How white is the sky? 

2021 ◽  
Author(s):  
Nedjeljka Žagar ◽  
Žiga Zaplotnik ◽  
Valentino Neduhal
Keyword(s):  
Kinetic Energy ◽  
Gravity Wave ◽  
Power Law ◽  
Gravity Waves ◽  
Global Analysis ◽  
Vertical Motion ◽  
Energy Spectra ◽  
Horizontal Wind ◽  
Unified Framework ◽  
Inertia Gravity Waves

<p>The energy spectrum of atmospheric horizontal motions has been extensively studied in observations and numerical simulations. Its canonical shape includes a transition from the -3 power law at synoptic scale to -5/3 power law at mesoscale. The transition is taking place at scales around 500 km that can be seen as the scale where energy associated with quasi-linear inertia-gravity waves exceeds the balanced (or Rossby wave) energy. In contrast to the horizontal spectrum, the spectrum of kinetic energy of vertical motions is poorly known since the vertical motion is not an observed quantity of the global observing system and vertical kinetic energy spectra from non-hydrostatic models are difficult to validate.</p> <p>Traditionally, vertical velocities associated with the Rossby and gravity waves have been treated separately using the quasi-geostrophic omega equations and polarization relations for the stratified Boussinesq fluid in the (x,z) plane, respectively. In the tropics, the Rossby and gravity  wave regimes are difficult to separate and their frequency gap, present in the extra-tropics, is filled with the Kelvin and mixed Rossby-gravity waves. A separate treatment of the Rossby and gravity wave regimes makes it challenging to quantify energies of their vertical motions and vertical momentum fluxes. A unified treatment and wave interactions is performed by high-resolution non-hydrostatic models but their understanding requires the toolkit of theory. </p> <p>This contribution presents a unified framework for the derivation of vertical velocities of the Rossby and inertia-gravity waves and associated kinetic energy spectra. Expressions for the Rossby and gravity wave vertical velocities are derived using the normal-mode framework in the hydrostatic atmosphere that can be considered applicable up to the scale around 10 km. The derivation involves the analytical evaluation of divergence of the horizontal wind associated with the Rossby and inertia-gravity eigensolutions of the linearized primitive equations. The new framework is applied to the global analysis data of the ECMWF system. Results confirm that the tropical vertical kinetic energy spectra associated with inertia-gravity waves are on average indeed white. Deviations from the white spectrum are discussed for latitude and altitude bands.</p>

The signature of the tropospheric gravity wave background in observed mesoscale motion

2021 ◽  
Author(s):  
Claudia Stephan ◽  
Alexis Mariaccia
Keyword(s):  
Gravity Waves ◽  
Functional Dependence ◽  
Vertical Motion ◽  
Numerical Data ◽  
Reanalysis Data ◽  
Horizontal Resolution ◽  
Energy Spectra ◽  
Equivalent Radius ◽  
Individual Wave ◽  
Inertia Gravity Waves

<p>How convection couples to mesoscale vertical motion and what determines these motions is poorly understood. We diagnose profiles of area-averaged mesoscale divergence from measurements of horizontal winds collected by an extensive upper-air sounding network of a recent campaign over the western tropical North Atlantic, the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC<sup>4</sup>A) campaign. Observed area-averaged divergence amplitudes scale approximately inversely with area equivalent radius. This functional dependence is also confirmed in reanalysis data and a global freely-evolving simulation run at 2.5 km horizontal resolution. Based on the numerical data it is demonstrated that the energy spectra of inertia gravity waves can explain the scaling of divergence amplitudes with area. At individual times, however, few waves can dominate the region. Nearly monochromatic tropospheric waves are diagnosed in the soundings by means of an optimized hodograph analysis. For one day, results suggest that an individual wave directly modulated the satellite observed cloud pattern. However, because such immediate wave impacts are rare, the systematic modulation of vertical motion due to inertia-gravity waves may be more relevant as a convection-modulating factor. We propose an analytic relationship between energy spectra and divergence amplitudes, which, if confirmed by future studies, could be used to design better external forcing methods for regional models.</p>

scholarly journals The signature of the tropospheric gravity wave background in observed mesoscale motion

