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

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


An analytical study of filtered tropical flows using an improvement of the longwave model

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


Olr observations

OLR Observations

-Filter out inertia-gravity waves

-OLR shows relative importance of wave types for MJO


Dispersion diagram

Dispersion Diagram

-Filters out inertia-gravity wave while retaining Kelvin waves


An analytical study of filtered tropical flows using an improvement of the longwave model

Rossby Dispersion Approximation

-Provides a better approximation of Rossby waves of all wavelengths


Analytical models

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


An analytical study of filtered tropical flows using an improvement of the longwave model

-Gill model neglects , we use

Gill Model vs. Filtered Model

Gill model equations

Filtered model equations


An analytical study of filtered tropical flows using an improvement of the longwave model

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


An analytical study of filtered tropical flows using an improvement of the longwave model

Potential Function

-Need to solve a master equation for potential function,

´ü¬

-1st order dispersion relation, instead of cubic

-Gill model dispersion relation does not contain


Forced model

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


An analytical study of filtered tropical flows using an improvement of the longwave model

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.


Horizontal structure

Horizontal structure


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