scholarly journals Effects of Horizontal Geometrical Spreading on the Parameterization of Orographic Gravity Wave Drag. Part I: Numerical Transform Solutions

2015 ◽  
Vol 72 (6) ◽  
pp. 2330-2347 ◽  
Author(s):  
Stephen D. Eckermann ◽  
Jun Ma ◽  
Dave Broutman
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Climate Models ◽  
Functional Form ◽  
Vertical Displacement ◽  
Wave Drag ◽  
Geometrical Spreading ◽  
Vertical Coordinate ◽  
Sheared Flow ◽  
Weather And Climate

Abstract Numerical transform solutions for hydrostatic gravity waves generated by both uniform and sheared flow over elliptical obstacles are used to quantify effects of horizontal geometrical spreading on amplitude evolution with height. Both vertical displacement and steepness amplitudes are considered because of their close connections to drag parameterizations in weather and climate models. Novel diagnostics quantify the location and value of the largest wavefield amplitudes most likely to break at each altitude. These horizontal locations do not stray far from the obstacle peak even at high altitudes. Resulting vertical profiles of wave amplitude are normalized to remove density and refraction effects, thereby quantifying the horizontal geometrical spreading contribution, currently absent from parameterizations. Horizontal geometrical spreading produces monotonic amplitude decreases with height through wave-action conservation as waves propagate into progressively larger horizontal areas. Accumulated amplitude reductions are appreciable for all but the most quasi-two-dimensional obstacles with long axes orthogonal to the flow, and even these are impacted appreciably if the obstacle is rotated by more than 20°–30°. Profiles are insensitive to the obstacle’s functional form but vary strongly in response to changes in its horizontal aspect ratio. Responses to background winds are captured by a vertical coordinate transformation that remaps profiles to a universal form for a given obstacle. These results show that horizontal geometrical spreading has comparable or larger effects on wave amplitudes as the refraction of vertical wavenumbers and thus is important for accurate parameterizations of wave breaking and drag.

Importance of gravity wave forcing for springtime southern polar vortex breakdown as revealed by ERA5

2021 ◽  
Author(s):  
Aman Gupta ◽  
Thomas Birner ◽  
Andreas Doernbrack ◽  
Inna Polichtchouk
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Zonal Wind ◽  
Planetary Wave ◽  
Climate Models ◽  
Vortex Breakdown ◽  
Polar Vortex ◽  
Wave Drag ◽  
Planetary Waves ◽  
The Mean

<p>Planetary waves and gravity waves are the key drivers of middle atmospheric circulation and variability. While planetary waves are well resolved in climate models, inaccuracies in representation of gravity waves in climate models persist. Inaccuracies in representation of gravity waves limit our understanding of the planetary wave-gravity wave interactions that can be crucial during the Antarctic polar vortex breakdown. Moreover, "missing" gravity wave drag around 60<sup>o</sup>S in the upper stratosphere is considered to be responsible for the "cold-pole" bias in comprehensive climate models that employ parameterizations to appproximately represent the gravity wave drag.</p><p>We illustrate the strength of the high-resolution ERA-5 reanalysis in resolving a broad spectrum of gravity waves in southern hemisphere midlatitudes and to estimate their contribution to the momentum budget around 60<sup>o</sup>S. We find that most of the resolved mountain waves excited over the Andes and Antarctic peninsula propagate away from their source and deposit momentum around 60<sup>o</sup>S over the Southern Ocean. Further, a composite analysis around 60<sup>o</sup>S during the vortex breakdown period using ERA-5 reveals considerably large fractional contribution of resolved + parameterized GWD towards the vortex deceleration. Upto 30 days prior to the breakdown, a balance between the Coriolis acceleration and the planetary wave deceleration provides a weak net deceleration of the mean winds, following which, they provide a net acceleration of the mean winds. The gravity waves, however, provide a steady deceleration of the mean winds throughout the breakdown period. The resolved drag in ERA-5 accounts for as much as one-fourth of the zonal wind deceleration at 60<sup>o</sup>S and 10 hPa, while the parameterized drag in ERA-5 accounts for more than one-half of the zonal wind deceleration.  The findings establish the crucial role of gravity waves in wintertime stratospheric circulation and opens avenues for further stratospheric gravity wave analysis using ERA-5.</p>

scholarly journals Diverse dynamical response to orographic gravity wave drag hotspots - a zonal mean perspective

2021 ◽  
Author(s):  
Petr Šácha ◽  
Aleš Kuchař ◽  
Roland Eichinger ◽  
Petr Pišoft ◽  
Christoph Jacobi ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Gravity Waves ◽  
Climate Models ◽  
Rossby Waves ◽  
Middle Atmosphere ◽  
Internal Gravity Waves ◽  
Wave Drag ◽  
Dynamical Response ◽  
Current Generation ◽  
Zonal Winds

