Inertia-gravity Waves Research Articles

A global survey of diurnal offshore propagation of rainfall

Diurnal rainfall offshore propagation (OP) shapes the timing and intensity of coastal rainfall and thus impacts both nature and society. Previous OP studies have rarely compared various coasts, and a consensus regarding physical mechanisms has not been reached on a global scale. Here, we provide the global climatology of observed OP, which propagates across ~78% of all coasts and accounts for ~59% of the coastal precipitation. Generally, OP is facilitated by low latitudes, high moisture conditions and offshore background winds. OP at low latitudes in a high-moisture environment is mainly caused by inertia–gravity waves due to the land–sea thermal contrast, whereas OP at higher latitudes is significantly influenced by background winds under trapped land–sea breeze circulation conditions. Slower near-shore OP might be modulated by density currents. Our results provide a guide for global OP hotspots and suggest relative contributions of mechanisms from a statistical perspective.

The Lower Thermospheric Winter‐To‐Summer Meridional Circulation: 1. Driving Mechanism

AbstractIn this study, the mechanism driving the narrow lower‐thermospheric winter‐to‐summer meridional circulation is thoroughly investigated for the first time using the Specified Dynamics configuration runs of the Whole Atmosphere Community Climate Model eXtended (SD‐WACCMX) simulations and the TIMED Doppler Interferometer (TIDI) observations. The mean meridional circulation in the SD‐WACCMX is qualitatively consistent with the TIDI measurements, though the magnitude in the SD‐WACCMX is about 50% weaker. The lower‐thermospheric winter‐to‐summer circulation is mainly driven by the resolved wave forcing, including the tides and internally generated inertia gravity waves (GWs). The momentum forcing from the parameterized sub‐grid scale GWs is not as significant as the resolved wave forcing in driving the lower‐thermospheric meridional circulation. The GW parameterization scheme in the SD‐WACCMX only includes GWs with phase velocities in the range of ±45 m/s, which might result in most of the parameterized sub‐grid GWs dissipating and breaking in the mesosphere and hardly impacting the lower thermosphere. Only including slow GWs in the SD‐WACCMX parameterization could potentially lead to the underestimation of the meridional wind in the model. Analysis also indicates the lower‐thermospheric meridional circulation is stronger in the summer hemisphere, which is attributed to the hemispheric asymmetry in the resolved wave momentum forcing. This study underlines the importance of the whole atmosphere coupling through wave propagation and dissipation. This understanding can guide the model development with an accurate representation of underlying physical processes in the mesosphere and lower thermosphere which drives the lower‐thermospheric circulation as well as the overall dynamics of this region.

Observations of Inertia Gravity Waves in the Western Pacific and Their Characteristic in the 2015/2016 Quasi‐Biennial Oscillation Disruption

AbstractThe statistical characteristics of inertia‐gravity waves (IGWs) in the troposphere (2–14 km) and lower stratosphere (18–28 km) are analyzed using daily radiosonde observations over six stations in the Western Pacific from 2013 to 2018. Stokes parameter method is used to extract the characteristic parameters of gravity waves (GWs), which are divided into upward and downward propagating waves, and compared with the results of hodograph analysis. In the stratosphere, due to the filtering effect of the background wind field, the IGWs generated in the troposphere mainly propagate eastward with lower frequency range. The tropospheric IGWs have obvious seasonal variation in spectral amplitude and energy, with the maximum in winter and the minimum in monsoon from 2013 to 2018. The stratospheric IGWs are enhanced during phase transition of the quasi‐biennial oscillation, when the enhanced easterly wind appears in the lowest stratosphere, accompanied by enhanced wave energy in the troposphere. During the quasi‐biennial oscillation disruption in late 2015 and early 2016, the tropospheric wave source excites more intense IGWs propagating upward. After reaching the stratosphere, IGWs with slower phase speed are absorbed by the mean flow, dissipating momentum to the lower stratosphere and generating additional enhanced westward forcing, which may have contributed to the development of the easterly wind within the westerly quasi‐biannual oscillation phase.

