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Abstract
The theory of empirical orthogonal functions (EOFs) is generalized in the context of normal modes on unidirectional sheared flows, at first using small disturbance to a monotonic potential vorticity basic state. A wave function is introduced (so called because of a partial analogy with quantum mechanical wave function), via the pseudomomentum, and is used to define the covariance matrix needed in an EOF analysis. The resulting new formalism comprises a fundamental, simpler and more physically insightful, version of EOF theory: it allows empirical reconstruction of the normal modes excited in an atmospheric time series, their respective variances, and phase speed relationship. This new approach permits quantitative and qualitative discussions of the underlying wave mechanisms present in a sheared flow. The theory is given for a hierarchy of models starting with the linearized quasigeostrophic equations. The extent to which these concepts carry over to nonlinear finite-amplitude disturbance is investigated. Included in these considerations are the nonlinear primitive equations in the hydrostatic approximation. The method is applied to 24 winters of the NMC dataset. The empirical results show the presence in the upper troposphere of normal modes, which oscillate in a statistical sense with their theoretically predicted natural frequencies. The normal modes are observed too with divergence e-folding times ranging between 2.5 and 4.5 days. The empirical normal-mode spectrum splits into a continuous and a discrete spectrum with oscillations of less than and greater than two weeks, respectively. The discrete spectrum is divided in forced meridional monopoles and meridional dipoles. In particular, the dipole with zonal wavenumber 2 shows a strong amplitude in phase space of the generalized EOF description for the North Atlantic blocking weather regimes.
Abstract
The theory of empirical orthogonal functions (EOFs) is generalized in the context of normal modes on unidirectional sheared flows, at first using small disturbance to a monotonic potential vorticity basic state. A wave function is introduced (so called because of a partial analogy with quantum mechanical wave function), via the pseudomomentum, and is used to define the covariance matrix needed in an EOF analysis. The resulting new formalism comprises a fundamental, simpler and more physically insightful, version of EOF theory: it allows empirical reconstruction of the normal modes excited in an atmospheric time series, their respective variances, and phase speed relationship. This new approach permits quantitative and qualitative discussions of the underlying wave mechanisms present in a sheared flow. The theory is given for a hierarchy of models starting with the linearized quasigeostrophic equations. The extent to which these concepts carry over to nonlinear finite-amplitude disturbance is investigated. Included in these considerations are the nonlinear primitive equations in the hydrostatic approximation. The method is applied to 24 winters of the NMC dataset. The empirical results show the presence in the upper troposphere of normal modes, which oscillate in a statistical sense with their theoretically predicted natural frequencies. The normal modes are observed too with divergence e-folding times ranging between 2.5 and 4.5 days. The empirical normal-mode spectrum splits into a continuous and a discrete spectrum with oscillations of less than and greater than two weeks, respectively. The discrete spectrum is divided in forced meridional monopoles and meridional dipoles. In particular, the dipole with zonal wavenumber 2 shows a strong amplitude in phase space of the generalized EOF description for the North Atlantic blocking weather regimes.
Abstract
A new time invariant of the shallow-water model on the f plane for an isolated distribution of vorticity is obtained. The physical interpretation of the new invariant and its relation to past studies is discussed. It corresponds to a global nonlinear geostrophic balance of the localized distribution of vorticity, and defines a manifold in spectral space where the inertial frequency is filtered out exactly for all time. The author argues that if the initial distribution of vorticity is not on this manifold, it is not in balance. Thus, an exact realization of a slow manifold generated by a number of finite constraints is obtained. The new time invariant is obtained with no assumption on the Froude number, the Rossby number, and the amplitude characterizing the distribution of vorticity.
Abstract
A new time invariant of the shallow-water model on the f plane for an isolated distribution of vorticity is obtained. The physical interpretation of the new invariant and its relation to past studies is discussed. It corresponds to a global nonlinear geostrophic balance of the localized distribution of vorticity, and defines a manifold in spectral space where the inertial frequency is filtered out exactly for all time. The author argues that if the initial distribution of vorticity is not on this manifold, it is not in balance. Thus, an exact realization of a slow manifold generated by a number of finite constraints is obtained. The new time invariant is obtained with no assumption on the Froude number, the Rossby number, and the amplitude characterizing the distribution of vorticity.
