Gerhard Schmitz

Energy Deposition and Turbulent Dissipation Owing to Gravity Waves in the Mesosphere

Abstract An attempt is made to define the thermodynamics of internal gravity waves breaking in the middle atmosphere on the basis of the energy conservation law for finite fluid volumes. Consistent with established turbulence theory, this method ultimately determines the turbulent dissipation to be equivalent to the frictional heating owing to the Reynolds stress tensor. The dynamic heating due to nonconservative wave propagation, that is, the energy deposition, consists of two terms: namely, convergence of the wave pressure flux and a residual work term that is due to the wave momentum flux and the vertical shear of the mean flow. Only if both heating terms are taken into account does the energy deposition vanish, by definition, for conservative quasi-linear wave propagation. The present form of the energy deposition can also be deduced from earlier studies of Hines and Reddy and from Lindzen. The role of the axiomatically defined heating rates in the heat budget of the middle atmosphere is estimated by ...

General circulation model results on migrating and nonmigrating tides in the mesosphere and lower thermosphere. Part I: comparison with observations

Abstract The general circulation model of the Department of Numerical Mathematics of the Russian Academy of Science ( Volodin and Schmitz, 2001 , Tellus 53A (2001) 300) from the surface to mesospheric and lower thermospheric heights has been used to analyse the diurnal and semi-diurnal tides. The GCM includes tropospheric and stratospheric tidal forcings due to absorption of the radiation and latent heat release and uses the gravity wave breaking parameterization of Hines (J. Atmos. Sol. Terr. Phys. 59 (1997a) 371; J. Atmos. Sol. Terr. Phys. 59 (1997b) 387). The model tides describe the observed tidal amplitudes and phases of eastward wind components at different northern hemispheric medium frequency radar sites (Andenes, Juliusruh, Saskatoon, Yamagawa and Hawaii) for January and July conditions. The separation of model tides into migrating and nonmigrating components shows that the nonmigrating part forms the total tide to a large extent, especially for the diurnal tide at low latitudes. The variability of diurnal and semi-diurnal tides is mostly determined by the variability of the nonmigrating part; the variability due to migrating tidal oscillations contributes only a small amount to the total variability. The nonmigrating diurnal model tide is strongly dependent on the longitude, with maxima in the western hemisphere at middle southern latitudes in January. In July, these tidal amplitudes are much weaker with maxima in the subtropics of the eastern hemisphere.

The Role of Stationary Waves in the Maintenance of the Northern Annular Mode as Deduced from Model Experiments

Abstract The influence of stationary waves on the maintenance of the tropospheric annular mode (AM) is examined in a simple global circulation model with perpetual January conditions. The presented model experiments vary in the configurations of stationary wave forcing by orography and land–sea heating contrasts. All simulations display an AM-like pattern in the lower troposphere. The zonal momentum budget shows that the feedback between eddies with periods less than 10 days and the zonal-mean zonal wind is generally the dominating process that maintains the AM. The kinetic energy of the high-frequency eddies depends on the stationary wave forcing, where orographic forcing reduces and thermal forcing enhances it. The AMs in the model experiments differ in the superposed anomalous stationary waves and in the strength of the zonally symmetric component. If only orographic stationary wave forcing is taken into account, the mountain torque decelerates the barotropic wind anomaly, and thus acts to weaken the A...

A troposphere–stratosphere–mesosphere general circulation model with parameterization of gravity waves: climatology and sensitivity studies

The climatology of the troposphere–stratosphere–mesosphere model of the Institute forNumerical Mathematics (INM) with the uppermost level at 0.003 hPa is presented. This modelis vertically extended from the upper level of 10 hPa for the earlier version, and a drag parameterizationdue to internal gravity waves (GW) is included. The model describes the mainfeatures of the mesospheric circulation: decreasing and reversion of westerly and easterly winds, equatorward shift of the westerly wind maximum with height and reversal of the meridionaltemperature gradient in the upper mesosphere. The model underestimates to some extent theamplitude of wave number 1 for stationary waves in the winter hemisphere. The same holdsfor the internal low-frequency variability in the winter stratosphere. The sensitivity of the modelclimate is studied with respect to the inclusion of orographic gravity wave drag and the variationof the source height of internal gravity waves.

