Large-scale Atmospheric Motions Research Articles

On the Quartic Korteweg–de Vries hierarchy of nonlinear Rossby waves and its dynamics

A long-standing challenge in exploring the dynamics of large-scale atmospheric or oceanic motions is to find more appropriate theoretical models. This paper aims at the mechanisms of nonlinear Rossby waves by a new obtained nonlinear evolutionary equation hierarchy approach. The multiple scales method and weak nonlinear perturbation method are adopted based on the quasi-geostrophic potential vorticity conservation law for large scale atmospheric or oceanic motions. It is the first time that a Quartic Korteweg–de Vries model equation is derived to describe the propagation of nonlinear Rossby waves amplitude, which provides a new acceptable theoretical model for the study of atmospheric blocking phenomena. Qualitative and quantitative analysis for the new Quartic KdV model are finished to disclose the evolutionary mechanisms of nonlinear Rossby waves. The corresponding results declares that the β effect, topographic features and detuning parameter are all important factors on the nonlinear Rossby waves.

Utilizing a Global Network of Telescopes to Update the Ephemeris for the Highly Eccentric Planet HD 80606 b and to Ensure the Efficient Scheduling of JWST

The transiting planet HD 80606 b undergoes a 1000 fold increase in insolation during its 111 days orbit due to it being highly eccentric (e = 0.93). The planet’s effective temperature increases from 400 to over 1400 K in a few hours as it makes a rapid passage to within 0.03 au of its host star during periapsis. Spectroscopic observations during the eclipse (which is conveniently oriented a few hours before periapsis) of HD 80606 b with the James Webb Space Telescope (JWST) are poised to exploit this highly variable environment to study a wide variety of atmospheric properties, including composition, chemical and dynamical timescales, and large scale atmospheric motions. Critical to planning and interpreting these observations is an accurate knowledge of the planet’s orbit. We report on observations of two full-transit events: 2020 February 7 as observed by the TESS spacecraft and 2021 December 7–8 as observed with a worldwide network of small telescopes. We also report new radial velocity observations which, when analyzed with a coupled model to the transits, greatly improves the planet’s orbital ephemeris. Our new orbit solution reduces the uncertainty in the transit and eclipse timing of the JWST era from tens of minutes to a few minutes. When combined with the planned JWST observations, this new precision may be adequate to look for non-Keplerian effects in the orbit of HD 80606 b.

No evidence for radius inflation in hot Jupiters from vertical advection of heat

Elucidating the radiative-dynamical coupling between the upper photosphere and deeper atmosphere may be key to our understanding of the abnormally large radii of hot Jupiters. Very long integration times of 3D general circulation models (GCMs) with self-consistent radiative transfer are needed to obtain a more comprehensive picture of the feedback processes between dynamics and radiation. Here, we present the longest 3D nongray GCM study to date (86000 d) of an ultra-hot Jupiter (WASP-76 b) that has reached a final converged state. Furthermore, we present a method that can be used to accelerate the path toward temperature convergence in the deep atmospheric layers. We find that the final converged temperature profile is cold in the deep atmospheric layers, lacking any sign of vertical transport of potential temperature by large-scale atmospheric motions. We therefore conclude that coupling between radiation and dynamics alone is not sufficient to explain the abnormally large radii of inflated hot gas giants.

Second-Order Approximate Equations of the Large-Scale Atmospheric Motion Equations and Symmetry Analysis for the Basic Equations of Atmospheric Motion

In this paper, symmetry properties of the basic equations of atmospheric motion are proposed. The results on symmetries show that the basic equations of atmospheric motion are invariant under space-time translation transformation, Galilean translation transformations and scaling transformations. Eight one-parameter invariant subgroups and eight one-parameter group invariant solutions are demonstrated. Three types of nontrivial similarity solutions and group invariants are proposed. With the help of perturbation method, we derive the second-order approximate equations for the large-scale atmospheric motion equations, including the non-dimensional equations and the dimensional equations. The second-order approximate equations of the large-scale atmospheric motion equations not only show the characteristics of physical quantities changing with time, but also describe the characteristics of large-scale atmospheric vertical motion.

