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 annual-cycle 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.