Westward-propagating Waves Research Articles

Influence of rossby wave in southern Indian Ocean on the low frequency variability of eddy kinetic energy within agulhas current system

The basin-scale wave propagation in the Southern Indian Ocean (SIO) is inferred to affect the low-frequency variability of eddy kinetic energy (EKE) within the Agulhas current system (ACS). Observations and numerical simulations indicate that westward-propagating waves, in the form of sea level variability from the east boundary, may cause “non-linear” oceanic responses (e.g., sea level and EKE) in the ACS. This is likely due to two factors: (i) the movement of wave crests and troughs continuously alters the stratification of the upper ocean, generating a positive baroclinic instability and prompting conversions of EKE from mean flow in the source regions, and (ii) wave-current interactions induce a rapid intension of an anticyclone gyre in the interior SIO and the corresponding EKE in the downstream regions. These basin-scale wave modulations may provide an additional perspective to the traditional wind driving view based on the barotropic Sverdrup relation. The local winds over the SIO play an important role in maintaining basin-scale Rossby waves in the southwest Indian Ocean and further modulating oceanic low-frequency variability in a “quasi-linear” way.

The Composite Response of Traveling Planetary Waves in the Middle Atmosphere Surrounding Sudden Stratospheric Warmings through an Overreflection Perspective

Abstract Traveling planetary waves surrounding sudden stratospheric warming events can result from direct propagation from below or in situ generation. They can have significant impacts on the circulation in the mesosphere and lower thermosphere. Our study runs a series of ensembles initialized from the Whole Atmosphere Community Climate Model, version 4, nudged up to 50 km by 6-hourly Modern-Era Retrospective Analysis for Research and Application, version 2, reanalysis to compile a library of sudden stratospheric warming events. To our knowledge, we present the first composite or ensemble study that attempts to link direct propagation and in situ generation by evaluating the wave geometries associated with the overreflection perspective, a framework used to describe how planetary waves interact with critical and turning levels. The present study looks at the evolution of these interactions through the onset of sudden stratospheric warmings with an elevated stratopause (ES-SSWs). Robust and unique features of ES-SSWs are determined by employing an ensemble study that compares ES-SSWs with normal winters. Our study evaluates the production and impacts of westward-propagating, quasi-stationary, and eastward-propagating planetary waves surrounding ES-SSWs. Our results show that eastward-propagating planetary waves are generated within the westward stratospheric wind layer after ES-SSW onset which aids in restoring the eastward stratospheric wind. The interaction of quasi-stationary and westward-propagating waves with the westward stratospheric wind is explored from an overreflection perspective and reaffirms that westward-propagating planetary waves are produced from instabilities at the top of the westward stratospheric wind reversal.

Two Types of Mid-High-Latitude Intraseasonal Oscillations in the Southern Hemisphere during Austral Summer

Abstract Using NCEP–NCAR reanalysis data, the atmospheric intraseasonal oscillation (ISO) over the mid-high latitudes in the Southern Hemisphere during austral summer is studied. Two types of 10–30-day eastward- and westward-propagating ISO at mid-high latitudes are extracted by extended empirical orthogonal functions. The analysis of wave activity flux reveals that the energy sources of the eastward-propagating wave train are in the southwest Pacific and southern Indian Ocean, and the westward-propagating wave train is over the east coast of South America. The diagnosis of geopotential height tendency shows that the zonal gradient of ISO relative vorticity guided by mean zonal wind plays a major role in the eastward propagation of the wave train, while the meridional gradient of mean relative vorticity and geostrophic vorticity guided by ISO meridional wind plays a major role in the westward propagation of the wave train. Energy analysis shows that the amplitude enhancement over the South Pacific is due to the ISO disturbance gaining energy from the mean flow. The eastward-propagating ISO obtains energy from the mean flow through kinetic and potential energy conversion, while the westward-propagating ISO cannot obtain energy through potential energy conversion. The surface air temperature and precipitation in South America are affected by the circulation and propagation corresponding to both types of ISO. The useful forecasting skills by the subseasonal-to-seasonal forecasting project for eastward- and westward-propagating types can reach to 17 days, while the potential forecasting skills improve to 20 and 19 days, respectively. Significance Statement The intraseasonal oscillation (ISO) has important effects on regional weather and climate, and we focus on the ISO over mid-high latitudes in the Southern Hemisphere, which has been paid little attention. We reveal two leading types of the mid-high-latitude ISO during austral summer, namely, the eastward- and westward-propagating types. Also, the characteristics and effects of the two types are explored. To understand their dynamical process, the geopotential height tendency and energy conversion are diagnosed. It is also found that the two ISO types can be predicted up to 17 days in advance by the subseasonal-to-seasonal project, which may provide guidance for the extended-range forecasts.

