Probing signals of atmospheric gravity waves excited by the July 29,2021 M_(W)8.2 Alaska earthquake

It is commonly believed that the atmosphere is decoupled from the solid Earth.Thus,it is difficult for the seismic wave energy inside the Earth to propagate into the atmosphere,and atmospheric pressure wave signals excited by earthquakes are unlikely to exist in atmospheric observations.An increasing number of studies have shown that earthquakes,volcanoes,and tsunamis can perturb the Earth's atmosphere due to various coupling effects.However,the observations mainly focus on acoustic waves with periods of less than 10 min and inertial gravity waves with periods of greater than 1 h.There are almost no clear observations of gravity waves that coincide with observations of low-frequency signals of the Earth's free oscillation frequency band within 1 h.This paper investigates atmospheric gravity wave signals within1 h of surface-atmosphere observations using the periodogram method based on seismometer and microbarometer observations from the global seismic network before and after the July 29,2021 M_(w)8.2 Alaska earthquake in the United States.The numerical results show that the atmospheric gravity wave signals with frequencies similar to those of the Earth's free oscillations _(0)S_(2) and _(0)T_(2) can be detected in the microbaro meter observations.The results con firm the existence of atmospheric gravity waves,indicating that the atmosphere and the solid Earth are not decoupled within this frequency band and that seismic wave energy excited by earthquakes can propagate from the interior of the Earth to the atmosphere and enhance the atmospheric gravity wave signals within 1 h.

Influence of topography on the fine structures of stratospheric gravity waves:An analysis using COSMIC-2 temperature data

We derive the potential energy of gravity waves(GWs)in the upper troposphere and stratosphere at 45°S-45°N from December 2019 to November 2022 by using temperature profiles retrieved from the Constellation Observing System for Meteorology,Ionosphere,and Climate-2(COSMIC-2)satellite.Owing to the dense sampling of COSMIC-2,in addition to the strong peaks of gravity wave potential energy(GWPE)above the Andes and Tibetan Plateau,we found weak peaks above the Rocky,Atlas,Caucasus,and Tianshan Mountains.The land-sea contrast is responsible for the longitudinal variations of the GWPE in the lower and upper stratosphere.At 40°N/S,the peaks were mainly above the topographic regions during the winter.At 20°N/S,the peaks were a slight distance away from the topographic regions and might be the combined effect of nontopographic GWs and mountain waves.Near the Equator,the peaks were mainly above the regions with the lowest sea level altitude and may have resulted from convection.Our results indicate that even above the local regions with lower sea level altitudes compared with the Andes and Tibetan Plateau,the GWPE also exhibits fine structures in geographic distributions.We found that dissipation layers above the tropopause jet provide the body force to generate secondary waves in the upper stratosphere,especially during the winter months of each hemisphere and at latitudes of greater than 20°N/S.

Analysis of gravity wave activity during stratospheric sudden warmings in the northern hemisphere

Due to the significant changes they bring to high latitude stratospheric temperature and wind,stratospheric sudden warmings(SSWs)can have an impact on the propagation and energy distribution of gravity waves(GWs).The variation characteristics of GWs during SSWs have always been an important issue.Using temperature data from January to March in 2014−2016,provided by the Constellation Observing System for Meteorology,Ionosphere and Climate(COSMIC)mission,we have analyzed global GW activity at 15−40 km in the Northern Hemisphere during SSW events.During the SSWs that we studied,the stratospheric temperature rose in one or two longitudinal regions in the Northern Hemisphere;the areas affected extended to the east of 90°W.During these SSWs,the potential energy density(E_(p)of GWs expanded and covered a larger range of longitude and altitude,exhibiting an eastward and downward extension.The E_(p)usually increased,while partially filtered by the eastward zonal winds.When zonal winds weakened or turned westward,E_(p)began to strengthen.After SSWs,the E_(p)usually decreased.These observations can serve as a reference for analyzing the interaction mechanism between SSWs and GWs in future work.

Application of higher-order KdV-mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Higher-order Korteweg-de Vries （KdV）-modified KdV （mKdV） equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.

Investigating the Dominant Source for the Generation of Gravity Waves during Indian Summer Monsoon Using Ground-based Measurements

Over the tropics, convection, wind shear （i.e., vertical and horizontal shear of wind and/or geostrophic adjustment comprising spontaneous imbalance in jet streams） and topography are the major sources for the generation of gravity waves. During the summer monsoon season （June August） over the Indian subcontinent, convection and wind shear coexist. To determine the dominant source of gravity waves during monsoon season, an experiment was conducted using mesosphere-stratosphere-troposphere （MST） radar situated at Gadanki （13.5°N, 79.2°E）, a tropical observatory in the southern part of the Indian subcontinent. MST radar was operated continuously for 72 h to capture high-frequency gravity waves. During this time, a radiosonde was released every 6 h in addition to the regular launch （once daily to study low-frequency gravity waves） throughout the season. These two data sets were utilized effectively to characterize the jet stream and the associated gravity waves. Data available from collocated instruments along with satellite-based brightness temperature （TBB） data were utilized to characterize the convection in and around Gadanki. Despite the presence of two major sources of gravity wave generation （i.e., convection and wind shear） during the monsoon season, wind shear （both vertical shear and geostrophic adjustment） contributed the most to the generation of gravity waves on various scales.