Tropical cyclone rapid intensification and the excitation of inertia-gravity waves on the edges of an evolving potential vorticity structure

The problem of tropical cyclone rapid intensification is reduced to a potential vorticity (PV) equation and a second order, inhomogeneous, partial differential equation for the azimuthal wind. The latter equation has the form of a Klein-Gordon equation, the right-hand side of which involves the radial derivative of the evolving PV field. When the PV field evolves rapidly, inertia-gravity waves are excited at the edges of the evolving PV structure. In contrast, when the PV field evolves slowly, the second order time derivative term in the Klein-Gordon equation is negligible, inertia-gravity waves are not excited, and the equation reduces to an invertibility principle for the PV. The above concepts are presented in the context of an axisymmetric shallow water model, in both its linear and nonlinear forms. The nonlinear results show a remarkable sensitivity of vortex intensification to the percentage of mass that is diabatically removed from the region inside a given absolute angular momentum surface.

Modeling Gas Flow Velocities in Soils Induced by Variations in Surface Pressure, Heat, and Moisture Dynamics

AbstractChanges in atmospheric pressure continuously ventilate soils and snowpacks. This physical process, known as pressure pumping, is a major factor in the exchange fluxes of H2O, CO2, and other trace gases between the soil and atmosphere. Thus models of pressure pumping are relevant to many areas of critical importance. This study compares the three principal models used to describe pressure pumping. Beginning with the fundamental physical principles and whether the flow field is compressible or incompressible, these models are categorized as linear parabolic (one model—compressible) or nonlinear hyperbolic (two models—incompressible). Using observed soil surface pressure data, measured vertical profiles of soil permeability and standard linear analysis and numerical methods, this study shows that nonlinear models produce advective velocities that are one to two orders of magnitude greater than those associated with the linear model. Incorporating soil temperature and moisture dynamics made very little difference to the linear model, but a significant difference in the nonlinear models suggesting that advective velocities induced by pressure changes associated with soil heating and moisture dynamics may not always be small enough to ignore. All numerical results are sensitive to the frequency of the pressure forcing, which was band‐pass filtered into low, mid and high frequencies with the greatest model differences at low frequencies. Partitioning the pressure forcing and model responses helped to establish that mid‐frequency weather‐related phenomena (empirically identified as inertia gravity waves and solitons) are important drivers of gas exchange between the soil and the atmosphere.

Transition from Balanced to Unbalanced Motion in the Eastern Tropical Pacific

Abstract Kinetic energy associated with inertia–gravity waves (IGWs) and other ageostrophic phenomena often overwhelms kinetic energy due to geostrophic motions for wavelengths on the order of tens of kilometers. Understanding the dependencies of the wavelength at which balanced (geostrophic) variability ceases to be larger than unbalanced variability is important for interpreting high-resolution altimetric data. This wavelength has been termed the transition scale. This study uses acoustic Doppler current profiler (ADCP) data along with auxiliary observations and a numerical model to investigate the transition scale in the eastern tropical Pacific and the mechanisms responsible for its regional and seasonal variations. One-dimensional kinetic energy wavenumber spectra are separated into rotational and divergent components, and subsequently into vortex and wave components. The divergent motions, most likely predominantly IGWs, account for most of the energy at wavelengths less than 100 km. The observed regional and seasonal patterns in the transition scale are consistent with those from a high-resolution global simulation. Observations, however, show weaker seasonality, with only modest wintertime increases in vortex energy. The ADCP-inferred IGW wavenumber spectra suggest that waves with near-inertial frequency dominate the unbalanced variability, while in model output, internal tides strongly influence the wavenumber spectrum. The ADCP-derived transition scales from the eastern tropical Pacific are typically in the 100–200-km range.