Abstract
Using the homogenized Canadian historical daily surface air temperature (SAT) for 210 relatively evenly distributed stations across Canada, the lagged composites and probability of the above- and below-normal SAT in Canada for different phases of the Madden–Julian oscillation (MJO) in the winter season are analyzed. Significant positive SAT anomalies and high probability of above-normal events in the central and eastern Canada are found 5–15 days following MJO phase 3, which corresponds to an enhanced precipitation over the Indian Ocean and Maritime Continent and a reduced convective activity near the tropical central Pacific. On the other hand, a positive SAT anomaly appears over a large part of northern and northeastern Canada about 5–15 days after the MJO is detected in phase 7. An analysis of the evolution of the 500-hPa geopotential height and sea level pressure anomalies indicates that the Canadian SAT anomaly is a result of a Rossby wave train associated with the tropical convection anomaly of the MJO. Hence, the MJO phase provides useful information for the extended-range forecast of Canadian winter surface air temperature. This result also provides an important reference for numerical model verifications.
Abstract
Using the homogenized Canadian historical daily surface air temperature (SAT) for 210 relatively evenly distributed stations across Canada, the lagged composites and probability of the above- and below-normal SAT in Canada for different phases of the Madden–Julian oscillation (MJO) in the winter season are analyzed. Significant positive SAT anomalies and high probability of above-normal events in the central and eastern Canada are found 5–15 days following MJO phase 3, which corresponds to an enhanced precipitation over the Indian Ocean and Maritime Continent and a reduced convective activity near the tropical central Pacific. On the other hand, a positive SAT anomaly appears over a large part of northern and northeastern Canada about 5–15 days after the MJO is detected in phase 7. An analysis of the evolution of the 500-hPa geopotential height and sea level pressure anomalies indicates that the Canadian SAT anomaly is a result of a Rossby wave train associated with the tropical convection anomaly of the MJO. Hence, the MJO phase provides useful information for the extended-range forecast of Canadian winter surface air temperature. This result also provides an important reference for numerical model verifications.
Abstract
The theory of empirical normal modes (ENMs) for a shallow water fluid is developed. ENMs are basis functions that both have the statistical properties of empirical orthogonal functions (EOFs) and the dynamical properties of normal modes. In fact, ENMs are obtained in a similar manner as EOFs but with the use of a quadratic form instead of the Euclidean norm. This quadratic form is a global invariant, the wave activity, of the linearized equations about a basic state. A general formulation is proposed for calculating normal modes from a generalized hermitian problem, even when the basic state is not zonal.
The projection coefficients of the flow onto a few leading ENWs generally have a more monochromatic behavior than that obtained for EOFS, which give them an intrinsically more predictable character. This property is illustrated by numerical experiments using the shallow water model on the sphere. It is shown, in particular, that the ENM coefficients, when used as predictors in a statistical linear model, provide better predictions of the behavior of the shallow water atmosphere than EOF coefficients. It is also shown that the choice of the basic state itself is crucial.
Abstract
The theory of empirical normal modes (ENMs) for a shallow water fluid is developed. ENMs are basis functions that both have the statistical properties of empirical orthogonal functions (EOFs) and the dynamical properties of normal modes. In fact, ENMs are obtained in a similar manner as EOFs but with the use of a quadratic form instead of the Euclidean norm. This quadratic form is a global invariant, the wave activity, of the linearized equations about a basic state. A general formulation is proposed for calculating normal modes from a generalized hermitian problem, even when the basic state is not zonal.
The projection coefficients of the flow onto a few leading ENWs generally have a more monochromatic behavior than that obtained for EOFS, which give them an intrinsically more predictable character. This property is illustrated by numerical experiments using the shallow water model on the sphere. It is shown, in particular, that the ENM coefficients, when used as predictors in a statistical linear model, provide better predictions of the behavior of the shallow water atmosphere than EOF coefficients. It is also shown that the choice of the basic state itself is crucial.