Characteristics of Tropical Convective Gravity Waves Resolved by ERA5 Reanalysis

Abstract The ERA5 reanalysis with hourly time steps and ∼30 km horizontal resolution resolves a substantially larger fraction of the gravity wave spectrum than its predecessors. Based on a representation of the two-sided zonal wavenumber–frequency spectrum, we show evidence of gravity wave signatures in a suite of atmospheric fields. Cross-spectrum analysis reveals (i) a substantial upward flux of geopotential for both eastward- and westward-propagating waves, (ii) an upward flux of westerly momentum in eastward-propagating waves and easterly momentum in westward-propagating waves, and (iii) anticyclonic rotation of the wind vector with time—all characteristics of vertically propagating gravity and inertio-gravity waves. Two-sided meridional wavenumber–frequency spectra, which are computed along individual meridians and then zonally averaged, exhibit characteristics similar to the spectra computed on latitude circles, indicating that these waves propagate in all directions. The three-dimensional structure of these waves is also documented in composites of the temperature field relative to grid-resolved, wave-induced downwelling events at individual reference grid points along the equator. It is shown that the waves radiate outward and upward relative to the respective reference grid points, and their amplitude decreases rapidly with time. Within the broad continuum of gravity wave phase speeds there are preferred values around ±49 and ±23 m s−1, the former associated with the first baroclinic mode in which the vertical velocity perturbations are of the same sign throughout the depth of the troposphere, and the latter with the second mode in which they are of opposing polarity in the lower and upper troposphere.

The Roles of Westward-Propagating Waves and the QBO in Limiting MJO Propagation

Abstract A recent study categorized the Madden–Julian oscillation (MJO) during boreal winter season into four types called stand, jump, slow, and fast MJO. This study focuses on the stand and jump MJO. Based on whether their convection penetrates the Maritime Continent (MC), stand and jump MJOs are seen as non-penetrating (NP) MJOs, while the other two are seen as eastward-penetrating (EP) MJOs. Results reveal the relative roles of the westward-propagating wave (WPW), as well as the QBO and ENSO, in limiting MJO propagation. Lack of the premoistening over the southern sea surface of the MC stops NP MJO from penetrating the MC. The active convection of the WPWs hinders the descending branch of the NP MJO circulation and therefore leads to the insufficient meridional advective moistening over the southern sea surface of the MC. The independent convection over the Pacific for jump MJOs is influenced by a combined effect of the QBO and ENSO. The tropopause instability induced by the MJO is found to significantly decouple from its convection over the Pacific in westerly QBO (QBOW) winters more than in easterly QBO (QBOE) winters. For jump MJOs, the independent convection over the central Pacific comes from local WPWs whose amplification and further development into deep convection are correlated to jump the MJOs’ decoupled tropopause instability. For stand MJOs, however, the seasonal-mean La Niña–like cool SST anomalies weaken the WPW activity over the central Pacific and confine WPWs within the western Pacific. Therefore, the decoupled tropopause instability of stand MJOs is out phase of WPWs and fails to induce an independent convection over the central Pacific.

Investigation of dominant traveling 10-day wave components using long-term MERRA-2 database

The eastward- and westward-traveling 10-day waves with zonal wavenumbers up to 6 from surface to the middle mesosphere during the recent 12 years from 2007 to 2018 are deduced from MERRA-2 data. On the basis of climatology study, the westward-propagating wave with zonal wave number 1 (W1) and eastward-propagating waves with zonal wave numbers 1 (E1) and 2 (E2) are identified as the dominant traveling ones. They are all active at mid- and high-latitudes above the troposphere and display notable month-to-month variations. The W1 and E2 waves are strong in the NH from December to March and in the SH from June to October, respectively, while the E1 wave is active in the SH from August to October and also in the NH from December to February. Further case study on E1 and E2 waves shows that their latitude–altitude structures are dependent on the transmission condition of the background atmosphere. The presence of these two waves in the stratosphere and mesosphere might have originated from the downward-propagating wave excited in the mesosphere by the mean flow instability, the upward-propagating wave from the troposphere, and/or in situ excited wave in the stratosphere. The two eastward waves can exert strong zonal forcing on the mean flow in the stratosphere and mesosphere in specific periods. Compared with E2 wave, the dramatic forcing from the E1 waves is located in the poleward regions.

