Energy Density Of Gravity Waves Research Articles

Assessment of Gravity Waves From Tropopause to Thermosphere and Ionosphere in High‐Resolution WACCM‐X Simulations

AbstractA new version of NCAR Whole Atmosphere Community Climate Model with thermosphere/ionosphere extension (WACCM‐X) has been developed. The main feature of this version is the species‐dependent spectral element (SE) dynamical core solved on a cubed sphere grid, eliminating the polar singularity and enabling simulations at high‐resolutions. Molecular viscosity and diffusion in the horizontal direction are also included. The Conservative Semi‐Lagrangian Multi‐Tracer Transport Scheme (CSLAM) is employed for the species transport. An efficient regridding scheme based on the Earth System Modeling Framework is used to map fields between the physics mesh and geomagnetic grid. Simulations have been performed at coarse (∼200 km and 0.25 scale height) and high (∼25 km and 0.1 scale height) resolutions. Spatial distribution of the resolved gravity waves from the high‐resolution simulations compares well with available observations in the middle and upper atmosphere. Analysis of the scale dependence of the gravity wave energy density and momentum flux shows that, while larger scale waves are dominant energetically at most latitudes, smaller scale waves contribute significantly to the total momentum flux, especially at mid‐high latitudes. The waves in the thermosphere are shown to be strongly modulated by the large‐scale wind through Doppler shift and molecular damping, and they cause large neutral atmosphere and plasma perturbations.

Winds and temperatures of the Arctic middle atmosphere during January measured by Doppler lidar

Abstract. We present an extensive data set of simultaneous temperature and wind measurements in the Arctic middle atmosphere. It consists of more than 300 h of Doppler Rayleigh lidar observations obtained during three January seasons (2012, 2014, and 2015) and covers the altitude range from 30 km up to about 85 km. The data set reveals large year-to-year variations in monthly mean temperatures and winds, which in 2012 are affected by a sudden stratospheric warming. The temporal evolution of winds and temperatures after that warming are studied over a period of 2 weeks, showing an elevated stratopause and the reformation of the polar vortex. The monthly mean temperatures and winds are compared to data extracted from the Integrated Forecast System of the European Centre for Medium-Range Weather Forecasts (ECMWF) and the Horizontal Wind Model (HWM07). Lidar and ECMWF data show good agreement of mean zonal and meridional winds below ≈ 55 km altitude, but we also find mean temperature, zonal wind, and meridional wind differences of up to 20 K, 20 m s−1, and 5 m s−1, respectively. Differences between lidar observations and HWM07 data are up to 30 m s−1. From the fluctuations of temperatures and winds within single nights we extract the potential and kinetic gravity wave energy density (GWED) per unit mass. It shows that the kinetic GWED is typically 5 to 10 times larger than the potential GWED, the total GWED increases with altitude with a scale height of ≈ 16 km. Since temporal fluctuations of winds and temperatures are underestimated in ECMWF, the total GWED is underestimated as well by a factor of 3–10 above 50 km altitude. Similarly, we estimate the energy density per unit mass for large-scale waves (LWED) from the fluctuations of nightly mean temperatures and winds. The total LWED is roughly constant with altitude. The ratio of kinetic to potential LWED varies with altitude over 2 orders of magnitude. LWEDs from ECMWF data show results similar to the lidar data. From the comparison of GWED and LWED, it follows that large-scale waves carry about 2 to 5 times more energy than gravity waves.

Low‐frequency oscillations of the gravity wave energy density in the lower atmosphere at low latitudes revealed by U.S. radiosonde data

AbstractWe adopted 14 year (from 1998 to 2011) radiosonde data from 16 stations at latitudes between 14.33°S to 29.37°N to investigate the low‐frequency oscillations of inertial gravity wave energy densities (including kinetic energy density, potential energy density, and total energy density) in the lower atmosphere from 2 km to 30 km. Apparent signatures of 11 year solar cycle and quasi‐biennial oscillation (QBO) were found in the gravity wave energy densities in the troposphere and lower stratosphere, respectively. Detailed analyses suggested that the 11 year oscillation and QBO of gravity wave activity might be due to the 11 year oscillation of convection activity and zonal wind QBO modulation, respectively. Besides, the gravity wave energy also showed a 35.2 month oscillation in the lower stratosphere, which might be generated by the interaction between the QBO (with the period of 26.7 months), and the 11 year solar cycle, while more possible causes are the direct modulation from the background zonal wind. Our results showed that the QBO signature in gravity wave total energy density could extend northward to over 20°N in the Northern Hemisphere, while the 11 year solar cycle in gravity wave activity could only extend to lower than 7.5°N. The oscillation with the period of 35.2 months may be a prolonged QBO in both gravity wave activity and background zonal wind.

