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.

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.

Research on internal gravity waves in the Martian atmosphere based on Tianwen-1 and Mars Global Surveyor occultation data

Internal gravity waves(IGWs)are critical in driving Martian atmospheric motion and phenomena.This study investigates Martian IGWs by using high-resolution data from China’s Tianwen-1 mission and the National Aeronautics and Space Administration’s Mars Global Surveyor(MGS)by the radio occultation(RO)technique.Key IGW parameters,such as vertical and horizontal wavelengths,intrinsic frequency,and energy density,are extracted based on vertical temperature profiles from the Martian surface to~50 km altitude.Data reveal that the Martian IGWs are predominantly small-scale waves,with vertical wavelengths between 6 and 13 km and horizontal wavelengths extending to thousands of kilometers.These waves propagate almost vertically and exhibit low intrinsic frequencies close to the inertial frequency,with the characteristic of low-frequency inertial IGWs.Tianwen-1 data indicate stronger IGW activity,higher energy density,and less dissipation than MGS data in the northern hemisphere.Moreover,MGS data in the southern hemisphere show higher buoyancy frequencies and lower vertical wavelengths,suggesting more stable atmospheric conditions conducive to IGW propagation.These extracted IGW characteristics can enhance our understanding of the atmospheric dynamics on Mars and contribute valuable information for parameterization in global circulation models.

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.

Gravity Wave Activity and Stratosphere-Troposphere Exchange During Typhoon Molave(2020)

To investigate the stratosphere-troposphere exchange(STE)process induced by the gravity waves(GWs)caused by Typhoon Molave(2020)in the upper troposphere and lower stratosphere,we analyzed the ERA5 reanalysis data provided by the European Centre for Medium-Range Weather Forecasts and the CMA Tropical Cyclone Best Track Dataset.We also adopted the mesoscale forecast model Weather Research and Forecasting model V4.3 for numerical simulation.Most of the previous studies were about typhoon-induced STE and typhoon-induced GWs,while our research focused on the STE caused by typhoon-induced gravity waves.Our analysis shows that most of the time,the gravity wave signal of Typhoon Molave appeared below the tropopause.It was stronger on the east side of the typhoon center(10°-20°N,110°-120°E)than on the west side,suggesting an eastward tilted structure with height increase.When the GWs in the upper troposphere and lower stratosphere region on the west side of the typhoon center broke up,it produced strong turbulence,resulting in stratosphere-troposphere exchange.At this time,the average potential vorticity vertical flux increased with the average ozone mass mixing ratio.The gravity wave events and STE process simulated by the WRF model were basically consistent with the results of ERA5 reanalysis data,but the time of gravity wave breaking was different.This study indicates that after the breaking of the GWs induced by typhoons,turbulent mixing will also be generated,and thus the STE.

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.

Analysis of the characteristics of gravity waves during a local rainstorm event in Foshan,China

A detailed analysis of the dynamic frequency spectrum characteristics of gravity waves(GWs)during a local heavy rainfall event on 20–21 November 2016 in Foshan,China,is presented.The results of this analysis,which was based on high-precision microbarograph data,indicate that GWs played a key role in generating the rainstorm.The GWs experienced two intermittent periods of amplitude enhancement and period widening.The largest amplitudes of the GWs were 80–160 Pa,with a corresponding period range of 140–270 min,which were approximately 4 h ahead of the rainstorm.The severe storms appeared to affect the GWs by augmenting the wave amplitudes with center amplitudes of approximately 80–100 Pa and periods ranging between 210 and 270 min;in particular,the amplitudes increased to approximately 10 Pa for GWs with shorter periods(less than 36 min).The pre-existing large-amplitude GWs may be precursors to severe storms;that is,these GWs occurred approximately 4 h earlier than the time radars and satellites identified convections.Thus,these results indicate that large-amplitude GWs constitute a possible mechanism for severe-storm warning.

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.

A Neural Network Based Single Footprint Temperature Retrieval for Atmospheric Infrared Sounder Measurements and Its Application to Study on Stratospheric Gravity Wave

Satellite hyperspectral infrared sounder measurements have better horizontal resolution than other sounding techniques as it boasts the stratospheric gravity wave(GW)analysis.To accurately and efficiently derive the three-dimensional structure of the stratospheric GWs from the single-field-of-view(SFOV)Atmospheric Infra Red Sounder(AIRS)observations,this paper firstly focuses on the retrieval of the atmospheric temperature profiles in the altitude range of 20-60 km with an artificial neural network approach(ANN).The simulation experiments show that the retrieval bias is less than 0.5 K,and the root mean square error(RMSE)ranges from 1.8 to 4 K.Moreover,the retrieval results from 20 granules of the AIRS observations with the trained neural network(AIRS_SFOV)and the corresponding operational AIRS products(AIRS_L2)as well as the dual-regression results from the Cooperative Institute for Meteorological Satellite Studies(CIMSS)(AIRS_DR)are compared respectively with ECMWF T799 data.The comparison indicates that the standard deviation of the ANN retrieval errors is significantly less than that of the AIRS_DR.Furthermore,the analysis of the typical GW events induced by the mountain Andes and the typhoon"Soulik"using different data indicates that the AIRS_SFOV results capture more details of the stratospheric gravity waves in the perturbation amplitude and pattern than the operational AIRS products do.

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.