Momentum Flux Spectrum of Convectively Forced Internal Gravity Waves and Its Application to Gravity Wave Drag Parameterization. Part I: Theory

Abstract

The phase-speed spectrum of momentum flux by convectively forced internal gravity waves is analytically formulated in two- and three-dimensional frameworks. For this, a three-layer atmosphere that has a constant vertical wind shear in the lowest layer, a uniform wind above, and piecewise constant buoyancy frequency in a forcing region and above is considered. The wave momentum flux at cloud top is determined by the spectral combination of a wave-filtering and resonance factor and diabatic forcing. The wave-filtering and resonance factor that is determined by the basic-state wind and stability and the vertical configuration of forcing restricts the effectiveness of the forcing, and thus only a part of the forcing spectrum can be used for generating gravity waves that propagate above cumulus clouds. The spectral distribution of the wave momentum flux is largely determined by the wave-filtering and resonance factor, but the magnitude of the momentum flux varies significantly according to spatial and time scales and moving speed of the forcing. The wave momentum flux formulation in the two-dimensional framework is extended to the three-dimensional framework. The three-dimensional momentum flux formulation is similar to the two-dimensional one except that the wave propagation in various horizontal directions and the three-dimensionality of forcing are allowed. The wave momentum flux spectrum formulated in this study is validated using mesoscale numerical model results and can reproduce the overall spectral structure and magnitude of the wave momentum flux spectra induced by numerically simulated mesoscale convective systems reasonably well.

A comprehensive observational filter for satellite infrared limb sounding of gravity waves

“…Here, we use exemplarily ray-tracing simulations based on convective sources. Offline simulation of global gravity waves was performed by coupling the convective GW source (CGWS) scheme (Song and Chun, 2005) and the gravity wave regional or global ray tracer (GROGRAT) (Marks and Eckermann, 1995;Eckermann and Marks, 1997). The CGWS scheme is formulated by applying a double Fourier transform in space and time to the perturbation solution of the primitive equations.…”

“…Different parameters for the CGWS scheme were considered. Parameter sets MF1 (δx = 5 km and δt = 20 min) and MF2 (δx = 25 km, δt = 60 min) were introduced by Song and Chun (2005) and Choi et al (2012), respectively. We introduce and investigate in this work an additional spectrum MF3 with a larger spatial scale (δx = 120 km and δt = 60 min).…”

A New Gravity Wave Parameterization Including Three-Dimensional Propagation

“…Currently, many varieties of GWP are used both for orographic and non-orographic GWs due to the growing demand for better representation of the middle atmosphere in climate projections (McLandress 1998;Kim et al 2003). Recent developments include source specifications of non-orographic GWs originating from convection (Beres et al 2005, Song andChun 2005) and jet-front systems (Charron and Manzini 2002;Richter et al 2010) based on physical processes and stochastic launching of GWs to imitate their intermittency (Eckermann 2011;Lott and Guez 2013;de la Camara and Lott 2015).…”

A computationally efficient nonstationary convective gravity‐wave drag parameterization for global atmospheric prediction systems

“…Among these studies, Chun and Baik assumed that the cloud-top wave stress is inversely proportional to the basic-state wind speed and the cubic buoyancy frequency for a given diabatic heating rate. Their parameterization considers GWs that are stationary relative to clouds, but it has been overhauled by Song and Chun [2005] to also include nonstationary GWs. Beres et al [2004] and Beres [2004] independently derived similar analytic formulations.…”

“…[6] The spectral parameterizations, developed for middle atmospheric climate simulation models [e.g., Alexander and Dunkerton, 1999], are generally computationally expensive and require to specify wave source at a height, remote from the source region near the surface, although some refined methods to specify the source spectrum have recently been introduced [e.g., Beres et al, 2004;Beres, 2004;Song and Chun, 2005]. For global weather forecast models that cover from the surface to the middle atmosphere, therefore, use of spectral GW parameterizations in current forms may not be very feasible due to its computational inefficiency and/or to the requirement for specifying wave source at the interface height, which may be too general or simple for real-time short or medium range forecasts.…”