<p>In the extratropical atmosphere, Rossby waves (RWs) and internal gravity waves (GWs) propagating from the troposphere mediate a coupling with the middle atmosphere by influencing the dynamics herein. In the current generation chemistry-climate models (CCMs), RW effects are well resolved while GW effects have to be parameterized. Here, we analyze orographic GW (OGW) interaction with resolved dynamics in a comprehensive CCM on the time scale of days. For this, we apply a recently developed method of strong OGW drag event composites for the three strongest northern hemisphere OGW hotspots. We show that locally-strong OGW events considerably alter the properties of resolved wave propagation into the middle atmosphere, which subsequently influences zonal winds and RW transience. Our results demonstrate that the influence of OGWs is critically dependent on the hotspot region, which underlines the OGW-resolved dynamics interaction being a two-way process.</p>

scholarly journals Effects of Horizontal Geometrical Spreading on the Parameterization of Orographic Gravity Wave Drag. Part II: Analytical Solutions

2015 ◽  
Vol 72 (6) ◽  
pp. 2348-2365 ◽  
Author(s):  
Stephen D. Eckermann ◽  
Dave Broutman ◽  
Harold Knight
Keyword(s):  
Analytical Solutions ◽  
Three Dimensional ◽  
Vertical Displacement ◽  
Wave Drag ◽  
Mean Value ◽  
Geometrical Spreading ◽  
Analytical Approximations ◽  
Approximate Analytical Solutions ◽  
Principal Axes ◽  
Analytical Relations

Abstract Effects of horizontal geometrical spreading on the amplitude variation with height of linear three-dimensional hydrostatic orographic gravity waves (OGWs) are quantified via relevant simplifications to the governing transform relations, leading to analytical solutions. The analysis is restricted to elliptical Gaussian obstacles with principal axes aligned parallel and perpendicular to unidirectional shear flow and to vertical displacement and steepness amplitudes, given their relevance to OGW drag parameterizations in global models. Two solutions are derived: a “small l” solution in which horizontal wavenumbers l orthogonal to the flow are taken to be much smaller than those parallel to the flow, and a “single k” solution in which horizontal wavenumbers k parallel to the flow have a single mean value. The resulting analytical relations, valid for arbitrary vertical profiles of upstream winds and stability, depend only on the obstacle’s elliptical aspect ratio β and a normalized height coordinate incorporating wind and stability variations. These analytical approximations accurately reproduce the salient features of the exact numerical transform solutions. These include monotonic decreases with height that asymptotically approach z−1/2 forms at large z and strong β dependence in amplitude diminution with height. Steepness singularities close to the surface are shown to be a mathematical consequence of the Hilbert transform approach to deriving complex wavefield solutions. These approximate analytical solutions for horizontal geometrical spreading effects on wave amplitude highlight the importance of this missing physics for current parameterizations of OGW drag and offer an accurate and efficient means of incorporating some of these omitted effects.

scholarly journals An Adaptive Vertical Coordinate Formulation for a Nonhydrostatic Model with Flux-Form Equations

2007 ◽  
Vol 135 (1) ◽  
pp. 228-239 ◽  
Author(s):  
Günther Zängl
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Three Dimensional ◽  
Vertical Position ◽  
Vertical Coordinate ◽  
Nonhydrostatic Model ◽  
Atmospheric Equations ◽  
Terrain Following ◽  
Tropopause Region ◽  
Model Layer

Abstract The concept of adaptive vertical coordinates is used to upgrade conventional terrain-following σ coordinates to arbitrary hybrid coordinates. Compared with previous approaches for implementing adaptive coordinates, the method presented here combines unrestricted applicability to nonhydrostatic models with the capability to integrate the atmospheric equations in flux form. The coordinate is based on a three-dimensional field carrying the vertical position of the coordinate surfaces, which is made time dependent by introducing a prognostic equation. As a specific example, the adaptive coordinate is used to emulate a hybrid isentropic system. Idealized tests in which the coordinate surfaces are artificially moved reveal that the ensuing spurious motions are small enough to be negligible in realistic applications. Mountain wave tests demonstrate that the hybrid coordinate remains numerically stable under strong forcing. However, the model layer distribution established with the hybrid isentropic coordinate is not optimal for representing the dynamics of breaking gravity waves because the vertical distance between the model levels tends to be too large in the wave breaking region. On the other hand, real case studies demonstrate that the hybrid coordinate significantly improves the representation of the tropopause because of enhanced vertical resolution in the tropopause region.

scholarly journals A Robust Mechanism for Strengthening of the Brewer–Dobson Circulation in Response to Climate Change: Critical-Layer Control of Subtropical Wave Breaking

