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.
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, 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 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.
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.
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, 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, 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, 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, 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.