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Yoshikazu Hayashi

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.

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Yoshikazu Hayashi

Abstract

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.

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Yoshikazu Hayashi

Abstract

Spectral formulas for analyzing transient waves are presented. Cross-spectral analysis of space-Fourier coefficients isolates travelling waves and standing wave oscillations, and provides statistical information concerning their structure and energetics.

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Yoshikazu Hayashi

Abstract

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).

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Yoshikazu Hayashi

Abstract

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.

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Yoshikazu Hayashi

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.

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Yoshikazu Hayashi

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 model are not spurious resonant waves resulting from an artificial reflection at the top of a finite-difference model.

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Yoshikazu Hayashi

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 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.

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Yoshikazu Hayashi

Abstract

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.

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Yoshikazu Hayashi

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.

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