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Gravity Wave Perturbations of Minor Constituents: A Parcel Advection Methodology

Stephen D. EckermannComputational Physics, Inc., Fairfax, Virginia

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Dorothy E. Gibson-WildeColorado Research Associates, Boulder, Colorado

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Julio T. BacmeisterE. O. Hulburt Center for Space Research, Naval Research Laboratory, Washington, D.C.

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Abstract

Existing analytical models of wave-induced minor constituent fluctuations result from linearized perturbation expansions of a rate equation governing either number density or mixing ratio, whereas many numerical models now use isentropic parcel advection methods to simulate these effects. Exact relationships between the two approaches are not currently clear for gravity waves. Here, the parcel advection method is formalized and applied to derive analytical formulas for the response of vertical constituent profiles of arbitrary shape to adiabatic gravity wave displacements. These relations are compared to corresponding formulas from standard linearized perturbation analyses. Both methods accurately model perturbations produced by nondissipating hydrostatic gravity waves within idealized vertical tracer profiles. Both methods can also model wave-induced perturbations of minor constituents with shorter chemical lifetimes. This is demonstrated by using the parcel method to reproduce previous results for wave-induced fluctuations in upper-stratospheric ozone. The parcel-based approach yields more accurate models of nondissipating hydrostatic gravity wave effects on tracer distibutions with sharp spatial gradients. The authors demonstrate this by using the method to model wave-induced modulations of sporadic sodium layers in the mesosphere and of ozone laminae in the lower stratosphere. Conversely, the parcel method does not accurately model tracer density perturbations produced by nonhydrostatic waves, or situations in which the photochemical response of the constituent leads to significant diabatic feedback on the perturbing wave.

* Current affiliation: E. O. Hulburt Center for Space Research, Naval Research Laboratory, Washington, D.C.

Corresponding author address: Dr. Stephen D. Eckermann, Computational Physics, Inc., Suite 600, 2750 Prosperity Avenue, Fairfax, VA 22031.

Email: eckerman@cpi.com.

Abstract

Existing analytical models of wave-induced minor constituent fluctuations result from linearized perturbation expansions of a rate equation governing either number density or mixing ratio, whereas many numerical models now use isentropic parcel advection methods to simulate these effects. Exact relationships between the two approaches are not currently clear for gravity waves. Here, the parcel advection method is formalized and applied to derive analytical formulas for the response of vertical constituent profiles of arbitrary shape to adiabatic gravity wave displacements. These relations are compared to corresponding formulas from standard linearized perturbation analyses. Both methods accurately model perturbations produced by nondissipating hydrostatic gravity waves within idealized vertical tracer profiles. Both methods can also model wave-induced perturbations of minor constituents with shorter chemical lifetimes. This is demonstrated by using the parcel method to reproduce previous results for wave-induced fluctuations in upper-stratospheric ozone. The parcel-based approach yields more accurate models of nondissipating hydrostatic gravity wave effects on tracer distibutions with sharp spatial gradients. The authors demonstrate this by using the method to model wave-induced modulations of sporadic sodium layers in the mesosphere and of ozone laminae in the lower stratosphere. Conversely, the parcel method does not accurately model tracer density perturbations produced by nonhydrostatic waves, or situations in which the photochemical response of the constituent leads to significant diabatic feedback on the perturbing wave.

* Current affiliation: E. O. Hulburt Center for Space Research, Naval Research Laboratory, Washington, D.C.

Corresponding author address: Dr. Stephen D. Eckermann, Computational Physics, Inc., Suite 600, 2750 Prosperity Avenue, Fairfax, VA 22031.

Email: eckerman@cpi.com.

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