Abstract
The theory of empirical normal modes (ENMs) is adapted to diagnose gravity waves generated by a relatively high-resolution numerical model solving the primitive equations. The ENM approach is based on the principal component analysis (which consists of finding the most efficient basis explaining the variance of a time series), except that it takes advantage of wave-activity conservation laws. In the present work, the small-amplitude version of the pseudoenergy is used to extract from data quasi-monochromatic three-dimensional empirical modes that describe atmospheric wave activity. The spatial distributions of these quasi-monochromatic modes are identical to the normal modes of the linearized primitive equations when the underlying dynamics can be described with a stochastic linear and forced model, thus establishing a bridge between statistics and dynamics. This diagnostic method is used to study inertia–gravity wave generation, propagation, transience, and breaking over the Rockies, the North Pacific, and Central America in the troposphere–stratosphere–mesosphere Geophysical Fluid Dynamics Laboratory SKYHI general circulation model at a resolution of 1° of latitude by 1.2° of longitude. Besides the action of mountains in exciting orographic waves, inertia–gravity wave activity has been found to be generated at the jet stream level as a possible consequence of a sustained nonlinear and ageostrophic flow. In the tropical region of the model (Central America), the inertia–gravity wave source mechanism produced mainly waves with a westward vertical tilt. A significant proportion of these inertia–gravity waves was able to reach the model mesosphere without much dissipation and absorption.
Abstract
The theory of empirical normal modes (ENMs) is adapted to diagnose gravity waves generated by a relatively high-resolution numerical model solving the primitive equations. The ENM approach is based on the principal component analysis (which consists of finding the most efficient basis explaining the variance of a time series), except that it takes advantage of wave-activity conservation laws. In the present work, the small-amplitude version of the pseudoenergy is used to extract from data quasi-monochromatic three-dimensional empirical modes that describe atmospheric wave activity. The spatial distributions of these quasi-monochromatic modes are identical to the normal modes of the linearized primitive equations when the underlying dynamics can be described with a stochastic linear and forced model, thus establishing a bridge between statistics and dynamics. This diagnostic method is used to study inertia–gravity wave generation, propagation, transience, and breaking over the Rockies, the North Pacific, and Central America in the troposphere–stratosphere–mesosphere Geophysical Fluid Dynamics Laboratory SKYHI general circulation model at a resolution of 1° of latitude by 1.2° of longitude. Besides the action of mountains in exciting orographic waves, inertia–gravity wave activity has been found to be generated at the jet stream level as a possible consequence of a sustained nonlinear and ageostrophic flow. In the tropical region of the model (Central America), the inertia–gravity wave source mechanism produced mainly waves with a westward vertical tilt. A significant proportion of these inertia–gravity waves was able to reach the model mesosphere without much dissipation and absorption.
Abstract
Previous studies have shown that the Madden–Julian oscillation (MJO) has a global impact that may provide an important source of skill for subseasonal predictions. The extratropical response was found to be the strongest when the tropical diabatic heating has a dipole structure with convection anomaly centers of opposite sign in the eastern Indian Ocean and the western Pacific. A positive (negative) MJO dipole heating refers to that with heating (cooling) in the eastern Indian Ocean and cooling (heating) in the western Pacific. In this study, two aspects of the extratropical response to the MJO are examined: 1) nonlinearity, which answers the question of whether the response to a positive MJO dipole heating is the mirror image of that to a negative MJO, and 2) sensitivity to the initial state, which explores the dependence of the extratropical response on the initial condition of the westerly jet.
Ensemble integrations using a primitive-equation global atmospheric circulation model are performed with anomalous tropical thermal forcings that resemble a positive MJO (+MJO) and a negative MJO (−MJO). The response in the first week is largely linear. After that, significant asymmetry is found between the response in the positive MJO and the negative MJO. The 500-hPa negative geopotential height response in the North Pacific of the −MJO run is located about 30° east of the positive height response of the +MJO run. There is also an eastward shift of the extratropical wave train in the Pacific–North American region. This simulated nonlinearity is in agreement with the observations. The two leading response patterns among the ensemble members are identified by an empirical orthogonal function (EOF) analysis. EOF1 represents an eastward shift of the wave train, which is positively correlated with strengthening of the East Asian subtropical upper-troposphere westerly jet in the initial condition. On the other hand, EOF2 represents an amplification of the response, which is associated with a southward shift of the westerly jet in the initial state.
Abstract
Previous studies have shown that the Madden–Julian oscillation (MJO) has a global impact that may provide an important source of skill for subseasonal predictions. The extratropical response was found to be the strongest when the tropical diabatic heating has a dipole structure with convection anomaly centers of opposite sign in the eastern Indian Ocean and the western Pacific. A positive (negative) MJO dipole heating refers to that with heating (cooling) in the eastern Indian Ocean and cooling (heating) in the western Pacific. In this study, two aspects of the extratropical response to the MJO are examined: 1) nonlinearity, which answers the question of whether the response to a positive MJO dipole heating is the mirror image of that to a negative MJO, and 2) sensitivity to the initial state, which explores the dependence of the extratropical response on the initial condition of the westerly jet.
