Search Results
You are looking at 1 - 10 of 15 items for :
- Author or Editor: Juliana Dias x
- Journal of the Atmospheric Sciences x
- Refine by Access: All Content x
Abstract
A number of studies suggest a two-way feedback between convectively coupled Kelvin waves (CCKWs) and the intertropical convergence zone (ITCZ). Viewed here as a proxy for deep convection, analysis of brightness temperature data reveals several aspects of these interdependencies. A wavenumber–frequency spectral analysis is applied to the satellite data in order to filter CCKWs. The ITCZ is characterized by a region of low brightness temperature and a proxy for both the ITCZ location and width are defined. The phase speed of CCKW data is determined using the Radon transform method. Linear regression techniques and probability density analysis are consistent with previous theoretical predictions and observational results. In particular, the fastest waves are found when the ITCZ is the farthest from the equator and the narrowest. Conversely, the slowest waves coincide with broad ITCZs that are located near the equator.
Abstract
A number of studies suggest a two-way feedback between convectively coupled Kelvin waves (CCKWs) and the intertropical convergence zone (ITCZ). Viewed here as a proxy for deep convection, analysis of brightness temperature data reveals several aspects of these interdependencies. A wavenumber–frequency spectral analysis is applied to the satellite data in order to filter CCKWs. The ITCZ is characterized by a region of low brightness temperature and a proxy for both the ITCZ location and width are defined. The phase speed of CCKW data is determined using the Radon transform method. Linear regression techniques and probability density analysis are consistent with previous theoretical predictions and observational results. In particular, the fastest waves are found when the ITCZ is the farthest from the equator and the narrowest. Conversely, the slowest waves coincide with broad ITCZs that are located near the equator.
Abstract
The dynamics of convectively coupled gravity waves traveling over a precipitating region are analyzed in an idealized model for the large-scale atmospheric circulation. The model is composed of a shallow water system coupled to an advection equation for moisture through the convection term, utilizing a quasi-equilibrium relaxation to moisture closure. Here the authors investigate the model in the strict quasi-equilibrium (SQE) of infinitely short relaxation time. This framework is applied to study the behavior of a disturbance propagating along a narrow precipitation band, similar to the intertropical convergence zone (ITCZ). For an ITCZ width on the order of the equatorial Rossby radius, Kelvin waves propagate at the moist gravity wave speed (about 15 m s−1), whereas for a narrow ITCZ, the propagation speed is comparable to the dry gravity wave (about 50 m s−1). It is also shown that a Kelvin wave propagating along a narrow precipitation region exhibits a meridional circulation that modulates the precipitation rate and affects the propagation speed of the wave.
Abstract
The dynamics of convectively coupled gravity waves traveling over a precipitating region are analyzed in an idealized model for the large-scale atmospheric circulation. The model is composed of a shallow water system coupled to an advection equation for moisture through the convection term, utilizing a quasi-equilibrium relaxation to moisture closure. Here the authors investigate the model in the strict quasi-equilibrium (SQE) of infinitely short relaxation time. This framework is applied to study the behavior of a disturbance propagating along a narrow precipitation band, similar to the intertropical convergence zone (ITCZ). For an ITCZ width on the order of the equatorial Rossby radius, Kelvin waves propagate at the moist gravity wave speed (about 15 m s−1), whereas for a narrow ITCZ, the propagation speed is comparable to the dry gravity wave (about 50 m s−1). It is also shown that a Kelvin wave propagating along a narrow precipitation region exhibits a meridional circulation that modulates the precipitation rate and affects the propagation speed of the wave.
Abstract
This paper presents a theoretical study of the effects of moist convection on geostrophic adjustment in an infinite channel. The governing equations correspond to a linearized shallow water system of equations for the atmosphere first vertical baroclinic mode, which is coupled to a vertically averaged moisture equation. The coupling is through a parameterization that represents precipitation. The transient behavior and final state of the flow initially at rest with active precipitation limited to half of the channel is investigated, both numerically and analytically. It is shown that an initial imbalance resulting from precipitation induces a circulation that dries out the nonprecipitating region and further enhances precipitation. This interaction between precipitation and dynamics leads to a sharper temperature gradient and stronger jet in the final state, when compared to the dry adjustment. Unlike in the dry case, the moist geostrophic adjustment cannot be entirely determined from the initial unbalanced flow, since it depends on the time scale for convection. Analytic approximations are derived in limits of both fast and slow convective adjustment time.
