Time Spectral Analysis for the Natural Variability of the Barotropic Model Atmosphere with Annual Cycle Forcing

Abstract

In this study, a long-term (1000 years) integration of a simple barotropic primitive equation model was carried out to investigate the typical magnitude and spectral features of natural variability of the model atmosphere.
The first experiment without an annual-cycle forcing shows no noticeable ultra-low-frequency variability. The frequency spectrum of the model atmosphere is characterized as a white noise for the low-frequency range beyond the period about 50 days. The spectrum then shifts sharply to a red noise for the period shorter than 50 days, indicating a characteristic -3 power slope over the frequency domain. Although no noticeable spectral peak is detected, we can find intraseasonal variability with a period of about 50 days in the time series of the model atmosphere as a result from the sharp transition from the red to white noise. Since the sole energy source of the system is a parameterized baroclinic instability of frequency about (5-day)^-1, we must have a reverse energy cascade from higher- to lower-frequency ranges along the -3 power slope of the red noise spectrum. It is discussed in this study that the spectrum tends to be red over the high-frequency range beyond (50-day)^-1 where a linear relation holds between life-time and spatial scales for prominent atmospheric phenomena. Beyond this period, the internal non-linear dynamics of the primitive equation can not sustain large energy because the spatial scale of the Earth is finite. As a result, the very-low-frequency variability results in the white noise spectrum.
Next, the same simple model is integrated with an annual-cycle forcing for 100 years to investigate the excitation of harmonics and subharmonics expected by the non-linear dynamic modulation of the annualcycle forcing. The results show, however, that the spectral features are not altered by the inclusion of the annual cycle, except for the isolated spectral peak associated with the annual-cycle forcing. We suggest from the results of this study that the harmonics and subharmonics, such as semiannual and biennial oscillations, are not excited solely by the non-linear dynamic modulation of the forced annual cycle in the atmosphere.