The Influences of Convectively Coupled Kelvin Waves on Multiscale Rainfall Variability over the South China Sea and Maritime Continent in December 2016

ABSTRACTWe studied the scale interactions of the convectively coupled Kelvin waves (KWs) over the South China Sea (SCS) and Maritime Continent (MC) during December 2016. Three KWs were observed near the equator in this month while the Madden–Julian oscillation (MJO) was inactive. The impacts of these KWs on the rainfall variability of various time scales are diagnosed, including synoptic disturbances, diurnal cycle (DC), and the onset of the Australian monsoon. Four interaction events between the KWs and the westward-propagating waves over the off-equatorial regions were examined; two events led to KW enhancements and the other two contributed to the formation of a tropical depression/tropical cyclone. Over the KW convectively active region of the MC, the DC of precipitation was enhanced in major islands and neighboring oceans. Over the land, the DC hot spots were modulated depending on the background winds and the terrain effects. Over the ocean, the “coastal regime” of the DC appeared at specific coastal areas. Last, the Australian summer monsoon onset occurred with the passage of a KW, which provided favorable conditions of low-level westerlies and initial convection over southern MC and the Arafura Sea. This effect may be helped by the warm sea surface temperature anomalies associated with the La Niña condition of this month. The current results showcase that KWs and their associated scale interactions can provide useful references for weather monitoring and forecast of this region when the MJO is absent.

Semidiurnal solar tide differences between fall and spring transition times in the Northern Hemisphere

Abstract. We present a study of the semidiurnal solar tide (S2) during the fall and spring transition times in the Northern Hemisphere. The tides have been obtained from wind measurements provided by three meteor radars located at Andenes (69∘ N, 16∘ E), Juliusruh (54∘ N, 13∘ E) and Tavistock (42∘ N, 81∘ W). During the fall, S2 is characterized by a sudden and pronounced decrease occurring every year and at all height levels. The spring transition also shows a decrease in S2, but not sudden and that ascends from lower to higher altitudes during an interval of ∼ 15 to 40 days. To assess contributions of different semidiurnal tidal components, we have examined a 20-year free-run simulation by the Hamburg Model of the Neutral and Ionized Atmosphere (HAMMONIA). We found that the differences exhibited by the S2 tide between equinox times are mainly due to distinct behaviors of the migrating semidiurnal and the non-migrating westward-propagating wave number 1 tidal components (SW2 and SW1, respectively). Specifically, during the fall both SW2 and SW1 decrease, while during the springtime SW2 decreases but SW1 remains approximately constant or decreases only slightly. The decrease shown by SW1 during the fall occurs later than that of SW2 and S2, which indicates that the behavior of S2 is mainly driven by the migrating component. Nonetheless, the influence of SW1 is necessary to explain the behavior of S2 during the spring. In addition, a strong shift in the phase of S2 (of SW2 in the simulations) is also observed during the fall. Our meteor radar wind measurements show more gravity wave activity in the fall than during the spring, which might be indicating that the fall decrease is partly due to interactions between SW2 and gravity waves.

Climatology of the quasi-2-day waves observed in the MLS/Aura measurements (2005–2014)

The paper presents the climatology and interannual variability of both eastward- and westward-propagating ∼2-day waves (QTDW) observed in the MLS/Aura geopotential height data for a period of 10 full years (2005–2014). The climatology of the QTDWs has been studied in two steps: (i) by using average 2D-wavelet spectra both the dominant modes of variability and how these modes vary in time and space have been determined, and (ii) by applying a 2D decomposition procedure, where all planetary waves are simultaneously extracted from the data, the average global spatio-temporal distributions of all defined by the 2D-wavelet analysis modes have been obtained. It is found that the westward-propagating waves at mid-high latitudes have zonal wave numbers 2, 3 and 4 and are observed mainly in summer hemisphere. Two different types of eastward-propagating waves have been identified: (i) waves at mid-high latitudes with zonal wave numbers 2 and 3 observed in the winter hemisphere, and (ii) waves observed predominantly over the equator with zonal wave number 2, which do not have a well-defined seasonal variability but show some enhancement in both solstices. While the climatological features of the MLS/Aura QTDWs for the considered period are robust the interannual variations have to be adopted cautiously. The primary reason is that the length of the considered period of 10 years is not enough for finding clear variability pattern. The only long-term variability which appears to have some robustness is that of the W3 wave in the Southern Hemisphere where the influence of the solar cycle has been distinguished.

