Numaguti, A, and Yoshikazu Hayashi, 2000: Gravity-wave dynamics of the hierarchical structure of super cloud clusters. Journal of the Meteorological Society of Japan, 78(4), 301-331. Abstract PDF
The hierarchical structures of eastward-moving tropical super cloud clusters (SCC) and embedded westward-moving quasi-periodic cloud clusters (QPCC) are successfully simulated by a simple longitude-height two-dimensional model with simple moist processes.
The model results clearly show a life cycle of cloud activity. The cloud area starts as a low-level shallow cloud, develops into deep convection, becomes a top-heavy cloud, and decays. Gravity-wave packets are excited by the growth and decay of this cloud and propagate both eastward and westward. The westward-propagating gravity waves are coupled with cloud activity and form westward-moving QPCC. On the other hand, the eastward propagating waves are not immediately coupled with deep convective activity. A deep convective cloud develops only after the low and middle troposphere is sufficiently moistened and cooled. The quasi-periodic energence of the new convective cloud to the east results in the eastward movement of the envelope of QPCC, forming an eastward-moving SCC.
It is suggested that the excitation of gravity waves of two vertical modes by grow and decay of the heating with top-heavy vertical profile is essential to this hierarchical structure. Especially, the net upward parcel displacement due to the shallow gravity-wave cell have an important role in the generation of new QPCC. Although both eastward-moving SCC and westward-moving SCC are possible in a non-rotating atmosphere with no external origins of east-west asymmetry, eastward-moving SCC can be selected under existence of some external asymmetry, such as the beta effect, mean zonal wind shear, or asymmetry of latent heat flux due to WISHE (wind-induced surface heat exchange) effect.
Hayashi, Yoshikazu, and Donald G Golder, 1997: United mechanisms for the generation of low- and high-frequency tropical waves. Part I: Control experiments with moist convective adjustment. Journal of the Atmospheric Sciences, 54(9), 1262-1276. Abstract PDF
To examine several mechanisms for the generation of low- and high-frequency tropical waves, numerical experiments are conducted using an idealized nine-level R21 spectral model with the original scheme of moist convective adjustment (MCA). The model prescribes globally uniform, time-independent distributions of sea surface temperatures and insolation, thereby excluding stationary waves and extratropical baroclinic waves. The idealized model, however, still produces tropical intraseasonal oscillations, superclusters, Kelvin waves, and mixed Rossby-gravity waves.
When eliminating the wind fluctuations in the parameterized surface fluxes of latent and sensible heat, the intraseasonal oscillations are profoundly weakened while other waves are not substantially weakened. Subsequently, the MCA scheme is modified to neutralize any conditionally unstable stratification that would otherwise develop during periods of nonsaturation. This modification suppresses the part of the MCA process that neutralizes, upon saturation, any preexisting unstable stratification. In spite of the presence of moisture convergence, all tropical transient waves then disappear, in contrast to the wave-CISK (conditional instability of the second kind) mechanism.
The above results are consistent with the united mechanisms proposed as follows: Intraseasonal oscillations are maintained primarily through the evaporation-wind feedback mechanism. Other waves are maintained primarily through the "saturation-triggering mechanism" and/or the lateral-triggering mechanism. The saturation-triggering mechanism hypothesizes that transient waves can be triggered by the intermittent onset of nonequilibrium moist convection, upon saturation, to neutralize any preexisting unstable stratification.
Hayashi, Yoshikazu, and Donald G Golder, 1997: United mechanisms for the generation of low- and high-frequency tropical waves. Part II: Theoretical Interpretations. Journal of the Meteorological Society of Japan, 75(4), 775-797. Abstract PDF
It is assumed that low- and high-frequency tropical waves are generated by the united mechanisms consisting of the evaporation-wind feedback (EWF), saturation-triggering (ST), and lateral-triggering mechanisms. Through the EWF mechanism, some waves become unstable owing to evaporation-wind feedback. Through the ST mechanism, other waves are triggered by the intermittent onset of moist convection, upon saturation, to neutralize any pre-existing conditionally unstable stratification. These mechanisms are theoretically interpreted by partitioning moist convective adjustment into two consecutive processes of diagnostic and prognostic adjustments. The two processes respectively restore and maintain convective equilibrium, and are crucial to the ST and EWF mechanisms.
As a step toward a unified theory, EWF instability is examined by the use of a theoretical Kelvin-wave model, which incorporates only the prognostic-adjustment process in the linearized perturbation equations, thereby excluding the ST mechanism. The solutions indicate that wave instability results from the EWF mechanism and not from the wave-CISK mechanism. For a plausible choice of adjustable parameters, one strongly unstable mode corresponds to the observed 40-50-day oscillation, while two weakly unstable modes correspond to the observed 25-30- day and 10-20- day oscillations.
These results are compared with those from the numerical experiments conducted in Part 1, using a nonlinear model incorporating the original moist convective adjustment scheme. It is then speculated that the 40-50 - and 25-30 -day modes can strongly grow through the linear and nonlinear EWF mechanisms respectively, while the 10-20- day mode can strongly amplify through the ST mechanism.
Hayashi, Yoshikazu, Donald G Golder, and P Jones, 1997: Tropical gravity waves and superclusters simulated by high-horizontal-resolution SKYHI general circulation models. Journal of the Meteorological Society of Japan, 75(6), 1125-1139. Abstract PDF
Tropical gravity waves and superclusters simulated by 40-level GFDL SKYHI general circulation model experiments with higher horizontal resolutions (0.6° longitude x 0.72° latitude) and (1.0° x 1.2°) are compared with those simulated by a lower-resolution (3.0° x 3.6°) experiment.
Results indicated that simulated precipitational heating appears to excite tropical gravity waves. At higher resolutions, precipitation is more confined in space and time, resulting in a broader wavenumber-frequency spectral distribution. Grid-scale precipitation, which is thought to mimic the precipitation associated with cloud clusters, is organized into larger-scale superclusters. The westward propagation of cloud clusters and eastward propagation of superclusters can be more clearly seen in the high-resolution experiments.
The high-resolution (0.6° x 0.72°) model indicates that the lower-stratospheric gravity-wave momentum flux is dominated by high-frequency components having periods shorter than one day. This flux doubles as the resolution is increased from (3.0° x 3.6°) to (0.6° x 0.72°). It is speculated that a further increase in both the horizontal and vertical resolutions could substantially enhance the gravity-wave momentum flux convergence, thus forcing a stronger quasi-biennial oscillation.
