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In light of the measurements from the TIMED spacecraft and coordinated ground-based observations, we discuss results from a modeling study with our Numerical Spectral Model (NSM), which specifically deals with the non-migrating tides generated in the mesosphere. The NSM extends from the ground to the thermosphere, incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GWs), and it describes the major dynamical features of the atmosphere including the wave driven equatorial oscillations (QBO and SAO), and the seasonal variations of tides and planetary waves (PWs). Accounting solely for the excitation Sources of the solar migrating tides, the NSM generates through nonlinear interactions also non-migrating tides in the mesosphere that are comparable in magnitude to those observed. (The important non-migrating tides generated explicitly by processes like tropospheric latent heat release and convection are not included.) Large non-migrating tides ire produced in the diurnal and semi-diurnal oscillations for the zonal mean (wave number m = 0) and in the semidiurnal oscillation for m = 1. In general, significant eastward and westward propagating tides are generated for all the zonal wave numbers m = 1-4. To identify the cause, the NSM is run without the solar heating for the zonal mean (m = 0), and the amplitudes of the resulting non-migrating tides are then negligibly small. In this case, the PWs generated by instabilities are artificially suppressed. This leads to the conclusion that the non-migrating tides are produced through nonlinear interactions between PWs and migrating tides, as had been previously proposed. In the accompanying paper, we present results from numerical experiments, which demonstrate that GW filtering contributes significantly to produce the nonlinear coupling that is involved. Published by Elsevier Ltd.

The Numerical Spectral Model (NSM) extends from the ground into the thermosphere and incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GWs). In the present version of the model we account for a tropospheric heat source in the zonal mean (m = 0), which reproduces qualitatively the observed zonal jets near the tropopause and the accompanying reversal in the latitudinal temperature variations. In the study presented here, we discuss the planetary waves (PWs) that are solely generated internally, i.e. without the explicit excitation sources related to tropospheric convection or topography. Our analysis shows that PWs are not produced when the zonally averaged heat source into the atmosphere is artificially suppressed, and that the PWs are generally weaker when the tropospheric source is not applied. Instabilities associated with the zonal mean temperature, pressure and wind fields, which still need to be explored, are exciting PWs that have amplitudes in the mesosphere comparable to those observed. Three classes of PWs are generated in the NSM. (1) Rossby type PWs, which slowly propagate westward relative to the mean zonal flow, are carried by the winds so that they appear (from the ground) to propagate, respectively, eastward and westward in the winter and summer hemispheres below 80 km. Depending on the zonal wave number and magnitudes of the zonal winds, and under the influence of the equatorial oscillations, these PWs typically have periods between 2 and 20 days. Their horizontal wind amplitudes can exceed 40 m/s in the lower mesosphere. (2) Rossby-gravity waves, which propagate westward at low latitudes and have periods around 2 days for zonal wave numbers m = 2 to 4. (3) Eastward propagating equatorial Kelvin waves, which are generated in the upper mesosphere with periods between 1 and 3 days depending on m. A survey of the PWs reveals that the largest wind amplitudes tend to occur below 80 km in the winter hemisphere; but above th

At high latitudes in the upper mesosphere, horizontal wind oscillations have been observed with periods around 10 h. Waves with such a period are generated in our Numerical Spectral Model (NSM), and they are identified as planetary-scale inertio gravity waves (IGW). These IGWs have periods between 9 and I I h and appear above 60 kin in the zonal mean (m=0), as well as in m=l to 4, propagating eastward and westward. Under the influence of the Coriolis force, the amplitudes of the waves propagating westward are larger at high latitudes than those propagating eastward. The waves grow in magnitude at least up to about 100 km and have vertical wavelengths around 25 km. Applying a running window of 15 days for spectral analysis, the amplitudes in the wind field are typically between 10 and 20 m/s and can reach 30m/s in the westward propagating component for m=1 at the poles. In the temperature perturbations, the wave amplitudes above 100 km are typically 5 K and as large as 10 K for m=0 at the poles. The IGWs are intermittent but reveal systematic seasonal variations, with the largest amplitudes occurring generally in late winter and spring. Numerical experiments show that such waves are also generated without excitation of the migrating tides. The amplitudes and periods then are similar, indicating that the tides are not essential to generate the waves. However, the seasonal variations without tides are significantly different, which leads to the conclusion that non linear interactions between the semidiurnal tide and planetary waves must contribute to the excitation of the IGWs. Directly or indirectly through the planetary waves, the IGWs are apparently excited by the instabilities that arise in the zonal mean circulation. When the solar heating is turned off for m=0, both the PWs and IGWs essentially disappear. That the IGWs and PWs have common roots in their excitation mechanism is also indicated by the striking similarity of their seasonal variations in the lower mes