Abstract
This paper presents a theoretical study of the effects of moist convection on geostrophic adjustment in an infinite channel. The governing equations correspond to a linearized shallow water system of equations for the atmosphere first vertical baroclinic mode, which is coupled to a vertically averaged moisture equation. The coupling is through a parameterization that represents precipitation. The transient behavior and final state of the flow initially at rest with active precipitation limited to half of the channel is investigated, both numerically and analytically. It is shown that an initial imbalance resulting from precipitation induces a circulation that dries out the nonprecipitating region and further enhances precipitation. This interaction between precipitation and dynamics leads to a sharper temperature gradient and stronger jet in the final state, when compared to the dry adjustment. Unlike in the dry case, the moist geostrophic adjustment cannot be entirely determined from the initial unbalanced flow, since it depends on the time scale for convection. Analytic approximations are derived in limits of both fast and slow convective adjustment time.
Abstract
Space–time spectral analysis of tropical cloudiness data shows strong evidence that convectively coupled n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) occur primarily within the western/central Pacific Ocean. Spectral filtering also shows that MRG and EIG cloudiness patterns are antisymmetric with respect to the equator, and they propagate coherently toward the west and east, respectively, with periods between 3 and 5 days, in agreement with Matsuno’s linear shallow-water theory. In contrast to the spectral approach, in a companion paper it has been shown that empirical orthogonal functions (EOFs) of 2–6-day-filtered cloudiness data within the tropical Pacific Ocean also suggest an antisymmetric pattern, but with the leading EOFs implying a zonally standing but poleward-propagating oscillation, along with the associated tropospheric flow moving to the west. In the present paper, these two views are reconciled by applying an independent approach based on a tracking method to assess tropical convection organization. It is shown that, on average, two-thirds of MRG and EIG events develop independently of one another, and one-third of the events overlap in space and time. This analysis also verifies that MRG and EIG cloudiness fields tend to propagate meridionally away from the equator. It is demonstrated that the lack of zonal propagation implied from the EOF analysis is likely due to the interference between eastward- and westward-propagating disturbances. In addition, it is shown that the westward-propagating circulation associated with the leading EOF is consistent with the expected theoretical behavior of an interference between MRGs and EIGs.
Abstract
Space–time spectral analysis of tropical cloudiness data shows strong evidence that convectively coupled n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) occur primarily within the western/central Pacific Ocean. Spectral filtering also shows that MRG and EIG cloudiness patterns are antisymmetric with respect to the equator, and they propagate coherently toward the west and east, respectively, with periods between 3 and 5 days, in agreement with Matsuno’s linear shallow-water theory. In contrast to the spectral approach, in a companion paper it has been shown that empirical orthogonal functions (EOFs) of 2–6-day-filtered cloudiness data within the tropical Pacific Ocean also suggest an antisymmetric pattern, but with the leading EOFs implying a zonally standing but poleward-propagating oscillation, along with the associated tropospheric flow moving to the west. In the present paper, these two views are reconciled by applying an independent approach based on a tracking method to assess tropical convection organization. It is shown that, on average, two-thirds of MRG and EIG events develop independently of one another, and one-third of the events overlap in space and time. This analysis also verifies that MRG and EIG cloudiness fields tend to propagate meridionally away from the equator. It is demonstrated that the lack of zonal propagation implied from the EOF analysis is likely due to the interference between eastward- and westward-propagating disturbances. In addition, it is shown that the westward-propagating circulation associated with the leading EOF is consistent with the expected theoretical behavior of an interference between MRGs and EIGs.