Hayashi, Yoshikazu, and Donald G Golder, 1995: The generation mechanism of tropical transient waves: control experiments and a unified theory with moist convective adjustment In Tenth Conference on Atmospheric and Oceanic Waves and Stability, Boston, MA, American Meteorological Society, 7-8.
Hayashi, Yoshikazu, and Donald G Golder, 1994: Kelvin and mixed Rossby-gravity waves appearing in the GFDL "SKYHI" general circulation model and the FGGE dataset: Implications for their generaton mechanism and role in the QBO. Journal of the Meteorological Society of Japan, 72(6), 901-935. Abstract PDF
To evaluate simulations and theories of equatorial Kelvin and mixed Rossby-gravity (MRG) waves, and to gain insight into their generation mechanism and role in the quasi-biennial oscillation, a space-time spectral analysis is performed on output data from the 40-level, three-degree latitude GFDL "SKYHI" general circulation model and on the GFDL FGGE dataset
The SKYHI and FGGE stratospheric Kelvin waves are dominated by an eastward- moving, wavenumber-one, 10-20 day period component in the lower stratosphere. These waves are accompanied by higher wavenumber-frequency components, which can be detected more clearly in the upper stratosphere than in the lower stratosphere. On the other hand, the SKYHI and FGGE MRG waves are dominated by a westward-moving wavenumber 3-5, 4-6 day component in the lower stratosphere. These waves are dominated by lower-wavenumbers (1-2) and shorter periods (2-4 days) in the upper stratosphere. The amplitudes of the SKYHI/FGGE Kelvin and MRG waves are comparable to those estimated from observed (non- FGGE) station data, whereas the SKYHI model produces only a very weak quasi- biennial oscillation. The SKYHI precipitation data intermittently exhibit grid-size pulses of precipitation, but do not clearly exhibit spectral peaks which correspond to Kelvin and MRG waves.
On the basis of the present analysis, it is proposed that Kelvin, MRG, and gravity waves result from wave-convection interactions and are intermittently triggered by random pulses of convective heating. It is speculated that the quasi-biennial oscillation is produced primarily by gravity waves and will increase in amplitude with horizontal resolution, as grid-size pulses of convective heating and small-scale gravity waves are more adequately produced in the model.
Hayashi, Yoshikazu, and Donald G Golder, 1993: Tropical 40-50- and 25-30-day oscillations appearing in realistic and idealized GFDL climate models and the ECMWF dataset. Journal of the Atmospheric Sciences, 50(3), 464-494. Abstract PDF
To clarify differences between the tropical 40-50- and 25-30 day oscillations and to evaluate simulations and various theories, space-time spectrum and filter analyses were performed on a nine-year dataset taken from the nine-level R30 spectral general circulation model and the nine-year (1979-1987) ECMWF four-dimensional analysis dataset. In addition, the 40-level SKYHI model was analyzed to examine the effect of increased vertical resolution, while an ocean-surface perpetual January R30 model was analyzed to examine the effects of the absence of geographical and seaonal variations.
The R30 model results indicate that the relative amplitude of the wavenumber-one component of the 40-50- and 25-30 day oscillations varies greatly from year to year. For the nine-year average, the simulated 40-50-day zonal velocity oscillations are as strong as observed, while the simulated 25-30 day zonal velocity oscillations are much stronger than observed. Although 40-50- and 25-30-day oscillations have similar structures, the 25-30 day oscillations exhibit a greater increase with height in their tropospheric amplitudes than the 40-50-day oscillations, resulting in different relative magnitudes at different levels. The time variance of the two oscillations has similar longitudinal distributions, implying that the two periods are not due to differences in local phase speeds. They appear to grow and decay independently without any coherent phase relationship, implying that the two periods are not a result of the seasonal modulation of an intrinsic 30-40 day period.
The SKYHI model indicates that 25-30 day oscillations still appear too strong. Nevertheless, this model reveals a longer vertical wavelength, a higher penetration of the 25-30-day amplitude above the level of convective heating, and a slightly greater height of the convective-heating amplitude, which cannot be detected in the R30 model. This implies that the two oscillations differ in their intrinsic vertical wavelengths.
The ocean-surface perpetual January R30 model indicates that not only the 25-30-day mode but also the 40-50-day mode can be simulated in the absence of geographical and seasonal modulations, while the wave-CISK and evaporation-wind feedback theories cannot explain the 40-50-day mode. Both R30 models indicate that daily precipitation is almost always associated with upward motion, being consistent with theoretical conditional heating. A comparison between the two R30 models suggests that the sea surface temperature geographically modulates the intrinsically eastward-moving wavenumber-one precipitation oscillations, resulting in their major Pacific and minor Atlantic local amplitudes. This in turn causes planetary-scale eastward-moving zonal-velocity oscillations and standing geopotential oscillations.
Sheng, J, and Yoshikazu Hayashi, 1990: Estimation of atmospheric energetics in the frequency domain during the FGGE year. Journal of the Atmospheric Sciences, 47(10), 1255-1268. Abstract PDF
The energetics of atmospheric motions are studied in the frequency domain using the two versions of the FGGE IIIb dataset, processed at GFDL and ECMWF. It is demonstrated that the frequency spectra of kinetic energy (KE) and available potential energy (APE) can be approximated by a power law. On a log-log diagram, a slope of minus one results for both KE and APE in the period range of 7 to 35 days, when integrated over the Northern Hemisphere.
The conversion from APE to KE is the major source of eddy kinetic energy for all the low and high frequency bands discussed. Through nonlinear interactions, motions of high frequencies (with periods shorter than 10 days) gain APE from, and lose KE to the motions of low frequencies (with periods longer than 10 days but shorter than the annual cycle). The nonlinear energy exchanges are relatively more important for the energy balance of low frequency modes. It is also shown that both high and low frequency transients extract APE from and supply KE to the time-mean flow. The intercomparisons between the two versions of FGGE data indicate an overall agreement between the energy cycles derived from the GFDL and ECMWF datasets, despite the differences in calculated values of spectral estimates.
Sheng, J, and Yoshikazu Hayashi, 1990: Observed and simulated energy cycles in the frequency domain. Journal of the Atmospheric Sciences, 47(10), 1243-1254. Abstract PDF
The analysis of spectral energetics in the frequency domain has been applied to several observed datasets and those simulated by a GFDL general circulation model. There exists good agreement on the directions of energy flows between the observed and the simulated atmospheres. The conversion from available potential energy to kinetic energy in the tropics and extratropics is the major source of eddy kinetic energy for all the low and high frequency bands discussed. The energy balance in the tropics has quite different characteristics from those in the extratropics. Instead of an up-scale decascade as in the case of the extratropics, kinetic energy is transferred in an opposite sense, namely from transients of longer time scales to those of shorter time scales.
