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- Author or Editor: Jacques Derome x

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## Abstract

The stability of free and forced planetary waves in a Î² plane channel is investigated with a barotropic model. The equilibrium flows that are considered have the gravest possible scale in the meridional direction and a zonal wavenumber of either 1 or 2. The equilibrium-forced waves are the result of the interaction of a constant mean zonal wind over finite-amplitude surface orography.

The frequency of all possible small-amplitude perturbations to the equilibrium flows are calculated as a function of the strength of the mean zonal wind and of the amplitude of the orography. The forced zonal-wavenumber-1 flow is found to have three major regions of instability in parameter space, two of which have stationary growing perturbations. The free Rossby wave of that scale is stable for all amplitudes. The forced zonal-wavenumber-2 wave has two adjacent instability domains one on each side of the resonant mean zonal wind. The free wave becomes unstable for sufficiently large amplitudes. The results are interpreted through the use of a severely truncated spectral model and are related to those of previous studies with infinite Î²-planes. We also report the existence of a traveling subresonant topographic instability, which seems to have gone unnoticed in previous studies.

## Abstract

The stability of free and forced planetary waves in a Î² plane channel is investigated with a barotropic model. The equilibrium flows that are considered have the gravest possible scale in the meridional direction and a zonal wavenumber of either 1 or 2. The equilibrium-forced waves are the result of the interaction of a constant mean zonal wind over finite-amplitude surface orography.

The frequency of all possible small-amplitude perturbations to the equilibrium flows are calculated as a function of the strength of the mean zonal wind and of the amplitude of the orography. The forced zonal-wavenumber-1 flow is found to have three major regions of instability in parameter space, two of which have stationary growing perturbations. The free Rossby wave of that scale is stable for all amplitudes. The forced zonal-wavenumber-2 wave has two adjacent instability domains one on each side of the resonant mean zonal wind. The free wave becomes unstable for sufficiently large amplitudes. The results are interpreted through the use of a severely truncated spectral model and are related to those of previous studies with infinite Î²-planes. We also report the existence of a traveling subresonant topographic instability, which seems to have gone unnoticed in previous studies.

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## Abstract

The interactions between low-frequency transients and synoptic-scale eddies are examined. The 300-mb data from 1981 to 1986 analyzed by the ECMWF are used to calculate the height tendency of the slow transients due to vorticity forcing by synoptic-scale eddies. It is found that the low-frequency transients are correlated with the forcing by the synoptic-scale eddies, most notably in the eastern part of the Pacific and Atlantic basins, where a significant portion of the time variance of the slow transient height field can be explained by the forcing. The lag correlation coefficients between the forcing and the slow transients indicate that the former leads the latter by a small phase difference (about one day).

The structure of the forcing is studied by an EOF analysis. The leading EOF mode in both oceanic sectors has a dipole structure. The pattern of the geopotential height field associated with each EOF mode of the forcing is also identified. The height pattern associated with the first Pacific forcing mode has a wave train structure, and the one associated with the first Atlantic forcing mode is a localized dipole. The correlation between the height pattern and the corresponding EOF mode in each sector is then examined, and no significant time phase shift can be found between the two.

Finally, a simple theoretical explanation is proposed to account for the phase relationship between the slow transients and their forcing by the synoptic-scale eddies.

## Abstract

The interactions between low-frequency transients and synoptic-scale eddies are examined. The 300-mb data from 1981 to 1986 analyzed by the ECMWF are used to calculate the height tendency of the slow transients due to vorticity forcing by synoptic-scale eddies. It is found that the low-frequency transients are correlated with the forcing by the synoptic-scale eddies, most notably in the eastern part of the Pacific and Atlantic basins, where a significant portion of the time variance of the slow transient height field can be explained by the forcing. The lag correlation coefficients between the forcing and the slow transients indicate that the former leads the latter by a small phase difference (about one day).

The structure of the forcing is studied by an EOF analysis. The leading EOF mode in both oceanic sectors has a dipole structure. The pattern of the geopotential height field associated with each EOF mode of the forcing is also identified. The height pattern associated with the first Pacific forcing mode has a wave train structure, and the one associated with the first Atlantic forcing mode is a localized dipole. The correlation between the height pattern and the corresponding EOF mode in each sector is then examined, and no significant time phase shift can be found between the two.

Finally, a simple theoretical explanation is proposed to account for the phase relationship between the slow transients and their forcing by the synoptic-scale eddies.