Radar Reflectivity–Based Model Initialization Using Specified Latent Heating (Radar-LHI) within a Diabatic Digital Filter or Pre-Forecast Integration

Abstract A technique for model initialization using three-dimensional radar reflectivity data has been developed and applied within the NOAA 13-km Rapid Refresh (RAP) and 3-km High-Resolution Rapid Refresh (HRRR) regional forecast systems. This technique enabled the first assimilation of radar reflectivity data for operational NOAA forecast models, critical especially for more accurate short-range prediction of convective storms. For the RAP, the technique uses a diabatic digital filter initialization (DFI) procedure originally deployed to control initial inertial gravity wave noise. Within the forward-model integration portion of diabatic DFI, temperature tendencies obtained from the model cloud/precipitation processes are replaced by specified latent heating–based temperature tendencies derived from the three-dimensional radar reflectivity data, where available. To further refine initial conditions for the convection-allowing HRRR model, a similar procedure is used in the HRRR, but without DFI. Both of these procedures, together called the “Radar-LHI” (latent heating initialization) technique, have been essential for initialization of ongoing precipitation systems, especially convective systems, within all NOAA operational versions of the 13-km RAP and 3-km HRRR models extending through the latest implementation upgrade at NCEP in 2020. Application of the latent heat–derived temperature tendency induces a vertical circulation with low-level convergence and upper-level divergence in precipitation systems. Retrospective tests of the Radar-LHI technique show significant improvement in short-range (0–6 h) precipitation system forecasts, as revealed by reflectivity verification scores. Results presented document the impact on HRRR reflectivity forecasts of the radar reflectivity initialization technique applied to the RAP alone, HRRR alone, and both the RAP and HRRR. Significance Statement The large forecast uncertainty of convective situations, even at short lead times, coupled with the hazardous weather they produce, makes convective storm prediction one of the most significant short-range forecast challenges confronting the operational numerical weather prediction community. Prediction of heavy precipitation events also requires accurate initialization of precipitation systems. An innovative assimilation technique using radar reflectivity data to initialize NOAA operational weather prediction models is described. This technique, which uses latent heating specified from radar reflectivity (and can accommodate lightning data and other convection/precipitation indicators), was first implemented in 2009 at NOAA/NCEP and continues to be used in 2022 in the NCEP-operational RAP and HRRR models, making it a backbone of the NOAA rapidly updated numerical weather prediction capability.

Influence of the interaction between different low‐ and mid‐level wind couplings and orography on the evolution of mesoscale convective systems in northwest China: A case study

A mesoscale convective systems (MCSs) event occurring in Northwest China is investigated to discuss the influences of interaction between different low- and mid-level winds couplings and orography on the evolution of MCSs, using high-resolution reanalysis data. The formation of a low-level anticyclonic circulation related to the plateau high caused the sequential occurrence of reverse and perpendicular low- and mid-level winds couplings and the stagnation and expansion of a high humidity zone originating from the mountains. In the case of reverse low- and mid-level winds coupling, mid-level winds were constantly lifted by low-level winds ascending the mountains, resulting in strong updrafts and relevant inertia-gravity waves occurring continuously in the upstream direction of mid-level winds. The unstable stratification generated by the high humidity zone prevented the inertia-gravity waves from propagating into the updrafts, leading to the maintenance and connection of the updrafts. Meanwhile, a strong downdraft occurred and maintained on the leeward side of the updrafts due to the coupling of the inertia-gravity waves associated with the uplift of mid-level winds with the inertia-gravity wave triggered by low-level winds ascending the mountains. Consequently, MCSs developed as they propagated into the updrafts, and perished abruptly when they reached the leeward-side downdraft. In the case of perpendicular low- and mid-level winds coupling, a broad and strong low-level updraft band formed and stayed on the windward side of mountain ridge due to terrain-induced uplift. Significant mid-level updraft and associated inertia-gravity wave were triggered on the side of the low-level updraft band blown by mid-level winds. The unstable stratification generated by the high humidity zone hindered the propagation of gravity wave into the low-level updraft band, leading to the maintenance of strength and continuity of the low-level updraft band. Consequently, MCSs maintained during their entire propagation along the low-level updraft band. This article is protected by copyright. All rights reserved.