Using a 5-year dataset from the ECMWF operational analysis, an energy cycle is obtained that is in general agreement with the one computed using the data of the FGGE year alone. The interannual variability of the spectral estimates is relatively small compared with the discrepancies caused by the variety of data origins.
To examine the effects of horizontal resolution on internal gravity waves simulated by the 40-level GFDL "SKYHI" general circulation model, a comparison is made between the 3 degree and 1 degree resolution models during late December. The stratospheric and mesospheric zonal flows in the winter and summer extratropical regions of the 1 degree model are much weaker and more realistic than the corresponding zonal flows of the 3 degree model. The weaker flows are consistent with the stronger Eliassen-Palm flux divergence (EPFD).
The increase in the magnitude of the EPFD in the winter and summer extratropical mesospheres is due mostly to the increase in the gravity wave VMFC. In the winter extratropical mesosphere, the increase of VMFC associated with large-scale eastward moving components also accounts for part of the increase in the gravity wave VMFC.
The gravity waves in the summer and winter mesosphere of the 1 degree model are associated with a broader frequency-spectra distribution, resulting in a more sporadic time-distribution of their VMFC. This broadening is due not only to the increase in resolvable horizontal wavenumbers but also occurs in the large-scale components owing to wave-wave interactions. It was found that the phase velocity and frequency of resolvable small-scale gravity waves are severely underestimated by finite difference approximations.
Hayashi, Yoshikazu, and Donald G Golder, 1988: Tropical intraseasonal oscillations appearing in a GFDL general circulation model and FGGE Data. Part II: Structure. Journal of the Atmospheric Sciences, 45(21), 3017-3033. Abstract PDF
Space-time spectral and filter analyses are made of the structure of the tropical intraseasonal oscillations appearing in a GFDL 30-wavenumber spectral general circulation model and the FGGE IIIb dataset.
The model's tropical zonal velocity exhibits spectral peaks with periods of 40-50 and 25-30 days at wavenumber 1 for six individual years, although the 40-50 day peak is not as pronounced as that found in the FGGE dataset. Both the eastward moving 40-50 and 25-30 day oscillations take the form of a Kelvin-Rossby wave pattern in the upper troposphere and a Rossby mode in the lower troposphere. They also take the form of a latitudinally tilted Walker cell which is modified by a meridional convergence in the boundary layer.
Hayashi, Yoshikazu, 1987: A modification of the atmospheric energy cycle. Journal of the Atmospheric Sciences, 44(15), 2006-2017. Abstract PDF
A modification is made of the conventional energy cycle by combining the eddy flux convergence and the mean meridional circulation terms in the mean momentum and heat equations. The combined terms are interpreted as the effective flux convergences in the extratropics where the steady state mean circulation is regarded as essentially being induced by eddies. In the presence of mean heating, the modified energy cycle is simpler and less misleading than the transformed energy cycle based on the transformed Eulerian-mean equations.
This modification suggests that the major energy source of tropospheric planetary waves can be traced to the thermal generation of mean potential energy and that the stratospheric planetary wave is maintained by the total (mean plus eddy) vertical flux of energy from the troposphere. The conventional energy cycle of observed tropospheric planetary waves is, however, not as complicated as that of theoretical planetary waves in the quasi-nonacceleration condition. This is due to the fact that the observed tropospheric eddy heat flux convergence is counterbalanced by the mean heating and does not induce a large mean circulation in the steady state.
Hayashi, Yoshikazu, and Donald G Golder, 1987: Effects of wave-wave and wave-mean flow interactions on the growth and maintenance of transient planetary waves in the presence of a mean thermal restoring force. Journal of the Atmospheric Sciences, 44(22), 3392-3401. Abstract PDF
In order to clarify the effects of wave-wave and wave-mean flow interactions on the growth and maintenance of extratropical tropospheric transient waves in the presence of a mean thermal restoring force, numerical experiments are conducted with the use of a dry general circulation model having a zonally uniform ocean surface. After the model has reached its steady state in the absence or presence of eddies, waves are allowed to grow from small disturbances by including all or some of the zonal wavenumber components.
In the presence of all wavenumbers (1-21), ultralong waves (wavenumber 1-3) and cyclone-scale waves (wavenumber 4-9) initially grow as fast as short-scale waves (wavenumber 10-21), whereas ultralong waves do not initially grow as fast in the absence of wave-wave interactions. However, in the mature stage, ultralong waves attain a smaller amplitude in the presence of higher wavenumber components than they do in the absence of these components. This smaller amplitude is due to the fact that the mean baroclinicity is reduced by ultralong waves together with the higher wavenumber components to maintain equilibrium.
It is found that wave-wave interactions energetically play a more important role in the growth of ultralong waves than in their maintenance, being consistent with their nonlinear growth. This implies that the wave-wave energy transfer is sensitive to phase relations and is more efficient in the growing stage. It is also found that the ratio between the kinetic and available potential energies of ultralong waves is increased in the presence of wave-wave interactions. This implies that ultralong waves become more barotropic due to the nonlinear growth of external Rossby waves.
Hayashi, Yoshikazu, and S Miyahara, 1987: A three-dimensional linear response model of the tropical intraseasonal oscillation. Journal of the Meteorological Society of Japan, 65(6), 843-852. Abstract PDF
The propagation and structure of the tropical intraseasonal oscillation are studied by the use of a three-dimensional linear response model and compared with those obtained from the FGGE data.
It is assumed that the imposed thermal forcing oscillates with a 40 day period and propogates eastward. Although the amplitude of the forcing is assumed to be large over a certain longitude band and small elsewhere, the responding zonal wind oscillation has significant components that propagate eastward around the earth as observed. This oscillation is also associated with an observed longitudinal node in the region of the maximum forcing. When the imposed forcing is strictly confined over some longitudes, the zonal wind oscillation propagates eastward and westward away from the forced region as in the case of a two-dimensional mode. The eastward moving wavenumber 1 component is associated with the observed wave pattern of the combined Kelvin-Rossby mode in the upper troposphere, while it is dominated by that of the Rossby mode in the lower troposphere. This component also takes the observed structure of the Walker cell modified by a frictional meridional convergence in the boundary layer. The dominance of the Rossby mode in the lower troposphere is due to the effect of surface friction.