Ensemble integrations using a primitive-equation global atmospheric circulation model are performed with anomalous tropical thermal forcings that resemble a positive MJO (+MJO) and a negative MJO (−MJO). The response in the first week is largely linear. After that, significant asymmetry is found between the response in the positive MJO and the negative MJO. The 500-hPa negative geopotential height response in the North Pacific of the −MJO run is located about 30° east of the positive height response of the +MJO run. There is also an eastward shift of the extratropical wave train in the Pacific–North American region. This simulated nonlinearity is in agreement with the observations. The two leading response patterns among the ensemble members are identified by an empirical orthogonal function (EOF) analysis. EOF1 represents an eastward shift of the wave train, which is positively correlated with strengthening of the East Asian subtropical upper-troposphere westerly jet in the initial condition. On the other hand, EOF2 represents an amplification of the response, which is associated with a southward shift of the westerly jet in the initial state.
Abstract
In the second phase of the Canadian Historical Forecasting Project (HFP2), four global atmospheric general circulation models (GCMs) were used to perform seasonal forecasts over the period of 1969–2003. Little predictive skill was found from the uncalibrated GCM ensemble seasonal predictions for the Canadian winter precipitation. This study is an effort to improve the precipitation forecasts through a postprocessing approach.
Canadian winter precipitation is significantly influenced by two of the most important atmospheric large-scale patterns: the Pacific–North American pattern (PNA) and the North Atlantic Oscillation (NAO). The time variations of these two patterns were found to be significantly correlated with those of the leading singular value decomposition (SVD) modes that relate the ensemble mean forecast 500-mb geopotential height over the Northern Hemisphere and the tropical Pacific SST in the previous month (November). A statistical approach to correct the ensemble forecasts was formulated based on the regression of the model’s leading forced SVD patterns and the observed seasonal mean precipitation. The performance of the corrected forecasts was assessed by comparing its cross-validated skill with that of the original GCM ensemble mean forecasts. The results show that the corrected forecasts predict the Canadian winter precipitation with statistically significant skill over the southern prairies and a large area of Québec–Ontario.
Abstract
In the second phase of the Canadian Historical Forecasting Project (HFP2), four global atmospheric general circulation models (GCMs) were used to perform seasonal forecasts over the period of 1969–2003. Little predictive skill was found from the uncalibrated GCM ensemble seasonal predictions for the Canadian winter precipitation. This study is an effort to improve the precipitation forecasts through a postprocessing approach.
Canadian winter precipitation is significantly influenced by two of the most important atmospheric large-scale patterns: the Pacific–North American pattern (PNA) and the North Atlantic Oscillation (NAO). The time variations of these two patterns were found to be significantly correlated with those of the leading singular value decomposition (SVD) modes that relate the ensemble mean forecast 500-mb geopotential height over the Northern Hemisphere and the tropical Pacific SST in the previous month (November). A statistical approach to correct the ensemble forecasts was formulated based on the regression of the model’s leading forced SVD patterns and the observed seasonal mean precipitation. The performance of the corrected forecasts was assessed by comparing its cross-validated skill with that of the original GCM ensemble mean forecasts. The results show that the corrected forecasts predict the Canadian winter precipitation with statistically significant skill over the southern prairies and a large area of Québec–Ontario.
Abstract
Data for 39 winters are used to compute the potential vorticity (PV) budget on the θ = 315 K isentropic surface over the Northern Hemisphere. The object is to compare the mechanisms that maintain the PV balance during normal winters with those that maintain the balance during winters with anomalies of the North Atlantic Oscillation (NAO) and Pacific–North American (PNA) types. On an isentropic surface that does not intersect the ground, which is usually the case for the 315 K surface, the mean seasonal flow must be such as to maintain a simple local balance between the diabatic and frictional sources/sinks of PV, the isentropic advection of PV by the mean seasonal flow, and the mean seasonal PV advection by the subseasonal transients.
