scholarly journals The MJO as a Dispersive, Convectively Coupled Moisture Wave: Theory and Observations

2016 ◽  
Vol 73 (3) ◽  
pp. 913-941 ◽  
Author(s):  
Ángel F. Adames ◽  
Daehyun Kim
Keyword(s):  
Group Velocity ◽  
Rossby Wave ◽  
Linear Regression Analysis ◽  
Phase Speed ◽  
Wave Theory ◽  
Reanalysis Data ◽  
Horizontal Wind ◽  
Model Parameters ◽  
Linear Wave ◽  
Zonal Wavenumber

Abstract A linear wave theory for the Madden–Julian oscillation (MJO), previously developed by Sobel and Maloney, is extended upon in this study. In this treatment, column moisture is the only prognostic variable and the horizontal wind is diagnosed as the forced Kelvin and Rossby wave responses to an equatorial heat source/sink. Unlike the original framework, the meridional and vertical structure of the basic equations is treated explicitly, and values of several key model parameters are adjusted, based on observations. A dispersion relation is derived that adequately describes the MJO’s signal in the wavenumber–frequency spectrum and defines the MJO as a dispersive equatorial moist wave with a westward group velocity. On the basis of linear regression analysis of satellite and reanalysis data, it is estimated that the MJO’s group velocity is ~40% as large as its phase speed. This dispersion is the result of the anomalous winds in the wave modulating the mean distribution of moisture such that the moisture anomaly propagates eastward while wave energy propagates westward. The moist wave grows through feedbacks involving moisture, clouds, and radiation and is damped by the advection of moisture associated with the Rossby wave. Additionally, a zonal wavenumber dependence is found in cloud–radiation feedbacks that cause growth to be strongest at planetary scales. These results suggest that this wavenumber dependence arises from the nonlocal nature of cloud–radiation feedbacks; that is, anomalous convection spreads upper-level clouds and reduces radiative cooling over an extensive area surrounding the anomalous precipitation.

scholarly journals Local Rossby Wave Packet Amplitude, Phase Speed, and Group Velocity: Seasonal Variability and Their Role in Temperature Extremes

2020 ◽  
Vol 33 (20) ◽  
pp. 8767-8787 ◽  
Author(s):  
Georgios Fragkoulidis ◽  
Volkmar Wirth
Keyword(s):  
Group Velocity ◽  
Rossby Wave ◽  
Model Simulation ◽  
Phase Speed ◽  
Meridional Wind ◽  
Reanalysis Data ◽  
Spatiotemporal Variability ◽  
Temperature Extremes ◽  
Time Period ◽  
Real Atmosphere

AbstractTransient Rossby wave packets (RWPs) are a prominent feature of the synoptic to planetary upper-tropospheric flow at the midlatitudes. Their demonstrated role in various aspects of weather and climate prompts the investigation of characteristic properties like their amplitude, phase speed, and group velocity. Traditional frameworks for the diagnosis of the two latter have so far remained nonlocal in space or time, thus preventing a detailed view on the spatiotemporal evolution of RWPs. The present work proposes a method for the diagnosis of horizontal Rossby wave phase speed and group velocity locally in space and time. The approach is based on the analytic signal of upper-tropospheric meridional wind velocity and RWP amplitude, respectively. The new diagnostics are first applied to illustrative examples from a barotropic model simulation and the real atmosphere. The main seasonal and interregional variability features of RWP amplitude, phase speed, and group velocity are then explored using ERA5 reanalysis data for the time period 1979–2018. Apparent differences and similarities in these respects between the Northern and Southern Hemispheres are also discussed. Finally, the role of RWP amplitude and phase speed during central European short-lived and persistent temperature extremes is investigated based on changes of their distribution compared to the climatology of the region. The proposed diagnostics offer insight into the spatiotemporal variability of RWP properties and allow the evaluation of their implications at low computational demands.