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## Abstract

A diagnostic algorithm, based on the empirical normal mode decomposition technique, is proposed as a diagnostic tool in studies of the atmospheric variability. It begins by analyzing the transient eddies in terms of empirical modes that are orthogonal with respect to wave activities. Time-dependent amplitudes together with wave activity spectra are used to classify the modes and compute their propagation properties.

The algorithm is applied to a sequence of four Northern Hemisphere winters taken from the National Centers for Environmental Prediction reanalyses, with a focus on the upper troposphere and lower stratosphere, giving a set of empirical modes of wind, pressure, specific volume, and potential vorticity. Results indicate that most of the wave activity is carried by large-scale, eastward-propagating modes centered at middle and high latitudes. Some properties of the leading modes, such as their average phase speeds, are in good agreement with the predictions of linear dynamics.

Characteristics of the leading wavenumber-5 mode, such as its dipolar pressure pattern near the summer hemisphere tropopause, its propagation speed of 12 m s^{âˆ’1} and decay rate of 3 days, can be explained by the theory of quasi modes, defined as superpositions of singular modes sharply peaked in the phase speed domain. Other large-scale, midlatitude modes also show properties compatible with the quasi-modal description, suggesting that quasi modes play an important role in the upper-troposphere dynamics.

## Abstract

A diagnostic algorithm, based on the empirical normal mode decomposition technique, is proposed as a diagnostic tool in studies of the atmospheric variability. It begins by analyzing the transient eddies in terms of empirical modes that are orthogonal with respect to wave activities. Time-dependent amplitudes together with wave activity spectra are used to classify the modes and compute their propagation properties.

The algorithm is applied to a sequence of four Northern Hemisphere winters taken from the National Centers for Environmental Prediction reanalyses, with a focus on the upper troposphere and lower stratosphere, giving a set of empirical modes of wind, pressure, specific volume, and potential vorticity. Results indicate that most of the wave activity is carried by large-scale, eastward-propagating modes centered at middle and high latitudes. Some properties of the leading modes, such as their average phase speeds, are in good agreement with the predictions of linear dynamics.

Characteristics of the leading wavenumber-5 mode, such as its dipolar pressure pattern near the summer hemisphere tropopause, its propagation speed of 12 m s^{âˆ’1} and decay rate of 3 days, can be explained by the theory of quasi modes, defined as superpositions of singular modes sharply peaked in the phase speed domain. Other large-scale, midlatitude modes also show properties compatible with the quasi-modal description, suggesting that quasi modes play an important role in the upper-troposphere dynamics.

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## 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, spaceâ€“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^{âˆ’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, spaceâ€“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^{âˆ’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.

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## Abstract

A dry primitive equation model is used to investigate the remote response to a fixed tropical heat source. The basic forcing for the model takes the form of time-independent terms added to the prognostic equations in two configurations. One produces a perturbation model, in which anomalies grow on a fixed basic state. The other gives a simple GCM, which can be integrated for a long time and delivers a realistic climate simulation with realistic storm tracks. A series of experiments is performed, including 15-day perturbation runs, ensemble experiments, and long equilibrium runs, to isolate different dynamical influences on the fully developed Pacificâ€“North American (PNA) type response to an equatorial heating anomaly centered on the date line.

The direct linear response is found to be very sensitive to changes in the basic state of the same order as the atmosphereâ€™s natural variability, and to the natural progression of the basic state over the time period required to set up the response. However, interactions with synoptic-scale noise in the ambient flow are found to have very little systematic effect on the linear response. Nonlinear interactions with a fixed basic state lead to changes in the position, but not the amplitude, of the response. Feedback with finite-amplitude transient eddies leads to downstream amplification of the PNA pattern, both within the setup time for the response and in a fully adjusted equilibrium situation.

Nonlinearity of the midlatitude dynamics gives rise to considerable asymmetry between the response to tropical heating and the response to an equal and opposite cooling.

## Abstract

A dry primitive equation model is used to investigate the remote response to a fixed tropical heat source. The basic forcing for the model takes the form of time-independent terms added to the prognostic equations in two configurations. One produces a perturbation model, in which anomalies grow on a fixed basic state. The other gives a simple GCM, which can be integrated for a long time and delivers a realistic climate simulation with realistic storm tracks. A series of experiments is performed, including 15-day perturbation runs, ensemble experiments, and long equilibrium runs, to isolate different dynamical influences on the fully developed Pacificâ€“North American (PNA) type response to an equatorial heating anomaly centered on the date line.