2021 ◽  
Vol 2 (2) ◽  
pp. 359-372
Author(s):  
Claudia Christine Stephan ◽  
Alexis Mariaccia
Keyword(s):  
Gravity Waves ◽  
Functional Dependence ◽  
Vertical Motion ◽  
Numerical Data ◽  
Reanalysis Data ◽  
Horizontal Resolution ◽  
Energy Spectra ◽  
Equivalent Radius ◽  
Individual Wave ◽  
Inertia Gravity Waves

Abstract. How convection couples to mesoscale vertical motion and what determines these motions is poorly understood. This study diagnoses profiles of area-averaged mesoscale divergence from measurements of horizontal winds collected by an extensive upper-air sounding network of a recent campaign over the western tropical North Atlantic, the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC4A) campaign. Observed area-averaged divergence amplitudes scale approximately inversely with area-equivalent radius. This functional dependence is also confirmed in reanalysis data and a global, freely evolving simulation run at 2.5 km horizontal resolution. Based on the numerical data it is demonstrated that the energy spectra of inertia gravity waves can explain the scaling of divergence amplitudes with area. At individual times, however, few waves can dominate the region. Nearly monochromatic tropospheric waves are diagnosed in the soundings by means of an optimized hodograph analysis. For one day, results suggest that an individual wave directly modulated the satellite-observed cloud pattern. However, because such immediate wave impacts are rare, the systematic modulation of vertical motion due to inertia–gravity waves may be more relevant as a convection-modulating factor. The analytic relationship between energy spectra and divergence amplitudes proposed in this article, if confirmed by future studies, could be used to design better external forcing methods for regional models.

scholarly journals The signature of the tropospheric gravity wave background in observed mesoscale motion

2020 ◽  
Author(s):  
Claudia Christine Stephan ◽  
Alexis Mariaccia
Keyword(s):  
Gravity Waves ◽  
Functional Dependence ◽  
Vertical Motion ◽  
Numerical Data ◽  
Reanalysis Data ◽  
Horizontal Resolution ◽  
Energy Spectra ◽  
Equivalent Radius ◽  
Individual Wave ◽  
Inertia Gravity Waves

Abstract. How convection couples to mesoscale vertical motion and what determines these motions is poorly understood. This study diagnoses profiles of area-averaged mesoscale divergence from measurements of horizontal winds collected by an extensive upper-air sounding network of a recent campaign over the western tropical North Atlantic, the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC4A) campaign. Observed area-averaged divergence amplitudes scale approximately inversely with area equivalent radius. This functional dependence is also confirmed in reanalysis data and a global freely-evolving simulation run at 2.5 km horizontal resolution. Based on the numerical data it is demonstrated that the energy spectra of inertia gravity waves can explain the scaling of divergence amplitudes with area. At individual times, however, few waves can dominate the region. Nearly monochromatic tropospheric waves are diagnosed in the soundings by means of an optimized hodograph analysis. For one day, results suggest that an individual wave directly modulated the satellite-observed cloud pattern. However, because such immediate wave impacts are rare, the systematic modulation of vertical motion due to inertia-gravity waves may be more relevant as a convection-modulating factor. The analytic relationship between energy spectra and divergence amplitudes proposed in this article, if confirmed by future studies, could be used to design better external forcing methods for regional models.

Further developments on estimating inertia-gravity-wave properties: Combining the Riesz transform with machine learning methods

2020 ◽  
Author(s):  
Mozhgan AmirAmjadi ◽  
Ali R. Mohebalhojeh ◽  
Mohammad Mirzaei
Keyword(s):  
Machine Learning ◽  
Wind Speed ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Riesz Transform ◽  
Wave Number ◽  
Horizontal Wind ◽  
Explanatory Variables ◽  
Wave Characteristics ◽  
Inertia Gravity Waves