Simulation of a torrential rainstorm in Xinjiang and gravity wave analysis

We used a weather research and forecasting model to simulate a torrential rainstorm that occurred in Xinjiang, China during June 16–17, 2016. The model successfully simulated the rainfall area, precipitation intensity, and changes in precipitation. We identified a clear wave signal using the two-dimensional fast Fourier transform method; the waves propagated westwards, with wavelengths of 45–20 km, periods of 50–120 min, and phase velocities mainly concentrated in the-25 m/s to-10 m/s range. The results of wavelet cross-spectral analysis further confirmed that the waves were gravity waves, peaking at 11：00 UTC, June 17, 2016. The gravity wave signal was identified along 79.17–79.93°E, 81.35–81.45°E and 81.5–81.83°E. The gravity waves detected along 81.5–81.83°E corresponded well with precipitation that accumulated in 1 h, indicating that gravity waves could be considered a rainstorm precursor in future precipitation forecasts.

Global static stability and its relation to gravity waves in the middle atmosphere

The global atmospheric static stability(N2)in the middle atmosphere and its relation to gravity waves(GWs)were investigated by using the temperature profiles measured by the Sounding of the Atmosphere using Broadband Emission Radiometry(SABER)instrument from 2002 to 2018.At low latitudes,a layer with enhanced N2 occurs at an altitude of^20 km and exhibits annual oscillations caused by tropopause inversion layers.Above an altitude of^70 km,enhanced N2 exhibits semiannual oscillations at low latitudes caused by the mesosphere inversion layers and annual oscillations at high latitudes resulting from the downward shift of the summer mesopause.The correlation coefficients between N2 and GW amplitudes can be larger than 0.8 at latitudes poleward of^40°N/S.This observation provides factual evidence that a large N2 supports large-amplitude GWs and indicates that N2 plays a dominant role in maintaining GWs at least at high latitudes of the middle atmosphere.This evidence also partially explains the previous results regarding the phase changes of annual oscillations of GWs at high latitudes.

Case study on stratospheric and mesospheric concentric gravity waves generated by deep convection

Concentric gravity waves(CGWs)in the middle and upper atmosphere show wave-coupling processes between the lower atmosphere and the middle and upper atmosphere.In this research,we analyzed a case of CGWs detected simultaneously by the AIRS(Atmospheric Infrared Sounder)and the VIIRS/DNB(Day/Night Band of the Visible Infrared Imager Radiometer Suite)in the stratosphere and mesosphere.Results showed that gravity waves(GWs)were generated by the collocated Hurricane Bejisa on the island of Mauritius.The AIRS data showed arc-like phase fronts of GWs with horizontal wavelengths of 190 and 150 km at 21:08 coordinated universal time(UTC)on 1 January 2014 and at 10:00 UTC on 2 January 2014,whereas the DNB observed arced GWs with horizontal wavelengths of 60 and 150 km in the same geographic regions at 22:24 UTC.The characteristics of CGW parameters in the stratosphere(~40 km)and the mesosphere(~87 km),such as the vertical wavelength,intrinsic frequency,and intrinsic horizontal phase speed,were first derived together with the background winds from ERA5 reanalysis data and Horizontal Wind Model data through the dispersion relationship of GWs and the wind-filtering theory.

Atmospheric frontal gravity waves observed in satellite SAR images of the Bohai Sea and Huanghai Sea

In the satellite synthetic aperture radar（SAR） images of the Bohai Sea and Huanghai Sea,the authors observe sea surface imprints of wave-like patterns with an average wavelength of 3.8 km.Comparing SAR observations with sea surface wind fields and surface weather maps,the authors find that the occurrence of the wave-like phenomena is associated with the passing of atmospheric front.The authors define the waves as atmospheric frontal gravity waves.The dynamical parameters of the wave packets are derived from statistics of 9 satellite SAR images obtained from 2002 to 2008.A two-dimensional linear physical wave model is used to analyze the generation mechanism of the waves.The atmospheric frontal wave induced wind variation across the frontal wave packet is compared with wind retrievals from the SAR images.The CMOD-5（C-band scatterometer ocean geophysical model function） is used for SAR wind retrievals VV（transmitted vertical and received vertical） for ENVISAT and HH（transmitted horizontally and received horizontally） for RADARSAT-1.A reasonable agreement between the analytical solution and the SAR observation is reached.This new SAR frontal wave observation adds to the school of SAR observations of sea surface imprints of AGWs including island lee waves,coastal lee waves,and upstream Atmospheric Gravity Waves（AGW）.