Multisite Remote Sensing for Tsunami-Induced Waves

In the 2011 Tohoku tsunamigenic earthquake, ionospheric anomalies generated by tsunami-induced gravity waves were observed by many types of instruments. Three digisondes and one Doppler receiver located in East Asia were applied to investigate the far-field ionospheric response to the westward-propagating gravity waves generated by the earthquake. Based on time–period spectrum analysis, oscillations between 20 and 36 min on the $fo\text{F}2$ (critical frequency of F2 layer) curves and Doppler variations of each observation location were identified. The horizontal group speed, generation time, and source location estimated with the ray-tracing method all indicated that the periodic disturbances recorded by the four radio systems were gravity waves induced by the tsunami following the 2011 Tohoku earthquake. The plasma frequency variations at five fixed altitudes in the ionospheric F2 layer over I-Cheon were used to investigate the vertical propagation of the tsunami-associated gravity waves. The measured phase progression in the vertical direction was opposite that of the energy transport, which further confirmed that the recorded waves were atmospheric gravity waves. The use of multisite remote sensing for examining tsunami-induced waves in the ionosphere may open new perspectives in oceanic monitoring and future tsunami warning systems.

Connection of sea level variability between the tropical western Pacific and the southern Indian Ocean during recent two decades

Based on the merged satellite altimeter data and in-situ observations, as well as a diagnosis of linear baroclinic Rossby wave solutions, this study analyzed the rapidly rise of sea level/sea surface height (SSH) in the tropical Pacific and Indian Oceans during recent two decades. Results show that the sea level rise signals in the tropical west Pacific and the southeast Indian Ocean are closely linked to each other through the pathways of oceanic waveguide within the Indonesian Seas in the form of thermocline adjustment. The sea level changes in the southeast Indian Ocean are strongly influenced by the low-frequency westward-propagating waves originated in the tropical Pacific, whereas those in the southwest Indian Ocean respond mainly to the local wind forcing. Analyses of the lead-lag correlation further reveal the different origins of interannual and interdecadal variabilities in the tropical Pacific. The interannual wave signals are dominated by the wind variability along the equatorial Pacific, which is associated with the El Nino-Southern Oscillation; whereas the interdecadal signals are driven mainly by the wind curl off the equatorial Pacific, which is closely related to the Pacific Decadal Oscillation.

Two-day wave observations over the middle and high latitudes in the NH and SH using COSMIC GPSRO measurements

The characteristics of the quasi-2-day wave (QTDW) in the upper stratosphere and lower mesospheric (USLM) altitudes over the northern hemisphere (NH) and southern hemisphere (SH) have been studied by using Global Positioning Radio Occultation (GPSRO) Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) temperature data from November 2006 to December 2010. We studied the seasonal, latitudinal, and interannual variability of the westward-propagating 2-day wave coincident with zonal wave number 3 in both hemispheres in the altitude range of 20–60km. The Lomb–Scargle periodogram (LSP) analysis indicates the dominance of the QTDW in the USLM in both the hemispheres. The observed amplitude of the wave is maximum during the winter season in middle and higher latitudes, with monthly mean amplitudes being as high as ∼8K. These amplitudes are found frequently during the late fall and peak to a maximum in the NH winter season. In the SH, QTDW amplitudes are found in the early winter season and appear till the early fall months. The QTDW varies from 49±3 to 48±1h in the NH and SH, respectively, with westward-propagating wave number 3. The amplitudes of the wave are large during winter in both the hemispheres, and, comparatively, the NH amplitudes are larger than those of the SH in higher latitudes.

The Continuous Mutual Evolution of Equatorial Waves and the Quasi-Biennial Oscillation of Zonal Flow in the Equatorial Stratosphere*

