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Andreas Dörnbrack

Abstract

Planetary waves disturbed the hitherto stable Arctic stratospheric polar vortex in the middle of January 2016 in such a way that unique tropospheric and stratospheric flow conditions for vertically and horizontally propagating mountain waves developed. Coexisting strong low-level westerly winds across almost all European mountain ranges plus the almost zonally aligned polar-front jet created these favorable conditions for deeply propagating gravity waves. Furthermore, the northward displacement of the polar night jet resulted in a widespread coverage of stratospheric mountain waves trailing across Northern Europe. This paper describes the particular meteorological setting by analyzing the tropospheric and stratospheric flows based on the ERA5 data. The potential of the flow for exciting internal gravity waves from nonorographic sources is evaluated across all altitudes by considering various indices to indicate flow imbalances as δ, Ro, Ro ζ , Ro, and ΔNBE. The analyzed gravity waves are described and characterized. The main finding of this case study is the exceptionally vast extension of the mountain waves trailing to high latitudes originating from the flow across the mountainous sources that are located at about 45°N. The magnitudes of the simulated stratospheric temperature perturbations attain values larger than 10 K and are comparable to values as documented by recent case studies of large-amplitude mountain waves over South America. The zonal means of the resolved and parameterized stratospheric wave drag during the mountain wave event peak at −4.5 and −32.2 m s−1 day−1, respectively.

Open access
Tyler Mixa
,
Andreas Dörnbrack
, and
Markus Rapp

Abstract

Horizontally dispersing gravity waves with horizontal wavelengths of 30–40 km were observed at mesospheric altitudes over Auckland Island by the airborne advanced mesospheric temperature mapper during a Deep Propagating Gravity Wave Experiment (DEEPWAVE) research flight on 14 July 2014. A 3D nonlinear compressible model is used to determine which propagation conditions enabled gravity wave penetration into the mesosphere and how the resulting instability characteristics led to widespread momentum deposition. Results indicate that linear tunneling through the polar night jet enabled quick gravity wave propagation from the surface up to the mesopause, while subsequent instability processes reveal large rolls that formed in the negative shear above the jet maximum and led to significant momentum deposition as they descended. This study suggests that gravity wave tunneling is a viable source for this case and other deep propagation events reaching the mesosphere and lower thermosphere.

Open access
Irina Strelnikova
,
Marwa Almowafy
,
Gerd Baumgarten
,
Kathrin Baumgarten
,
Manfred Ern
,
Michael Gerding
, and
Franz-Josef Lübken

Abstract

We present gravity wave climatologies based on 7 years (2012–18) of lidar and Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperatures and reanalysis data at 54° and 69°N in the altitude range 30–70 km. We use 9452 (5044) h of lidar observations at Kühlungsborn [Arctic Lidar Observatory for Middle Atmosphere Research (ALOMAR)]. Filtering according to vertical wavelength (λ z < 15 km) or period (τ < 8 h) is applied. Gravity wave potential energy densities (GWPED) per unit volume (E pV) and per unit mass (E pm) are derived. GWPED from reanalysis are smaller compared to lidar. The difference increases with altitude in winter and reaches almost two orders of magnitude around 70 km. A seasonal cycle of E pV with maximum values in winter is present at both stations in nearly all lidar and SABER measurements and in reanalysis data. For SABER and for lidar (with λ < 15 km) the winter/summer ratios are a factor of ~2–4, but are significantly smaller for lidar with τ < 8 h. The winter/summer ratios are nearly identical at both stations and are significantly larger for E pm compared to E pV. Lidar and SABER observations show that E pV is larger by a factor of ~2 at Kühlungsborn compared to ALOMAR, independent of season and altitude. Comparison with mean background winds shows that simple scenarios regarding GW filtering, etc., cannot explain the Kühlungsborn–ALOMAR differences. The value of E pV decreases with altitude in nearly all cases. Corresponding E pV-scale heights from lidar are generally larger in winter compared to summer. Above ~55 km, E pV in summer is almost constant with altitude at both stations. The winter–summer difference of E pV scale heights is much smaller or absent in SABER and in reanalysis data.

Open access
Gergely Bölöni
,
Young-Ha Kim
,
Sebastian Borchert
, and
Ulrich Achatz

Abstract

Current gravity wave (GW) parameterization (GWP) schemes are using the steady-state assumption, in which an instantaneous balance between GWs and mean flow is postulated, thereby neglecting transient, nondissipative interactions between the GW field and the resolved flow. These schemes rely exclusively on wave dissipation, by GW breaking or near critical layers, as a mechanism leading to forcing of the mean flow. In a transient GWP, without the steady-state assumption, nondissipative wave–mean-flow interactions are enabled as an additional mechanism. Idealized studies have shown that this is potentially important, and therefore the transient GWP Multiscale Gravity Wave Model (MS-GWaM) has been implemented into a state-of-the-art weather and climate model. In this implementation, MS-GWaM leads to a zonal-mean circulation that agrees well with observations and increases GW momentum-flux intermittency as compared with steady-state GWPs, bringing it into better agreement with superpressure balloon observations. Transient effects taken into account by MS-GWaM are shown to make a difference even on monthly time scales: in comparison with steady-state GWPs momentum fluxes in the lower stratosphere are increased and the amount of missing drag at Southern Hemispheric high latitudes is decreased to a modest but nonnegligible extent. An analysis of the contribution of different wavelengths to the GW signal in MS-GWaM suggests that small-scale GWs play an important role down to horizontal and vertical wavelengths of 50 km (or even smaller) and 200 m, respectively.

Full access
Young-Ha Kim
,
Gergely Bölöni
,
Sebastian Borchert
,
Hye-Yeong Chun
, and
Ulrich Achatz

Abstract

In a companion paper, the Multiscale Gravity Wave Model (MS-GWaM) has been introduced and its application to a global model as a transient subgrid-scale parameterization has been described. This paper focuses on the examination of intermittency of gravity waves (GWs) modeled by MS-GWaM. To introduce the variability and intermittency in wave sources, convective GW sources are formulated, using diabatic heating diagnosed by the convection parameterization, and they are coupled to MS-GWaM in addition to a flow-independent source in the extratropics accounting for GWs due neither to convection nor to orography. The probability density function (PDF) and Gini index for GW pseudomomentum fluxes are assessed to investigate the intermittency. Both are similar to those from observations in the lower stratosphere. The intermittency of GWs over tropical convection is quite high and is found not to change much in the vertical direction. In the extratropics, where nonconvective GWs dominate, the intermittency is lower than that in the tropics in the stratosphere and comparable to that in the mesosphere, exhibiting a gradual increase with altitude. The PDFs in these latitudes seem to be close to the lognormal distributions. Effects of transient GW–mean-flow interactions on the simulated GW intermittency are assessed by performing additional simulations using the steady-state assumption in the GW parameterization. The intermittency of parameterized GWs over tropical convection is found to be overestimated by the assumption, whereas in the extratropics it is largely underrepresented. Explanation and discussion of these effects are included.

Full access
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.

Free access
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.

Free access
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.

Full access
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
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.

Full access