An Optical Flow Approach to Tracking Ship Track Behavior Using GOES-R Satellite Imagery

Ship emissions can form linear cloud structures, or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ship tracks</i> , when atmospheric water vapor condenses on aerosols in the ship exhaust. These structures are of interest because they are observable and traceable examples of MCB, a mechanism that has been studied as a potential approach for solar climate intervention. Ship tracks can be observed throughout the diurnal cycle via space-borne assets like the advanced baseline imagers on the national oceanic and atmospheric administration geostationary operational environmental satellites, the GOES-R series. Due to complex atmospheric dynamics, it can be difficult to track these aerosol perturbations over space and time to precisely characterize how long a single emission source can significantly contribute to indirect radiative forcing. We propose an optical flow approach to estimate the trajectories of ship-emitted aerosols after they begin mixing with low boundary layer clouds using GOES-17 satellite imagery. Most optical flow estimation methods have only been used to estimate large scale atmospheric motion. We demonstrate the ability of our approach to precisely isolate the movement of ship tracks in low-lying clouds from the movement of large swaths of high clouds that often dominate the scene. This efficient approach shows that ship tracks persist as visible, linear features beyond 9 h and sometimes longer than 24 h.

The long-term transport and radiative impacts of the 2017 British Columbia pyrocumulonimbus smoke aerosols in the stratosphere

Abstract. Interactions of meteorology with wildfires in British Columbia, Canada, during August 2017 led to three major pyrocumulonimbus (pyroCb) events that resulted in the injection of large amounts of smoke aerosols and other combustion products at the local upper troposphere and lower stratosphere (UTLS). These plumes of UTLS smoke with elevated values of aerosol extinction and backscatter compared to the background state were readily tracked by multiple satellite-based instruments as they spread across the Northern Hemisphere (NH). The plumes were observed in the lower stratosphere for about 8–10 months following the fire injections, with a stratospheric aerosol e-folding time of about 5 months. To investigate the radiative impacts of these events on the Earth system, we performed a number of simulations with the Goddard Earth Observing System (GEOS) atmospheric general circulation model (AGCM). Observations from multiple remote-sensing instruments were used to calibrate the injection parameters (location, amount, composition and heights) and optical properties of the smoke aerosols in the model. The resulting simulations of three-dimensional smoke transport were evaluated for a year from the day of injections using daily observations from OMPS-LP (Ozone Mapping Profiler Suite Limb Profiler). The model-simulated rate of ascent, hemispheric spread and residence time (or e-folding time) of the smoke aerosols in the stratosphere are in close agreement with OMPS-LP observations. We found that both aerosol self-lofting and the large-scale atmospheric motion play important roles in lifting the smoke plumes from near the tropopause altitudes (∼ 12 km) to about 22–23 km into the atmosphere. Further, our estimations of the radiative impacts of the pyroCb-emitted smoke aerosols showed that the smoke caused an additional warming of the atmosphere by about 0.6–1 W/m2 (zonal mean) that persisted for about 2–3 months after the injections in regions north of 40∘ N. The surface experienced a comparable magnitude of cooling. The atmospheric warming is mainly located in the stratosphere, coincident with the location of the smoke plumes, leading to an increase in zonal mean shortwave (SW) heating rates of 0.02–0.04 K/d during September 2017.

Physical limits of wind energy within the atmosphere and its use as renewable energy: From the theoretical basis to practical implications

How much wind energy does the atmosphere generate, and how much of it can at best be used as renewable energy? This review aims to give first-order estimates and sensitivities to answer these questions that are consistent with those obtained from numerical simulation models. The first part describes how thermodynamics determines how much wind energy the atmosphere is physically capable of generating at large scales from the solar radiative forcing. The work done to generate and maintain large-scale atmospheric motion can be seen as the consequence of an atmospheric heat engine, which is driven by the difference in solar radiative heating between the tropics and the poles. The resulting motion transports heat, which depletes this differential solar heating and the associated, large-scale temperature difference. This interaction between the thermodynamic driver and the resulting dynamics leads to a maximum in the global mean kinetic energy generation rate of about 1.7 W m$^{-2}$, which matches rates inferred from observations of about 2.1 - 2.5 W m$^{-2}$ very well. The second part focuses on the limits of converting the kinetic energy of the atmosphere into renewable energy. The momentum balance of the lower atmosphere shows that at large-scales, only a fraction of about 26% of the kinetic energy can at most be converted to renewable energy, yielding a typical resource potential of about 0.5 W m$^{-2}$ per surface area. The apparent discrepancy with much higher yields of small wind farms can be explained by the spatial scale of about 100 km at which kinetic energy near the surface is being dissipated and replenished. I close with a discussion of how these insights are compatible to established meteorological concepts, inform practical applications, and can set the basis for doing climate science in a simple, analytical, and transparent way.

