THE POWER SPECTRAL DENSITY OF ATMOSPHERIC TEMPERATURE FROM TIME SCALES OF 10-2 TO 106 YR

Abstract

After removing annual variability, power spectral analyses of local atmospheric temperature from hundreds of stations and ice core records have been carried out from time scales of 10−2 to 106 yr. A clear sequence of power-law behaviors is found as follows: (1) from 40 ka to 1 Ma a flat spectrum is observed; (2) from 2 ka to 40 ka the spectrum is proportional to f−2 where f is the frequency; and (3) below time scales of 2 ka the power spectrum is proportional to f−1/2. At time scales less than 1 month we observe that the power spectra of continental stations become proportional to f−3/2 while maritime stations continue to have power spectra proportional to f−1/2 down to time scales of 1 day. To explain these observations, we model the vertical transport of heat in the atmosphere as a stochastic diffusion process. The power spectrum of temperature fluctuations at the earth's surface expected from this model equation in a two-layer geometry with thermal and eddy diffusion properties appropriate to the atmosphere and the ocean and a radiation condition at the top of the atmosphere agrees with the observed spectrum. The difference in power spectra between continental and marine stations can be understood with this approach as a consequence of the air mass above a maritime station exchanging heat with both the atmosphere above and the ocean below while a continental station exchanges heat mostly with the atmosphere above.