Review Article
Middle atmosphere dynamics with gravity wave interactions in the numerical spectral model: Tides and planetary waves

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Abstract

As Lindzen (1981) had shown, small-scale gravity waves (GW) produce the observed reversals of the zonal-mean circulation and temperature variations in the upper mesosphere. The waves also play a major role in modulating and amplifying the diurnal tides (DT) (e.g., Waltersheid, 1981; Fritts and Vincent, 1987, Fritts, 1995a). We summarize here the modeling studies with the mechanistic numerical spectral model (NSM) with Doppler spread parameterization for GW (Hines, 1997a, Hines, 1997b), which describes in the middle atmosphere: (a) migrating and non-migrating DT, (b) planetary waves (PW), and (c) 10-h global-scale inertio gravity waves. Numerical experiments are discussed, which illuminate the influence of GW filtering and nonlinear interactions between DT, PW, and zonal mean variations.

Research highlights

► Theoretical model simulates middle atmosphere tides, planetary waves (PW), 10-h oscillations. ► Model studies with parameterized gravity waves (GW) provide understanding of observed phenomena. ► GW interactions producing stratospheric QBO amplify mesospheric tides, PW, 10-h oscillations. ► GW filtering with amplification of tides and PW generate seasonal and inter-annual variations. ► GW generate non-migrating tides through nonlinear interaction between migrating tides and PW.

Introduction

The fundamental properties of diurnal tides (DT) and planetary waves (PW) are well understood (Chapman and Lindzen, 1970, Holton, 1979, Kato, 1980, Volland, 1988). Measurements from the ground and with spacecraft have shown that the DT in the mesosphere and lower thermosphere exhibit large seasonal and inter-annual variations, and that they are modulated by PW (e.g., Avery et al., 1989, Manson et al., 1989; Vincent et al., 1998; Gille et al., 1991, Hays et al., 1994, Burrage et al., 1995a, Burrage et al., 1995b, McLandress et al., 1996, Wu et al., 1998, Leblanc et al., 1999a, Leblanc et al., 1999b, Vincent et al., 1998, Huang and Reber, 2003, Huang and Reber, 2004, Wu and Jiang, 2005, Manson et al., 2002, Zhang et al., 2006, Mukhtarov et al., 2009, Huang et al., 2006, Huang et al., 2010).

In the mesosphere, the DT, PW, and small-scale gravity waves (GW) attain large amplitudes, and their interactions have been the subject of theoretical studies (e.g., Walterscheid, 1981, Fritts, 1984, Fritts, 1995a, Fritts, 1995b, Fritts and Vincent, 1987, Vial and Forbes, 1989, Forbes et al., 1991, Forbes, 1995). Numerical models have been employed to study the DT under the influence of the zonal-mean circulation, eddy viscosity, and GW interactions (e.g., Lindzen and Hong, 1974, Forbes and Hagan, 1988, Forbes and Vial, 1989, Akmaev et al., 1996, Miyahara and Forbes, 1991, Hagan, 1996, Hagan et al., 1993, Hagan et al., 1997, Hagan et al., 1999a, 1997; Jacobi et al., 1999, Yudin et al., 1997, McLandress, 1997a, McLandress, 2002a, McLandress, 2002b, Miyahara et al., 1993, Miyahara et al., 1999, Geller et al., 1997, Mayr et al., 1998, Akmaev, 2001a, Akmaev, 2001b).

We deal with wave-mean flow interactions in a global scale model, where the GW processes need to be parameterized. With this approach, Lindzen (1981) showed that GW interactions with the zonal circulation can produce the observed temperatures in the upper mesosphere, which are lower in summer than in winter. Wave interactions like that are also involved in generating the quasi-biennial oscillation (QBO) in the lower stratosphere that can be produced with planetary waves (e.g., Lindzen and Holton, 1968). Modeling studies with observed planetary waves have led to the conclusion that GW must also be important for the QBO, and this has been confirmed in studies with the numerical spectral model (NSM), which are summarized in Mayr et al. (2010), referred to as Part I. The QBO is produced in the NSM through critical level absorption of GW, applying the parameterization developed by Hines, 1997a, Hines, 1997b. Walterscheid (1981) proposed that wave mean flow interactions generating the QBO could also amplify the tides, and this has been confirmed in our GW studies with the NSM, which are summarized in the present companion paper.