The climatology over the 39 winters shows that the main positive PV centers over the east coasts of Asia and Canada are maintained through a three-way balance among the upstream diabatic/frictional sources of PV, the PV advection by the mean seasonal flow, and that by the subseasonal transients. The transients with periods between 2 and 10 days and those with periods between 10 and 90 days are found to contribute about equally to the PV balance. The PV balance of NAO and PNA winter anomalies reveals that the PV advection by the subseasonal transients more systematically opposes the advection by the seasonal mean flow, so that the local PV source term is proportionately much less important than it is in the maintenance of climatological PV centers.
The calculations were also made on the θ = 350 K and 450 K isentropes. The results are presented only briefly to highlight the main similarities and differences with those obtained at 315 K.
Abstract
Data for 39 winters are used to compute the potential vorticity (PV) budget on the θ = 315 K isentropic surface over the Northern Hemisphere. The object is to compare the mechanisms that maintain the PV balance during normal winters with those that maintain the balance during winters with anomalies of the North Atlantic Oscillation (NAO) and Pacific–North American (PNA) types. On an isentropic surface that does not intersect the ground, which is usually the case for the 315 K surface, the mean seasonal flow must be such as to maintain a simple local balance between the diabatic and frictional sources/sinks of PV, the isentropic advection of PV by the mean seasonal flow, and the mean seasonal PV advection by the subseasonal transients.
The climatology over the 39 winters shows that the main positive PV centers over the east coasts of Asia and Canada are maintained through a three-way balance among the upstream diabatic/frictional sources of PV, the PV advection by the mean seasonal flow, and that by the subseasonal transients. The transients with periods between 2 and 10 days and those with periods between 10 and 90 days are found to contribute about equally to the PV balance. The PV balance of NAO and PNA winter anomalies reveals that the PV advection by the subseasonal transients more systematically opposes the advection by the seasonal mean flow, so that the local PV source term is proportionately much less important than it is in the maintenance of climatological PV centers.
The calculations were also made on the θ = 350 K and 450 K isentropes. The results are presented only briefly to highlight the main similarities and differences with those obtained at 315 K.
Abstract
The output of two global atmospheric models participating in the second phase of the Canadian Historical Forecasting Project (HFP2) is utilized to assess the forecast skill of the Madden–Julian oscillation (MJO). The two models are the third generation of the general circulation model (GCM3) of the Canadian Centre for Climate Modeling and Analysis (CCCma) and the Global Environmental Multiscale (GEM) model of Recherche en Prévision Numérique (RPN). Space–time spectral analysis of the daily precipitation in near-equilibrium integrations reveals that GEM has a better representation of the convectively coupled equatorial waves including the MJO, Kelvin, equatorial Rossby (ER), and mixed Rossby–gravity (MRG) waves. An objective of this study is to examine how the MJO forecast skill is influenced by the model’s ability in representing the convectively coupled equatorial waves.
The observed MJO signal is measured by a bivariate index that is obtained by projecting the combined fields of the 15°S–15°N meridionally averaged precipitation rate and the zonal winds at 850 and 200 hPa onto the two leading empirical orthogonal function (EOF) structures as derived using the same meridionally averaged variables following a similar approach used recently by Wheeler and Hendon. The forecast MJO index, on the other hand, is calculated by projecting the forecast variables onto the same two EOFs.
With the HFP2 hindcast output spanning 35 yr, for the first time the MJO forecast skill of dynamical models is assessed over such a long time period with a significant and robust result. The result shows that the GEM model produces a significantly better level of forecast skill for the MJO in the first 2 weeks. The difference is larger in Northern Hemisphere winter than in summer, when the correlation skill score drops below 0.50 at a lead time of 10 days for GEM whereas it is at 6 days for GCM3. At lead times longer than about 15 days, GCM3 performs slightly better. There are some features that are common for the two models. The forecast skill is better in winter than in summer. Forecasts initialized with a large amplitude for the MJO are found to be more skillful than those with a weak MJO signal in the initial conditions. The forecast skill is dependent on the phase of the MJO at the initial conditions. Forecasts initialized with an MJO that has an active convection in tropical Africa and the Indian Ocean sector have a better level of forecast skill than those initialized with a different phase of the MJO.