Abstract The continuous mutual evolution of equatorial waves and the background quasi-biennial oscillation (QBO) is demonstrated using daily NCEP–U.S. Department of Energy (DOE) reanalysis for the period from 1 January 1979 to 31 December 2010. Using a novel diagnostic technique, the phase speed, vertical tilting, and form stress of equatorial waves in the stratosphere are obtained continuously on a daily basis. The results indicate that, on top of a weak-amplitude annual-cycle signal, all of these wave properties have a pronounced QBO signal with a downward propagation that evolves continuously together with the background QBO. The analysis also highlights the potential role of wave-induced form stress in driving the QBO regime change. Dominant waves in the equatorial stratosphere propagate very slowly relative to the ground at all times, implying that their observed intrinsic phase speed evolution follows the background QBO nearly exactly but with opposite sign, as the established theory predicts. By revealing the continuous evolution of the form stress associated with the vertically tilted waves, the new diagnostic method also demonstrates the dominance of eastward-tilted, eastward-propagating waves contributing to a deceleration of easterly flow at high altitudes, which causes a downward propagation of the easterly flow signal. Similarly, the dominance of westward-tilted, westward-propagating waves acts to reverse westerly flow to easterly flow and causes a downward propagation of westerly flow signal. The results suggest that in addition to the wave-breaking processes, such continuously alternating downward transfer of westerly and easterly angular momentum by westward-tilted, westward-propagating waves and eastward-tilted, eastward-propagating waves contributes to the wave–mean flow interaction mechanism for the QBO.

Assessing model representations of stratospheric equatorial waves

Some westward‐propagating Rossby‐gravity waves and eastward Kelvin waves can travel up through the atmosphere following their formation in the tropical troposphere. Once they reach the stratosphere, these waves dissipate, releasing their energy. Known as stratospheric equatorial waves, these Rossby‐gravity and Kelvin waves are an important aspect driving the quasi‐biennial oscillation (QBO), a roughly monthly reversal, in the direction of the equatorial stratospheric winds. Similar to other atmospheric systems, such as the El Niño–Southern Oscillation or the North Atlantic Oscillation, the phase of the QBO affects global weather patterns, particularly in North America and western Europe.

The Transition to a Subtropical Jet Regime and Its Maintenance

Abstract An abrupt transition from a merged jet regime to a subtropical jet regime is analyzed using a two-layer modified quasigeostrophic (QG) spherical model. Unlike the common version of QG models, this model includes advection of the zonal mean momentum by the ageostrophic mean meridional circulation, allowing for a relatively realistic momentum balance in the tropics and subtropics. The merged jet is a single jet inside the Ferrel cell created by a merging of the subtropical and eddy-driven jets, and the subtropical jet is a mainly thermally driven jet at the Hadley cell edge. The maintenance of each type of jet depends on the dominant baroclinic modes. In the merged jet regime, the spectrum is dominated by intermediate-scale (wavenumbers 4–6) fast waves at the midlatitudes that grow close to the jet maximum. In the subtropical jet regime, the spectrum is dominated by long (wavenumbers 1–3) slow westward-propagating waves at high latitudes and somewhat weaker intermediate-scale slow waves at the midlatitudes. In the subtropical jet regime, waves equilibrate at weaker amplitudes than in the merged jet regime. A mechanism is found that explains why baroclinic instability is weaker in the subtropical jet regime, although the vertical shear of the mean flow is stronger, which has to do with the lower-level potential vorticity (PV) structure. The relevance of these results to the real atmosphere seams to hold in local zonal sections but not for the zonal mean.

A Multiscale Model for the Modulation and Rectification of the ITCZ

Abstract The authors introduce the modulation of the ITCZ equations (M-ITCZ), which describes the multiscale dynamics of the ITCZ on diurnal to monthly time scales in which mesoscale convectively coupled Rossby waves in the ITCZ are modulated by a large-scale gravity wave that is also generated by convection. Westward-propagating disturbances are observed to cause ITCZ breakup over the course of a few days, and the M-ITCZ meso-/planetary-scale coupled waves provide a mechanism for this interaction, thereby providing a framework to study the modulation and rectification of the Hadley circulation over long zonal length scales in the ITCZ. The authors consider examples of zonally symmetric heating profiles in the M-ITCZ system and generate a Hadley circulation consistent with the observed winds. Zonally localized heating creates a wind response throughout the tropics that is carried by a pair of zonally propagating gravity bores driving mean easterlies at the base and mean westerlies at the top of the troposphere. The bores carry low-temperature and upward velocity perturbations to the west of the heating and high-temperature and downward velocity perturbations to the east, making the westward-propagating branch favorable to convective triggering and the eastward-propagating branch favorable to convective suppression. The mesoscale dynamics of the M-ITCZ describe convectively forced, nonlinear Rossby waves propagating in the zonal winds created by the planetary-scale gravity wave. The authors suggest that convective coupling slows the westward-propagating gravity wave, thereby creating a coupled gravity–Rossby wave that is similar to the westward-propagating disturbances seen in the ITCZ.