Hayashi, Yoshikazu, 1986: Statistical interpretations of ensemble-time mean predictability. Journal of the Meteorological Society of Japan, 64(2), 167-181. Abstract
Statistical interpretation of ensemble-time mean forecasts by the use of a dynamical model with unchanging external conditions are discussed. For this purpose, three kinds of variances are defined and their interrelations are clarified. It is proposed to define the predictability limit of the ensemble-time mean forecasts as the period when their error variance surpasses that of the climate-time mean forecasts. It is shown that, for a large ensemble of forecasts, this limit is close to Shukla's (1981) limit of individual time mean forecasts. The latter limit is defined as the period when the variance of the time mean forecasts with slightly different initial perturbations approaches that of the time mean forecasts from widely different basic initial conditions.
The statistical significance of ensemble-time mean predictability is also discussed and the interpretation of the analysis of variance is clarified. It is emphasized that a null hypothesis of unpredictability should not be readily accepted unless the confidence intervals are sufficiently small. It is shown by the use of confidence intervals that the number of Shukla's predictability experiments with a general circulation model is too small to statistically support his conclusion that the 31-60 day means are not dynamically predictable.
Hayashi, Yoshikazu, and Donald G Golder, 1986: Tropical intraseasonal oscillations appearing in a GFDL general circulation model and FGGE Data. Part I: Phase propagation. Journal of the Atmospheric Sciences, 43(24), 3058-3067. Abstract PDF
Space-time spectrum and filter analyses are made of the tropical intraseasonal oscillations in the northern summer appearing in a GFDL 30-wavenumber spectral general circulation model and the FGGE IIIb data.
The model exhibits major and minor wavenumber 1 spectral peaks in the equatorial zonal velocity at eastward-moving periods of 40-50 and 25-30 days in agreement with the FGGE data. Both the 40-50 and 25-30 day oscillations are associated with a similar spatial structure. In particular, both of these oscillations exhibit a phase reversal between the 200 and 800 mb zonal velocities. They propagate eastward with a node near the dateline and an antinode in the western hemisphere. Their wave patterns take the form of an eastward-moving Kelvin mode near the equator and an eastward-moving Rossby mode away from the equator.
Both spectral peaks are also detectable in the model's precipitation, corresponding to those in the observed outgoing longwave radiation. The 40-50 and 25-30 day precipitation oscillations are in phase with the vertical velocity and propagate northeastward with major and minor antinodes in the eastern and western hemispheres, respectively.
The present results demonstrate that the intraseasonal oscillations can be simulated in a model without air-sea interactions and cloud-radiation feedbacks.
Miyahara, S, Yoshikazu Hayashi, and Jerry D Mahlman, 1986: Interactions between gravity waves and planetary-scale flow simulated by the GFDL "SKYHI" general circulation model. Journal of the Atmospheric Sciences, 43(17), 1844-1861. Abstract PDF
In order to study interactions between gravity waves and planetary scale flow in the middle atmosphere, a 3 degree latitude by 3.6 degree longitude version of the 40-level GFDL "SKYHI" general circulation model is analyzed using bihourly sampled output data.
It is shown by a space-time spectral analysis that gravity waves in the mean zonal westerlies (easterlies) mainly consist of westward-(eastward-) moving components, and carry easterly (westerly) momentum upward, and decelerate the mean zonal westerlies (easterlies) in the mesosphere.
Zonal momentum flux convergence due to gravity waves accounts for nearly all of the Eliassen-Palm (E-P) flux divergence in the summer mesosphere. This convergence accounts for 30%-50% of that in the winter upper mesosphere. However, this percentage is probably an underestimate, since the convergence is significantly enhanced in a high resolution (1 degree x 1.2 degree) model currently being integrated.
Vertical propagation of gravity waves is affected not only by the mean zonal wind but also by velocity perturbations associated with planetary waves. The drag force due to gravity waves acts to suppress stationary planetary waves in the winter mesosphere.
Hayashi, Yoshikazu, 1985: Theoretical interpretations of the Eliassen-Palm diagnostics of wave-mean flow interaction. Part I: Effects of the lower boundary. Journal of the Meteorological Society of Japan, 64(4), 497-511. Abstract
In order to theoretically interpret the Eliassen-Palm diagnostics of wave-mean flow interactions, necessary and sufficient conditions are derived for the Eliassen-Palm flux divergence to approximate the zonal acceleration in the absence of mean damping.
It is shown by a simple analytical model that a violation of these conditions due to the effect of the lower boundary condition may explain why some observational diagnostic studies indicate that transient eddies accelerate westerlies in the mid-latitude upper troposphere in the absence of mean damping, although the transient E-P flux divergence is easterly there.
It is also suggested on the basis of simple diagnostic relations that the steady state upper tropospheric westerlies can be either enhanced or reduced by transient eddies depending on mean damping and radiative heating.
Hayashi, Yoshikazu, 1985: Theoretical interpretations of the Eliassen-Palm diagnostics of wave-mean flow interaction. Part II: Effects of mean damping. Journal of the Meteorological Society of Japan, 63(4), 513-521. Abstract
In order to theoretically interpret the Eliassen-Palm diagnostics of wave-mean flow interaction, necessary and sufficient conditions are derived for the Eliassen-Palm flux divergence to balance the steady state residual circulations induced by eddies in the presence of mean damping. It is shown by a simple analytical model that this balance holds for stratospheric planetary waves when the mean Rayleigh friction coefficient is one order smaller than the mean Newtonian cooling coefficient, although the tall mean flow condition (Andrews and McIntyre, 1976) is not violated. In this case, the Eliassen-Palm flux divergence can be interpreted as approximating the steady state residual circulations (~ Lagrangian mean circulations) induced by eddies as well as the net mean acceleration in the absence of mean damping. This balance is consistent with the stratospheric circulations of a dynamical model (Holton and Wehrbein, 1980a, b) and the GFDL "SKYHI" general circulation model (Andrews et al., 1983).
Hayashi, Yoshikazu, and Donald G Golder, 1985: Nonlinear energy transfer between stationary and transient waves simulated by a GFDL spectral general circulation model. Journal of the Atmospheric Sciences, 42(12), 1340-1344. Abstract PDF
A wavenumber spectral analysis has been made of the nonlinear energy transfer between the tropospheric stationary (January mean) and transient waves in the midlatitudes simulated by a GFDL 9-level spectral general circulation model with 30 zonal wavenumbers.