Chan et al., 1994, Chan et al., 1995 introduced the NSM, which is fully nonlinear and is integrated from the surface into the thermosphere. Formulated in terms of vector spherical harmonics, the model allows us to study the individual and interacting dynamical components with zonal wave numbers m=0–4, as illustrated in Fig. 1 of Part I. The zonal-mean (m=0) heating rates for the middle atmosphere are taken from Strobel (1978), and the excitation rates for the migrating DT in the troposphere and stratosphere are taken from Forbes and Garrett (1978). Solar EUV heating is applied in the thermosphere. The planetary waves (PW) are generated internally by instabilities. Newtonian cooling describes radiative loss (Wehrbein and Leovy, 1982, Zhu, 1989). Starting with Mengel et al. (1995), the NSM has been run with the GW Doppler spread parameterization (DSP) of Hines, 1997a, Hines, 1997b. In the DSP formulation, GW momentum is strictly conserved, which is important for wave filtering and the associated nonlinear interactions. The DSP comes with uncertainties that affect the height dependent GW momentum source and eddy viscosity, and the input parameters were changed over the years as documented in the literature. In all DSP applications, for simplicity, the GW source at the initial height was chosen to be isotropic, time independent, and hemispherically symmetric.

By way of introduction, we present in Fig. 1 numerical results from 2D (a) and 3D (b) versions of the NSM. Applying the same GW source at the initial height, the zonal-mean (m=0) winds are shown, which describe the quasi-biennial oscillation (QBO) and semi-annual oscillation (SAO) near the equator. From the 2D model (Fig. 1a), the winds are much larger than those in 3D (Fig. 1b). The GW in 2D are solely available to generate and amplify the QBO and SAO. In 3D, the GW apparently amplify the tides and planetary waves at the expense of the equatorial oscillations. This illustrates how GW interactions can influence, and couple, the dynamical components of the atmosphere.

In the following we show how GW processes affect the tides and planetary waves as enumerated in Fig. 2. Numerical experiments are presented that provide understanding.

Section snippets

Diurnal tides

Generated primarily by solar heating, the dominant diurnal tides propagate with the Sun westward and are referred to as migrating tides. The non-migrating tides, not propagating with the Sun, are generated in the NSM with planetary waves (PW)—and they are later discussed. Here we deal primarily with migrating tides with inclusion of weaker non-migrating oscillations.

For the fundamental 24-h diurnal tide, the basic effect of GW momentum deposition is demonstrated in numerical results taken from

Non-migrating tides

The so-called diurnal and semi-diurnal migrating tides (MT) propagate westward with the Sun, occupy m=1 and 2, and have periods of 24 and 12 h, respectively. The non-migrating tides (NMT) also have periods of 24 and 12 h, commensurated with solar heating. But unlike the MT, the NMT can also propagate eastward, be stationary (m=0), or occupy any wave number.

Non-migrating tides (NMT) have been observed in the middle atmosphere with satellite borne wind and temperature measurements (e.g., Lieberman,

Planetary-scale inertio gravity waves

In the upper mesosphere, oscillations with periods around 10 h have been observed with different measurement techniques. Analyzing radar wind data at Saskatoon (52°N), Manson et al. (1982) and Manson and Meek (1990) discovered persistent oscillations with periods of 9–10 and 16 h, which were attributed to nonlinear coupling between the semi-diurnal tide and planetary waves. Such oscillations were also reported by Ruster (1994) and Sivjee et al. (1994). In optical measurements of winds and

Planetary waves

The dynamical properties of planetary waves (PW) are well understood and are discussed in the textbook literature (e.g., Holton, 1979, Volland, 1988). Topographic forcing and tropical convection can produce the PW originating in the troposphere, and the baroclinic instability has been invoked for the PW generated in the mesosphere (Plumb, 1983, Pfister, 1985). As the PW propagate up through the middle atmosphere, they attain large amplitudes in the upper mesosphere as observed with ground-based

Summary

We summarize numerical results from the numerical spectral model (NSM) that is integrated from the ground into the thermosphere. The spectral formulation allows us to analyze the individual, and interacting, dynamical components with different zonal wave numbers, which describe the zonal-mean variations, tides, and planetary waves.

The NSM employs the Doppler spread parameterization (DSP) for small-scale gravity waves (GW) developed by Hines, 1997a, Hines, 1997b. With the DSP formulation, the

Acknowledgement

The authors are greatly indebted to a reviewer for constructive comments and pointing out the paper of Larsen (2002), which contributed significantly to improve the paper.

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