becomes less damped and finally begins to grow Unstable modes appear to be rooted in Kelvin modes Modified by dynamic coupling with Rossby waves Acts as an efficient brake on eastward propagation Suppresses unrealistically fast growth

17. Limitations of the model CISK closure not very convincing Essentially implies direct dependence of convective heating upon moisture convergence “Shallow circulation” may exist at the equator

18. Thank You

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