It is shown that the wavenumber energy spectra are fairly well simulated, although the kinetic energy of simulated ultralong waves is about 60% of that observed. In particular, both simulated and observed ultralong waves are maintained primarily by energy transfer from zonal available potential energy. The model's energy spectra are then partitioned into stationary and transient wave parts. It is found that stationary ultralong waves gain kinetic energy but lose available potential energy through the nonlinear interaction with transient waves. Since this loss is much larger that the gain, transient waves act to destroy stationary wave energy which is maintained primarily by conversion from the zonal available potential energy, being consistent with observations. On the other hand, transient ultralong waves gain both kinetic and available potential energy through wave-wave interactions. This gain is comparable to the gain from the zonal available potential energy.
A space-time spectral analysis is made of large-scale equatorial disturbances simulated by the 40-level, 5 degree latitude GFDL "SKYHI" general circulation model with annual mean conditions. Three kinds of eastward moving waves with wavenumbers 1-2 are found in the lower and upper stratosphere and mesosphere. These waves are characterized by small meridional winds and an eastward tilt with height and are identifiable with observed Kelvin waves. A time-height section reveals their vertical group propagation.
The lower stratospheric Kelvin wave is associated with periods of 10-30 days (eastward phase speed 15-46 m s-1) for wavenumber 1 and a vertical wavelength of ~10 km, corresponding to that observed in 1968 by Wallace and Kousky. The upper stratospheric Kelvin wave is associated with periods of 5-7 days (66-92 m s-1) for wavenumber 1 and a vertical wavelength of ~20 km, corresponding to that observed by Hirota. The mesospheric Kelvin wave is associated with periods of 3-4 days (115-154 m s-1) for wavenumber 1 and a vertical wavelength of ~40 km, corresponding to that recently discovered by Salby and others. All these Kelvin waves transport energy and eastward momentum upward and contribute to the maintenance of the eastward flow.
In addition, gravity waves of zonal wavenumbers 1-30 and periods of 0.7-2 days have been found, particularly in the model's equatorial stratosphere and mesosphere. Their eastward and westward moving components transport eastward and westward momentum upward and contribute to the momentum balance as much as, or even more than, Kelvin waves with periods longer than two days.
Yamagata, T, and Yoshikazu Hayashi, 1984: A simple diagnostic model for the 30-50 day oscillation in the tropics. Journal of the Meteorological Society of Japan, 62(5), 709-717. Abstract
A theoretical discussion is given of the structure of observed 30-50 day atmospheric oscillation in the tropics by the use of a simple linear diagnostic model based on primitive, shallow water, Beta-plane equations with the long wave approxiation. It is assumed that this oscillation is forced by a localized heat source pulsating with a 40-day period. The response of the model shows that the zonal wind oscillation consists of a standing wave with a phase jump in the region of heating and traveling waves with slow zonal phase variations elsewhere. The pressure field is, however, not associated with a phase jump in agreement with observations.
Hayashi, Yoshikazu, 1983: Modified methods of estimating space-time spectra from polar-orbiting satellite data Part I: The frequency transform method. Journal of the Meteorological Society of Japan, 61(2), 254-261. Abstract PDF
A simplification is made of the nonorthogonal Fourier transform method (Salby, 1982) for estimating space-time spectra from uneven twice-daily data sampled by a polar-orbiting satellite. The modified method transforms frequency only by the use of the Galilean transformation, while Salby's method transforms both frequency and wavenumber. Space-time spectra are obtained from the time-Fourier transform with respect to the Doppler-shifted frequency as viewed from the satellite. The wavenumber-frequency aliasing characteristics are examined and the computer code is exemplified.
Hayashi, Yoshikazu, 1983: Modified methods of estimating space-time spectra from polar-orbiting satellite data Part II: The wavenumber transform method. Journal of the Meteorological Society of Japan, 61(2), 263-268. Abstract PDF
In order to estimate space-time spectra correctly from uneven twice-daily data sampled by a polar-orbiting satellite, the wavenumber transform method (Hayashi, 1980) is modified by the use of a nonorthogonal Fourier inversion. The space-time spectra are obtained from the time-Fourier coefficients of the space-Fourier transforms of the asynoptic field with respect to its frequency-shifted wavenumber. Since this method requires the spatial interpolation of asynoptic data, it is effective only for ultralong waves. The wavenumber-frequency aliasing characteristics are examined and the computer code is exemplified.
Hayashi, Yoshikazu, and Donald G Golder, 1983: Transient planetary waves simulated by GFDL spectral general circulation models. Part 1: Effects of mountains. Journal of the Atmospheric Sciences, 40(4), 941-950. Abstract PDF
Space-time spectral analysis over a three year data set is made of transient planetary waves simulated by Geophysical Fluid Dynamics Laboratory (GFDL) spectral general circulation models with and without mountains.
In both models westward moving ultralong waves have larger geopotential amplitude than eastward moving ultralong waves, being in agreement with observations. In both models westward moving ultralong waves are associated with little vertical tilt and a large meridional wavelength, while eastward moving ultralong waves are associated with some vertical tilt and a small meridional wavelength.
In the absence of mountains westward moving ultralong waves are somewhat decreased, while eastward moving ultralong waves are somewhat increased, and eastward moving wavenumbe 4-6 components are markedly increased in the Northern Hemisphere .
Hayashi, Yoshikazu, and Donald G Golder, 1983: Transient planetary waves simulated by GFDL spectral general circulation models. Part 2: Effects of nonlinear energy transfer. Journal of the Atmospheric Sciences, 40(4), 951-957. Abstract PDF
In order to study how transient planetary waves in the midlatitude troposphere are maintained, a space-time spectral analysis over a 1-year data set is made of a GFDL spectral general circulation model.
It is found that the kinetic energy (Kn) of both westward and eastward moving ultralong waves with periods less than 20 days is maintained primarily through conversion from wave available-potential energy (An).
In particular, An of the westward moving ultralong waves is comparable to that of Kn and is maintained primarily through the wave-wave transfer of An. In contrast, An of the eastward moving ultralong waves is larger than Knand is maintained primarily through the zonal-wave transfer of An and partly through the wave-wave transfer of An. These conclusions also hold in the absence of stationary-transient wave interactions as confirmed by a model with a uniform surface.
Hayashi, Yoshikazu, 1982: Confidence intervals of a climatic signal. Journal of the Atmospheric Sciences, 39(9), 1895-1905. Abstract PDF
In order to interpret climate statistics correctly, the definitions of climate change, signal-to-noise ratio and statistical significance are clarified.
It is proposed to test the significance of climate statistics by the use of confidence intervals, since they are more informative than merely testing the null hypothesis that the true response is zero. The confidence intervals of the mean difference, variance ratio and signal-to-noise ratio are formulated and applied to a climate sensitivity study.