In the polar region of the upper mesosphere, horizontal wind oscillations have been observed with periods around 10 hours. Waves with such periods are generated in our Numerical Spectral Model (NSM), and they are identified as planetary-scale inertio gravity waves (IGW). These waves have periods between 9 and 11 hours and appear above 70 km in the zonal mean (m = 0), as well as in m = 1 to 4 propagating eastward and westward. They grow in magnitude to altitudes near 100 km and have vertical wavelengths of about 25 km. The m = 1 westward IGWs have the largest amplitudes, up to 30 m/s at the poles. The IGWs occur intermittently but reveal systematic seasonal variations. Their amplitudes generally are largest in late winter and spring. Numerical experiments show that the waves also appear without tidal excitation. Like the planetary waves in the model, the IGWs are produced by instabilities that arise in the mean zonal circulation.

We report results from our Numerical Spectral Model (NSM) that incorporates Hines' parameterization for small-scale gravity waves (GW). The NSM generates non-migrating tides in the mesosphere having amplitudes comparable to those observed, and we demonstrate that they arise from interactions between migrating tides and planetary waves (PW). We examine this mechanism for the large m = 0 diurnal tide, which was proposed to be generated with m = 1 PWs. The NSM is run for comparison without the zonal mean heat source, which suppresses the PWs that normally are excited by instabilities. The resulting amplitudes of the stationary tide are then negligibly small. When the time dependent GW momentum source for m = 0 is turned off, the stationary tide is significantly reduced. This indicates that, in the NSM, GWs play an important role in generating the nonlinear interactions between migrating tides and PWs that are necessary to produce the non-migrating tides.

In our Numerical Spectral Model (NSM) that incorporates Hines' Doppler Spread Parameterization, small-scale gravity waves (GW) propagating in the east/west direction can generate the essential features of the observed equatorial oscillations in the zonal circulation and in particular the QBO extending from the stratosphere into the upper mesosphere. We report here that the NSM also produces in the zonally symmetric (wavenumber=0) meridional circulation intraseasonal oscillations on time scales of a few months. A distinct but variable meridional wind oscillation (MWO) is generated, which appears to be the counterpart to the quasi-biennial oscillation (QBO). With a vertical grid-point resolution of about 0.5 km, the NSM produces the MWO through momentum deposition of GWs propagating in the north/south direction. The resulting momentum source represents a non-linear function of the meridional winds that is of third (generally odd) order, and this enables the oscillation, as is the case for the zonal winds in the QBO. Since the meridional winds are relatively small compared to the zonal winds. however, the vertical scale-length for the MWO is much smaller, i.e., only about 10 km instead of 40 km for the QBO. Consistent with the associated increase of the viscous stress, the period of the MWO is then short compared with that of the QBO, i.e., only about 1-4 months. Measurements with the HRDI instrument on LIARS show evidence of the MWO with periods between 2 and 3 months (Huang and Reber, J. Geophys. Res. (2003)). Depending on the strength of the GW forcing, the computed amplitudes of the MWO are typically 5 m/s in the upper stratosphere and mesosphere, and the associated temperature amplitudes are about 3 K. These amplitudes may be observable with the instruments on the TIMED spacecraft. Extended computer simulations with the NSM in 2D and 3D reveal that the MWO is modulated by and in turn influences the QBO. (C) 2003 Elsevier Ltd. All rights reserved.