Abstract
The dynamics of convectively coupled equatorial waves (CCEWs) is analyzed in an idealized model of the large-scale atmospheric circulation. The model is composed of a linear rotating shallow-water system with a variable equivalent height, or equivalent gravity wave speed, which varies in space. This model is based on the hypothesis that moist convection acts to remove convective instability, therefore modulating the equivalent height of a shallow-water system. Asymptotic solutions are derived in the case of a small perturbation around a constant coefficient, which is assumed to be a mean moist equivalent height derived from satellite observations. The first-order solutions correspond to the free normal modes of the linear shallow-water system and the second-order flow is derived solving a perturbation eigenvalue problem. The asymptotic solutions are documented in the case of a zonally varying equivalent height and for wavenumbers and frequencies that are consistent with observations of CCEWs. This analysis shows that the dynamics of the secondary divergence and its impact on the full divergence varies mode by mode. For instance, for a negative equivalent height anomaly, which is interpreted as a moister background, the secondary divergence is nearly in phase with the primary divergence in the case of Kelvin waves—in contrast to mixed Rossby–gravity waves where the secondary divergence acts to attenuate the primary divergence. While highly idealized, the modeled waves share some features with observations, providing a mechanism for the relationship between CCEWs phase speed, amplitude, and horizontal structure.
Abstract
The dynamics of convectively coupled equatorial waves (CCEWs) is analyzed in an idealized model of the large-scale atmospheric circulation. The model is composed of a linear rotating shallow-water system with a variable equivalent height, or equivalent gravity wave speed, which varies in space. This model is based on the hypothesis that moist convection acts to remove convective instability, therefore modulating the equivalent height of a shallow-water system. Asymptotic solutions are derived in the case of a small perturbation around a constant coefficient, which is assumed to be a mean moist equivalent height derived from satellite observations. The first-order solutions correspond to the free normal modes of the linear shallow-water system and the second-order flow is derived solving a perturbation eigenvalue problem. The asymptotic solutions are documented in the case of a zonally varying equivalent height and for wavenumbers and frequencies that are consistent with observations of CCEWs. This analysis shows that the dynamics of the secondary divergence and its impact on the full divergence varies mode by mode. For instance, for a negative equivalent height anomaly, which is interpreted as a moister background, the secondary divergence is nearly in phase with the primary divergence in the case of Kelvin waves—in contrast to mixed Rossby–gravity waves where the secondary divergence acts to attenuate the primary divergence. While highly idealized, the modeled waves share some features with observations, providing a mechanism for the relationship between CCEWs phase speed, amplitude, and horizontal structure.
Abstract
The relationship between n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) from Matsuno’s shallow-water theory on an equatorial beta plane is studied using statistics of satellite brightness temperature T b and dynamical fields from ERA-Interim data. Unlike other observed convectively coupled equatorial waves, which have spectral signals well separated into eastward and westward modes, there is a continuum of MRG–EIG power standing above the background that peaks near wavenumber 0. This continuum is also present in the signals of dry stratospheric MRGs. While hundreds of papers have been written on MRGs, very little work on EIGs has appeared in the literature to date. The authors attribute this to the fact that EIG circulations are much weaker than those of MRGs for a given amount of divergence, making them more difficult to observe even though they strongly modulate convection.
Empirical orthogonal function (EOF) and cross-spectral analysis of 2–6-day-filtered T b isolate zonally standing modes of synoptic-scale convection originally identified by Wallace in 1971. These display antisymmetric T b signals about the equator that propagate poleward with a period of around 4 days, along with westward-propagating MRG-like circulations that move through the T b patterns. Further analysis here and in Part II shows that these signatures are not artifacts of the EOF approach but result from a mixture of MRG or EIG modes occurring either in isolation or at the same time.
Abstract
The relationship between n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) from Matsuno’s shallow-water theory on an equatorial beta plane is studied using statistics of satellite brightness temperature T b and dynamical fields from ERA-Interim data. Unlike other observed convectively coupled equatorial waves, which have spectral signals well separated into eastward and westward modes, there is a continuum of MRG–EIG power standing above the background that peaks near wavenumber 0. This continuum is also present in the signals of dry stratospheric MRGs. While hundreds of papers have been written on MRGs, very little work on EIGs has appeared in the literature to date. The authors attribute this to the fact that EIG circulations are much weaker than those of MRGs for a given amount of divergence, making them more difficult to observe even though they strongly modulate convection.
Empirical orthogonal function (EOF) and cross-spectral analysis of 2–6-day-filtered T b isolate zonally standing modes of synoptic-scale convection originally identified by Wallace in 1971. These display antisymmetric T b signals about the equator that propagate poleward with a period of around 4 days, along with westward-propagating MRG-like circulations that move through the T b patterns. Further analysis here and in Part II shows that these signatures are not artifacts of the EOF approach but result from a mixture of MRG or EIG modes occurring either in isolation or at the same time.