It is also proposed to make a multivariate test of a response pattern by the use of joint confidence intervals, since they are more informative than merely testing the null hypothesis that the true response is everywhere zero. These intervals can also be applied to test the joint significance of the amplitude and phase of the seasonal cycles of a response.
Hayashi, Yoshikazu, 1982: Interpretations of space-time spectral energy equations. Journal of the Atmospheric Sciences, 39(3), 685-688. Abstract PDF
Interpretations are given of two different formulations of space-time spectral energy equations derived by Kao (1968) and Hayashi (1980).
Contrary to Kao's interpretation, it is argued that his formulation does not describe how spectral energy is maintained, since his equation corresponds to the imaginary part of the energy equation of space-time Fourier components which governs the frequency (time change of phase).
On the other hand, Hayashi's formulation is consistent with Saltzman's (1957) wavenumber spectral energy equation, since his formulation corresponds to the real part which governs the growth rate (time change of amplitude).
Hayashi, Yoshikazu, 1982: Space-time spectral analysis and its applications to atmospheric waves. Journal of the Meteorological Society of Japan, 60(1), 156-171. Abstract PDF
Space-time spectral analysis methods and their applications to large-scale atmospheric waves are reviewed.
Space-time spectral analysis resolves transient waves into eastward and westward moving components and is mathematically analogous to rotary spectral analysis which resolves two-dimensional velocity vectors into clockwise and anticlockwise components. Space-time spectral analysis can also resolve transient waves consisting of multiple wavenumbers into standing and traveling wave packets. Space-time energy spectra are governed by space-time spectral energy equations which consist of linear and nonlinear energy transfer spectra.
Space-time spectra can be estimated by either the lag correlation method, direct Fourier transform method or the maximum entropy method depending on the length of the time record. By use of the modified space-Fourier transform these spectra can be estimated correctly from polar-orbiting satellite data which are sampled globally at different hours of the day.
Space-time spectral analysis has been extensively applied to data generated by GFDL general circulation models to determine the wave characteristics, structure and energetics of transient planetary waves, to verify the model with observations and to clarify their generation mechanisms by means of controlled experiments.
Hayashi, Yoshikazu, 1981: Space-time cross spectral analysis using the maximum entropy method. Journal of the Meteorological Society of Japan, 59(5), 620-624. Abstract PDF
Space-time cross spectra are experimentally estimated from given sinusoidal waves by use of the multivariate maximum entropy method. This method gives not only power spectra but also cospectra, phase difference and coherence with fine frequency resolutions from short time records. As an example of its application, a space-time spectral analysis is made of external Rossby waves simulated by a GFDL spectral general circulation model.
Hayashi, Yoshikazu, 1981: Vertical-zonal propagation of a stationary planetary wave packet. Journal of the Atmospheric Sciences, 38(6), 1197-1205. Abstract PDF
In order to explain why the Aleutian high stands out in the winter stratosphere, a complex Fourier analysis is made of simulated and observed stationary waves. It is found that in the troposphere the envelope of the time mean geopotential height consisting of wavenumbers 1 ~ 3 attains its major and minor maxima in the Pacific and Atlantic, respectively. The major maximum is dominated by wavenumbers 1 ~ 2 and shifts eastward with height in the stratosphere in the approximate direction of the group velocity and strengthens the Aleutian high. The minor maximum is dominated by wavenumber 3 and is confined in the troposphere.
Hayashi, Yoshikazu, and Donald G Golder, 1981: The effects of condensational heating on midlatitude transient waves in their mature stage: Control experiments with a GFDL general circulation model. Journal of the Atmospheric Sciences, 38(11), 2532-2539. Abstract PDF
The effects of condensational heating on midlatitude transient waves in their mature stage are re-examined by comparing moist and dry GFDL spectral general circulation models, both of which have all ocean surfaces with prescribed zonally uniform temperature. The zonal mean states of both models are fixed in time so as to be identical throughout the time integration.The effects of condensational heating on midlatitude transient waves in their mature stage are re-examined by comparing moist and dry GFDL spectral general circulation models, both of which have all ocean surfaces with prescribed zonally uniform temperature. The zonal mean states of both models are fixed in time so as to be identical throughout the time integration.
It is found that the transient eddy kinetic energy is significantly enhanced for all wavenumbers by the effect of latent heat release. This increase is primarily due to an increase in baroclinic conversion from the zonal available potential energy and only partly due to the generation of eddy available potential energy by condensational heating.
Hayashi, Yoshikazu, 1980: Estimation of nonlinear energy transfer spectra by the cross-spectral method. Journal of the Atmospheric Sciences, 37(2), 299-307. Abstract PDF
Spectral formulas are derived to compute nonlinear energy transfer spectra by use of the cross-spectral technique. Nonlinear product terms are calculated directly from dependent variables without using the conventional interaction Fourier coefficients. The proposed method of computation is simpler than the conventional method and is applicable not only to wavenumber spectra but also to frequency or wavenumber-frequency spectra. Nonlinear aliasing errors associated with this approach can be either neglected or completely eliminated by Fourier interpolation. An example of the application of this method to atmospheric waves is given.
Hayashi, Yoshikazu, 1980: A method of estimating space-time spectra from polar-orbiting satellite data. Journal of the Atmospheric Sciences, 37(6), 1385-1392. Abstract PDF
Space-time spectral formulas are modified to estimate wavenumber-frequency spectra correctly from space-time series data sampled at the same local time but at different hours of a day by a polar-orbiting satellite.
It is shown that a significant error occurs in the wavenumber-frequency spectra of the space-time series for wave periods less than 10 days. This error can be eliminated without time interpolation by taking a space-Fourier transform with respect to the frequency-shifted wavenumbers measured at the same local time.
Hayashi, Yoshikazu, and Donald G Golder, 1980: The seasonal variation of tropical transient planetary waves appearing in a GFDL general circulation model. Journal of the Atmospheric Sciences, 37(4), 705-716. Abstract PDF
The seasonal variation of tropical transient planetary waves appearing in an 11-layer GFDL general circulation model is investigated. Space-time power spectra are estimated for every month by use of the maximum entropy method which can be applied to a short time record. The identification of equatorial wave modes is confirmed by space-time rotary spectral analysis which resolves traveling vortices into clockwise and anticlockwise components as well as eastward and westward moving components. It is found that the model's stratospheric Kelvin and mixed Rossby-gravity waves attain their primary and secondary maxima around July and January, respectively.
