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.
An Analytical Study of Filtered Tropical Flows Using an Improvement of the Longwave Model
Alex O. Gonzalez
Wayne Schubert, Matt Masarik, Levi Silvers, Jonathan Vigh, CMMAP, and SOARS Program
-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
Wave Types Improvement of the Longwave Model
-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
-Filter out inertia-gravity waves
-OLR shows relative importance of wave types for MJO
-Filters out inertia-gravity wave while retaining Kelvin waves
Rossby Dispersion Approximation Improvement of the Longwave Model
-Provides a better approximation of Rossby waves of all wavelengths
Matsuno Primitive Model
-Two important models: Matsuno and Gill
-Want to improve Gill model because it distorts short Rossby waves
Gill Longwave Model
-Shallow-water primitive equations without forcings
-Gill model neglects , we use Improvement of the Longwave Model
Gill Model vs. Filtered Model
Gill model equations
Filtered model equations
Gill Model vs. Filtered Model Improvement of the Longwave 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
Potential Function Improvement of the Longwave Model
-Need to solve a master equation for potential function,
-1st order dispersion relation, instead of cubic
-Gill model dispersion relation does not contain
-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
References Improvement of the Longwave Model
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.