Solar cycle activity effects (SCAE) in the lower and middle atmosphere, reported in several studies, are difficult to explain on the basis of the small changes in solar radiation that accompany the 11-year cycle. It is therefore natural to speculate that dynamical processes may come into play to produce a leverage. Such a leverage may be provided by the quasi-biennial oscillation (QBO) in the zonal circulation of the stratosphere, which has been linked to solar activity variations (e.g., Labitzke (J. Meteorol. Soc. Jpn. 60 (1982) 124; Geophys. Res. Lett. 14 (1987) 135); Labitzke and Van Loon (J. Atm. Terr. Phys. 50 (1988) 197; J. Atm. Terr. Phys. 54 (1992) 1453)). Driven primarily by wave mean flow interaction, the QBO period and its amplitude are variable but are also strongly influenced by the seasonal cycle in the solar radiation. This influence extends to low altitudes and is referred to as "downward control". Small changes in the solar radiative forcing may produce small changes in the period and phase of the QBO, but these in turn may produce measurable differences in the wind field. Thus, the QBO may be an amplifier of solar activity variations and a natural conduit of these variations to lower altitudes. To test this hypothesis, we conducted experiments with a 2D version of our numerical spectral model that incorporates Hines' Doppler spread parameterization for small-scale gravity waves (GW). Solar cycle radiance variations (SCRV) are accounted for by changing the radiative heating rate on a logarithmic scale from 0.1\% at the surface to 1\% at 50 km to 10\% at 100 km. With and without SCRV, but with the same GW flux, we then conduct numerical experiments to evaluate the magnitude of the SCAE in the zonal circulation. The numerical results show that, under certain conditions, the SCAE is significant and can extend to lower altitudes where the SCRV is small. For a modeled QBO period of 30 months, we find that the seasonal cycle in the solar forcing acts as a

Quasi-decadal oscillations (QDO) have been observed in the stratosphere and have been linked to the quasi-biennial oscillation (QBO) in the zonal circulation and to the 11-year solar activity cycle. With the use of a 2D version of our numerical spectral model that incorporates Hines' Doppler spread parameterization for gravity waves (GW), we demonstrate that beat periods between 9 and 11 years can be generated by the QBO as it interacts through GW filtering with the annual oscillation (AO) or semi-annual oscillation (SAO). Results are discussed from model runs covering up to 50 years, and our analyses lead to the following conclusions. A QDO is generated in the zonal circulation of the upper mesosphere. The largest signature of the QDO, however, appears in the form of amplitude modulations of the QBO, AO and SAO, and these extend into the lower stratosphere. The downward control that characterizes the QBO apparently comes into play, and the longer time constants for diffusion and radiative loss at lower altitudes facilitate the QDO response. Although excited by the QBO, which is confined to low latitudes, the QDO is shown to extend to high latitudes. The effect is particularly large for a QBO with period around 33 months (near the upper limit of observations), which interacts with the SAO to produce a hemispherically symmetric QDO. (The same dynamical condition also holds for a 28-month QBO.) Our analysis indicates that the QDO is transferred to high latitudes by the meridional circulation, which prominently exhibits this periodicity particularly in the amplitude modulation of the AO. (C) 2003 Elsevier Ltd. All rights reserved.

We present results from a non-linear, 3D, time dependent numerical spectral model, which extends from the ground up to the thermosphere and incorporates Hines' Doppler spread parameterization for small-scale gravity waves (GWs). Our focal point is the mesosphere, which is dominated by wave interactions. We discuss diurnal and semi-diurnal tides in the present paper (Part I) and planetary waves (PWs) in a companion paper (Part II). To study the seasonal variations of tides, in particular with regard to GW forcing, numerical experiments are performed that lead to the following conclusions: (1) The large semi-annual variations in the diurnal tide (DT), with peak amplitudes observed around equinox, are produced to a significant extent by GW interactions that involve, in part, PWs. (2) The DT, like PWs, is amplified by GW momentum deposition, which reduces also the vertical wavelength. (3) Variations in eddy viscosity associated with GW interactions may also influence the DT. (4) The semidiurnal tide (SDT), and its phase in particular, is strongly influenced by the zonal mean circulation. (5) Without the DT present, the SDT is amplified by GWs; but the DT filters out GWs such that the wave interaction significantly reduces the amplitude of the SDT during equinox, effectively producing a strong non-linear interaction between the DT and the SDT. (6) PWs generated internally by the baroclinic instability and GW forcing produce large amplitude modulations of the DT and SDT. (C) 2001 Published by Elsevier Science Ltd.