The direct linear response is found to be very sensitive to changes in the basic state of the same order as the atmosphereâ€™s natural variability, and to the natural progression of the basic state over the time period required to set up the response. However, interactions with synoptic-scale noise in the ambient flow are found to have very little systematic effect on the linear response. Nonlinear interactions with a fixed basic state lead to changes in the position, but not the amplitude, of the response. Feedback with finite-amplitude transient eddies leads to downstream amplification of the PNA pattern, both within the setup time for the response and in a fully adjusted equilibrium situation.

Nonlinearity of the midlatitude dynamics gives rise to considerable asymmetry between the response to tropical heating and the response to an equal and opposite cooling.

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## Abstract

The resonance of stationary waves forced by topography is examined using a quasi-geostrophic model on a beta-plane channel. It is shown analytically that among the factors favoring the resonance of large, rather than synoptic or small, scale waves is the fact that the sensitivity of the large resonant responses to a change of zonal wind decreases as the scale of the resonant wave increases. A numerical model is used to examine resonance in the presence of topography having zonal wavenumber 2 with zonal flows having horizontal and vertical shear and including the effects of damping and nonlinear interactions. Although the effects of resonance are found to be important even in the presence of damping mechanisms, linear experiments with topographical forcing of reasonable amplitude indicate that a period or several weeks is required for a resonant internal mode to achieve large amplitude in the troposphere. However, as the structure of the resonant mode is such that it has much larger amplitudes in the upper atmosphere than in the troposphere, the interaction between this growing resonant mode and the mean flow which occurs when nonlinear effects are permitted triggers a stratospheric warming and zonal wind reversal. These events, which drive the system off resonance, occur long before large wave amplitudes are achieved in the lower atmosphere. The barotropic mode of zonal wavenumber 2 is shown not to resonate for reasonable values of our mean zonal wind primarily because the latter has the same (sinusoidal) meridional structure as the topography.

## Abstract

The resonance of stationary waves forced by topography is examined using a quasi-geostrophic model on a beta-plane channel. It is shown analytically that among the factors favoring the resonance of large, rather than synoptic or small, scale waves is the fact that the sensitivity of the large resonant responses to a change of zonal wind decreases as the scale of the resonant wave increases. A numerical model is used to examine resonance in the presence of topography having zonal wavenumber 2 with zonal flows having horizontal and vertical shear and including the effects of damping and nonlinear interactions. Although the effects of resonance are found to be important even in the presence of damping mechanisms, linear experiments with topographical forcing of reasonable amplitude indicate that a period or several weeks is required for a resonant internal mode to achieve large amplitude in the troposphere. However, as the structure of the resonant mode is such that it has much larger amplitudes in the upper atmosphere than in the troposphere, the interaction between this growing resonant mode and the mean flow which occurs when nonlinear effects are permitted triggers a stratospheric warming and zonal wind reversal. These events, which drive the system off resonance, occur long before large wave amplitudes are achieved in the lower atmosphere. The barotropic mode of zonal wavenumber 2 is shown not to resonate for reasonable values of our mean zonal wind primarily because the latter has the same (sinusoidal) meridional structure as the topography.

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## Abstract

Three-dimensional flows for which *q*=âˆ’Î»(*p*)Ïˆ where *q* is the potential vorticity, Ïˆ the stream function and Î» some arbitrary function of pressure, are examined. It is found that flows which satisfy this condition and are quite similar to atmospheric blocking patterns can be generated by the superposition of a zonal current independent of the meridional coordinate plus two eddy components. These flows, for which the Jacobian of Ïˆ and *q* is zero, are of interest because 1) in the absence of forcing they constitute steady state solutions of the potential vorticity equation; and 2) the possibility exists that they can be forced resonantly to a finite amplitude by means of a potential vorticity source. The arbitrariness in the choice of Î» is removed by specifying the vertical profile of the diabatic heating. It is shown that when the latter is a linear function of Pressure the resultant forced flow is nearly equivalent barotropic, stable to small amplitude perturbations, with a tendency for the blocking patterns to become somewhat move prominent with increasing pressure, in rather good agreement with observations of blocking highs.

