Uncertainties of Estimates of Inertia–Gravity Energy in the Atmosphere. Part II: Large-Scale Equatorial Waves

2009 ◽  
Vol 137 (11) ◽  
pp. 3858-3873 ◽  
Author(s):  
N. Žagar ◽  
J. Tribbia ◽  
J. L. Anderson ◽  
K. Raeder
Keyword(s):  
Large Scale ◽  
Normal Modes ◽  
Lower Troposphere ◽  
Physical Space ◽  
Significant Degree ◽  
Hadley Cell ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Energy Propagation ◽  
Zonal Wavenumber

Abstract This paper analyzes the spectra and spatiotemporal features of the large-scale inertia-gravity (IG) circulations in four analysis systems in the tropics. Of special interest is the Kelvin wave (KW), which represents between 7% and 25% of the total IG wave (zonal wavenumber k ≠ 0) energy. The mixed Rossby–gravity (MRG) mode comprises between 4% and 15% of the IG wave energy. At the longest scales, the KW spectra are fitted by a law while the MRG energy spectrum appears flat. At shorter scales both modes follow a −3 law. Energy spectra of the total IG wave motion at long zonal scales (zonal wavenumber smaller than 7) have slopes close to −1. The average circulation associated with KW is characterized by reverse flows in the upper and lower troposphere consistent with the ideas behind simple tropical models. The inverse projection is used to quantify the role of Kelvin and MRG waves in current analysis systems in the upper troposphere over the Indian Ocean. At these levels, easterlies between 10°S and 30°N are represented by the KW to a significant degree while the cross-equatorial flow toward the descending branch of the Hadley cell at 10°S is associated with the MRG waves. The transient structure of equatorial waves is presented in the space of normal modes defined by the zonal wavenumbers, meridional Hough functions, and the vertical eigenfunctions. The difference in the depth of the model domain in DART–CAM and NCEP–NCAR on one hand and ECMWF and NCEP on the other appears to be one reason for different wave propagation properties. In the latter case the vertical energy propagation is diagnosed by filtering the propagating KW modes back to physical space. The results agree with the linear theory of vertically propagating equatorial waves.

scholarly journals Effect of Overturning Circulation on Long Equatorial Waves: A Low-Frequency Cutoff

2018 ◽  
Vol 75 (5) ◽  
pp. 1721-1739 ◽  
Author(s):  
Amanda Back ◽  
Joseph A. Biello
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Meridional Circulation ◽  
Low Frequency ◽  
Hadley Cell ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Background Flow ◽  
Overturning Circulation ◽  
Equatorial Wave

Zonally long tropical waves in the presence of a large-scale meridional and vertical overturning circulation are studied in an idealized model based on the intraseasonal multiscale moist dynamics (IMMD) theory. The model consists of a system of shallow-water equations describing barotropic and first baroclinic vertical modes coupled to one another by the zonally symmetric, time-independent background circulation. To isolate the effects of the meridional circulation alone, an idealized background flow is chosen to mimic the meridional and vertical components of the flow of the Hadley cell; the background flow meridionally converges and rises at the equator. The resulting linear eigenvalue problem is a generalization of the long-wave-scaled version of Matsuno’s equatorial wave problem with the addition of meridional and vertical advection. The results demonstrate that the meridional circulation couples equatorially trapped baroclinic Rossby waves to planetary, barotropic free Rossby waves. The meridional circulation also causes the Kelvin wave to develop an equatorially trapped barotropic component, imparting a westward-tilted vertical structure to the wave. The total energy of the linear system is positive definite, so all waves are shown to be neutrally stable. A critical layer exists at latitudes where the meridional background flow vanishes, resulting in a minimum frequency cutoff for physically feasible waves. Therefore, linear Matsuno waves with periods longer than the vertical transport time of the meridional circulation do not exist in the equatorial waveguide. This implies a low-frequency cutoff for long equatorial waves.

scholarly journals A simple nonlinear model of low frequency (interseasonal) oscillations in the tropical atmosphere

1996 ◽  
Vol 3 (1) ◽  
pp. 29-40 ◽  
Author(s):  
D. Luo
Keyword(s):  
Nonlinear Interaction ◽  
Wave Equations ◽  
Narrow Range ◽  
Lower Troposphere ◽  
Equatorial Region ◽  
Wave Number ◽  
Convective Heating ◽  
Kelvin Wave ◽  
Intensity Parameter ◽  
Zonal Wavenumber