Determining the parameters of wave disturbances of the middle atmosphere from lidar measurements

Altitude profiles of temperature of the middle atmosphere (30–60 km) are determined from data of lidar sensing at wavelengths of 355 and 532 nm using a modified Rayleigh method. Temperature disturbances are discriminated against the background of average profiles, using a smoothing spline. The altitude profiles of the potential energy density of gravity waves are calculated directly according to temperature fluctuations. A continuous wavelet analysis is used to determine the spectral characteristics of wave disturbances, including local power spectra of temperature fluctuations and potential energy, as well as vertical phase velocity and period for extracted wavelengths. The developed software tools make it possible to determine the characteristics of the wave disturbances localized in time and identified with respect to wavelengths of wave disturbances (wave packets). Lidar measurements in Obninsk are described.

Seasonal variations in lower stratospheric gravity wave energy above the Falkland Islands

AbstractThe gravity wavefield in the lower stratosphere (between 15 km and 22 km altitude) above Mount Pleasant Airport (51°49′S, 58°26′W) on the Falkland Islands is studied using over 2100 high‐resolution radiosonde soundings from 2002 to 2010. The seasonal variation in vertical direction of propagation shows a small decrease in numbers of upward propagating waves that is related to critical level filtering; however, there is a very large increase in numbers of downward propagating waves between July and September; this is attributed to the proximity of the edge of the polar vortex. There is a seasonal variation in gravity wave energy density, with a large peak during the austral autumn equinox; this is markedly different to results in the literature both from Rothera, on the Antarctic Peninsula, and stations on the main Antarctic continent. This seasonal pattern has been shown to be linked to variations in the sources of upward propagating gravity waves. The seasonal variation in gravity wave characteristics above Mount Pleasant Airport seen in our results suggests that the gravity wavefield in this region is determined by a combination of different gravity wave sources located above and below the lower stratosphere.

Diagnosis of tropical cyclone activity through gravity wave energy density in the southwest Indian Ocean

Tropical cyclone (TC) activity is diagnosed through convective gravity waves (GWs) observed in the upper troposphere (UT)/lower stratosphere (LS) above Tromelin island (15.53°S, 54.31°E) in the tropical southwest Indian Ocean. Monthly and weekly GW total energy densities derived from daily GPS windsonde data are compared with Outgoing Longwave Radiation (OLR) and TC hours in the vicinity of Tromelin. A relationship between GW energy density and TC activity is observed in the LS, for the TC season 2001/2002. Moreover TCs (local convection) produce GWs with total energy density mostly higher (lower) than 12 J kg−1. A 10‐season climatology (1997/1998–2006/2007) confirms that large values of GW total energy density in the LS are associated with weak values of OLR during the TC passage. Monthly total, kinetic and potential GW energy densities within 2000 km radius of Tromelin can be estimated using linear relationships with TC hours for a threshold of above 6 TC days per month. A linear relationship also exists between weekly GW total energy density in the LS and the activity of intense TCs above a threshold of 2 TC days per week within 1000 km radius of Tromelin. GW energy density in the LS could be used as a possible index to investigate TC activity in the UT/LS.

Climatology of gravity wave activity during the West African Monsoon

Abstract. Gravity wave activity is analysed in the lower stratosphere using 6 year radiosonde data (2001–2006) above two meteorological stations in the West African tropical region such as Niamey (13.47° N; 2.16° E) and Ouagadougou (12.35° N; 1.51° W). Monthly total energy density of gravity waves is computed with temperature and horizontal wind perturbations to highlight the West African Monsoon period from June to September. Comparison with monthly total energy density calculated with temperature only supports that observed small-scale temperature and wind perturbations are mostly associated with gravity waves in the lower stratosphere especially for large values during the wet season. Above the two sites, monthly evolution of gravity wave total energy density reveals a maximum intensity of gravity wave activity in July during the West African Monsoon period. Indicators of convective activity such as mean Outgoing Longwave Radiation (OLR) and Tropical Rainfall Measuring Mission (TRMM) rain rates reveal to be adequate monsoon proxies to be compared to gravity wave energy intensity during the West African Monsoon.

Seasonal and nightly variations of gravity-wave energy density in the middle atmosphere measured by the Purple Crow Lidar

Abstract. The Purple Crow Lidar (PCL) is a large power-aperture product monostatic Rayleigh-Raman-Sodium-resonance-fluorescence lidar, which has been in operation at the Delaware Observatory (42.9° N, 81.4° W, 237 m elevation) near the campus of The University of Western Ontario since 1992. Kinetic-energy density has been calculated from the Rayleigh-scatter system measurements of density fluctuations at temporal-spatial scales relevant for gravity waves, e.g. soundings at 288 m height resolution and 9 min temporal resolution in the upper stratosphere and mesosphere. The seasonal averages from 10 years of measurements show in all seasons some loss of gravity-wave energy in the upper stratosphere. During the equinox periods and summer the measurements are consistent with gravity waves growing in height with little saturation, in agreement with the classic picture of the variations in the height at which gravity waves break given by Lindzen (1981). The mean values compare favourably to previous measurements when computed as nightly averages, but the high temporal-spatial resolution measurements show considerable day-to-day variability. The variability over a night is often extremely large, with typical RMS fluctuations of 50 to 100% at all heights and seasons common. These measurements imply that using a daily or nightly-averaged gravity-wave energy density in numerical models may be highly unrealistic.