NUMERICAL INVESTIGATION OF THE NONLINEAR FRACTIONAL OSTROVSKY EQUATION

This research paper investigates the numerical solutions of the nonlinear fractional Ostrovsky equation through five recent numerical schemes (Adomian decomposition (AD), El Kalla (EK), Cubic B-Spline (CBS), extended Cubic B-Spline (ECBS), exponential Cubic B-Spline (ExCBS) schemes). We investigate the obtained computational solutions via the generalized Jacobi elliptical functional (JEF) and modified Khater (MK) methods. This model is considered as a mathematical modification model of the Korteweg–de Vries (KdV) equation with respect to the effects of background rotation. The solitary solutions of the well-known mathematical model (KdV equation) usually decay and are replaced by radiating inertia gravity waves. The obtained solitary solutions show the localized wave packet as a persistent and dominant feature. The accuracy of the obtained numerical solutions is investigated by calculating the absolute error between the exact and numerical solutions. Many sketches are given to illustrate the matching between the exact and numerical solutions.

Atmospheric Energy Spectra in Global Kilometre-Scale Models

Eleven 40-day long integrations of five different global models with horizontal resolutions of less than 9 km are compared in terms of their global energy spectra. The method of normal-mode function decomposition is used to distinguish between balanced (Rossby wave; RW) and unbalanced (inertia-gravity wave; IGW) circulation. The simulations produce the expected canonical shape of the spectra, but their spectral slopes at mesoscales, and the zonal scale at which RW and IGW spectra intersect differ significantly. The partitioning of total wave energies into RWs an IGWs is most sensitive to the turbulence closure scheme and this partitioning is what determines the spectral crossing scale in the simulations, which differs by a factor of up to two. It implies that care must be taken when using simple spatial filtering to compare gravity wave phenomena in storm-resolving simulations, even when the model horizontal resolutions are similar. In contrast to the energy partitioning between the RWs and IGWs, changes in turbulence closure schemes do not seem to strongly affect spectral slopes, which only exhibit major differences at mesoscales. Despite their minor contribution to the global (horizontal kinetic plus potential available) energy, small scales are important for driving the global mean circulation. Our results support the conclusions of previous studies that the strength of convection is a relevant factor for explaining discrepancies in the energies at small scales. The models studied here produce the major large-scale features of tropical precipitation patterns. However, particularly at large horizontal wavenumbers, the spectra of upper tropospheric vertical velocity, which is a good indicator for the strength of deep convection, differ by factors of three or more in energy. High vertical kinetic energies at small scales are mostly found in those models that do not use any convective parameterisation.

Oceanic Internal Waves and Internal Tides in the East Asian Marginal Seas

Inertia-gravity waves or internal waves (IWs) are ubiquitous in the stratified, rotating ocean [...]

Bedymo: a combined quasi-geostrophic and primitive equation model in <i>σ</i> coordinates

Abstract. This paper introduces the Bergen Dynamical Model (Bedymo), an idealized atmospheric circulation model, which combines the quasi-geostrophic approximation and the hydrostatic primitive equations into one modelling framework. The model is designed such that the two systems of equations are solved as similarly as possible, such that differences can be unambiguously attributed to the different approximations, rather than the model formulation or the numerics. As a consequence, but in contrast to most other quasi-geostrophic models, Bedymo uses σ coordinates in the vertical. In addition to the atmospheric core, Bedymo also includes a slab ocean model with options for prescribed and wind-induced currents. Further, Bedymo has a graphical user interface, making it particularly useful for teaching. Bedymo is evaluated for four atmosphere-only test cases and one coupled test case including the slab ocean component. The atmosphere-only test cases comprise the growth of a cyclonic disturbance in a baroclinic environment and the excitation of Rossby waves and inertia–gravity waves by isolated orography, as well as the simulation of a mid-latitude storm track, all in a mid-latitude channel. The atmosphere–ocean coupled test case is based on an equatorial channel and evaluates the coupled response to an isolated equatorial temperature anomaly in the ocean mixed layer. For all test cases, results agree well with expectations from theory and results obtained with more complex models.

Vertical Momentum Transfer Induced by Internal Inertial-Gravity Waves in Flow with Account of Turbulent Viscosity and Diffusion

Vertical Momentum Transfer Induced by Internal Inertial-Gravity Waves in Flow with Account of Turbulent Viscosity and Diffusion

Destabilizing resonances of precessing inertia-gravity waves.