Hayashi, Yoshikazu, 1979: A generalized method of resolving transient disturbances into standing and traveling waves by space-time spectral analysis. Journal of the Atmospheric Sciences, 36(6), 1017-1029. Abstract PDF
Space-time spectral formulas are generalized to partition the time power spectrum of transient disturbances consisting of multiple wavenumbers into standing and traveling parts by assuming that these parts are incoherent with each other.
This technique is useful in interpreting the spatial variation of wave amplitude in terms of standing and traveling waves. An example of its application to the analysis of transient planetary waves is given.
Hayashi, Yoshikazu, 1979: Space-time spectral analysis of rotary vector series. Journal of the Atmospheric Sciences, 36(5), 757-766. Abstract PDF
The analogy between space-time spectra and rotary spectra is discussed. The space-time spectra can be interpreted as the rotary spectra of a wave vector. These spectra are combined to resolve a rotary vector into clockwise and anticlockwise components as well as progressive and retrogressive components. The space-time rotary spectrum analysis is useful for a statistical identification of traveling vortices.
Hayashi, Yoshikazu, and Donald G Golder, 1978: The generation of equatorial transient planetary waves: control experiments with a GFDL general circulation model. Journal of the Atmospheric Sciences, 35(11), 2068-2082. Abstract PDF
In order to study the generation of transient planetary waves in the tropics, the effects of topography, midlatitude disturbances and condensational heat are eliminated one by one from a GFDL general circulation model during the period June and July. The time development and three-dimensional propagation of waves are examined by a space-time spectral analysis using the maximum entropy method.
It is found that the characteristic scale and period of Kelvin and mixed Rossby-gravity waves do not depend on land-sea contrast or the zonal variation of sea surface temperature. Even if midlatitude disturbances are eliminated, both these waves appear in the stratosphere due to the effect of latent heat release in the troposphere. In contrast to Kelvin waves, however, mixed Rossby-gravity waves can be significantly intensified by westward moving midlatitude disturbances which are found to propagate intermittently toward the equator.
Hayashi, Yoshikazu, 1977: On the coherence between progressive and retrogressive waves and a partition of space-time power spectra into standing and traveling parts. Journal of Applied Meteorology, 16(4), 368-373. Abstract PDF
A formula is derived to express the PR coherence between the progressive and retrogressive components in terms of the CS coherence between the cosine and sine space-Fourier coefficients. By the use of the PR coherence the space-time power spectra are partitioned into standing and traveling wave parts.
If the PR coherence is zero, the progressive and retrogressive components do not interfere with each other to form standing wave oscillations with nodes. In this case the CS coherence also becomes zero, if and only if these components have equal amplitudes.
Hayashi, Yoshikazu, 1977: Space-time power spectral analysis using the maximum entropy method. Journal of the Meteorological Society of Japan, 55(4), 415-420. Abstract
A spectral formula in complex representation is derived to compute space-time power spectrum by applying the maximum entropy method. This method gives finer spectral resolutions for shorter time records than conventional methods and is particularly useful in analyzing waves whose amplitude and frequency vary with time. Examples of its application and computer code are also given.
Hayashi, Yoshikazu, and Donald G Golder, 1977: Space-time spectral analysis of mid-latitude disturbances appearing in a GFDL general circulation model. Journal of the Atmospheric Sciences, 34(2), 237-262. Abstract PDF
A space-time spectral analysis is applied to the Northern Hemisphere winter of an 11-layer GFDL general circulation model with seasonal variation. A statistical study is made of the stationary and transient ultralong waves and transient long waves with respect to their wave characteristics, three-dimensional structure and energetics.
The stratospheric stationary waves attain their maximum amplitude in geopotential at the latitudes of the stratospheric jet in agreement with observations and theories, although their amplitude is too large. The tropospheric stationary waves corresponding to the Siberian high and the Aleutian low are characterized by large eddy available potential energy which is mainly converted from zonal available potential energy. On the other hand, the tropospheric stationary wave corresponding to the local intensification of the subtropical jet is characterized by large eddy kinetic energy which is supplied by the energy flux from the region of large eddy energy conversion occurring to the north of the latitude of the Tibetan Plateau.
The transient ultra-long waves are too weak in the troposphere and are associated with a more eastward moving component contrary to those observed in the troposphere. They are characterized by baroclinic energy conversion in the troposphere and barotropic conversion in the stratosphere.
The transient long waves corresponding to cyclones are well simulated and their phase relations agree with both observations and linear theories. Their kinetic energy is largest around 300 mb in agreement with observations, but contrary to linear theories. Their kinetic energy maxima occur over the Pacific and the Atlantic to the east of the maximum latitudinal gradient of the time mean temperature.
Hayashi, Yoshikazu, 1976: Non-singular resonance of equatorial waves under the radiation condition. Journal of the Atmospheric Sciences, 33(2), 183-201. Abstract PDF
A response of large-scale equatorial waves to a thermal or a lateral forcing confined in the troposphere is examined analytically by imposing the radiation condition based on an equatorial beta-plane model without wind shear.
A resonant response with large finite amplitude occurs under the radiation condition, when the vertical scale of the wave coincides with that of the forcing. This "non-singular resonance" is associated with a sharp spectral peak for equatorial waves which are characterized by a small variation of the frequency with the vertical wavenumber. However, such resonant equatorial waves are not realistic, since their vertical velocity is not in phase with the imposed convective heating and their pressure is not in geostrophic balance with the meridional wind of the imposed mid-latitude disturbances.
This study suggests that the forcing cannot be imposed arbitrarily regardless of its feedback. It assures on the other hand that the equatorial waves simulated by a general circulation model are not spurious resonant waves resulting from an artificial reflection at the top of a finite-difference model.
Hayashi, Yoshikazu, 1974: Spectral analysis of tropical disturbances appearing in a GFDL general circulation model. Journal of the Atmospheric Sciences, 31(1), 180-218. Abstract PDF
A space-time cross spectrum analysis is applied to the 11-layer, 2.4 degree mesh GFDL general circulation model with seasonal variation, extending the work of Manabe, et al. A statistical study is made of the model's tropical disturbances during the period July through October with respect to their wave characteristics, three-dimensional structure, energetics, and their role in the general circulation.
Four types of equatorial traveling waves are isolated from stationary waves and ultra-long waves extending from middle latitudes. They are identifiable with observed mixed Rossby-gravity waves (Yanai waves), Kelvin waves, equatorial Rossby-type waves, and easterly waves.