Abstract. In this paper, for a prescribed normalized vertical convective heating profile, nonlinear Kelvin wave equations with wave-CISK heating over equatorial region is reduced to a sixth-order nonlinear ordinary differential equation by using the Galerkin spectral method in the case of considering nonlinear interaction between first and second baroclinic modes. Some numerical calculations are made with the fourth- order Rung-Kutta scheme. It is found that in a narrow range of the heating intensity parameter b, 30-60-day oscillation can occur through linear coupling between first and second baroclinic Kelvin wave-CISK modes for zonal wave-number one when the convective heating is confined to the lower and middle tropospheres. While for zonal wavenumber two, 30-60-day oscillation can be observed in a narrow range of b only when the convective heating is confined to the lower troposphere. However, in a wider range of this heating intensity parameter, 30-60-day oscillation can occur through nonlinear interaction between the first and second baroclinic Kelvin wave-CISK modes with zonal wavenumber one for three vertical convective heating profiles having a maximum in the upper, middle and lower tropospheres, and the total streamfield of the nonlinear first and second baroclinic Kelvin wave-CISK modes possesses a phase reversal between the upper- and lower-tropospheric wind fields. While for zonal wavenumber two, no 30-60-day oscillations can be found. Therefore, it appears that nonlinear interaction between vertical Kelvin wave-CISK modes favours the occurrence of 30-60-day oscillations, particularly, the importance of the vertical distribution of convective heating is re-emphasised.

scholarly journals Linear and Weakly Nonlinear Energetics of Global Nonhydrostatic Normal Modes

2019 ◽  
Vol 76 (12) ◽  
pp. 3831-3846 ◽  
Author(s):  
Carlos F. M. Raupp ◽  
André S. W. Teruya ◽  
Pedro L. Silva Dias
Keyword(s):  
Normal Modes ◽  
Physical Space ◽  
Wave Mode ◽  
Finite Amplitude ◽  
Vertical Acceleration ◽  
Wave Interactions ◽  
Weakly Nonlinear ◽  
Resonant Wave ◽  
Zonal Wavenumber ◽  
Resonant Triads

Abstract Here the theory of global nonhydrostatic normal modes has been further developed with the analysis of both linear and weakly nonlinear energetics of inertia–acoustic (IA) and inertia–gravity (IG) modes. These energetics are analyzed in the context of a shallow global nonhydrostatic model governing finite-amplitude perturbations around a resting, hydrostatic, and isothermal background state. For the linear case, the energy as a function of the zonal wavenumber of the IA and IG modes is analyzed, and the nonhydrostatic effect of vertical acceleration on the IG waves is highlighted. For the nonlinear energetics analysis, the reduced equations of a single resonant wave triad interaction are obtained by using a pseudoenergy orthogonality relation. Integration of the triad equations for a resonance involving a short harmonic of an IG wave, a planetary-scale IA mode, and a short IA wave mode shows that an IG mode can allow two IA modes to exchange energy in specific resonant triads. These wave interactions can yield significant modulations in the dynamical fields associated with the physical-space solution with periods varying from a daily time scale to almost a month long.

scholarly journals Changes in the Austral Winter Hadley Circulation and the Impact on Stationary Rossby Waves Propagation

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ana Carolina Vasques Freitas ◽  
Tércio Ambrizzi
Keyword(s):  
Indian Ocean ◽  
South America ◽  
Rossby Waves ◽  
Wave Train ◽  
Hadley Circulation ◽  
Opposite Polarity ◽  
Hadley Cell ◽  
Energy Propagation ◽  
Zonal Wavenumber ◽  
The Impact

The present study investigates how changes in the Hadley Cell (HC) intensity impact the stationary Rossby waves energy propagation in the Southern Hemisphere (SH) extratropics. Composites for weak and strong HC Intensity Index (HCI) were used in this analysis. The results for weak HC cases showed a wave train emanating from the subtropical central-west Indian Ocean in an arc-like route, with zonal wavenumber three in the polar jet waveguide, and reaching the north of South America. For strong HC cases, the wave train is also trapped inside the polar jet waveguide with zonal wavenumber four, emanating from subtropical central-east Indian Ocean and reaching the subtropical west coast of Africa. A weaker zonally oriented wave train with zonal wavenumber five has been found in the subtropical region with opposite polarity for weak and strong HC cases. Over the South America, the results show that an HC weakening can lead to a very cold and rainy winter in the southwest of the continent and a mild warm and dry winter on Brazilian states of Minas Gerais and Bahia. A pattern almost opposite was observed when the CH strengthens.