Instabilities in stratified precessing fluid are investigated. We extend the study by Mahalov [Phys. Fluids A 5, 891 (1993)0899-821310.1063/1.858635] in the stably stratified Boussinesq framework, with an external Coriolis force (with rate Ω_{p}) altering the base flow through the distortion of the circular streamlines of the unperturbed axially stratified rotating columns (with constant vorticity 2Ω.) It is shown that the inviscid part of the modified velocity flow (0,Ωr,-2ɛΩrsinφ) and buoyancy with gradient N^{2}(-2ɛcosφ,2ɛsinφ,1) are an exact solution of Boussinesq-Euler equations. Here (r,φ,z) is a cylindrical coordinate system, with ɛ=Ω_{p}/Ω being the Poincaré number and N the Brunt-Väisälä frequency. The base flow is transformed into a Cartesian coordinate system, and the stability of a superimposed perturbation is studied in terms of Fourier (or Kelvin) modes. The resulting Floquet system for the Fourier modes has three parameters: ɛ, N=N/Ω, and μ, which is the angle between the wave vector k and the solid-body rotation axis in the limit ɛ=0. In this limit, there are inertia-gravity waves propagating with frequency ±ω and the resonant cases are those for which 2ω=nΩ, n being an integer. We perform an asymptotic analysis to leading order in ɛ and characterize the destabilizing resonant case of order n=1 (i.e., the subharmonic instability) which exists and for 0≤N<Ω/2. In this range, the subharmonic instability remains the strongest with a maximal growth rate σ_{m}=[ɛ(5sqrt[15]/8)sqrt[1-4N^{2}]/(4-N^{2})]. Stable stratification acts in such a way as to make the subharmonic instability less efficient, so as it disappears for N≥0.5Ω. The destabilizing resonant cases of order n=2,3,4,5 are investigated in detail by numerical computations. The effect of viscosity on these instabilities is briefly addressed assuming the diffusive coefficients (kinematic and thermal) are equal. Likewise, we briefly investigate the case where N^{2}<0 and show that the instability associated to the mode with k_{3}=0 is the strongest.

Geophysical fluid models with simple energy backscatter: explicit flows and unbounded exponential growth

Motivated by numerical schemes for large-scale geophysical flow, we consider the rotating shallow water and Boussinesq equations on the whole space with horizontal kinetic energy backscatter source terms built from negative viscosity and stabilising hyperviscosity with constant parameters. We study the impact of this energy input through various explicit flows, which are simultaneously solving the nonlinear equations and the linear equations that arise upon dropping the transport nonlinearity, i.e. the linearisation in the zero state. These include barotropic, parallel and Kolmogorov flows as well as monochromatic inertia gravity waves. With focus on stable stratification, we find that the backscatter generates numerous solutions of this type that grow exponentially and unboundedly, also with vertical structure. This signifies the possibility of undesired energy concentration into specific modes due to the backscatter. Families of steady-state flows of this type arise as well and superposition principles in the nonlinear equations provide explicit sufficient conditions for instability of some of these. For certain steady barotropic flows of this type, we provide numerical evidence of eigenmodes whose growth rates are proportional to the amplitude factor of the flow. For all other arising steady solutions, we prove that this is not possible.

Inertia-gravity wave energy and instability drive turbulence: evidence from a near-global high-resolution radiosonde dataset

Inertia-gravity wave energy and instability drive turbulence: evidence from a near-global high-resolution radiosonde dataset

A Statistical Investigation of Inertia Gravity Wave Activity Based on MST Radar Observations at Xianghe (116.9°E, 39.8°N), China

