1. An Analytical Study of Filtered Tropical Flows Using an Improvement of the Longwave Model Acknowledgements Wayne Schubert, Matt Masarik, Levi Silvers, Jonathan Vigh, CMMAP, and SOARS Program Alex O. Gonzalez

2. Overview -Theoretical studies vital because lack of numerical data in tropics -Analytical model using different filtering techniques -Use equatorial wave theory (on beta-plane) to gain insight on atmospheric phenomena such as MJO

3. -4 types of atmospheric waves in equatorial region: -Inertia gravity, Mixed-Rossby gravity, Rossby, and Kelvin waves -Most concerned with Rossby and Kelvin waves for MJO Wave Types

4. OLR Observations -Filter out inertia-gravity waves -OLR shows relative importance of wave types for MJO

5. Dispersion Diagram -Filters out inertia-gravity wave while retaining Kelvin waves

6. -Provides a better approximation of Rossby waves of all wavelengths Rossby Dispersion Approximation

7. -Two important models: Matsuno and Gill -Want to improve Gill model because it distorts short Rossby waves Analytical Models Matsuno Primitive Model Filtered Model Gill Longwave Model -Shallow-water primitive equations without forcings

8. -Gill model neglects, we use Gill Model vs. Filtered Model Gill model equationsFiltered model equations

9. Gill Model vs. Filtered Model -Using Ripa (1994) method of separating and h into Kelvin and non-Kelvin parts Gill using Ripa methodFiltered using Ripa method -Can do this because v=0 for Kelvin waves

10. -Need to solve a master equation for potential function, -1 st order dispersion relation, instead of cubic -Gill model dispersion relation does not contain Potential Function 

11. -Not easy to solve shallow-water equations with convective coupling, need to make assumptions -Follow framework of Ripa (1994) -Use arguments of PV, Geostrophic Flow, and Divergence -Learn more about importance of Rossby and Kelvin modes in MJO Forced Model

12. Gill, A. E. 1980. Some simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteor. Soc., 447-462. Matsuno, T. 1966: Quasi-Geostrophic Motions in the Equatorial Area. J. Meteor. Soc. Japan, 14, 25-42. Ripa, P. 1994: Horizontal wave propagation in the equatorial waveguide. J. Fluid Mech., 271, 267-284 Schubert, W. H., M. T. Masarik, L. G. Silvers, and A. O. Gonzalez 2008: A Filtered Model of Tropical Wave Motions. Q. J. R. Meteorol. Soc. (2008), 134, pp. 1-10. In Progress. Stevens, P. L., H.-C. Kuo, W. H. Schubert, and P. Ciesielski, 1990: Quasi-balanced dynamics in the tropics. J. Atmos. Sci., 47, 2262-2273. Wheeler, M.C., 2002: Tropical Meteorology: Equatorial Waves. In: J. Holton, J. Curry, and J. Pyle (eds), Encyclopedia of Atmospheric Sciences. Academic Press, 2313-2325. References

13. Horizontal structure