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Christoph Zülicke and Dieter Peters

Abstract

The link between poleward-breaking Rossby waves and stratospheric inertia–gravity waves is examined. With a visual inspection of Ertel’s potential vorticity maps based on ECMWF analyses it was found that Rossby wave–breaking events occurred over northern Europe in about 40% of the winter days in 1999–2003. The majority of them were breaking poleward downstream. A total of 10 field campaigns were performed in the winters of 1999–2002 at Kühlungsborn, Germany (54°N, 12°E). They are related to such events and can be considered as representative for poleward-breaking Rossby waves. Inertia–gravity wave properties are diagnosed from radiosonde observations. They appeared to be shallower, slower, and stronger than the climatological mean for the north German lowlands. Hence, Rossby wave–breaking events are linked with strong stratospheric inertia–gravity wave activity. A novel parameterization of inertia–gravity wave generation and propagation is proposed. The stratospheric inertia–gravity wave action in the 16–20-km height range was parameterized with the synoptic-scale cross-stream ageostrophic wind, which accounts for imbalances in the upper-tropospheric jet streak. This empirical relationship is supported with quasigeostrophic theory. Effects of damping and critical level absorption are taken into account with Wentzel–Kramers–Brillouin theory. For verification of the parameterization with homogeneous meteorological fields in space and time, the 10 field campaigns were hindcasted with the nonhydrostatic fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model. About 80% of the variance in inertia–gravity wave action was found to be explained. For the 10 campaigns a close link was found between the poleward-breaking Rossby waves and the strong stratospheric inertia–gravity waves. The role of the polar vortex was twofold: first, it forced the poleward-oriented Rossby waves to break downstream and to form strong tropospheric jet streaks generating inertia–gravity waves. Second, the strong winds in the stratosphere favored the upward propagation of the inertia–gravity waves. The proposed new parameterization of inertia–gravity wave generation and propagation was validated and can be used to deduce mesoscale wave intensity from synoptic flow characteristics during poleward Rossby wave–breaking events.

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Christoph Zülicke and Dieter Peters

Abstract

Poleward-breaking Rossby waves often induce an upper-level jet streak over northern Europe. Dominant inertia–gravity wave packets are observed downstream of this jet. The physical processes of their generation and propagation, in such a configuration, are investigated with a mesoscale model.

The study is focused on an observational campaign from 17 to 19 December 1999 over northern Germany. Different simulations with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) have been performed. For a high-resolution process study, three domains were set up that encompass the evolution of Rossby waves and that of inertia–gravity waves. To minimize the impact of model damping, the horizontal and vertical resolution has been adjusted appropriately.

With a novel statistical approach, the properties of inertia–gravity wave packets have been estimated. This method uses the horizontal divergence field and takes into account the spatial extension of a wave packet. It avoids the explicit treatment of the background field and works for arbitrary wavelength. Two classes of inertia–gravity waves were found: subsynoptic waves with a horizontal wavelength of about 500 km and mesoscale waves with a horizontal wavelength of about 200 km. The subsynoptic structures were also detected in radiosonde observations during this campaign. The similarity between simulated and observed wavelengths and amplitudes suggests that the simulations can be considered as near realistic.

Spontaneous radiation from unbalanced flow is an important process of inertia–gravity wave generation. Synoptic-scale imbalances in the exit region of the upper-tropospheric jet streak were identified with the smoothed cross-stream Lagrangian Rossby number. In a number of simulations with different physics, it was found that the inertia–gravity wave activity was related to the tropospheric jet, orography, and moist convection. The upward propagation of inertia–gravity waves was favored during this event of a poleward-breaking Rossby wave. The presence of the polar vortex induced background winds exceeding the critical line. Consequently, the activity of inertia–gravity waves in the lower stratosphere increased by an order of magnitude during the case study.

The successful simulation of the complex processes of generation and propagation showed the important role of poleward Rossby wave breaking for the appearance of inertia–gravity waves in the midlatitudes.

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Mohammad Mirzaei, Ali R. Mohebalhojeh, Christoph Zülicke, and Riwal Plougonven

Abstract

Quantification of inertia–gravity waves (IGWs) generated by upper-level jet–surface front systems and their parameterization in global models of the atmosphere relies on suitable methods to estimate the strength of IGWs. A harmonic divergence analysis (HDA) that has been previously employed for quantification of IGWs combines wave properties from linear dynamics with a sophisticated statistical analysis to provide such estimates. A question of fundamental importance that arises is how the measures of IGW activity provided by the HDA are related to the measures coming from the wave–vortex decomposition (WVD) methods. The question is addressed by employing the nonlinear balance relations of the first-order δγ, the Bolin–Charney, and the first- to third-order Rossby number expansion to carry out WVD. The global kinetic energy of IGWs given by the HDA and WVD are compared in numerical simulations of moist baroclinic waves by the Weather Research and Forecasting (WRF) Model in a channel on the f plane. The estimates of the HDA are found to be 2–3 times smaller than those of the optimal WVD. This is in part due to the absence of a well-defined scale separation between the waves and vortical flows, the IGW estimates by the HDA capturing only the dominant wave packets and with limited scales. It is also shown that the difference between the HDA and WVD estimates is related to the width of the IGW spectrum.