Local diagnostics of Rossby wave packet properties – Seasonal variability and their role in temperature extremes

2020 ◽  
Author(s):  
Georgios Fragkoulidis ◽  
Volkmar Wirth
Keyword(s):  
Group Velocity ◽  
Rossby Wave ◽  
Phase Speed ◽  
Meridional Wind ◽  
Reanalysis Data ◽  
Diagnostic Methods ◽  
Temperature Extremes ◽  
Time Period ◽  
Tropospheric Circulation ◽  
Systematic Biases

<p>Transient Rossby wave packets (RWPs) are a prominent feature of the synoptic to planetary upper-tropospheric flow at the mid-latitudes. This prompts the development of diagnostic methods to identify and investigate the spatiotemporal evolution of key RWP properties. Such properties include the RWP phase speed and group velocity, the diagnosis of which has so far remained non-local in space and/or time. To this end, a novel diagnostic approach is presented here, which is based on the analytic signal of upper-tropospheric meridional wind velocity and thus allows the evaluation of RWP properties locally in space and time. The detailed insight into these properties can be utilized toward a better understanding of the upper-tropospheric circulation, its interplay with local weather features, and its model representation. In particular, climatologies of RWP amplitude, wavenumber, phase speed, and group velocity are investigated using reanalysis data for the time period 1979 – 2018. Pronounced features of seasonal and interregional variability are highlighted. Moreover, the role of RWP amplitude and phase speed in the occurrence and duration of temperature extremes in Europe is explored. Finally, indications of systematic biases in medium-range forecasts of these fields suggest that a correct representation of the RWP evolution is crucial for the predictability of temperature extreme events.</p>

A Methodology to Characterize Internal Solitons in the Ocean

2018 ◽  
Author(s):  
Henrique Coelho ◽  
Zhong Peng ◽  
Dave Sproson ◽  
Jill Bradon
Keyword(s):  
Internal Waves ◽  
Large Scale ◽  
Numerical Models ◽  
Phase Speed ◽  
Selection Procedure ◽  
Wave Theory ◽  
Tidal Energy ◽  
Internal Tides ◽  
Linear Wave ◽  
Soliton Generation

Internal waves in the ocean occur in stably stratified fluids when a water parcel is vertically displaced by some external forcing and is restored by buoyancy forces. A specific case of such internal waves is internal tides and their associated currents. These currents can be significant in areas where internal waves degenerate into nonlinear solitary waves, known as solitons. Solitons are potentially hazardous for offshore engineering constructions, such as oil/gas pipelines and floating platforms. The most efficient mechanism of soliton generation is the tidal energy conversion from barotropic to baroclinic component over large-scale oceanic bottom obstructions (shelf breaks, seamounts, canyons and ridges). In this paper, a methodology is provided to compute diagnostics and prognostics for soliton generation and propagation, including the associated currents. The methodology comprises a diagnostic tool which, through the use of a set of theoretical and empirical formulations, selects areas where solitons are likely to occur. These theoretical and empirical formulations include the computation of the integral body force (1), the linear wave theory to compute the phase speed and the empirical model proposed by (2). After the selection procedure, the tool provides initial and boundary conditions for non-hydrostatic numerical models. The numerical models run in 2D-V configuration (vertical slices) with horizontal and vertical resolutions ranging from 50 to 200 m and 5 to 10 m, respectively. Examples are provided for an open ocean location over the Mascarene Plateau in the Indian Ocean. Validation of diagnostics and prognostics are provided against ADCP and satellite data.

scholarly journals Equatorial Waves in Opposite QBO Phases

2011 ◽  
Vol 68 (4) ◽  
pp. 839-862 ◽  
Author(s):  
Gui-Ying Yang ◽  
Brian J. Hoskins ◽  
Julia M. Slingo
Keyword(s):  
Group Velocity ◽  
Lower Stratosphere ◽  
Phase Speed ◽  
Kelvin Waves ◽  
Western Hemisphere ◽  
Equatorial Waves ◽  
Vertical Wavelength ◽  
Quasi Biennial Oscillation ◽  
Zonal Wavenumber ◽  
The Waves

