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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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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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Mark Schlutow

Abstract

Stationary gravity waves, such as mountain lee waves, are effectively described by Grimshaw’s dissipative modulation equations even in high altitudes where they become nonlinear due to their large amplitudes. In this theoretical study, a wave-Reynolds number is introduced to characterize general solutions to these modulation equations. This nondimensional number relates the vertical linear group velocity with wavenumber, pressure scale height, and kinematic molecular/eddy viscosity. It is demonstrated by analytic and numerical methods that Lindzen-type waves in the saturation region, that is, where the wave-Reynolds number is of order unity, destabilize by transient perturbations. It is proposed that this mechanism may be a generator for secondary waves due to direct wave–mean-flow interaction. By assumption, the primary waves are exactly such that altitudinal amplitude growth and viscous damping are balanced and by that the amplitude is maximized. Implications of these results on the relation between mean-flow acceleration and wave breaking heights are discussed.

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Junhong Wei, Gergely Bölöni, and Ulrich Achatz

Abstract

This paper compares two different approaches for the efficient modeling of subgrid-scale inertia–gravity waves in a rotating compressible atmosphere. The first approach, denoted as the pseudomomentum scheme, exploits the fact that in a Lagrangian-mean reference frame the response of a large-scale flow can only be due to forcing momentum. Present-day gravity wave parameterizations follow this route. They do so, however, in an Eulerian-mean formulation. Transformation to that reference frame leads, under certain assumptions, to pseudomomentum-flux convergence by which the momentum is to be forced. It can be shown that this approach is justified if the large-scale flow is in geostrophic and hydrostatic balance. Otherwise, elastic and thermal effects might be lost. In the second approach, called the direct scheme and not relying on such assumptions, the large-scale flow is forced both in the momentum equation, by anelastic momentum-flux convergence and an additional elastic term, and in the entropy equation, via entropy-flux convergence. A budget analysis based on one-dimensional wave packets suggests that the comparison between the abovementioned two schemes should be sensitive to the following two parameters: 1) the intrinsic frequency and 2) the wave packet scale. The smaller the intrinsic frequency is, the greater their differences are. More importantly, with high-resolution wave-resolving simulations as a reference, this study shows conclusive evidence that the direct scheme is more reliable than the pseudomomentum scheme, regardless of whether one-dimensional or two-dimensional wave packets are considered. In addition, sensitivity experiments are performed to further investigate the relative importance of each term in the direct scheme, as well as the wave–mean flow interactions during the wave propagation.

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Claudia Christine Stephan, Cornelia Strube, Daniel Klocke, Manfred Ern, Lars Hoffmann, Peter Preusse, and Hauke Schmidt

Abstract

Large uncertainties remain with respect to the representation of atmospheric gravity waves (GWs) in general circulation models (GCMs) with coarse grids. Insufficient parameterizations result from a lack of observational constraints on the parameters used in GW parameterizations as well as from physical inconsistencies between parameterizations and reality. For instance, parameterizations make oversimplifying assumptions about the generation and propagation of GWs. Increasing computational capabilities now allow GCMs to run at grid spacings that are sufficiently fine to resolve a major fraction of the GW spectrum. This study presents the first intercomparison of resolved GW pseudomomentum fluxes (GWMFs) in global convection-permitting simulations and those derived from satellite observations. Six simulations of three different GCMs are analyzed over the period of one month of August to assess the sensitivity of GWMF to model formulation and horizontal grid spacing. The simulations reproduce detailed observed features of the global GWMF distribution, which can be attributed to realistic GWs from convection, orography, and storm tracks. Yet the GWMF magnitudes differ substantially between simulations. Differences in the strength of convection may help explain differences in the GWMF between simulations of the same model in the summer low latitudes where convection is the primary source. Across models, there is no evidence for a systematic change with resolution. Instead, GWMF is strongly affected by model formulation. The results imply that validating the realism of simulated GWs across the entire resolved spectrum will remain a difficult challenge not least because of a lack of appropriate observational data.