Latitudinal and seasonal variability of gravity-wave energy in the South-West Indian Ocean

Abstract. Vertical temperature profiles obtained by radiosonde and Raman lidar measurements are used to investigate a climatology of total energy density of gravity waves (GW) in the Upper Troposphere (UT) and the Lower Stratosphere (LS) from 1992 to 2004 above Mahé (4° S, 55° E), Tromelin (15° S, 54° E) and La Réunion (21° S, 55° E) located in the tropical South-West Indian Ocean. The commonly used spectral index value (p≈5/3) of the intrinsic frequency spectrum is used for calculating estimated total energy density in the UT and LS. Estimated total energy density provides good estimation of total energy density in the LS but underestimates total energy density by one half in the UT above Mahé and Tromelin probably due to the activity of near-inertial frequency waves. Estimated total energy density reveals a strong seasonal variability as a function of latitude and convection as an evident active source of GW activity in the LS in austral summer. Above La Réunion, a semi-annual GW activity is observed in the LS with the signature of the subtropical barrier in the UT. Moreover, radiosondes and Raman lidar provide consistent GW surveys in the UT/LS at heights<23 km above La Réunion.

Energy density and pressure of long wavelength gravitational waves

Inflation leads us to expect a spectrum of gravitational waves (tensor perturbations) extending to wavelengths much bigger than the present observable horizon. Although these gravity waves are not directly observable, the energy density that they contribute grows in importance during the radiation- and dust-dominated ages of the universe. We show that the back reaction of tensor perturbations during matter domination is limited from above, since gravitational waves of wavelength $\lambda$ have a share of the total energy density $\Delta \rho(\lambda)/\rho$ during matter domination that is at most equal to the share of the total energy density that they had when the mode $\lambda$ exited the Hubble radius $H^{-1}$ during inflation. This work is to be contrasted to that of Sahni, who analyzed the energy density of gravity waves only insofar as their wavelengths are smaller than $H^{-1}$. Such a cut-off in the spectral energy of gravity waves leads to the breakdown of energy conservation, and we show that this anomaly is eliminated simply by taking into account the energy density and pressure of long wavelength gravitational waves as well as short wavelength ones.

Limits on a stochastic background of gravitational waves from gravitational lensing.

We compute the effects of a stochastic background of gravitational waves on multiply imaged systems or on weak lensing. There are two possible observable effects: a static relative deflection of images or shear, and an induced time-dependent shift or proper motion. We evaluate the rms magnitude of these effects for a COBE normalized, scale-invariant spectrum, which is an upper limit on spectra produced by inflation. Previous work has shown that large-scale structure may cause a relative deflection large enough to affect observations, but we find that the corresponding effect of gravity waves is smaller by \ensuremath{\sim}${10}^{4}$ and so cannot be observed. This results from the oscillation in time as well as the redshifting of the amplitude of gravity waves. We estimate the magnitude of the proper motion induced by deflection of light due to large-scale structure, and find it to be \ensuremath{\sim}${10}^{\ensuremath{-}8}$ arcsec per year. This corresponds to \ensuremath{\sim}50 km/s at cosmological distances, which is quite small compared to typical peculiar velocities. The COBE normalized gravity wave spectrum produces motions smaller still by \ensuremath{\sim}${10}^{2}$. We conclude that light deflection due to these cosmological perturbations cannot produce observable proper motions of lensed images. On the other hand, there are only a few known observational limits on a stochastic background of gravity waves at shorter, astrophysical wavelengths. We calculate the expected magnitudes of the effects of lensing by gravity waves of such wavelengths, and find that they are too small to yield interesting limits on the energy density of gravity waves.

Energy density of relic gravity waves from inflation.

We evaluate both the spectral energy density and the total energy density for relic gravity waves produced during the transition from an early inflationary phase to a matter-dominated Friedmann-Robertson-Walker-type expansion: $a\ensuremath{\sim}{t}^{c} (c<1)$. We find that for power-law inflation the spectral energy density for gravity waves has more power on larger scales than for purely exponential inflation. Evaluating the energy density of created massless particles (both gravitons and massless scalars) we find that in the case of exponential inflation the ratio of the density of created particles to the total density of matter is a constant, if $c\ensuremath{\ge}\frac{1}{2}$. This unusual behavior is a consequence of the fact that the equation of state for created particles mimics the equation of state for matter driving the expansion of the Universe. As a result, self-consistent solutions of the Einstein equations can be found, in which the expansion of the Universe is sustained solely by the ongoing production of massless particles, so that ${G}_{\ensuremath{\mu}\ensuremath{\nu}}=8\ensuremath{\pi}G〈{T}_{\ensuremath{\mu}\ensuremath{\nu}}〉$. In the case of power-law and quasiexponential inflation we find that the ratio of the energy density of gravity waves to the background matter density increases with time, as gravity waves with longer wavelengths and larger amplitudes enter the horizon at successively later epochs. This could lead to the energy density of gravity waves becoming comparable to the energy density of matter at late times, if inflation commenced at Planckian energies.