By integration of a three-level beta-plant model in time, it is shown that it is indeed possible, in the absence of dissipation, to thermally fore the above types of flows at resonance and to generate flow patterns that are quite similar to atmospheric blocking patterns. It is also shown that even when a rather broad spectrum of modes is thermally forced, the above resonant modes tend to dominate the flow, in spite of the possible interaction among modes. This would imply that provided the mean zonal flow has the proper strength to produce a resonance condition, the thermal forcing field need not have a very special structure to produce a finite amplitude disturbance through resonance.

## Abstract

Three-dimensional flows for which *q*=âˆ’Î»(*p*)Ïˆ where *q* is the potential vorticity, Ïˆ the stream function and Î» some arbitrary function of pressure, are examined. It is found that flows which satisfy this condition and are quite similar to atmospheric blocking patterns can be generated by the superposition of a zonal current independent of the meridional coordinate plus two eddy components. These flows, for which the Jacobian of Ïˆ and *q* is zero, are of interest because 1) in the absence of forcing they constitute steady state solutions of the potential vorticity equation; and 2) the possibility exists that they can be forced resonantly to a finite amplitude by means of a potential vorticity source. The arbitrariness in the choice of Î» is removed by specifying the vertical profile of the diabatic heating. It is shown that when the latter is a linear function of Pressure the resultant forced flow is nearly equivalent barotropic, stable to small amplitude perturbations, with a tendency for the blocking patterns to become somewhat move prominent with increasing pressure, in rather good agreement with observations of blocking highs.

By integration of a three-level beta-plant model in time, it is shown that it is indeed possible, in the absence of dissipation, to thermally fore the above types of flows at resonance and to generate flow patterns that are quite similar to atmospheric blocking patterns. It is also shown that even when a rather broad spectrum of modes is thermally forced, the above resonant modes tend to dominate the flow, in spite of the possible interaction among modes. This would imply that provided the mean zonal flow has the proper strength to produce a resonance condition, the thermal forcing field need not have a very special structure to produce a finite amplitude disturbance through resonance.

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## Abstract

An algorithm based on the empirical normal mode analysis is used in a comparative study of the climatology and variability in dynamical-core experiments of the Global Environmental Multiscale model. The algorithm is proposed as a means to assess properties of the model's dynamical core and to establish objective criteria for model intercomparison studies. In this paper, the analysis is restricted to the upper troposphere and lower stratosphere. Two dynamical-core experiments are considered: one with the forcing proposed by Held and Suarez, later modified by Williamson et al. (called HSW experiment), and the other with a forcing inspired by the prescriptions of Boer and Denis (BD). Results are also compared with those of an earlier diagnosis of NCEP reanalyses. Normal modes and wave-activity spectra are similar to those found in the reanalysis data, although details depend on the forcing. For instance, wave-energy amplitudes are higher with the BD forcing, and an approximate energy equipartition is observed in the spectrum of wavenumber-1 modes in the NCEP data and the BD experiment but not in the HSW experiment. The HSW forcing has a relatively strong relaxation acting on the complete temperature field, whereas the BD forcing only acts on the zonal-mean temperature, letting the internal dynamics alone drive the wave-activity spectral cascade. This difference may explain why the BD forcing is more successful in reproducing the observed wave activity in the upper troposphere and lower stratosphere.

## Abstract

An algorithm based on the empirical normal mode analysis is used in a comparative study of the climatology and variability in dynamical-core experiments of the Global Environmental Multiscale model. The algorithm is proposed as a means to assess properties of the model's dynamical core and to establish objective criteria for model intercomparison studies. In this paper, the analysis is restricted to the upper troposphere and lower stratosphere. Two dynamical-core experiments are considered: one with the forcing proposed by Held and Suarez, later modified by Williamson et al. (called HSW experiment), and the other with a forcing inspired by the prescriptions of Boer and Denis (BD). Results are also compared with those of an earlier diagnosis of NCEP reanalyses. Normal modes and wave-activity spectra are similar to those found in the reanalysis data, although details depend on the forcing. For instance, wave-energy amplitudes are higher with the BD forcing, and an approximate energy equipartition is observed in the spectrum of wavenumber-1 modes in the NCEP data and the BD experiment but not in the HSW experiment. The HSW forcing has a relatively strong relaxation acting on the complete temperature field, whereas the BD forcing only acts on the zonal-mean temperature, letting the internal dynamics alone drive the wave-activity spectral cascade. This difference may explain why the BD forcing is more successful in reproducing the observed wave activity in the upper troposphere and lower stratosphere.