Open access
Martina Bramberger, Andreas Dörnbrack, Henrike Wilms, Steffen Gemsa, Kevin Raynor, and Robert Sharman

Abstract

Stall warnings at flight level 410 (12.5 km) occurred unexpectedly during a research flight of the High Altitude and Long Range Research Aircraft (HALO) over Italy on 12 January 2016. The dangerous flight situation was mitigated by pilot intervention. At the incident location, the stratosphere was characterized by large horizontal variations in the along-track wind speed and temperature. On this particular day, strong northwesterly winds in the lower troposphere in concert with an aligned polar front jet favored the excitation and vertical propagation of large-amplitude mountain waves at and above the Apennines in Italy. These mountain waves carried large vertical energy fluxes of 8 W m−2 and propagated without significant dissipation from the troposphere into the stratosphere. While turbulence is a well-acknowledged hazard to aviation, this case study reveals that nonbreaking, vertically propagating mountain waves also pose a potential hazard, especially to high-flying aircraft. It is the wave-induced modulation of the ambient along-track wind speed that may decrease the aircraft speed toward the minimum needed stall speed.

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Jannik Wilhelm, T. R. Akylas, Gergely Bölöni, Junhong Wei, Bruno Ribstein, Rupert Klein, and Ulrich Achatz

Abstract

As present weather forecast codes and increasingly many atmospheric climate models resolve at least part of the mesoscale flow, and hence also internal gravity waves (GWs), it is natural to ask whether even in such configurations subgrid-scale GWs might impact the resolved flow and how their effect could be taken into account. This motivates a theoretical and numerical investigation of the interactions between unresolved submesoscale and resolved mesoscale GWs, using Boussinesq dynamics for simplicity. By scaling arguments, first a subset of submesoscale GWs that can indeed influence the dynamics of mesoscale GWs is identified. Therein, hydrostatic GWs with wavelengths corresponding to the largest unresolved scales of present-day limited-area weather forecast models are an interesting example. A large-amplitude WKB theory, allowing for a mesoscale unbalanced flow, is then formulated, based on multiscale asymptotic analysis utilizing a proper scale-separation parameter. Purely vertical propagation of submesoscale GWs is found to be most important, implying inter alia that the resolved flow is only affected by the vertical flux convergence of submesoscale horizontal momentum at leading order. In turn, submesoscale GWs are refracted by mesoscale vertical wind shear while conserving their wave-action density. An efficient numerical implementation of the theory uses a phase-space ray tracer, thus handling the frequent appearance of caustics. The WKB approach and its numerical implementation are validated successfully against submesoscale-resolving simulations of the resonant radiation of mesoscale inertia GWs by a horizontally as well as vertically confined submesoscale GW packet.

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Tanja C. Portele, Andreas Dörnbrack, Johannes S. Wagner, Sonja Gisinger, Benedikt Ehard, Pierre-Dominique Pautet, and Markus Rapp

Abstract

The impact of transient tropospheric forcing on the deep vertical mountain-wave propagation is investigated by a unique combination of in situ and remote sensing observations and numerical modeling. The temporal evolution of the upstream low-level wind follows approximately a shape and was controlled by a migrating trough and connected fronts. Our case study reveals the importance of the time-varying propagation conditions in the upper troposphere and lower stratosphere (UTLS). Upper-tropospheric stability, the wind profile, and the tropopause strength affected the observed and simulated wave response in the UTLS. Leg-integrated along-track momentum fluxes () and amplitudes of vertical displacements of air parcels in the UTLS reached up to 130 kN m−1 and 1500 m, respectively. Their maxima were phase shifted to the maximum low-level forcing by ≈8 h. Small-scale waves ( km) were continuously forced, and their flux values depended on wave attenuation by breaking and reflection in the UTLS region. Only maximum flow over the envelope of the mountain range favored the excitation of longer waves that propagated deeply into the mesosphere. Their long propagation time caused a retarded enhancement of observed mesospheric gravity wave activity about 12–15 h after their observation in the UTLS. For the UTLS, we further compared observed and simulated with fluxes of 2D quasi-steady runs. UTLS momentum fluxes seem to be reproducible by individual quasi-steady 2D runs, except for the flux enhancement during the early decelerating forcing phase.

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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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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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