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

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-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

0

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hyv

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u

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hyu

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-Gill model neglects , we use

Gill Model vs. Filtered Model

Gill model equations Filtered model equations

0

x

hyv

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uβ

0

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hyu

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vβ

02

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uc

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h

0

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hyv

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uβ

0~

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hyu

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vβ

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h

Gill Model vs. Filtered Model

-Using Ripa (1994) method of separating and h into Kelvin and non-Kelvin parts

Gill using Ripa method Filtered using Ripa method

-Can do this because v=0 for Kelvin waves

,,vu

-Need to solve a master equation for potential function,

-1st 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. 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-balanceddynamics 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

Horizontal structure