Abstract
The organization of tropical convection is assessed through an object-based analysis of satellite brightness temperature data Tb , a proxy for convective activity. The analysis involves the detection of contiguous cloud regions (CCRs) in the three-dimensional space of latitude, longitude, and time where Tb falls below a given threshold. A range of thresholds is considered and only CCRs that satisfy a minimum size constraint are retained in the analysis. Various statistical properties of CCRs are documented including their zonal speed of propagation, which is estimated using a Radon transformation technique. Consistent with previous studies, a majority of CCRs are found to propagate westward, typically at speeds of around 15 m s−1, regardless of underlying Tb threshold. Most of these zonally propagating CCRs have lifetimes less than 2 days and zonal widths less than 800 km, implying aggregation of just a few individual mesoscale convective systems. This object-based perspective is somewhat different than that obtained in previous Fourier-based analyses, which primarily emphasize the organization of convection on synoptic and planetary scales via wave–convection coupling. To reconcile these contrasting views, an object-based data reconstruction is developed that objectively demonstrates how the spectral peaks of synoptic- to planetary-scale waves can be attributed to the organization of CCRs into larger-scale wave envelopes. A novel method based on the randomization of CCRs in physical space leads to an empirical background spectrum for organized tropical convection that does not rely on any smoothing in spectral space. Normalization by this background reveals spectral peaks associated with synoptic- and planetary-scale waves that are consistent with previous studies.
Abstract
The organization of tropical convection is assessed through an object-based analysis of satellite brightness temperature data Tb , a proxy for convective activity. The analysis involves the detection of contiguous cloud regions (CCRs) in the three-dimensional space of latitude, longitude, and time where Tb falls below a given threshold. A range of thresholds is considered and only CCRs that satisfy a minimum size constraint are retained in the analysis. Various statistical properties of CCRs are documented including their zonal speed of propagation, which is estimated using a Radon transformation technique. Consistent with previous studies, a majority of CCRs are found to propagate westward, typically at speeds of around 15 m s−1, regardless of underlying Tb threshold. Most of these zonally propagating CCRs have lifetimes less than 2 days and zonal widths less than 800 km, implying aggregation of just a few individual mesoscale convective systems. This object-based perspective is somewhat different than that obtained in previous Fourier-based analyses, which primarily emphasize the organization of convection on synoptic and planetary scales via wave–convection coupling. To reconcile these contrasting views, an object-based data reconstruction is developed that objectively demonstrates how the spectral peaks of synoptic- to planetary-scale waves can be attributed to the organization of CCRs into larger-scale wave envelopes. A novel method based on the randomization of CCRs in physical space leads to an empirical background spectrum for organized tropical convection that does not rely on any smoothing in spectral space. Normalization by this background reveals spectral peaks associated with synoptic- and planetary-scale waves that are consistent with previous studies.
Abstract
The intrusion of lower-stratospheric extratropical potential vorticity into the tropical upper troposphere in the weeks surrounding the occurrence of sudden stratospheric warmings (SSWs) is examined. The analysis reveals that SSW-related PV intrusions are significantly stronger, penetrate more deeply into the tropics, and exhibit distinct geographic distributions compared to their climatological counterparts. While climatological upper-tropospheric and lower-stratospheric (UTLS) PV intrusions are generally attributed to synoptic-scale Rossby wave breaking, it is found that SSW-related PV intrusions are governed by planetary-scale wave disturbances that deform the extratropical meridional PV gradient maximum equatorward. As these deformations unfold, planetary-scale wave breaking along the edge of the polar vortex extends deeply into the subtropical and tropical UTLS. In addition, the material PV deformations also reorganize the geographic structure of the UTLS waveguide, which alters where synoptic-scale waves break. In combination, these two intrusion mechanisms provide a robust explanation describing why displacement and split SSWs—or, more generally, anomalous stratospheric planetary wave events—produce intrusions with unique geographic distributions: displacement SSWs have a single PV intrusion maximum over the Pacific Ocean, while split SSWs have intrusion maxima over the Pacific and Indian Oceans. It is also shown that the two intrusion mechanisms involve distinct time scales of variability, and it is highlighted that they represent an instantaneous and direct link between the stratosphere and troposphere. This is in contrast to higher-latitude stratosphere–troposphere coupling that occurs indirectly via wave–mean flow feedbacks.