Abstract A methodology for identifying equatorial waves is used to analyze the multilevel 40-yr ECMWF Re-Analysis (ERA-40) data for two different years (1992 and 1993) to investigate the behavior of the equatorial waves under opposite phases of the quasi-biennial oscillation (QBO). A comprehensive view of 3D structures and of zonal and vertical propagation of equatorial Kelvin, westward-moving mixed Rossby–gravity (WMRG), and n = 1 Rossby (R1) waves in different QBO phases is presented. Consistent with expectation based on theory, upward-propagating Kelvin waves occur more frequently during the easterly QBO phase than during the westerly QBO phase. However, the westward-moving WMRG and R1 waves show the opposite behavior. The presence of vertically propagating equatorial waves in the stratosphere also depends on the upper tropospheric winds and tropospheric forcing. Typical propagation parameters such as the zonal wavenumber, zonal phase speed, period, vertical wavelength, and vertical group velocity are found. In general, waves in the lower stratosphere have a smaller zonal wavenumber, shorter period, faster phase speed, and shorter vertical wavelength than those in the upper troposphere. All of the waves in the lower stratosphere show an upward group velocity and downward phase speed. When the phase of the QBO is not favorable for waves to propagate, their phase speed in the lower stratosphere is larger and their period is shorter than in the favorable phase, suggesting Doppler shifting by the ambient flow and a filtering of the slow waves. Tropospheric WMRG and R1 waves in the Western Hemisphere also show upward phase speed and downward group velocity, with an indication of their forcing from middle latitudes. Although the waves observed in the lower stratosphere are dominated by “free” waves, there is evidence of some connection with previous tropical convection in the favorable year for the Kelvin waves in the warm water hemisphere and WMRG and R1 waves in the Western Hemisphere, which is suggestive of the importance of convective forcing for the existence of propagating coupled Kelvin waves and midlatitude forcing for the existence of coupled WMRG and R1 waves.

The Effects of Midlatitude Waves over and around the Tibetan Plateau on Submonthly Variability of the East Asian Summer Monsoon

2009 ◽  
Vol 137 (7) ◽  
pp. 2286-2304 ◽  
Author(s):  
Hatsuki Fujinami ◽  
Tetsuzo Yasunari
Keyword(s):  
Tibetan Plateau ◽  
Rossby Wave ◽  
Large Scale ◽  
Southern China ◽  
Phase Speed ◽  
The Tibetan Plateau ◽  
Low Level ◽  
Zonal Wavenumber ◽  
Upper Level ◽  
Southward Migration

Convective variability at submonthly time scales (7–25 days) over the Yangtze and Huaihe River basins (YHRBs) and associated large-scale atmospheric circulation during the mei-yu season were examined using interpolated outgoing longwave radiation (OLR) and NCEP–NCAR reanalysis data for 12 yr having active submonthly convective fluctuation over the YHRBs within the period 1979–2004. Correlations between convection anomalies over the YHRBs and upper-level streamfunction anomalies at every grid point show two contrasting patterns. One pattern exhibits high correlations along the northern to eastern peripheries of the Tibetan Plateau (defined as the NET pattern), whereas the other has high correlations across the Tibetan Plateau (defined as the AT pattern). Composite analysis of the NET pattern shows slow southward migration of convection anomalies from the northeastern periphery of the Tibetan Plateau to southern China, in relation to southward migration of the mei-yu front caused by simultaneous amplification of upper- and low-level waves north of the YHRBs. In the AT pattern, convection anomalies migrate eastward from the western Tibetan Plateau to the YHRBs. A low-level vortex is created at the lee of the plateau by eastward-moving upper-level wave packets and associated convection from the plateau. Rossby wave trains along the Asian jet characterize the upper-level circulation anomalies in the two patterns. The basic state of the Asian jet during the mei-yu season differs between the two patterns, especially around the Tibetan Plateau. The Asian jet has a northward arclike structure in NET years, while a zonal jet dominates in AT years. These differences could alter the Rossby wave train propagation route. Furthermore, the larger zonal wavenumber of AT waves (∼7–8) than of NET waves (∼6) means faster zonal phase speed relative to the ground in the AT pattern than in the NET pattern. These differences likely explain the meridional amplification of waves north of the YHRBs in the NET pattern and the eastward wave movement across the plateau in the AT pattern.