We present results from a non-linear, 3D, time dependent numerical spectral model (NSM), which extends from the ground up to the thermosphere and incorporates Hines' Doppler spread parameterization for small-scale gravity waves (GWs). Our focus is the mesosphere where wave interactions play a prominent role. We discuss planetary waves (PWs) in the present paper (Part II) and diurnal and semi-diurnal tides in the companion paper (Part I). Without external, time-dependent energy or momentum sources, PWs are generated in the model for zonal wavenumbers 1-4, which have amplitudes in the mesosphere above 50 km as large as 30 m/s and periods between 2 and 15 days. The waves are generated primarily during solstice, which indicates that the baroclinic instability (associated with the GW driven reversal in the latitudinal temperature gradient) plays an important role. Results from a numerical experiment show that GWs are also significantly involved directly in generating the PWs. For the zonal wavenumber m = 1, the predominant wave periods at mid latitudes in summer cover a wide range around 7 days and peak in winter around 4 days. For m = 2, the periods in summer and winter are around 4 and 3 days, respectively. For m = 3, 4 the predominant wave periods are in both seasons close to 2 days. At low latitudes, these waves have the characteristics of Rossby gravity waves, with large meridional winds at the equator and propagating westward. A common feature of the PWs (m = I to 4) generated in the summer and winter hemispheres is that their vertical wavelengths throughout the mesosphere are large, which indicates that the waves are not propagating freely but are generated (and absorbed) throughout the region. Another common feature is that the PWs propagate preferentially westward in summer and eastward in winter. being launched from the westward and eastward zonal winds that prevail, respectively, in the summer and winter hemispheres at altitudes below 80 km. As shown in Part 1

In this paper we present an extension for the 2D (zonal mean) version of our numerical spectral mode (NSM) that incorporates Hines' Doppler spread parameterization (DSP) for small-scale gravity waves (GW). This model is applied to describe the seasonal variations and the semi-annual and quasi-biennial oscillations (SAO and QBO). Our earlier model reproduced the salient features of the mean zonal circulation in the middle atmosphere, including the QBO extension into the upper mesosphere inferred from UARS measurements. The model is extended to reproduce the upwelling at equatorial latitudes that is associated with the Brewer-Dobson circulation - which affects significantly the dynamics of the stratosphere as Dunkerton had pointed out. In the presence of GW, this upwelling is produced in our model with tropospheric heating, which generates also zonal jets outside the tropics similar to those observed. The resulting upward vertical winds increase the period of the QBO. To compensate for that, one needs to increase the eddy diffusivity and the GW momentum flux, bringing the latter closer to values recommended in the DSP. The QBO period in the model is 30 months (mo), which is conducive to synchronize this oscillation with the seasonal cycle of solar forcing. Associated with this QBO are interannual and interseasonal variations that become increasingly more important at higher altitudes - and this variability is interpreted in terms of GW filtering that effectively couples the dynamical components of the mesosphere. The computed temperature amplitudes for the SAO and QBO are in substantial agreement with observations at equatorial and extra-tropical latitudes. At high latitudes, however, the observed QBO amplitudes are significantly larger, which may be a signature of propagating planetary waves not included in the present model. The assumption of hydrostatic equilibrium not being imposed, we find that the effects from the vertical Coriolis force associated with the equa

The Doppler Spread Parameterization (DSP) for gravity waves (GW) developed by Hines is applied to the zonal momentum budget at the equator. For sufficiently large oscillation amplitudes in the background zonal winds, comparable to the GW induced wind variability, the momentum source is intermittent and as such it represents a nonlinearity of third or generally odd order. This kind of nonlinearity generates, besides higher harmonics, the fundamental harmonic itself which is retained in a simplified analytical solution that can describe self-sustained oscillations without invoking external, time dependent forcing. The formulation is discussed to provide some understanding of the numerical results presented in the companion paper. (C) 1998 Elsevier Science Ltd.

