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Mohammad Mirzaei, Ali R. Mohebalhojeh, and Farhang Ahmadi-Givi

Abstract

The spontaneous adjustment emission of inertia–gravity waves is investigated by examining the amount of imbalance generated during the evolution of unstable jets in an isentropic two-layer primitive equation model on the sphere. To determine the balance and thus the imbalance, potential vorticity (PV) inversion by means of the first-, second-, and third-order plain-δδ, plain-δγ, and plain-γγ balance relations, as well as the Bolin–Charney balance relations, is applied. Five sets of experiments are carried out by (i) changing the upper-layer potential temperature with a fixed initial jet speed and (ii) changing the initial jet speed with a fixed upper-layer potential temperature. For each set, the relation between the optimal measure of imbalance with the corresponding measure of balanced vortical flow is sought at the peak of instability. The minimal imbalance obtained by 1 of the above 10 PV inversion procedures is considered as the optimal.

The focus herein is on the magnitude of imbalance and its scaling with various measures of balanced flow. It is shown that for the magnitude of imbalance it is always possible to find the proper measure with an exponentially small scaling. For the imbalance-to-balance ratio, however, a power law is obtained when either the jet or the stratification is weak. The latter difference in scaling behavior of the imbalance and imbalance-to-balance ratio may be an artifact of the inevitable numerical errors whose effects are felt more strongly when the signature of vortical flow is weak.

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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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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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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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