scholarly journals Midlatitude Baroclinic Rossby Waves in a High-Resolution OGCM Simulation

2009 ◽  
Vol 39 (9) ◽  
pp. 2264-2279 ◽  
Author(s):  
Kunihiro Aoki ◽  
Atsushi Kubokawa ◽  
Hideharu Sasaki ◽  
Yoshikazu Sasai
Keyword(s):  
Rossby Wave ◽  
Vertical Structure ◽  
Phase Speed ◽  
Wave Theory ◽  
Bottom Pressure ◽  
Background Flow ◽  
Flat Bottom ◽  
Long Wave ◽  
Wavenumber Spectrum ◽  
Dominant Peak

Abstract The effects of background baroclinic zonal flow and bottom pressure decoupling on midlatitude oceanic Rossby wave dynamics using a high-resolution OGCM simulation are investigated. To examine these effects, the phase speed and vertical structure of the simulated wave are compared with each of the different linear Rossby wave solutions obtained for two different circumstances (with or without background flow) and two different boundary conditions (a flat bottom or a bottom pressure decoupling condition). First, a frequency–wavenumber spectrum is examined for depth anomaly of the permanent thermocline (27.0σθ surface) along 32°S. Most of the energy is distributed along the theoretical dispersion curve including the effects of background flow and bottom pressure decoupling. The authors focus on a secondary dominant peak (appearing at a frequency greater than 1 cycle per year) at which the differences between the dispersion curves are large enough to discuss the relation between the spectral peak and the dispersion curves. The phase speed of this peak is nearly 1.5 times larger than that of the standard long-wave theory (flat bottom and no background flow), which is similar to results from previous observational studies. The extended long-wave theory including background flow and bottom pressure decoupling effects overestimates the phase speed. However, taking into account finite wavelength effects, this theory provides a phase speed much closer to that of the secondary dominant peak. The vertical structure corresponding to the wave of the secondary dominant peak extracted by composite analysis is intensified in the surface layer, a result similar to that from the theory including background flow and bottom pressure decoupling effects. The authors also compare the latitudinal distribution of midlatitude phase speed estimated by the frequency–wavenumber spectrum with theoretical results. The theory including background flow, bottom pressure decoupling, and finite wavelength effects reproduces the latitudinal distribution well, suggesting that these effects are important for explaining Rossby wave speed. The dominant factor enhancing the phase speed is bottom pressure decoupling related to rough bottom topography, while north of 30°N the background flow makes a strong contribution to the phase speed enhancement.

scholarly journals Global Patterns of Low-Mode Internal-Wave Propagation. Part II: Group Velocity

2007 ◽  
Vol 37 (7) ◽  
pp. 1849-1858 ◽  
Author(s):  
Matthew H. Alford ◽  
Zhongxiang Zhao
Keyword(s):  
Group Velocity ◽  
Standing Waves ◽  
Deep Ocean ◽  
Wave Theory ◽  
Internal Tides ◽  
Linear Wave ◽  
Frequency Spectra ◽  
Tidal Waves ◽  
Latitudinal Dependence ◽  
Group Speed

Abstract Using a set of 80 globally distributed time series of near-inertial and semidiurnal energy E and energy flux F computed from historical moorings, the group velocity ĉg ≡ FE−1 is estimated. For a single free wave, observed group speed |ĉg| should equal that expected from linear wave theory. For comparison, the latitude dependence of perceived group speed for perfectly standing waves is also derived. The latitudinal dependence of observed semidiurnal |ĉg| closely follows that expected for free waves at all latitudes, implying that 1) low-mode internal tides obey linear theory and 2) standing internal-tidal waves are rare in the deep ocean for latitudes equatorward of about 35°. At higher latitudes, standing waves cannot be easily distinguished from free waves using this method because their expected group speeds are similar. Near-inertial waves exhibit scattered |ĉg| values consistent with the passage of events generated at various latitudes, with implied frequencies ω ≈ 1.05–1.25 × f, as typically observed in frequency spectra.