Nonlinear interactions of nearly non-dispersive equatorial shallow-water waves

Abstract This paper is concerned with nonlinear interactions of fundamental equatorial modes. In order to understand the mechanism of large-scale atmospheric motions in the near equator regime—especially the observed wavenumber-frequency spectrum—we develop novel models describing interactions among Kelvin, Yanai and Poincaré waves. Based on the methods of multiple scales and Galerkin projection, the primitive equations can be simplified to model equations which reduce the complexity and cost of computation significantly. Subsequently, the detailed numerical results indicate that wave interactions between the aforementioned modes in the non-dispersive regime depends on initial amplitude and relative phase and that the eastward Yanai wave can be generated from the second Poincaré mode. We also compare the simplified models to an advanced finite element approximation for the primitive equations. The fact that results of the latter are in good agreement, at least qualitatively, with those of the simplified models, indicates that reduced models capture most of the wave interaction mechanisms in the nearly non-dispersive regime.

Scale Interactions in Turbulence for Mountain Blowing Snow

Abstract Blowing snow particle transport responds to wind motions across many length and time scales. This coupling is nonlinear by nature and complicated in atmospheric flows where eddies of many sizes are superimposed. In mountainous terrain, wind flow descriptions are further complicated by topographically influenced or enhanced flows. To improve the current understanding and modeling of blowing snow transport in complex terrain, statistically significant timing and frequencies of wind–snow coupling were identified in high-frequency observations of surface blowing snow and near-surface turbulence from a mountain field site in the Canadian Rockies. Investigation of the mechanisms influencing near-surface, high-frequency turbulence and snow concentration fluctuations provided strong evidence for amplitude modulation from large-scale motions. The large-scale atmospheric motions modulating near-surface turbulence and snow transport were then compared to specific quadrant analysis structures recently identified as relevant for outdoor blowing snow transport. The results suggest that large atmospheric structures modulate the amplitude of high-frequency turbulence and modify turbulence statistics typically used to model blowing snow. Additionally, blowing snow was preferentially redistributed under the footprint of these same sweep motions, with both low- and high-frequency coherence increasing in their presence.

Predictability of large-scale atmospheric motions: Lyapunov exponents and error dynamics.

The deterministic equations describing the dynamics of the atmosphere (and of the climate system) are known to display the property of sensitivity to initial conditions. In the ergodic theory of chaos, this property is usually quantified by computing the Lyapunov exponents. In this review, these quantifiers computed in a hierarchy of atmospheric models (coupled or not to an ocean) are analyzed, together with their local counterparts known as the local or finite-time Lyapunov exponents. It is shown in particular that the variability of the local Lyapunov exponents (corresponding to the dominant Lyapunov exponent) decreases when the model resolution increases. The dynamics of (finite-amplitude) initial condition errors in these models is also reviewed, and in general found to display a complicated growth far from the asymptotic estimates provided by the Lyapunov exponents. The implications of these results for operational (high resolution) atmospheric and climate modelling are also discussed.

Understanding dynamics of large-scale atmospheric vortices with moist-convective shallow water model

Atmospheric jets and vortices which, together with inertia-gravity waves, constitute the principal dynamical entities of large-scale atmospheric motions, are well described in the framework of one- or multi-layer rotating shallow water models, which are obtained by vertically averaging of full “primitive” equations. There is a simple and physically consistent way to include moist convection in these models by adding a relaxational parameterization of precipitation and coupling precipitation with convective fluxes with the help of moist enthalpy conservation. We recall the construction of moist-convective rotating shallow water model (mcRSW) model and give an example of application to upper-layer atmospheric vortices.

Study on some partial differential equations in the atmospheric and oceanic dynamics

We review some development of study on some partial differential equations in the atmospheric and oceanic dynamics. Firstly, we give some mathematical results of the surface quasi-geostrophic equations. Secondly, we recall some results on the global well-posedness and long-time dynamics for the three-dimensional viscous primitive equations describing the large-scale atmospheric and oceanic motions. At last, we review some results of stochastical partial differential equations in the atmospheric and oceanic dynamics, which include the existence and uniqueness of global strong solutions to the initial boundary value problem for the stochastic primitive equations, and the existence of random attractors for the corresponding random dynamical system.