Large variations are observed in the Semi-Annual Oscillation (SAO) and Quasi-Biennial Oscillation (QBO) near the equator that are not well understood. We had shown earlier that small scale gravity waves (GW) can generate these oscillations. Here we demonstrate that GW filtering can also produce the variability. Our model incorporates Hines' Doppler Spread Parameterization (DSP) for GW. In the present version, we employ a larger GW flux and a more realistic description of Newtonian cooling. This model produces a QBO with amplitudes close to 15 m/s at 25 km and periods around 33 months. At higher altitudes, the model produces a SAO with amplitudes varying between 5 and 30 m/s. We interpret these variations in terms of GW filtering by the QBO that produces bear periods between 4 and 8.5 years. To provide better understanding, we present also a case in which the QBO period is virtually locked at 18 months. The SAO amplitude then varies with a regular pattern having a period of 18 months, and the Annual Oscillation (AO) amplitude varies with a period of 36 months. For QBO's with periods of 18 (or 30) months, the phase relationship with the seasonal cycle of solar forcing would tend to synchronize and stabilize the oscillations.

Gravity Waves (GW) as described with the Doppler Spread Parameterization (DSP) of Hines have been shown to produce significant Quasi-biennial and Semi-annual oscillations (QBO and SAO) in the zonal circulation at equatorial latitudes. To elucidate the process involved, we discuss computer experiments performed without the external, seasonal variations in solar differential heating, and the conclusions are summarized here. (1) As reported earlier, two kinds of oscillations are then generated spontaneously: one at lower altitudes in the stratosphere which has a long period approaching that of the QBO, the other one al higher altitudes in the mesosphere which has a shorter period close to that of the SAO. The amplitudes of these oscillations are weaker, however, than those generated with seasonal heating. (2) When the time independent solar healing is turned off, the oscillations continue but with significantly reduced period in the mesosphere where the vertical winds driven by solar differential heating produce Doppler shifting. The associated temperature variations are then small, consistent with the one dimensional prototype calculations discussed by Lindzen and Holton. (3) When the GW momentum source is turned off above 40 km to suppress the short-period oscillation, the long-period oscillation below continues with enhanced amplitude and period. When the source is turned off below 35 km, the amplitude of the short-period oscillation increases at higher altitudes, indicative of increased acceleration. (4) The wind oscillations change systematically and dramatically with changing eddy diffusivity/viscosity (K). The amplitudes and periods of both short- and long-period oscillations decrease (increase) with increasing (decreasing) K, and above a certain value of viscosity, both oscillations completely cease. Lowering K thus helps in generating a larger and longer period QBO at lower altitudes, but can be detrimental to the SAO when the natural oscillation period increa

Wind measurements with the UARS spacecraft show that between 90 and 100 km altitude the fundamental diurnal tide is modulated semi-annually with peak amplitudes of almost 100 m/s near equinox, more than a factor of two larger than during solstice. Applying Hines' Doppler-Spread Parameterization (DSP) for small scale gravity waves (GW), we present results from a Numerical Spectral Model (NSM) to describe the seasonal variations in the mean zonal circulation interacting self consistently with the diurnal tide. With the DSP, the GW momentum source increases the amplitude of the tide at altitudes above 70 km, in contrast to the Rayleigh friction parameterization that causes damping. Since the tide absorbs GW momentum, it reduces the wave-generated semi-annual oscillations (SAO) in the mean zonal winds at equatorial latitudes. Outside the tropics, GW momentum is absorbed by the mean zonal winds that peak near the summer and winter solstices. As a result, the GW reach the upper mesosphere with more momentum during equinox periods and thus cause a seasonal modulation of the tide that is predominately semi-annual.

Mayr et al. [this issue] discussed a two-dimensional version of the numerical spectral model (NSM) of Chan et al. [1994a, b] that incorporates the Doppler spread parameterization (DSP) for momentum deposition by small-scale gravity waves (GW) developed by Hines [1997a, b] and presented numerical results describing the global scale seasonal variations in the temperature and wind fields of the middle atmosphere. Even with the simplest assumptions for the GW flux emanating from the troposphere, to be isotropic and independent of latitude and season, this model also produces significant oscillations in the equatorial zonal circulation which are discussed here. Our model results lead to the following conclusions: (1) At altitudes above 40 km, a periodicity of 6 month dominates, resembling the observed semiannual oscillation (SAO). The peak amplitude of this oscillation is close to 18 m/s near 50 km (20-30 m/s observed). A secondary maximum is excited near 80 km with an amplitude of about 11 m/s (15-25 m/s observed), whose phase is opposite to that at 50 km. In this altitude range, the downward phase progression is about 9 km/month, in agreement with observations. The computed SAO is confined to equatorial latitudes, as observed. (2) At altitudes below 40 km, the period of the computed oscillation is almost 21 months, approaching that of the observed quasi-biennial oscillation (QBO). The maximum wind amplitudes are close to 8 m/s (20 m/s observed), and the downward phase progression is about 1.6 km/month (1.3 km/month observed). The model also produces a QBO in the upper mesosphere, in qualitative agreement with recent UARS measurements [Burrage et al., 1996]. (3) When the eddy diffusivity is reduced by a factor of two, the QBO period increases to 30 months and the maximum wind amplitude approaches 13 m/s. Computer experiments are discussed for constant, equinoctial solar heating to elucidate the GW excitation mechanism for the equatorial oscillations in the zonal circula