LINEAR THEORY OF GRAVITY WAVES ON A VOIGT VISCOELASTIC MEDIUM

Linear surface gravity waves on a semi-infinite incompressible Voigt medium are studied in this paper.Three dimensionless parameters,the dimensionless viscoelastic parameter (?),the dimensionless wave number and the dimensionless sur- face tension are introduced.A dimensionless characteristic equation describing the waves is derived.This is a sixth order complex algebraic equation which is solved to give the complex dispersion relation.Based on the numerical solution, two critical values of (?),(?)_A=0.607 and (?)_R=2.380,which represent the appearance of the cutoff region and the disappearance of the strong dispersion region,are found.The effects of (?) on the characteristic equation and the properties of the waves are discussed.

A class of coupled nonlinear Schrdinger equations:Painlev'e property,exact solutions,and application to atmospheric gravity waves

The Painleve integrability and exact solutions to a coupled nonlinear Schrodinger （CNLS） equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painleve test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

Application of deep learning to estimate stratospheric gravity wave potential energy

One of the most important dynamic processes in the middle and upper atmosphere,gravity waves(GWs)play a key role in determining global atmospheric circulation.Gravity wave potential energy(GW Ep)is an important parameter that characterizes GW intensity,so it is critical to understand its global distribution.In this paper,a deep learning algorithm(DeepLab V3+)is used to estimate the stratospheric GW Ep.The deep learning model inputs are ERA5 reanalysis datasets and GMTED2010 terrain data.GW Ep averaged over 20−30 km from 60°S−60°N,calculated by COSMIC radio occultation(RO)data,is used as the measured value corresponding to the model output.The results show that(1)this method can effectively estimate the zonal trend of GW Ep.However,the errors between the estimated and measured value of Ep are larger in low-latitude regions than in mid-latitude regions,possibly due to the large number of convolution operations used in the deep learning model.Additionally,the measured Ep has errors associated with interpolation to the grid;this tends to be amplified in low-latitude regions because the GW Ep is larger and the RO data are relatively sparse,affecting the training accuracy.(2)The estimated Ep shows seasonal variations,which are stronger in the winter hemisphere and weaker in the summer hemisphere.(3)The effect of quasi-biennial oscillation(QBO)can be clearly observed in the monthly variation of estimated GW Ep,and its QBO amplitude may be less than that of the measured Ep.

Inertial gravity waves observed by a Doppler wind LiDAR and their possible sources

In this paper,we use wind observations by a Doppler wind LiDAR near Delingha(37.4°N,97.4°E),Qinghai,Northwestern China to study the characteristics of inertial gravity waves in the stratosphere.We focus on 10–12 December 2013,a particularly interesting case study.Most of the time,the inertial gravity waves extracted from the LiDAR measurements were stationary with vertical wavelengths of about 9–11 km and horizontal wavelengths of about 800–1000 km.However,for parts of the observational period in this case study,a hodograph analysis indicates that different inertial gravity wave propagation features were present at lower and upper altitudes.In the middle and upper stratosphere(~30–50 km),the waves propagated downward,especially during a period of stronger winds,and to the northwest–southeast.In the lower stratosphere and upper troposphere(~10–20 km),however,waves with upward propagation and northeast–southwest orientation were dominant.By taking into account reanalysis data and satellite observations,we have confirmed the presence of different wave patterns in the lower and upper stratosphere during this part of the observational period.The combined data sets suggest that the different wave patterns at lower and upper height levels are likely to have been associated with the presence of lower and upper stratospheric jet streams.

Gravity wave activities in Tibet observed by COSMIC GPS radio occultation

The Gravity waves activities in the Tibetan Plateau are very complex with different effects and natures that are not clear due to the lack of high resolution data from space and also from ground. In this paper,using COSMICGPS radio occultation data from 2006 to 2014, the atmospheric gravity waves activities and climatologic behaviors in Tibetan stratosphere are studied and analyzed, which show different characteristics. Most of the gravity waves with potential energy(Ep) at altitude of 17-24 km are associated with mountain waves. A good correlation between gravity wave activities and zonal wind flow is found. The distribution of gravity wave(GW) activities in Tibet is strongly connected with zonal wind variation and topography. GW activities are enhanced in winter seasons and decreased in summer seasons since strong western winds persist at all heights of the Tibetan troposphere. The gravity waves generated in the Tibetan area are mostly related to the orography of the area. The vertical wavelengths of GWS are shorter.Gravity waves in the Northwest have different vertical wavelengths in the Southeastern part of Tibetan Plateau, and dominant wavelengths are 3-5 km in the Northwest and 2-3 km in the Southeast,respectively. In the summer, the Northwestern part is the main source of wave generation while in the winter the GW is generated almost from all peaks of the Tibetan Plateau. Gravity waves in the region are clearly related to deep convection, which can also be proved by the inverse relation of Outgoing long wave radiation(OLR) and potential energy(Ep).

