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Diabatic Balance Model for the Equatorial Atmosphere

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  • 1 Department of Physics, University of Toronto, Toronto, Ontario, Canada
  • | 2 Department of Meteorology, University of Reading, Reading, Berkshire, United Kingdom
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Abstract

Using an asymptotic expansion, a balance model is derived for the shallow-water equations (SWE) on the equatorial β plane that is valid for planetary-scale equatorial dynamics and includes Kelvin waves. In contrast to many theories of tropical dynamics, neither a strict balance between diabatic heating and vertical motion nor a small Froude number is required. Instead, the expansion is based on the smallness of the ratio of meridional to zonal length scales, which can also be interpreted as a separation in time scale. The leading-order model is characterized by a semigeostrophic balance between the zonal wind and meridional pressure gradient, while the meridional wind υ vanishes; the model is thus asymptotically nondivergent, and the nonzero correction to υ can be found at the next order. Importantly for applications, the diagnostic balance relations are linear for winds when inferring the wind field from mass observations and the winds can be diagnosed without direct observations of diabatic heating. The accuracy of the model is investigated through a set of numerical examples. These examples show that the diagnostic balance relations can remain valid even when the dynamics do not, and the balance dynamics can capture the slow behavior of a rapidly varying solution.

Corresponding author address: Ian Chan, Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada. E-mail: ianchan@atmosp.physics.utoronto.ca

Abstract

Using an asymptotic expansion, a balance model is derived for the shallow-water equations (SWE) on the equatorial β plane that is valid for planetary-scale equatorial dynamics and includes Kelvin waves. In contrast to many theories of tropical dynamics, neither a strict balance between diabatic heating and vertical motion nor a small Froude number is required. Instead, the expansion is based on the smallness of the ratio of meridional to zonal length scales, which can also be interpreted as a separation in time scale. The leading-order model is characterized by a semigeostrophic balance between the zonal wind and meridional pressure gradient, while the meridional wind υ vanishes; the model is thus asymptotically nondivergent, and the nonzero correction to υ can be found at the next order. Importantly for applications, the diagnostic balance relations are linear for winds when inferring the wind field from mass observations and the winds can be diagnosed without direct observations of diabatic heating. The accuracy of the model is investigated through a set of numerical examples. These examples show that the diagnostic balance relations can remain valid even when the dynamics do not, and the balance dynamics can capture the slow behavior of a rapidly varying solution.

Corresponding author address: Ian Chan, Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada. E-mail: ianchan@atmosp.physics.utoronto.ca
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