Abstract
The intrusion of lower-stratospheric extratropical potential vorticity into the tropical upper troposphere in the weeks surrounding the occurrence of sudden stratospheric warmings (SSWs) is examined. The analysis reveals that SSW-related PV intrusions are significantly stronger, penetrate more deeply into the tropics, and exhibit distinct geographic distributions compared to their climatological counterparts. While climatological upper-tropospheric and lower-stratospheric (UTLS) PV intrusions are generally attributed to synoptic-scale Rossby wave breaking, it is found that SSW-related PV intrusions are governed by planetary-scale wave disturbances that deform the extratropical meridional PV gradient maximum equatorward. As these deformations unfold, planetary-scale wave breaking along the edge of the polar vortex extends deeply into the subtropical and tropical UTLS. In addition, the material PV deformations also reorganize the geographic structure of the UTLS waveguide, which alters where synoptic-scale waves break. In combination, these two intrusion mechanisms provide a robust explanation describing why displacement and split SSWs—or, more generally, anomalous stratospheric planetary wave events—produce intrusions with unique geographic distributions: displacement SSWs have a single PV intrusion maximum over the Pacific Ocean, while split SSWs have intrusion maxima over the Pacific and Indian Oceans. It is also shown that the two intrusion mechanisms involve distinct time scales of variability, and it is highlighted that they represent an instantaneous and direct link between the stratosphere and troposphere. This is in contrast to higher-latitude stratosphere–troposphere coupling that occurs indirectly via wave–mean flow feedbacks.
Abstract
The exponential increase in precipitation with increasing column saturation fraction (CSF) is used to investigate the role of moisture in convective coupling. This simple empirical relationship between precipitation and CSF is shown to capture nearly all MJO-related variability in TRMM precipitation, ~80% of equatorial Rossby wave–related variability, and ~75% of east Pacific easterly wave–related variability. In contrast, this empirical relationship only captures roughly half of TRMM precipitation variability associated with Kelvin waves, African easterly waves, and mixed Rossby–gravity waves, suggesting coupling mechanisms other than moisture are playing leading roles in these phenomena. These latter phenomena have strong adiabatically forced vertical motions that could reduce static stability and convective inhibition while simultaneously moistening, creating a more favorable convective environment. Cross-spectra of precipitation and column-integrated dry static energy show enhanced coherence and an out-of-phase relationship in the Kelvin wave, mixed Rossby–gravity wave, and eastward inertio-gravity wave bands, supporting this narrative. The cooperative modulation of precipitation by moisture and temperature anomalies is shown to shorten the convective adjustment time scale (i.e., time scale by which moisture and precipitation are relaxed toward their “background” state) of these phenomena. Speeding the removal of moisture anomalies relative to that of temperature anomalies may allow the latter to assume a more important role in driving moist static energy fluctuations, helping promote the gravity wave character of these phenomena.
Abstract
The exponential increase in precipitation with increasing column saturation fraction (CSF) is used to investigate the role of moisture in convective coupling. This simple empirical relationship between precipitation and CSF is shown to capture nearly all MJO-related variability in TRMM precipitation, ~80% of equatorial Rossby wave–related variability, and ~75% of east Pacific easterly wave–related variability. In contrast, this empirical relationship only captures roughly half of TRMM precipitation variability associated with Kelvin waves, African easterly waves, and mixed Rossby–gravity waves, suggesting coupling mechanisms other than moisture are playing leading roles in these phenomena. These latter phenomena have strong adiabatically forced vertical motions that could reduce static stability and convective inhibition while simultaneously moistening, creating a more favorable convective environment. Cross-spectra of precipitation and column-integrated dry static energy show enhanced coherence and an out-of-phase relationship in the Kelvin wave, mixed Rossby–gravity wave, and eastward inertio-gravity wave bands, supporting this narrative. The cooperative modulation of precipitation by moisture and temperature anomalies is shown to shorten the convective adjustment time scale (i.e., time scale by which moisture and precipitation are relaxed toward their “background” state) of these phenomena. Speeding the removal of moisture anomalies relative to that of temperature anomalies may allow the latter to assume a more important role in driving moist static energy fluctuations, helping promote the gravity wave character of these phenomena.