scholarly journals A Toy Model of the Instability in the Equatorially Trapped Convectively Coupled Waves on the Equatorial Beta Plane

2008 ◽  
Vol 65 (12) ◽  
pp. 3736-3757 ◽  
Author(s):  
Joseph Allan Andersen ◽  
Zhiming Kuang
Keyword(s):  
Growth Rates ◽  
Wave Spectrum ◽  
Phase Speed ◽  
Wave Theory ◽  
Linear Instability ◽  
Kelvin Wave ◽  
Convectively Coupled Waves ◽  
Beta Plane ◽  
Zonal Wavenumber ◽  
Wave Modes

Abstract The equatorial atmospheric variability shows a spectrum of significant peaks in the wavenumber–frequency domain. These peaks have been identified with the equatorially trapped wave modes of rotating shallow water wave theory. This paper addresses the observation that the various wave types (e.g., Kelvin, Rossby, etc.) and wavenumbers show differing signal strength relative to a red background. It is hypothesized that this may be due to variations in the linear stability of the atmosphere in response to the various wave types depending on both the specific wave type and the wavenumber. A simple model of the convectively coupled waves on the equatorial beta plane is constructed to identify processes that contribute to this dependence. The linear instability spectrum of the resulting coupled system is evaluated by eigenvalue analysis. This analysis shows unstable waves with phase speeds, growth rates, and structures (vertical and horizontal) that are broadly consistent with the results from observations. The linear system, with an idealized single intertropical convergence zone (ITCZ) as a mean state, shows peak unstable Kelvin waves around zonal wavenumber 7 with peak growth rates of ∼0.08 day−1 (e-folding time of ∼13 days). The system also shows unstable mixed Rossby–gravity (MRG) and inertio-gravity waves with significant growth in the zonal wavenumber range from −15 (negative indicates westward phase speed) to +10 (positive indicates eastward phase speed). The peak MRG n = 0 eastward inertio-gravity wave (EIG) growth rate is around one-third that of the Kelvin wave and occurs at zonal wavenumber 3. The Rossby waves in this system are stable, and the Madden–Julian oscillation is not observed. Within this model, it is shown that in addition to the effect of the ITCZ configuration, the differing instabilities of the different wave modes are also related to their different efficiency in converting input energy into divergent flow. This energy conversion efficiency difference is suggested as an additional factor that helps to shape the observed wave spectrum.

Planetary (Rossby), Inertia-Gravity (Poincaré) and Kelvin waves on the f-plane and β-plane in the presence of a uniform zonal flow

2021 ◽  
Author(s):  
Yair De-Leon ◽  
Chaim I. Garfinkel ◽  
Nathan Paldor
Keyword(s):  
Numerical Solutions ◽  
Bottom Topography ◽  
Phase Speed ◽  
Zonal Flow ◽  
Dispersion Curves ◽  
Kelvin Waves ◽  
Linear Wave ◽  
Hermite Function ◽  
Mean Flow ◽  
Zonal Wavenumber

<p>A linear wave theory of the Rotating Shallow Water Equations (RSWE) is developed in a channel on either the mid-latitude f-plane/β-plane or on the equatorial β-plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. We show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f-plane similar to the generation of these waves by PV sources such as the β–effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting planetary (Rossby), Inertia-Gravity (Poincaré) and Kelvin-like waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the “no mean-flow” phase speeds does not account for the difference in phase speeds, and the meridional structure does not often oscillate across the channel but is trapped near one the channel's boundaries in mid latitudes or behaves as Hermite function in the case of an equatorial channel. The phase speed of Kelvin-like waves is modified by the presence of a mean flow compared to the classical gravity wave speed but their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincaré modes are not uniform but change with the zonal wavenumber, and the convexity of the dispersion curves also changes with the zonal wavenumber. In some cases, the Kelvin-like dispersion curve crosses those of Poincaré modes, but it is not an evidence for the existence of instability since the Kelvin waves are not part of the solutions of an eigenvalue problem. </p>

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

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