<p>One of the remaining issues in the parameterization of inertia-gravity waves is the estimation of wave characteristics such as wavenumber and intrinsic frequency. In this survey, we explore a new way to estimate the wave characteristics at the launch level. To this end, we retrieve the wavenumber using the Riesz Transform which is the generalized form of the Hilbert Transform applicable in the multi-dimensional analysis. For this purpose, the high-resolution horizontal divergence field has been employed since it filters the background flow and thus provides a reasonable representation of the inertia-gravity wave signal. This is followed by the application of machine learning to reconstruct the retrieved wavenumber using the coarse-grained resolvable variables including the horizontal wind speed, the large scale vertical velocity, the cross-stream ageostrophic wind speed, the frontogenesis function and the latent heat released during condensation as explanatory variables at the launch level.<br>We have employed the ERA5 dataset in this survey, having observed that the dataset can directly resolve the inertia-gravity waves at its full resolution. In order to avoid mountain waves and focus on non-orographic inertia-gravity waves, two areas far from the significant obstacles over the midlatitude of the Atlantic Ocean and Northern Pacific Ocean are considered from December 2018 to February 2019. The results show a reasonable correlation between the reconstructed wavenumber using low-resolution explanatory variables and the retrieved one using the Riesz Transform so that this method can be utilized to estimate the inertia-gravity wave number at the launch level.</p>

Turbulent kinetic energy spectra and cascades in the polar atmosphere of Saturn

2021 ◽  
Author(s):  
Peter L. Read ◽  
Arrate Antuñano ◽  
Simon Cabanes ◽  
Greg Colyer ◽  
Teresa del Rio-Gaztelurrutia ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
High Latitude ◽  
Deep Convection ◽  
Baroclinic Instability ◽  
Polar Vortex ◽  
Energy Spectra ◽  
Horizontal Wind ◽  
Polar Regions ◽  
Zonal Wavenumber ◽  
Cloud Tops

<p>The regions of Saturn’s cloud-covered atmosphere polewards of 60<sup>o</sup> latitude are dominated in each hemisphere near the cloud tops by an intense, cyclonic polar vortex surrounded by a strong, high latitude eastward zonal jet. In the north, this high latitude jet takes the form of a remarkably regular zonal wavenumber m=6 hexagonal pattern that has been present at least since the Voyager spacecraft encounters with Saturn in 1980-81, and probably much longer. The origin of this feature, and the absence of a similar feature in the south, has remained poorly understood since its discovery. In this work, we present some new analyses of horizontal wind measurements at Saturn’s cloud tops polewards of 60 degrees in both the northern and southern hemispheres, previously published by Antuñano et al. (2015) using images from the Cassini mission, in which we compute kinetic energy spectra and the transfer rates of kinetic energy (KE) and enstrophy between different scales. 2D KE spectra are consistent with a zonostrophic regime, with a steep (~n<sup>-5</sup>) spectrum for the mean zonal flow (n is the total wavenumber) and a shallower Kolmogorov-like KE spectrum (~n<sup>-5/3</sup>) for the residual (eddy) flow, much as previously found for Jupiter’s atmosphere (Galperin et al. 2014; Young & Read 2017). Three different methods are used to compute the energy and enstrophy transfers, (a) as latitude-dependent zonal spectral fluxes, (b) as latitude-dependent structure functions and (c) as spatially filtered energy fluxes. The results of all three methods are largely in agreement in indicating a direct (forward) enstrophy cascade across most scales, averaged across the whole domain, an inverse kinetic energy cascade to large scales and a weak direct KE cascade at the smallest scales. The pattern of transfers has a more complex dependence on latitude, however. But it is clear that the m=6 North Polar Hexagon (NPH) wave was transferring KE into its zonal jet at 78<sup>o</sup> N (planetographic) at a rate of ∏<sub>E</sub> ≈ 1.8 x 10<sup>-4</sup> W kg<sup>-1</sup> at the time the Cassini images were acquired. This implies that the NPH was not maintained by a barotropic instability at this time, but may have been driven via a baroclinic instability or possibly from deep convection. Further implications of these results will be discussed.</p><p> </p><p>References</p><p>Antuñano, A., T. del Río-Gaztelurrutia, A. Sánchez-Lavega, and R. Hueso (2015), Dynamics of Saturn’s polar regions, J. Geophys. Res. Planets, 120, 155–176, doi:10.1002/2014JE004709.</p><p>Galperin, B., R. M.B. Young, S. Sukoriansky, N. Dikovskaya, P. L. Read, A. J. Lancaster & D. Armstrong (2014) Cassini observations reveal a regime of zonostrophic macroturbulence on Jupiter, Icarus, 229, 295–320.doi: 10.1016/j.icarus.2013.08.030</p><p>Young, R. M. B. & Read, P. L. (2017) Forward and inverse kinetic energy cascades in Jupiter’s turbulent weather layer, Nature Phys., 13, 1135-1140. Doi:10.1038/NPHYS4227</p><div> <div> <div> </div> </div> <div> <div> </div> </div> <div> <div> </div> </div> <div> <div> </div> </div> </div>