scholarly journals Enhanced Persistence of Equatorial Waves via Convergence Coupling in the Stochastic Multicloud Model

2015 ◽  
Vol 72 (12) ◽  
pp. 4701-4720 ◽  
Author(s):  
Noah D. Brenowitz ◽  
Yevgeniy Frenkel ◽  
Andrew J. Majda
Keyword(s):  
Large Scale ◽  
Heat Fluxes ◽  
Sea Surface ◽  
Theoretical Studies ◽  
Equatorial Waves ◽  
Moist Convection ◽  
Kelvin Wave ◽  
Surface Heat Fluxes ◽  
Walker Cell ◽  
Conditional Instability

Abstract Recent observational and theoretical studies show a systematic relationship between tropical moist convection and measures related to large-scale convergence. It has been suggested that cloud fields in the column stochastic multicloud model compare better with observations when using predictors related to convergence rather than moist energetics (e.g., CAPE) as per Peters et al. Here, this work is extended to a fully prognostic multicloud model. A nonlocal convergence-coupled formulation of the stochastic multicloud model is implemented without wind-dependent surface heat fluxes. In a series of idealized Walker cell simulations, this convergence coupling enhances the persistence of Kelvin wave analogs in dry regions of the domain while leaving the dynamics in moist regions largely unaltered. This effect is robust for changes in the amplitude of the imposed sea surface temperature (SST) gradient. In essence, this method provides a soft convergence coupling that allows for increased interaction between cumulus convection and the large-scale circulation but does not suffer from the deleterious wave–conditional instability of the second kind (CISK) behavior of the Kuo-type moisture-convergence closures.

Uncertainties of Estimates of Inertia–Gravity Energy in the Atmosphere. Part I: Intercomparison of Four Analysis Systems

2009 ◽  
Vol 137 (11) ◽  
pp. 3837-3857 ◽  
Author(s):  
N. Žagar ◽  
J. Tribbia ◽  
J. L. Anderson ◽  
K. Raeder
Keyword(s):  
Three Dimensional ◽  
Normal Modes ◽  
Atmospheric Model ◽  
Kelvin Wave ◽  
Energy Field ◽  
Inverse Projection ◽  
Zonal Wavenumber ◽  
The Difference ◽  
Analysis System ◽  
The Tropics

Abstract This paper presents the application of the normal-mode functions to diagnose the atmospheric energy spectra in terms of balanced and inertia–gravity (IG) contributions. A set of three-dimensional orthogonal normal modes is applied to four analysis datasets from July 2007. The datasets are the operational analysis systems of NCEP and ECMWF, the NCEP–NCAR reanalyses, and the Data Assimilation Research Testbed–Community Atmospheric Model (DART–CAM), an ensemble analysis system developed at NCAR. The differences between the datasets can be considered as a measure of uncertainty of the IG contribution to the global energetics. The results show that the percentage of IG motion in the present NCEP, ECMWF, and DART–CAM analysis systems is between 1% and 2% of the total energy field. In the wave part of the flow (zonal wavenumber k ≠ 0), the IG energy contribution is between 9% and 15%. On the contrary, the NCEP–NCAR reanalyses contain more IG motion, especially in the Southern Hemisphere extratropics. Each analysis contains more energy in the eastward IG motion than in its westward counterpart. The difference is about 2%–3% of the total wave energy and it is associated with the motions projected onto the Kelvin wave in the tropics. The selected truncation parameters of the expansion (zonal, meridional, and vertical truncation) ensure that the projection provides the optimal fit to the input data on model levels. This approach is different from previous applications of the normal modes and under the linearity assumption it allows the application of the inverse projection to obtain details of circulation associated with a selected type of motion. The bulk of the IG motion is confined to the tropics. For the successful reproduction of three-dimensional circulations by the normal modes it is important that the expansion includes a number of vertical modes.

scholarly journals Convectively Coupled Equatorial Waves. Part III: Synthesis Structures and Their Forcing and Evolution