Abstract
The output of two global atmospheric models participating in the second phase of the Canadian Historical Forecasting Project (HFP2) is utilized to assess the forecast skill of the Madden–Julian oscillation (MJO). The two models are the third generation of the general circulation model (GCM3) of the Canadian Centre for Climate Modeling and Analysis (CCCma) and the Global Environmental Multiscale (GEM) model of Recherche en Prévision Numérique (RPN). Space–time spectral analysis of the daily precipitation in near-equilibrium integrations reveals that GEM has a better representation of the convectively coupled equatorial waves including the MJO, Kelvin, equatorial Rossby (ER), and mixed Rossby–gravity (MRG) waves. An objective of this study is to examine how the MJO forecast skill is influenced by the model’s ability in representing the convectively coupled equatorial waves.
The observed MJO signal is measured by a bivariate index that is obtained by projecting the combined fields of the 15°S–15°N meridionally averaged precipitation rate and the zonal winds at 850 and 200 hPa onto the two leading empirical orthogonal function (EOF) structures as derived using the same meridionally averaged variables following a similar approach used recently by Wheeler and Hendon. The forecast MJO index, on the other hand, is calculated by projecting the forecast variables onto the same two EOFs.
With the HFP2 hindcast output spanning 35 yr, for the first time the MJO forecast skill of dynamical models is assessed over such a long time period with a significant and robust result. The result shows that the GEM model produces a significantly better level of forecast skill for the MJO in the first 2 weeks. The difference is larger in Northern Hemisphere winter than in summer, when the correlation skill score drops below 0.50 at a lead time of 10 days for GEM whereas it is at 6 days for GCM3. At lead times longer than about 15 days, GCM3 performs slightly better. There are some features that are common for the two models. The forecast skill is better in winter than in summer. Forecasts initialized with a large amplitude for the MJO are found to be more skillful than those with a weak MJO signal in the initial conditions. The forecast skill is dependent on the phase of the MJO at the initial conditions. Forecasts initialized with an MJO that has an active convection in tropical Africa and the Indian Ocean sector have a better level of forecast skill than those initialized with a different phase of the MJO.
Abstract
A long integration of a primitive equation dry atmospheric model with time-independent forcing under boreal winter conditions is analyzed. A variety of techniques such as time filtering, space–time spectral analysis, and lag regressions are used to identify tropical waves. It is evident that oscillations with intraseasonal time scales and a Kelvin wave structure exist in the model tropical atmosphere. Coherent eastward propagations in the 250-hPa velocity potential and zonal wind are found, with a speed of about 15 m s−1. The oscillation is stronger in the Eastern Hemisphere than in the Western Hemisphere.
Interactions between the tropical and extratropical flows are found to be responsible for the simulated intraseasonal variability. Wave activity flux analysis reveals that a tropical influence occurs in the North Pacific region where a northeastward wave activity flux is found associated with the tropical divergent flow in the western and central Pacific. In the North Atlantic sector, on the other hand, a strong extratropical influence is observed with a southward wave activity flux into the Tropics. The extratropical low-frequency variability develops by extracting kinetic energy from the basic mean flow and through interactions with synoptic-scale transient eddies. Linear experiments show that the tropical atmospheric response to the extratropical forcing in the North Atlantic leads to an eastward-propagating wave in the tropical easterly mean flow of the Eastern Hemisphere.
Abstract
A long integration of a primitive equation dry atmospheric model with time-independent forcing under boreal winter conditions is analyzed. A variety of techniques such as time filtering, space–time spectral analysis, and lag regressions are used to identify tropical waves. It is evident that oscillations with intraseasonal time scales and a Kelvin wave structure exist in the model tropical atmosphere. Coherent eastward propagations in the 250-hPa velocity potential and zonal wind are found, with a speed of about 15 m s−1. The oscillation is stronger in the Eastern Hemisphere than in the Western Hemisphere.
Interactions between the tropical and extratropical flows are found to be responsible for the simulated intraseasonal variability. Wave activity flux analysis reveals that a tropical influence occurs in the North Pacific region where a northeastward wave activity flux is found associated with the tropical divergent flow in the western and central Pacific. In the North Atlantic sector, on the other hand, a strong extratropical influence is observed with a southward wave activity flux into the Tropics. The extratropical low-frequency variability develops by extracting kinetic energy from the basic mean flow and through interactions with synoptic-scale transient eddies. Linear experiments show that the tropical atmospheric response to the extratropical forcing in the North Atlantic leads to an eastward-propagating wave in the tropical easterly mean flow of the Eastern Hemisphere.