2011 ◽  
Vol 68 (4) ◽  
pp. 784-797 ◽  
Author(s):  
Theodore G. Shepherd ◽  
Charles McLandress
Keyword(s):  
Climate Change ◽  
Wave Breaking ◽  
Climate Models ◽  
Lower Stratosphere ◽  
Climate Model ◽  
Baroclinic Instability ◽  
Wave Drag ◽  
Dynamical Mechanism ◽  
Rossby Wave Breaking ◽  
Critical Layers

Abstract Climate models consistently predict a strengthened Brewer–Dobson circulation in response to greenhouse gas (GHG)-induced climate change. Although the predicted circulation changes are clearly the result of changes in stratospheric wave drag, the mechanism behind the wave-drag changes remains unclear. Here, simulations from a chemistry–climate model are analyzed to show that the changes in resolved wave drag are largely explainable in terms of a simple and robust dynamical mechanism, namely changes in the location of critical layers within the subtropical lower stratosphere, which are known from observations to control the spatial distribution of Rossby wave breaking. In particular, the strengthening of the upper flanks of the subtropical jets that is robustly expected from GHG-induced tropospheric warming pushes the critical layers (and the associated regions of wave drag) upward, allowing more wave activity to penetrate into the subtropical lower stratosphere. Because the subtropics represent the critical region for wave driving of the Brewer–Dobson circulation, the circulation is thereby strengthened. Transient planetary-scale waves and synoptic-scale waves generated by baroclinic instability are both found to play a crucial role in this process. Changes in stationary planetary wave drag are not so important because they largely occur away from subtropical latitudes.

Angular Momentum Conservation and Gravity Wave Drag Parameterization: Implications for Climate Models

2007 ◽  
Vol 64 (1) ◽  
pp. 190-203 ◽  
Author(s):  
Tiffany A. Shaw ◽  
Theodore G. Shepherd
Keyword(s):  
Gravity Wave ◽  
Wave Breaking ◽  
Climate Models ◽  
Middle Atmosphere ◽  
Momentum Conservation ◽  
Wave Drag ◽  
Source Spectrum ◽  
Wave Source ◽  
Radiative Perturbation ◽  
Spurious Response

Abstract The robustness of the parameterized gravity wave response to an imposed radiative perturbation in the middle atmosphere is examined. When momentum is conserved and for reasonable gravity wave drag parameters, the response to a polar cooling induces polar downwelling above the region of the imposed cooling, with consequent adiabatic warming. This response is robust to changes in the gravity wave source spectrum, background flow, gravity wave breaking criterion, and model lid height. When momentum is not conserved, either in the formulation or in the implementation of the gravity wave drag parameterization, the response becomes sensitive to the above-mentioned factors—in particular to the model lid height. The spurious response resulting from nonconservation is found to be nonnegligible in terms of the total gravity wave drag–induced downwelling.

scholarly journals Theoretical Studies of Convectively Forced Mesoscale Flows in Three Dimensions. Part II: Shear Flow with a Critical Level

2010 ◽  
Vol 67 (3) ◽  
pp. 694-712 ◽  
Author(s):  
Ji-Young Han ◽  
Jong-Jin Baik
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Wind Direction ◽  
Critical Level ◽  
Deep Convection ◽  
Vertical Wind Shear ◽  
Finite Depth ◽  
Vertical Displacement ◽  
Two Dimensions ◽  
Three Dimensions

Abstract Convectively forced mesoscale flows in a shear flow with a critical level are theoretically investigated by obtaining analytic solutions for a hydrostatic, nonrotating, inviscid, Boussinesq airflow system. The response to surface pulse heating shows that near the center of the moving mode, the magnitude of the vertical velocity becomes constant after some time, whereas the magnitudes of the vertical displacement and perturbation horizontal velocity increase linearly with time. It is confirmed from the solutions obtained in present and previous studies that this result is valid regardless of the basic-state wind profile and dimension. The response to 3D finite-depth steady heating representing latent heating due to cumulus convection shows that, unlike in two dimensions, a low-level updraft that is necessary to sustain deep convection always occurs at the heating center regardless of the intensity of vertical wind shear and the heating depth. For deep heating across a critical level, little change occurs in the perturbation field below the critical level, although the heating top height increases. This is because downward-propagating gravity waves induced by the heating above, but not near, the critical level can hardly affect the flow response field below the critical level. When the basic-state wind backs with height, the vertex of V-shaped perturbations above the heating top points to a direction rotated a little clockwise from the basic-state wind direction. This is because the V-shaped perturbations above the heating top is induced by upward-propagating gravity waves that have passed through the layer below where the basic-state wind direction is clockwise relative to that above.

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