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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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Gergely Bölöni
,
Bruno Ribstein
,
Jewgenija Muraschko
,
Christine Sgoff
,
Junhong Wei
, and
Ulrich Achatz

Abstract

With the aim of contributing to the improvement of subgrid-scale gravity wave (GW) parameterizations in numerical weather prediction and climate models, the comparative relevance in GW drag of direct GW–mean flow interactions and turbulent wave breakdown are investigated. Of equal interest is how well Wentzel–Kramer–Brillouin (WKB) theory can capture direct wave–mean flow interactions that are excluded by applying the steady-state approximation. WKB is implemented in a very efficient Lagrangian ray-tracing approach that considers wave-action density in phase space, thereby avoiding numerical instabilities due to caustics. It is supplemented by a simple wave-breaking scheme based on a static-instability saturation criterion. Idealized test cases of horizontally homogeneous GW packets are considered where wave-resolving large-eddy simulations (LESs) provide the reference. In all of these cases, the WKB simulations including direct GW–mean flow interactions already reproduce the LES data to a good accuracy without a wave-breaking scheme. The latter scheme provides a next-order correction that is useful for fully capturing the total energy balance between wave and mean flow. Moreover, a steady-state WKB implementation as used in present GW parameterizations where turbulence provides by the noninteraction paradigm, the only possibility to affect the mean flow, is much less able to yield reliable results. The GW energy is damped too strongly and induces an oversimplified mean flow. This argues for WKB approaches to GW parameterization that take wave transience into account.

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