Real-time prediction of atmospheric Lagrangian coherent structures based on forecast data: An application and error analysis

The language of Lagrangian coherent structures (LCSs) provides a new means for studying transport and mixing of passive particles advected by an atmospheric flow field. Recent observations suggest that LCSs govern the large-scale atmospheric motion of airborne microorganisms, paving the way for more efficient models and management strategies for the spread of infectious diseases affecting plants, domestic animals, and humans. In addition, having reliable predictions of the timing of hyperbolic LCSs may contribute to improved aerobiological sampling of microorganisms with unmanned aerial vehicles and LCS-based early warning systems. Chaotic atmospheric dynamics lead to unavoidable forecasting errors in the wind velocity field, which compounds errors in LCS forecasting. In this study, we reveal the cumulative effects of errors of (short-term) wind field forecasts on the finite-time Lyapunov exponent (FTLE) fields and the associated LCSs when realistic forecast plans impose certain limits on the forecasting parameters. Objectives of this paper are to (a) quantify the accuracy of prediction of FTLE–LCS features and (b) determine the sensitivity of such predictions to forecasting parameters. Results indicate that forecasts of attracting LCSs exhibit less divergence from the archive-based LCSs than the repelling features. This result is important since attracting LCSs are the backbone of long-lived features in moving fluids. We also show under what circumstances one can trust the forecast results if one merely wants to know if an LCS passed over a region and does not need to precisely know the passage time.

Atmospheric transport of persistent semi-volatile organic chemicals to the Arctic and cold condensation in the mid-troposphere – Part 2: 3-D modeling of episodic atmospheric transport

Abstract. Two 3-dimensional global atmospheric transport models for persistent organic pollutants (POPs) have been employed to investigate the association between the large-scale atmospheric motions and poleward transports of persistent semi-volatile organic chemicals (SVOCs). We examine the modeled daily air concentration of α- and γ-hexachlorocyclohexane (HCH) over a period from 1997 through 1999 during which a number of episodic atmospheric transport events were detected in this modeling study. These events provide modeling evidence for improving the interpretation on the cold condensation effect and poleward atmospheric transport of SVOCs in the mid-troposphere. Two episodic transport events of γ-HCH (lindane) to the high Arctic (80–90° N), one from Asian and another from Eurasian sources, are reported in this paper. Both events suggest that the episodic atmospheric transports occurring in the mid-troposphere (e.g. from 3000 m to 5500 m height) are driven by atmospheric horizontal and vertical motions. The association of the transport events with atmospheric circulation is briefly discussed. Strong southerly winds, forced by the evolution of two semi-permanent high pressure systems over mid-high latitudes in the Northern Hemisphere, play an important role in the long-range transport (LRT) of HCHs to the high latitudes from its sources. Being consistent with the cold condensation effect and poleward atmospheric transport in a mean meridional atmospheric circulation simulated by a 2-D atmospheric transport model, as reported by the first part of this study, this modeling study indicates that cold condensation is likely occurring more intensively in the mid-troposphere where rapid declining air temperature results in condensed phase of the chemical over and near its source regions and where stronger winds convey the chemical more rapidly to the polar region during the episodic poleward atmospheric transport events.

Predictability during the Onset Period of a Euro-Atlantic Blocking Event during 12-21 December 2007

The predictability of large-scale atmospheric motions during the onset period of a prominent atmospheric blocking event occurring over the Euro-Atlantic sector during 12-21 December 2007 is examined using Japanese 25-year Reanalysis (JRA25)/JMA Climate Data Assimilation System (JCDAS) dataset and one-week ensemble forecast dataset provided by the Japan Meteorological Agency (JMA). First, it is found that the predictability in the blocking region is temporarily reduced during the onset period of the blocking event. Second, a simple sensitivity analysis introduced by Enomoto et al. (2007) indicates that low-frequency variations associated with a quasi-stationary Rossby wave train significantly affect the prediction of the blocking onset in comparison with high-frequency variations. This is also confirmed by the time evolution of the spread among ensemble members based on 300-hPa height field. Finally, the predicted vorticity flux divergence by the low-frequency variations, rather than the high-frequency variations, is also found to significantly correlate with the predicted blocking strength, which stresses the importance of the low-frequency variations for the prediction of the onset of this blocking event.