scholarly journals Ageostrophic instability in rotating, stratified interior vertical shear flows

2014 ◽  
Vol 755 ◽  
pp. 397-428 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Claire Ménesguen
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gravity Waves ◽  
Shear Flows ◽  
Vertical Shear ◽  
Mean Flow ◽  
Efficient Energy Transfer ◽  
The Mean ◽  
Inertia Gravity Waves

AbstractThe linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ($\mathit{Ro}$). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ($k,l$) that are far from $l= 0$ or $k = 0$, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.

scholarly journals Inertia–gravity-wave radiation by a sheared vortex

2008 ◽  
Vol 596 ◽  
pp. 169-189 ◽  
Author(s):  
E. I. ÓLAFSDÓTTIR ◽  
A. B. OLDE DAALHUIS ◽  
J. VANNESTE
Keyword(s):  
Gravity Wave ◽  
Couette Flow ◽  
Gravity Waves ◽  
Dimensional Structure ◽  
Analytic Description ◽  
Wave Radiation ◽  
Rossby Number ◽  
Spontaneous Radiation ◽  
Initial State ◽  
Inertia Gravity Waves

We consider the linear evolution of a localized vortex with Gaussian potential vorticity that is superposed on a horizontal Couette flow in a rapidly rotating strongly stratified fluid. The Rossby number, defined as the ratio of the shear of the Couette flow to the Coriolis frequency, is assumed small. Our focus is on the inertia–gravity waves that are generated spontaneously during the evolution of the vortex. These are exponentially small in the Rossby number and hence are neglected in balanced models such as the quasi-geostrophic model and its higher-order generalizations. We develop an exponential-asymptotic approach, based on an expansion in sheared modes, to give an analytic description of the three-dimensional structure of the inertia–gravity waves emitted by the vortex. This provides an explicit example of the spontaneous radiation of inertia–gravity waves by localized balanced motion in the small-Rossby-number regime.The inertia–gravity waves are emitted as a burst of four wavepackets propagating downstream of the vortex. The approach employed reduces the computation of inertia–gravity-wave fields to a single quadrature, carried out numerically, for each spatial location and each time. This makes it possible to unambiguously define an initial state that is entirely free of inertia–gravity waves, and circumvents the difficulties generally associated with the separation between balanced motion and inertia–gravity waves.

scholarly journals Simulation of Inertia–Gravity Waves in a Poleward-Breaking Rossby Wave

2006 ◽  
Vol 63 (12) ◽  
pp. 3253-3276 ◽  
Author(s):  
Christoph Zülicke ◽  
Dieter Peters
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Mesoscale Model ◽  
Wave Packets ◽  
The Impact ◽  
Jet Streak ◽  
Horizontal Wavelength ◽  
Inertia Gravity Waves