Attributing Tropical Cyclogenesis to Equatorial Waves in the Western North Pacific

Abstract Tropical cyclogenesis is attributed to an equatorial wave when the filtered rainfall anomaly exceeds a threshold value at the genesis location. It is argued that 0 mm day−1 (simply requiring a positive anomaly) is too small a threshold because unrelated noise can produce a positive anomaly. A threshold of 6 mm day−1 is too large because two-thirds of storms would have no precursor disturbance. Between these extremes, consistent results are found for a range of thresholds from 2 to 4 mm day−1. Roughly twice as many tropical cyclones are attributed to tropical depression (TD)-type disturbances as to equatorial Rossby waves, mixed Rossby–gravity waves, or Kelvin waves. The influence of the Madden–Julian oscillation (MJO) is even smaller. The use of variables such as vorticity and vertical wind shear in other studies gives a larger contribution for the MJO. It is suggested that its direct influence on the rainfall in forming tropical cyclones is less than for other variables. The impacts of tropical cyclone–related precipitation anomalies are also presented. Tropical cyclones can contribute more than 20% of the warm-season rainfall and 50% of its total variance. The influence of tropical cyclones on the equatorial wave spectrum is generally small. The exception occurs in shorter-wavelength westward-propagating waves, for which tropical cyclones represent up to 27% of the variance. Tropical cyclones also significantly contaminate wave-filtered rainfall anomalies in their immediate vicinity. To mitigate this effect, the tropical cyclone–related anomalies were removed before filtering in this study.

Extratropical Rossby Waves in the Presence of Buoyancy Mixing

AbstractThe propagation of Rossby waves on a midlatitude β plane is investigated in the presence of density diffusion with the aid of linear hydrostatic theory. The search for wave solutions in a vertically bounded medium subject to horizontal (vertical) diffusion leads to an eigenvalue problem of second (fourth) order. Exact solutions of the problem are obtained for uniform background stratification (N), and approximate solutions are constructed for variable N using the Wentzel–Kramers–Brillouin method. Roots of the eigenvalue relations for free waves are found and discussed.The barotropic wave of adiabatic theory is also a solution of the eigenvalue problem as this is augmented with density diffusion in the horizontal or vertical direction. The barotropic wave is undamped as fluid parcels in the wave move only horizontally and are therefore insensitive to the vortex stretching induced by mixing. On the other hand, density diffusion modifies the properties of baroclinic waves of adiabatic theory. In the presence of horizontal diffusion the baroclinic modes are damped but their vertical structure remains unaltered. The ability of horizontal diffusion to damp baroclinic waves stems from its tendency to counteract the deformation of isopycnal surfaces caused by the passage of these waves. The damping rate increases (i) linearly with horizontal diffusivity and (ii) nonlinearly with horizontal wavenumber and mode number. In the presence of vertical diffusion the baroclinic waves suffer both damping and a change in vertical structure. In the long-wave limit the damping is critical (wave decay rate numerically equal to wave frequency) and increases as the square roots of vertical diffusivity and zonal wavenumber. Density diffusion in the horizontal or vertical direction reduces the amplitude of the phase speed of westward-propagating waves. Observational estimates of eddy diffusivities suggest that horizontal and vertical mixing strongly attenuates baroclinic waves in the ocean but that vertical mixing is too weak to notably modify the vertical structure of the gravest modes.

A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere

AbstractA global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.

Multi-scale Organization of Convection in a Global Numerical Simulation of the December 2006 MJO Event Using Explicit Moist Processes

Multi-scale convective organization in a Madden-Julian Oscillation (MJO) event that occurred during December 2006 and January 2007 was studied by global numerical experiments using explicit moist physics. The simulations successfully reproduced the eastward-propagating (∼5 m s-1) convective envelope of the MJO with a zonal scale of 5000-10,000 km, which included eastward-propagating (10-15 m s-1) disturbances (EPDs) and westward-propagating cloud clusters (CCs) with zonal scales of 1000-2000 km and O (100 km), respectively.The simulated EPDs were composed of CCs, with new clusters growing to the east of older ones. When the large-scale circulation associated with the MJO intensified, the EPDs formed well-organized squall-type clusters (rainbands). The dynamical structure of the simulated EPDs was reminiscent of moist Kelvin waves. Relevance of westward-propagating wave disturbances including cross-equatorial flow to convective organization in the EPDs was also suggested.