2007 ◽  
Vol 64 (10) ◽  
pp. 3438-3451 ◽  
Author(s):  
Gui-Ying Yang ◽  
Brian Hoskins ◽  
Julia Slingo
Keyword(s):  
Lower Troposphere ◽  
Wave Activity ◽  
Equatorial Region ◽  
Western Hemisphere ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Upper Troposphere ◽  
Convectively Coupled Equatorial Waves ◽  
Eastern Hemisphere ◽  
Equatorial Wave

Abstract Building on Parts I and II of this study, the structures of eastward- and westward-moving convectively coupled equatorial waves are examined through synthesis of projections onto standard equatorial wave horizontal structures. The interaction between these equatorial wave components and their evolution are investigated. It is shown that the total eastward-moving fields and their coupling with equatorial convection closely resemble the standard Kelvin wave in the lower troposphere, with intensified convection in phase with anomalous westerlies in the Eastern Hemisphere (EH) and with anomalous convergence in the Western Hemisphere (WH). However, in the upper troposphere, the total fields show a mixture of the Kelvin wave and higher (n = 0 and 1) wave structures, with strong meridional wind and its divergence. The equatorial total fields show what may be described as a modified first internal Kelvin wave vertical structure in the EH, with a tilt in the vertical and a third peak in the midtroposphere. There is evidence that the EH midtropospheric Kelvin wave is closely associated with SH extratropical eastward-moving wave activity, the vertical velocity associated with the wave activity stretching into the equatorial region in the mid–upper troposphere. The midtropospheric zonal wind and geopotential height show a pattern that may be associated with a forced wave. The westward-moving fields associated with off-equatorial convection show very different behaviors between the EH midsummer and the WH transition seasons. In the EH midsummer, the total fields have a baroclinic structure, with the off-equatorial convection in phase with relatively warm air, suggesting convective forcing of the dynamical fields. The total structures exhibit a mixture of the n = 0, 1 components, with the former dominating to the east of convection and the latter to the west of convection. The n = 0 component is found to be closely connected to the lower-level n = 1 Rossby (R1) wave that appears earlier and seems to provide organization for the convection, which in turn forces the n = 0 wave. In the WH transition season the total fields have a barotropic structure and are dominated by the R1 wave. There is evidence that this barotropic R1 wave, as well as the associated tropical convection, is forced by the NH upper-tropospheric extratropical Rossby wave activity. In the EH, westward-moving lower-level wind structures associated with equatorial convection resemble the R1 wave, with equatorial westerlies in phase with the intensified convection. However, westward-moving n = −1 and n = 0 structures are also involved.

scholarly journals Convectively Coupled Equatorial Waves Simulated on an Aquaplanet in a Global Nonhydrostatic Experiment

2008 ◽  
Vol 65 (4) ◽  
pp. 1246-1265 ◽  
Author(s):  
Tomoe Nasuno ◽  
Hirofumi Tomita ◽  
Shinichi Iga ◽  
Hiroaki Miura ◽  
Masaki Satoh
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Lower Troposphere ◽  
Moisture Flux ◽  
Moisture Distribution ◽  
Convective System ◽  
Dynamical Structure ◽  
Kelvin Wave ◽  
Free Atmosphere ◽  
Low Level

Abstract Large-scale tropical convective disturbances simulated in a 7-km-mesh aquaplanet experiment are investigated. A 40-day simulation was executed using the Nonhydrostatic Icosahedral Atmospheric Model (NICAM). Two scales of eastward-propagating disturbances were analyzed. One was tightly coupled to a convective system resembling super–cloud clusters (SCCs) with a zonal scale of several thousand kilometers (SCC mode), whereas the other was characterized by a planetary-scale dynamical structure (40 000-km mode). The typical phase velocity was 17 (23) m s−1 for the SCC (40 000 km) mode. The SCC mode resembled convectively coupled Kelvin waves in the real atmosphere around the equator, but was accompanied by a pair of off-equatorial gyres. The 40 000-km mode maintained a Kelvin wave–like zonal structure, even poleward of the equatorial Rossby deformation radius. The equatorial structures in both modes matched neutral eastward-propagating gravity waves in the lower troposphere and unstable (growing) waves in the upper troposphere. In both modes, the meridional mass divergence exceeded the zonal component, not only in the boundary layer, but also in the free atmosphere. The forcing terms indicated that the meridional flow was primarily driven by convection via deformation in pressure fields and vertical circulations. Moisture convergence was one order of magnitude greater than the moisture flux from the sea surface. In the boundary layer, frictional convergence in the (anomalous) low-level easterly phase accounted for the buildup of low-level moisture leading to the active convective phase. The moisture distribution in the free atmosphere suggested that the moisture–convection feedback operated efficiently, especially in the SCC mode.