Abstract
The composite structure of the Madden–Julian oscillation (MJO) has long been known to feature pronounced Rossby gyres in the subtropical upper troposphere, whose existence can be interpreted as the forced response to convective heating anomalies in the presence of a subtropical westerly jet. The question of interest here is whether these forced gyre circulations have any subsequent effects on divergence patterns in the tropics and the Kelvin-mode component of the MJO. A nonlinear spherical shallow water model is used to investigate how the introduction of different background jet profiles affects the model’s steady-state response to an imposed MJO-like stationary thermal forcing. Results show that a stronger jet leads to a stronger Kelvin-mode response in the tropics up to a critical jet speed, along with stronger divergence anomalies in the vicinity of the forcing. To understand this behavior, additional calculations are performed in which a localized vorticity forcing is imposed in the extratropics, without any thermal forcing in the tropics. The response is once again seen to include pronounced equatorial Kelvin waves, provided the jet is of sufficient amplitude. A detailed analysis of the vorticity budget reveals that the zonal-mean zonal wind shear plays a key role in amplifying the Kelvin-mode divergent winds near the equator, with the effects of nonlinearities being of negligible importance. These results help to explain why the MJO tends to be strongest during boreal winter when the Indo-Pacific jet is typically at its strongest.
Significance Statement
The MJO is a planetary-scale convectively coupled equatorial disturbance that serves as a primary source of atmospheric predictability on intraseasonal time scales (30–90 days). Due to its dominance and spontaneous recurrence, the MJO has a significant global impact, influencing hurricanes in the tropics, storm tracks, and atmosphere blocking events in the midlatitudes, and even weather systems near the poles. Despite steady improvements in subseasonal-to-seasonal (S2S) forecast models, the MJO prediction skill has still not reached its maximum potential. The root of this challenge is partly due to our lack of understanding of how the MJO interacts with the background mean flow. In this work, we use a simple one-layer atmospheric model with idealized heating and vorticity sources to understand the impact of the subtropical jet on the MJO amplitude and its horizontal structure.
Abstract
The composite structure of the Madden–Julian oscillation (MJO) has long been known to feature pronounced Rossby gyres in the subtropical upper troposphere, whose existence can be interpreted as the forced response to convective heating anomalies in the presence of a subtropical westerly jet. The question of interest here is whether these forced gyre circulations have any subsequent effects on divergence patterns in the tropics and the Kelvin-mode component of the MJO. A nonlinear spherical shallow water model is used to investigate how the introduction of different background jet profiles affects the model’s steady-state response to an imposed MJO-like stationary thermal forcing. Results show that a stronger jet leads to a stronger Kelvin-mode response in the tropics up to a critical jet speed, along with stronger divergence anomalies in the vicinity of the forcing. To understand this behavior, additional calculations are performed in which a localized vorticity forcing is imposed in the extratropics, without any thermal forcing in the tropics. The response is once again seen to include pronounced equatorial Kelvin waves, provided the jet is of sufficient amplitude. A detailed analysis of the vorticity budget reveals that the zonal-mean zonal wind shear plays a key role in amplifying the Kelvin-mode divergent winds near the equator, with the effects of nonlinearities being of negligible importance. These results help to explain why the MJO tends to be strongest during boreal winter when the Indo-Pacific jet is typically at its strongest.
Significance Statement
The MJO is a planetary-scale convectively coupled equatorial disturbance that serves as a primary source of atmospheric predictability on intraseasonal time scales (30–90 days). Due to its dominance and spontaneous recurrence, the MJO has a significant global impact, influencing hurricanes in the tropics, storm tracks, and atmosphere blocking events in the midlatitudes, and even weather systems near the poles. Despite steady improvements in subseasonal-to-seasonal (S2S) forecast models, the MJO prediction skill has still not reached its maximum potential. The root of this challenge is partly due to our lack of understanding of how the MJO interacts with the background mean flow. In this work, we use a simple one-layer atmospheric model with idealized heating and vorticity sources to understand the impact of the subtropical jet on the MJO amplitude and its horizontal structure.