Normal Modes of the Atmosphere as Estimated by Principal Oscillation Patterns and Derived from Quasigeostrophic Theory

Abstract The principal oscillation pattern (POP) analysis is a technique to empirically identify time-dependent spatial patterns in a multivariate time series of geophysical or other data. In order to investigate medium-scale and synoptic waves in the atmosphere it has been applied to tropospheric geopotential height fields of ECMWF analyses from 1984 to 1987. The data have been subjected to zonal Fourier decomposition and to time filtering so that variations with periods between 3 and 25 days were retained. Analyses have been performed separately for each zonal wavenumber 5–9 on the Northern Hemisphere in winter and on the Southern Hemisphere in summer (DJF). P0Ps can be seen as normal modes of a linear approximation to a more complex dynamical system. The system matrix is estimated from observations of nature. This concept is compared with conventional stability analysis where the system matrix of the linear system is derived from theoretical, in this case quasigeostrophic, reasoning. Only the mean basi...

Shear and Static Instability of Inertia–Gravity Wave Packets: Short-Term Modal and Nonmodal Growth

Abstract The problem of nonmodal instabilities of inertia–gravity waves (IGW) in the middle atmosphere is addressed, within the framework of a Boussinesq model with realistic molecular viscosity and thermal diffusion, by singular-vector analysis of horizontally homogeneous vertical profiles of wind and buoyancy obtained from IGW packets at their statically least stable or most unstable horizontal location. Nonmodal growth is always found to be significantly stronger than that of normal modes, most notably at wave amplitudes below the static instability limit where normal-mode instability is very weak, whereas the energy gain between the optimal perturbation and singular vector after one Brunt–Vaisala period can be as large as two orders of magnitude. Among a multitude of rapidly growing singular vectors for this optimization time, small-scale (wavelengths of a few 100 m) perturbations propagating in the horizontal parallel to the IGW are most prominent. These parallel optimal perturbations are amplified b...

Optimal Growth in Inertia–Gravity Wave Packets: Energetics, Long-Term Development, and Three-Dimensional Structure

Abstract Using a hierarchy of three models of increasing realism and complexity, and expanding on a previous study, optimal perturbations of inertia–gravity wave (IGW) packets are studied with respect to several aspects. It is shown that normal modes are comparatively less able to extract energy from the IGW over finite time due to their time-invariant structure, while singular vectors (SVs) can adjust their dynamical fields flexibly so as to optimize the statically enhanced roll and Orr mechanisms by which they grow. On longer time scales, where the time dependence of the IGW packet precludes a normal-mode analysis, optimal growth is found to further amplify suitable perturbations. The propagation characteristics of these exhibit critical layer interactions for horizontal propagation directions transverse with respect to the IGW, preventing significant vertical propagation, while parallel and obliquely propagating perturbations of sufficiently long horizontal scales are found to radiate gravity waves int...

The effect of a regional increase in ocean surface roughness on the tropospheric circulation: a GCM experiment

The sensitivity of the atmospheric circulation to an increase in ocean surface roughness in the Southern Hemisphere storm track is investigated in a paired general circulation model experiment. Such a change in sea roughness could be induced by ocean waves generated by storms. Two extended permanent-July runs are made. One with standard sea surface roughness, the other with ten times as a large surface roughness over open sea poleward of 40° S. The regional increase in ocean surface roughness significantly modifies the tropospheric circulation in the Southern Hemisphere. The strongest effect is the reduction of tropospheric winds (by 2 m/s or 10%) above the area with increased roughness. The poleward eddy momentum flux is reduced in the upper troposphere and the meridional eddy sensible heat flux is reduced in the lower troposphere. Zonal mean and eddy kinetic energy are consistently reduced.