All these traveling waves are maintained primarily by the conversion of available potential energy generated by condensational heating. This heat is associated with traveling rainfall disturbances localized, in particular, in the western Pacific of the northern summer hemisphere where the sea surface is relatively warm.
Hayashi, Yoshikazu, 1973: A method of analyzing transient waves by space-time cross spectra. Journal of Applied Meteorology, 12(2), 404-408. Abstract PDF
Spectral formulas for analyzing transient waves are presented. Cross-spectral analysis of space-Fourier coefficients isolates traveling waves and standing wave oscillations, and provides statistical information concerning their structure and energetics.
Hayashi, Yoshikazu, 1971: Frictional convergence due to large-scale equatorial waves in a finite-depth Ekman layer. Journal of the Meteorological Society of Japan, 49(6), 450-457. Abstract
Frictional convergence due to large-scale equatorial waves discussed by Holton, et al. (1971) and Yamasaki (1971) is re-examined diagnostically on the assumption that the Ekman layer solution does not extend to infinite height. It is found that frictional convergence is not singular but extreme at the critical latitude where the Coriolis frequency is equal to the wave frequency for even meridional modes, while it attains its maximum at the equator for odd modes contrary to the result by Holton, et al. (1971).
Hayashi, Yoshikazu, 1971: A generalized method of resolving disturbances into progressive and retrogressive waves by space fourier and time cross-spectral analyses.. Journal of the Meteorological Society of Japan, 49(2), 125-128.
Hayashi, Yoshikazu, 1971: Instability of large-scale equatorial waves under the radiation condition. Journal of the Meteorological Society of Japan, 49(4), 316-320.
Hayashi, Yoshikazu, 1971: Instability of large-scale equatorial waves with a frequency-dependent CISK parameter. Journal of the Meteorological Society of Japan, 49(1), 59-62.
Hayashi, Yoshikazu, 1971: Large-scale equatorial waves destabilized by convective heating in the presence of surface friction. Journal of the Meteorological Society of Japan, 49(6), 458-466. Abstract
The effect of surface friction is incorporated into a previous model (Hayashi, 1970) of large-scale equatorial waves destabilized by convective heating.
It is found that the growth rate of Rossby type waves is enhanced and that the wave structure in the surface layer is significantly affected by the surface friction. However, the essential features of the previous model are not much altered.
Hayashi, Yoshikazu, 1970: A theory of large-scale equatorial waves generated by condensation heat and accelerating the zonal wind. Journal of the Meteorological Society of Japan, 48(2), 140-160. Abstract
For the purpose of extending the theoretical interpretation of the large-scale equatorial waves discovered by Yanai and Maruyama (1966), a three-dimensional linearized primitive equation model of unstable waves is constructed on an equatorial beta plane. It is assumed that the release of latent heat due to moist convection in the troposphere is disturbed in proportion to the horizontal convergence in the subcloud layer responding to large-scale equatorial waves.
It is found that Mode HB in the theory of unstable low latitude disturbances by Yamasaki (1969) is characterized by complex equivalent depth which simulates many aspects of Yanai-Maruyama waves. This mode is further classified into various meridional modes, following Matsuno (1966).
When the heat in the upper troposphere exceeds a critical value, unstable waves of free internal mode come into existence. Their growth rate increases with increasing heat in the upper troposphere. With the exception of inertio-gravity waves and Kelvin waves, mixed Rossby-gravity waves are the most unstable. The period corresponding to the observed wavelength of 10,000 km coincides with the observed period of about 4 days. The e-folding time is of the order of 10 days which, however, decreases with increasing wavelength.
The energy and momentum budgets are also examined in detail. It is shown that a non-linear forcing by Rossby type waves results in easterly acceleration of the mean zonal wind in the lower stratosphere, while Kelvin waves accelerate a westerly flow.
Yanai, M, and Yoshikazu Hayashi, 1969: Large-scale equatorial waves penetrating from the upper troposphere into the lower stratosphere. Journal of the Meteorological Society of Japan, 47(3), 167-182. Abstract
The three-dimensional structure of large-scale disturbances found in the lower stratosphere and the upper troposphere in the equatorial Pacific is studied in detail by power spectral and synoptic analyses, using the special upper-air observations during the period April through July 1962. It is found that the sharp spectral peak of the meridional component of the wind near the 4.5-day period in the upper troposphere and the lower stratosphere is caused by the westward movement of large-scale eddies which are centered over the equator and penetrating through the tropopause with their axes tilting westward with height.
A spectral method of estimating vertical and horizontal transports of energy is devised, by which energy flux is obtained from the correlation between horizontal wind and temperature or the tilt of phase lines. It is shown that the westward tilt of vertical phase lines or poleward transport of heat indicates the upward transport of wave energy. The large-scale waves in the upper troposphere provide the lower stratosphere with energy of the order of 6 ergs per cm2 sec and the vertical convergence of energy of the order of 1 erg per cm2 sec km occurs at the levels from 15 to 20 km. In the lower stratosphere horizontal convergence of wave energy occurs near the equator.
Yanai, M, T Marayama, T Nitta, and Yoshikazu Hayashi, 1968: Power spectra of large-scale disturbances over the tropical Pacific. Journal of the Meteorological Society of Japan, 46(4), 308-323. Abstract
The power spectra of the meridional component of the wind from the ground to the 30-km level at 17 stations in the tropical and sub-tropical Pacific are studied based on special upper wind observations taken during the period April through July 1962.
In equatorial latitudes, the power spectra show a peak at a period close to 4 days corresponding to the passage of "equatorial waves" in the lower tropospheric easterlies. A very large spectral density is found at the periods 4 to 5 days throughout the upper troposphere and the lower stratosphere where the mean wind is from the west. The peak spectral density reaches a maximum at about the 17-km level near the tropopause. The spectral density gradually decreases with height in the stratosphere where the mean wind is from the east.
In sub-tropical latitudes, large disturbance energy is associated with the upper tropospheric westerlies and a large portion of the spectral density is contained in the wave period longer than 5 days. A sharp suppression of the spectral density takes place at the lower boundary of the stratospheric easterlies.
From the computation of the coherence and the phase difference of the meridional component of the wind, the vertical and horizontal structure of the disturbances is studied. The large horizontal extent and the westward inclination of phase lines of the disturbances in the upper troposphere and in the lower stratosphere are revealed. The horizontal coherence of the lower tropospheric disturbances in the east-west direction is very low. The phase lines of the lower tropospheric disturbances are inclined eastward with height. The average wavelength of the disturbances at various levels is estimated from the relation between the phase difference and the longitudinal difference of the stations.