The MJO and Convectively Coupled Waves in a Coarse-Resolution GCM with a Simple Multicloud Parameterization

2011 ◽  
Vol 68 (2) ◽  
pp. 240-264 ◽  
Author(s):  
Boualem Khouider ◽  
Amik St-Cyr ◽  
Andrew J. Majda ◽  
Joseph Tribbia
Keyword(s):  
General Circulation ◽  
Large Scale ◽  
Deep Convection ◽  
General Circulation Models ◽  
Moisture Gradient ◽  
Kelvin Wave ◽  
The Third ◽  
Coarse Resolution ◽  
Convectively Coupled Waves ◽  
Zonal Wavenumber

Abstract The adequate representation of the dominant intraseasonal and synoptic-scale variability in the tropics, characterized by the Madden–Julian oscillation (MJO) and convectively coupled waves, is still problematic in current operational general circulation models (GCMs). Here results are presented using the next-generation NCAR GCM—the High-Order Methods Modeling Environment (HOMME)—as a dry dynamical core at a coarse resolution of about 167 km, coupled to a simple multicloud parameterization. The coupling is performed through a judicious choice of heating vertical profiles for the three cloud types—congestus, deep, and stratiform—that characterize organized tropical convection. Important control parameters that affect the types of waves that emerge are the background vertical gradient of the moisture and the stratiform fraction in the multicloud parameterization, which set the strength of large-scale moisture convergence and unsaturated downdrafts in the wake of deep convection, respectively. Three numerical simulations using different moisture gradients and different stratiform fractions are considered. The first experiment uses a large moisture gradient and a small stratiform fraction and provides an MJO-like example. It results in an intraseasonal oscillation of zonal wavenumber 2, moving eastward at a constant speed of roughly 5 m s−1. The second uses a weaker background moisture gradient and a large stratiform fraction and yields convectively coupled Rossby, Kelvin, and two-day waves, embedded in and interacting with each other; and the third experiment combines the small stratiform fraction and the weak background moisture gradient to yield a planetary-scale (wavenumber 1) second baroclinic Kelvin wave. While the first two experiments provide two benchmark examples that reproduce several key features of the observational record, the third is more of a demonstration of a bad MJO model solution that exhibits very unrealistic features.

Large-Scale Rossby Normal Modes during Some Recent Northern Hemisphere Winters

2012 ◽  
Vol 69 (3) ◽  
pp. 820-839 ◽  
Author(s):  
F. Sassi ◽  
R. R. Garcia ◽  
K. W. Hoppel
Keyword(s):  
Northern Hemisphere ◽  
Large Scale ◽  
Normal Modes ◽  
Background Spectrum ◽  
Zonal Wavenumber ◽  
Free Mode ◽  
Real Atmosphere ◽  
Height Fields ◽  
The Waves ◽  
Spectral Location

Abstract Large-scale Rossby normal modes are studied for the Northern Hemisphere winters of 2005, 2006, 2008, and 2009 using global observational meteorological analyses spanning the 0–92-km altitude range. Spectral analysis of geopotential height fields shows pronounced peaks at westward-propagating zonal wavenumber 1 near the theoretical locations of the free Rossby waves at 25, 16, 10, and 5 days that, in some cases, have amplitudes significantly larger than the estimated background spectrum. Evidence is also found for a wavenumber-2 free mode near 4 days. A coherence analysis is used to extract the amplitude and phase of the waves, and to isolate those regions of the latitude/altitude plane where the signals are statistically significant. Although the spectral location, temporal evolution, and vertical structure of several of these waves are suggestive of the presence of Rossby normal modes, this study shows that in the real atmosphere the waves only occasionally have the global properties of classical normal modes. Moreover, no evidence is found that the amplitudes of these modes are enhanced during stratospheric sudden warmings.

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