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An Analytical Study of Filtered Tropical Flows Using an Improvement of the Longwave Model

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

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An Analytical Study of Filtered Tropical Flows Using an Improvement of the Longwave Model

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

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

  3. Wave Types -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

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

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

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

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

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

  11. Forced Model -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

  12. References 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.

  13. Horizontal structure

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