Particle Motion in Surface Gravity Waves

Fluid particles in translating surface gravity waves have an orbital motion which decreases in size with increasing mean depth. These wave characteristics came from observations and were not forecast theoretically. The classical potential flow model is incapable of explaining the particle movement due to the irrotational assumption and to a flaw in carrying out the method. When a wave passes by an observer from left to right, the particles move clockwise under a crest and a trough. This correct conclusion is consistent with what the incorrect standard theory implies but should not be considered to have been derived from it.

LINEAR GRAVITY WAVES ON MAXWELL FLUIDS OF FINITE DEPTH

Linear surface gravity waves on Maxwell viscoelastic fluids with finite depth are studied in this paper.A dispersion equation describing the spatial decay of the gravity wave in finite depth is derived.A dimensionless memory(time)number θ is introduced.The dispersion equation for the pure viscous fluid will be a specific case of the dispersion equation for the viscoelastic fluid as θ=0.The complex dispersion equation is numerically solved to investigate the dispersion relation.The influences of θ and water depth on the dispersion characteristics and wave decay are discussed.It is found that the role of elasticity for the Maxwell fluid is to make the surface gravity wave on the Maxwell fluid behave more like the surface gravity wave on the inviscid fluid.

Gravity Wave Activity and Spectra in the Upper Mesosphere at Wuhan,China During Early March 1996

Sodium layers (75–105 km) were measured by Na lidar on three nights from 1 to 3 of March 1996. The lidar data were used to calculate the relative atmospheric density perturbations and their spectra. The average r. m. s. density perturbations for early March at Wuhan are 5%. The Vertical wave number spectra exhibit power-law shapes with an average slpoes of ?2. 12 in the upper mesosphere when the associated density mean quantity of the day was used.

A nonlinear Schrodinger equation for gravity waves slowly modulated by linear shear flow

Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schr?dinger equation(NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple-scale analysis method. The gravity waves are influenced by a linear shear flow, which is composed of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of the NLSE is analyzed, and the region of the MI for gravity waves(the necessary condition for existence of freak waves) is identified. In this work, the uniform background flows along or against wave propagation are referred to as down-flow and up-flow, respectively. Uniform up-flow enhances the MI, whereas uniform down-flow reduces it. Positive vorticity enhances the MI, while negative vorticity reduces it. Hence, the influence of positive(negative)vorticity on MI can be balanced out by that of uniform down(up) flow. Furthermore, the Peregrine breather solution of the NLSE is applied to freak waves. Uniform up-flow increases the steepness of the free surface elevation, while uniform down-flow decreases it. Positive vorticity increases the steepness of the free surface elevation, whereas negative vorticity decreases it.

Proof of Six-Wave Resonance Conditions of Ocean Surface Gravity Waves in Deep Water

A necessary big step up in the modern water wave theories and their widespread application in ocean engineering is how to obtain 6-wave resonance conditions and to prove it. In the light of the existing forms and characteristics of 3-wave, 4-wave and 5-wave resonance conditions, the 6-wave resonance conditions are proposed and proved for currently a maximum wave-wave resonance interactions of the ocean surface gravity waves in deep water, which will be indispensable to both the Kolmogorov spectrum of the corresponding universal wave turbulence and a synthetic 4-5-6-wave resonant model for the ocean surface gravity waves.

Joint observation of the concentric gravity wave event on the Tibetan Plateau

A concentric gravity wave event was captured by a photographer in NagarzêCounty(90.28°N,28.33°E)between 02:00 and 04:00(local time)on May 11,2019.This concentric gravity wave event was also observed by the Suomi National Polar-orbiting Partnership satellite and the all-sky airglow imager at Yangbajing station(90.5°E,30.1°N).The temporal and spatial information on gravity waves from the photographs provided a rare opportunity to study the propagation of gravity waves over the Tibetan Plateau.According to wind and temperature data from the MERRA-2 reanalysis(Modern-Era Retrospective analysis for Research and Applications,Version 2)and empirical models(NRLMSISE-00[Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere]and HWM[horizontal wind model]),we inversely derived the propagation trajectory from the observed wave pattern to the source region by using the ray-tracing method.The source of the concentric gravity wave was identified as deep convection in Bangladesh(90.6°E,25.0°N).The maximum background wind speed in the propagation direction(31.05 m/s)was less than the phase speed of 53 m/s,which is consistent with the wind-filtering theory.