In our solar system, convective atmospheres are as common as those that are stable, and convective and stable regions sometimes coexist in the same atmosphere. There is a need to develop circulation models that can handle convection and stable-layer flows simultaneously and efficiently. This paper represents an approach to the construction of such a model. Taking advantages of the simplicity of implementing implicit time stepping in spectral models, we solve a non-hydrostatic, fully compressible version of the hydrodynamic equations without the time step restrictions imposed by acoustic and gravity waves. To simplify the nonlinear terms and to conserve the total mass and total angular momentum to round-off accuracy, we introduce a "stratified'' approximation which limits the nonlinearity of the equations to quadratic. The linear terms remain intact so that all the linear waves are preserved. The set of assumptions made by the "stratified'' approximation is a subset of those of the anelastic approximation. It offers more generality and accuracy while the computational overhead is relatively low. Tests are presented to illustrate the capabilities and advantages of the present model. (C) 1994 Academic Press, Inc.

We report on the application of a newly developed spectral code to the study of the middle upper atmosphere. The spectral approach offers conceptual and practical convenience for analyzing the generation and interaction of different components of atmospheric activity through the decomposition of the dynamical fields into components with different zonal wave numbers (m). As examples and tests. we obtain solutions for the m = 0 (the mean circulation) and 1 (the diurnal tides) components separately (no mutual interactions), as well as the m = 1 component under the influence of the mean circulation. By simulating gravity wave effects with Rayleigh friction and eddy diffusion peaking near 90 km altitude, the mean circulation thus generated can reproduce the observed mesospheric temperature anomaly under solstice conditions. The computed diurnal tides are in good agreement with results obtained earlier by other authors. The large temperature gradient (associated with the m = 0 component) set up by the mesospheric temperature anomaly under solstice conditions creates a condition favorable for the development of baroclinic instabilities in the mesopause layer, especially near the summer pole. In our time dependent calculation, waves with approximately 4-day period are generated in the m = 1 component, superimposing with the 1-day period tides.

The Hadley mechanism is adopted to describe the axisymmetric four day superrotation in the Venus atmosphere, with solar driven meridional winds redistributing energy and momentum, and eddy diffusion describing the actions of three dimensional transient eddies. We address the question how the eddy diffusion coefficients are related to the properties of the circulation. For the atmosphere of a slowly rotating planet such as Venus, we show that a form of the non-linear closure is suggested by the mixing length hypothesis, which constrains the magnitude of the eddy diffusion coefficients. Combining this constraint with the concept of the Rossby radius of deformation yields zonal velocities on the order of 100 m sec -1. A steady state, non-linear, one-layer spectral model is used for a parametric study to find a relationship between heat source, meridional circulation and eddy diffusion coefficients, which yields the large zonal velocities observed. This analysis leads to the following conclusions: (1) Proportional changes in the heat source and eddy diffusion coefficients do not significantly change the zonal velocities. (2) The meridional velocity is virtually constant for large eddy diffusion coefficients. (3) Below a threshold in the diffusion rate, the meridional velocity decreases, commensurate with the mixing length hypothesis. Eddy heat conduction becomes important and shares with the Hadley cell advection in balancing the solar heating. The zonal velocities then reach large values near 100 m sec -1. (4) For large eddy diffusion and small heating rates, the zonal velocities decrease with decreasing planetary rotation rates. However, under condition (3), the zonal velocities are independent of the planetary rotation rate. Ramifications are discussed for related parameterizations in GCMs, emphasizing that eddy diffusion coefficients are governed by solar forcing and cannot be chosen independently. © 1988 D. Reidel Publishing Company.