Yoshikazu Hayashi

Space-Time Spectral Analysis of Rotary Vector Series

Abstract 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.

Spectral Analysis of Tropical Disturbances Appearing in a GFDL General Circulation Model

Abstract A space-time cross spectrum analysis is applied to the 11-layer, 2.4° mesh GFDL general circulation model with seasonal variation, extending the work of Manabe et al. A statistical study is made of the models 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.

Confidence Intervals of a Climatic Signal

Abstract 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.

Estimation of Nonlinear Energy Transfer Spectra by the Cross-Spectral Method

Abstract 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.

Observed and Simulated Energy Cycles in the Frequency Domain

Abstract 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 relati...

Non-Singular Resonance of Equatorial Waves Under the Radiation Condition

Abstract 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 ...

Estimation of Atmospheric Energetics in the Frequency Domain during the FGGE Year

Abstract 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...

A Method of Estimating Space-Time Spectra from Polar-Orbiting Satellite Data

Abstract 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.

Vertical-Zonal Propagation of a Stationary Planetary Wave Packet

Abstract 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.

Interpretations of Space-Time Spectral Energy Equations

Abstract Interpretations are given of two different formulations of space-time spectral energy equations derived by Kao (1968) and Hayashi (1980). Contrary to Kaos 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, Hayashis formulation is consistent with Saltzmans (1957) wavenumber spectral energy equation, since his formulation corresponds to the real part which governs the growth rate (time change of amplitude).