Existence of the solutions and the attractors for the large-scale atmospheric equations

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

Analysis of Discrete Shallow-Water Models on Geodesic Delaunay Grids with C-Type Staggering

AbstractThe properties of C-grid staggered spatial discretizations of the shallow-water equations on regular Delaunay triangulations on the sphere are analyzed. Mass-conserving schemes that also conserve either energy or potential enstrophy are derived, and their features are analogous to those of the C-grid staggered schemes on quadrilateral grids. Results of numerical tests carried out with explicit and semi-implicit time discretizations show that the potential-enstrophy-conserving scheme is able to reproduce correctly the main features of large-scale atmospheric motion and that power spectra for energy and potential enstrophy obtained in long model integrations display a qualitative behavior similar to that predicted by the decaying turbulence theory for the continuous system.

Experimental studies of turbulent helicity and its spectrum in the atmospheric boundary layer

1. In this paper, we present results of the first measurements of turbulent helicity in the atmospheric boundary layer. The spectra obtained are analyzed within the framework of the problem of helicity turbulent cascades towards small scales. For the scales being considered in this study, the helicity spectrum turns out to be similar to the passive-admixture spectrum. Helicity is defined as a scalar product of the velocity v and the vorticity: w = ∇ × v . A difference of helicity from zero implies the violation of the flow mirror symmetry that exists, e.g., in the Ekman’s atmospheric boundary layer. Helicity plays a significant role in processes of magnetic-fields generation in a conducting liquid, and it is one of the important characteristics of large-scale atmospheric motions [1‐5]. At the same time, the role of helicity in hydrodynamic turbulence has not yet been entirely revealed, although we may assume that the turbulization of spiral flows results in the helicity of turbulent velocity pulsations. Within the inviscid limit, the Navier‐Stokes equations conserve kinetic energy and helicity. For turbulent flows, the presence of two quadratic invariants indicates the possible existence of both double cascades (when cascades of the energy and helicity are realized in different segments of wave numbers by analogy with the twodimensional turbulence) and the helicity cascade in parallel with the energy cascade towards small scales [6]. In particular, the existence of the exact relation connecting double and triple velocity correlations, which was later referred to as the 2/15 law (by analogy with Kolmogorov’s 4/5 law) [7], is associated with the helicity cascade.

Energy Spectrum and Energy Flow of the Arctic Oscillation in the Phase Speed Domain

In this study, energy spectrum and energy flow of the large-scale atmospheric motions are examined in reference to the Arctic Oscillation index. Attention is concentrated to the barotropic component of the atmosphere in the framework of the 3D normal mode decomposition.According to the result of the observational analysis in the phase speed domain, the Arctic Oscillation (AO) is characterized as the energy increase at the meridional index l=3 with simultaneous decrease at l=5 of the zonal field. The result is consistent with the theory of the AO by the singular eigenmode of the global atmosphere. The accumulation of energy at the eigenmode of the AO is explained by the enhanced energy flux FZi associated with the zonal-wave interaction.It is found in this study that the energy flux FZi comes from eddies at the spherical Rhines speed cR where the planetary-scale Rossby wave becomes stationary. The result suggests that the low-frequency variability associated with the AO is maintained by energy flux from cR, which is compensated by the up-scale energy cascade from synoptic eddies in addition to the forced stationary planetary waves by topography.

Energy spectrum proportional to the squared phase speed of Rossby modes in the general circulation of the atmosphere

[1] In this study, energy spectrum of the large-scale atmospheric motions is examined in the framework of the 3D normal mode decomposition. The horizontal scale of disturbance is measured by the phase speed of a Rossby mode c. According to the analysis result for the barotropic component of the atmosphere, we obtain a characteristic energy spectrum with distinct slopes for the turbulence and wave regimes separated by the spherical Rhines speed. In order to explain the observational finding that the energy spectrum is proportional to c2, we put forward a hypothesis based on the criterion of Rossby wave breaking such that the local meridional gradient of potential vorticity becomes negative, ∂q/∂y < 0, somewhere in the domain. With a constant m describing a total mass of the atmosphere for unit area, we have shown that the barotropic energy spectrum of the general circulation E can be represented as E = mc2.