Poleward-breaking Rossby waves often induce an upper-level jet streak over northern Europe. Dominant inertia–gravity wave packets are observed downstream of this jet. The physical processes of their generation and propagation, in such a configuration, are investigated with a mesoscale model. The study is focused on an observational campaign from 17 to 19 December 1999 over northern Germany. Different simulations with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) have been performed. For a high-resolution process study, three domains were set up that encompass the evolution of Rossby waves and that of inertia–gravity waves. To minimize the impact of model damping, the horizontal and vertical resolution has been adjusted appropriately. With a novel statistical approach, the properties of inertia–gravity wave packets have been estimated. This method uses the horizontal divergence field and takes into account the spatial extension of a wave packet. It avoids the explicit treatment of the background field and works for arbitrary wavelength. Two classes of inertia–gravity waves were found: subsynoptic waves with a horizontal wavelength of about 500 km and mesoscale waves with a horizontal wavelength of about 200 km. The subsynoptic structures were also detected in radiosonde observations during this campaign. The similarity between simulated and observed wavelengths and amplitudes suggests that the simulations can be considered as near realistic. Spontaneous radiation from unbalanced flow is an important process of inertia–gravity wave generation. Synoptic-scale imbalances in the exit region of the upper-tropospheric jet streak were identified with the smoothed cross-stream Lagrangian Rossby number. In a number of simulations with different physics, it was found that the inertia–gravity wave activity was related to the tropospheric jet, orography, and moist convection. The upward propagation of inertia–gravity waves was favored during this event of a poleward-breaking Rossby wave. The presence of the polar vortex induced background winds exceeding the critical line. Consequently, the activity of inertia–gravity waves in the lower stratosphere increased by an order of magnitude during the case study. The successful simulation of the complex processes of generation and propagation showed the important role of poleward Rossby wave breaking for the appearance of inertia–gravity waves in the midlatitudes.

scholarly journals Gravity wave transmission diagram

2015 ◽  
Vol 33 (12) ◽  
pp. 1479-1484 ◽  
Author(s):  
Y. Tomikawa
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Phase Speed ◽  
Propagation Direction ◽  
Wave Transmission ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Wave Power ◽  
Power Spectral ◽  
Horizontal Wavelength

Abstract. A new method of obtaining power spectral distribution of gravity waves as a function of ground-based horizontal phase speed and propagation direction from airglow observations has recently been proposed. To explain gravity wave power spectrum anisotropy, a new gravity wave transmission diagram was developed in this study. Gravity wave transmissivity depends on the existence of critical and turning levels for waves that are determined by background horizontal wind distributions. Gravity wave transmission diagrams for different horizontal wavelengths in simple background horizontal winds with constant vertical shear indicate that the effects of the turning level reflection are significant and strongly dependent on the horizontal wavelength.

scholarly journals Derivation of gravity wave intrinsic parameters and vertical wavelength using a single scanning OH(3-1) airglow spectrometer

2018 ◽  
Vol 11 (5) ◽  
pp. 2937-2947 ◽  
Author(s):  
Sabine Wüst ◽  
Thomas Offenwanger ◽  
Carsten Schmidt ◽  
Michael Bittner ◽  
Christoph Jacobi ◽  
...  
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Spatial Information ◽  
Rotational Transition ◽  
Horizontal Wind ◽  
Vertical Temperature ◽  
Vertical Wavelength ◽  
Broadband Emission ◽  
Wind Measurements ◽  
First Time

Abstract. For the first time, we present an approach to derive zonal, meridional, and vertical wavelengths as well as periods of gravity waves based on only one OH* spectrometer, addressing one vibrational-rotational transition. Knowledge of these parameters is a precondition for the calculation of further information, such as the wave group velocity vector. OH(3-1) spectrometer measurements allow the analysis of gravity wave ground-based periods but spatial information cannot necessarily be deduced. We use a scanning spectrometer and harmonic analysis to derive horizontal wavelengths at the mesopause altitude above Oberpfaffenhofen (48.09∘ N, 11.28∘ E), Germany for 22 nights in 2015. Based on the approximation of the dispersion relation for gravity waves of low and medium frequencies and additional horizontal wind information, we calculate vertical wavelengths. The mesopause wind measurements nearest to Oberpfaffenhofen are conducted at Collm (51.30∘ N, 13.02∘ E), Germany, ca. 380 km northeast of Oberpfaffenhofen, by a meteor radar. In order to compare our results, vertical temperature profiles of TIMED-SABER (thermosphere ionosphere mesosphere energetics dynamics, sounding of the atmosphere using broadband emission radiometry) overpasses are analysed with respect to the dominating vertical wavelength.

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