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

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

-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

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

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

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

-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

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

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

-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 

-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

Gill, A. E Some simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteor. Soc., Matsuno, T. 1966: Quasi-Geostrophic Motions in the Equatorial Area. J. Meteor. Soc. Japan, 14, Ripa, P. 1994: Horizontal wave propagation in the equatorial waveguide. J. Fluid Mech., 271, 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 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, Wheeler, M.C., 2002: Tropical Meteorology: Equatorial Waves. In: J. Holton, J. Curry, and J. Pyle (eds), Encyclopedia of Atmospheric Sciences. Academic Press, References

Horizontal structure