AbstractUsing three‐dimensional wind observations from a Mesosphere‐Stratosphere‐Troposphere radar at Xianghe for two years from September 2011 to August 2013, we study inertia gravity wave (IGW) activity in the two height segments of 3–10 and 15–25 km to reveal the characteristics of waves in the source region at midlatitude. Case investigation indicates that three‐dimensional wind fluctuations are usually dominated by a strong IGW. Statistics on 15,617 IGWs extracted show that most waves have typical horizontal scales of tens to thousands of kilometers, the vertical scale of a few kilometers, intrinsic frequencies in 1–4 times the inertial frequency, and amplitudes of 1–4 ms−1 in horizontal winds but less than 0.3 ms−1 in the vertical wind. In the lower region, occurrence possibilities of upward and downward propagating waves are almost the same throughout the year. Whereas in the upper region, IGWs display a predominant upward propagation with a maximum of 85.3% in February but a minimum of 63.6% in July, and a preferential propagation in the zonal direction relative to the meridional direction. Meanwhile, wave energy has a prominent seasonal cycle with the maximum in winter and the minimum in summer. Subtropical jet, as wave source and propagation condition, plays an important role in these different features between the two regions. The annual average of momentum flux indicates that the IGWs in the lower stratosphere can apply a persistent eastward drag on the background flow at higher altitudes through momentum transported by these waves.

Computational and numerical simulations of nonlinear fractional Ostrovsky equation

This article investigates the accuracy of the obtained analytical solutions of the nonlinear fractional Ostrovsky (NLFO.) equation. The researched solutions are obtained by exploiting the well-known generalized Tanh–function (GTF.) method with the Atengana– conformable fractional (ACF.) derivative in the wave transformation. Five–numerical schemes (Adomian decomposition (AD), El Kalla (EK), cubic B-Spline (CBS), extended cubic B-Spline (ECBS), and exponential cubic B-Spline (ExCBS)) handle these solutions to check their solutions. The investigated fractional model is a general form of the KdV equation; however, the KdV equation’s solutions replace this effect with radiating inertia gravity waves. This model also describes a weak description of nonlinear ocean wave processes considering Earth rotation. The obtained analytical and numerical results are sketched through Mathematica 12 in different plot types to explain the waves’ dynamical behavior. Additionally, the computational obtained solutions’ stability is investigated. Finally, the paper’s contribution and obtained results’ novelty are demonstrated by comparing our solutions with those that have been obtained in previous scientific articles.

Faster and Slower Soliton Phase Shift: Oceanic Waves Affected by Earth Rotation

This research paper investigates the accuracy of a novel computational scheme (Khater II method) by applying this new technique to the fractional nonlinear Ostrovsky (FNO) equation. The accuracy of the obtained solutions was verified by employing the Adomian decomposition (AD) and El Kalla (EK) methods. The AD and EK methods are considered as two of the most accurate semi-analytical schemes. The FNO model is a modified version of the well-known Korteweg–de Vries (KdV) equation that considers the effects of rotational symmetry in space. However, in the KdV model, solutions to the KdV equations substitute this effect with radiating inertia gravity waves, and thus this impact is ignored. The analytical, semi-analytical, and accuracy between solutions are represented in some distinct plots. Additionally, the paper’s novelty and its contributions are demonstrated by comparing the obtained solutions with previously published results.

Toward a Numerical Laboratory for Investigations of Gravity Wave–Mean Flow Interactions in the Atmosphere

AbstractIdealized integral studies of the dynamics of atmospheric inertia–gravity waves (IGWs) from their sources in the troposphere (e.g., by spontaneous emission from jets and fronts) to dissipation and mean flow effects at higher altitudes could contribute to a better treatment of these processes in IGW parameterizations in numerical weather prediction and climate simulation. It seems important that numerical codes applied for this purpose are efficient and focus on the essentials. Therefore, a previously published staggered-grid solver for f-plane soundproof pseudoincompressible dynamics is extended here by two main components. These are 1) a semi-implicit time stepping scheme for the integration of buoyancy and Coriolis effects, and 2) the incorporation of Newtonian heating consistent with pseudoincompressible dynamics. This heating function is used to enforce a temperature profile that is baroclinically unstable in the troposphere and it allows the background state to vary in time. Numerical experiments for several benchmarks are compared against a buoyancy/Coriolis-explicit third-order Runge–Kutta scheme, verifying the accuracy and efficiency of the scheme. Preliminary mesoscale simulations with baroclinic wave activity in the troposphere show intensive small-scale wave activity at high altitudes, and they also indicate there the expected reversal of the zonal-mean zonal winds.