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Mohammad Mirzaei, Christoph Zülicke, Ali R. Mohebalhojeh, Farhang Ahmadi-Givi, and Riwal Plougonven

Abstract

The impact of moisture on inertia–gravity wave generation is assessed for an idealized unstable baroclinic wave using the Weather Research and Forecasting Model (WRF) in a channel on the f plane. The evolution of these waves in a moist simulation is compared with a dry simulation. The centers of action for inertia–gravity wave activity are identified as the equatorward-moving upper-level front and the poleward-progressing upper-level jet–surface front system. Four stratospheric wave packets are found, which are significantly more intense in the moist simulation and have slightly higher frequency. They are characterized by their structure and position during the baroclinic wave life cycle and are related to forcing terms in jet, front, and convection systems.

By exploring the time series of mass and energy, it is shown that the release of latent heat leads to a change in enthalpy, an increase in the eddy kinetic energy, and an intensification of the inertia–gravity wave energy. The ratio of the inertia–gravity wave energy to the eddy kinetic energy is estimated to be about 1/200 for the moist simulation, which is 3 times larger than that for the dry simulation. An empirical parameterization scheme for the inertia–gravity wave energy is proposed, based on the fast large-scale ageostrophic flow associated with the jet, front, and convection. The diagnosed stratospheric inertia–gravity wave energy is well captured by this parameterization in six WRF simulations with different moisture and resolutions. The approach used to construct the parameterization may serve as a starting point for state-dependent nonorographic gravity wave drag schemes in general circulation models.

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Mahnoosh Haghighatnasab, Mohammad Mirzaei, Ali R. Mohebalhojeh, Christoph Zülicke, and Riwal Plougonven

Abstract

The parameterization of inertia–gravity waves (IGWs) is of considerable importance in general circulation models. Among the challenging issues faced in studies concerned with parameterization of IGWs is the estimation of diabatic forcing in a way independent of the physics parameterization schemes, in particular, convection. The requirement is to estimate the diabatic heating associated with balanced motion. This can be done by comparing estimates of balanced vertical motion with and without diabatic effects. The omega equation provides the natural method of estimating balanced vertical motion without diabatic effects, and several methods for including diabatic effects are compared. To this end, the assumption of spatial-scale separation between IGWs and balanced flows is combined with a suitable form of the balanced omega equation. To test the methods constructed for estimating diabatic heating, an idealized numerical simulation of the moist baroclinic waves is performed using the Weather Research and Forecasting (WRF) Model in a channel on the f plane. In overall agreement with the diabatic heating of the WRF Model, in the omega-equation-based estimates, the maxima of heating appear in the warm sector of the baroclinic wave and in the exit region of the upper-level jet. The omega-equation-based method with spatial smoothing for estimating balanced vertical motion is thus presented as the proper way to evaluate diabatic forcing for parameterization of IGWs.

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Mozhgan Amiramjadi, Ali R. Mohebalhojeh, Mohammad Mirzaei, Christoph Zülicke, and Riwal Plougonven

Abstract

The way the large-scale flow determines the energy of the nonorographic mesoscale inertia–gravity waves (IGWs) is theoretically significant and practically useful for source parameterization of IGWs. The relations previously developed on the f plane for tropospheric sources of IGWs including jets, fronts, and convection in terms of associated secondary circulations strength are generalized for application over the globe. A low-pass spatial filter with a cutoff zonal wavenumber of 22 is applied to separate the large-scale flow from the IGWs using the ERA5 data of ECMWF for the period 2016–19. A comparison with GRACILE data based on satellite observations of the middle stratosphere shows reasonable representation of IGWs in the ERA5 data despite underestimates by a factor of smaller than 3. The sum of the energies, which are mass-weighted integrals in the troposphere from the surface to 100 hPa, as given by the generalized relations is termed initial parameterized energy. The corresponding energy integral for the IGWs is termed the diagnosed energy. The connection between the parameterized and diagnosed IGW energies is explored with regression analysis for each season and six oceanic domains distributed over the globe covering the Northern and Southern Hemispheres and the tropics. While capturing the seasonal cycle, the domain area-average seasonal mean initial parameterized energy is weaker than the diagnosed energy by a factor of 3. The best performance in regression analysis is obtained by using a combination of power and exponential functions, which suggests evidence of exponential weakness.

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Christoph Zülicke, Erich Becker, Vivien Matthias, Dieter H. W. Peters, Hauke Schmidt, Han-Li Liu, Laura de la Torre Ramos, and Daniel M. Mitchell

Abstract

The vertical coupling between the stratosphere and the mesosphere is diagnosed from polar cap temperatures averaged over 60°–90°N with a new method: the joint occurrence of a warm stratosphere at 10 hPa and a cold mesosphere at 0.01 hPa. The investigation of an 11-yr-long dataset (2004–15) from Aura-MLS observations shows that such mesospheric coupling days appear in 7% of the winter. During major sudden stratospheric warming events mesospheric couplings are present with an enhanced average daily frequency of 22%. This daily frequency changes from event to event but broadly results in five of seven major warmings being classified as mesospheric couplings (2006, 2008, 2009, 2010, and 2013). The observed fraction of mesospheric coupling events (71%) is compared with simulations of the Kühlungsborn Mechanistic Circulation Model (KMCM), the Hamburg Model of the Neutral and Ionized Atmosphere (HAMMONIA), and the Whole Atmosphere Community Climate Model (WACCM). The simulated fraction of mesospheric coupling events ranges between 57% and 94%, which fits the observations. In searching for causal relations weak evidence is found that major warming events with strong intensity or split vortices favor their coupling with the upper mesosphere. More evidence is found with a conceptual model: an effective vertical coupling between 10 and 0.01 hPa is provided by deep zonal-mean easterlies at 60°N, which are acting as a gravity-wave guide. The explained variance is above 40% in the four datasets, which indicates a near-realistic simulation of this process.

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