The power spectral density of atmospheric temperature from time scales of 10^-2 to 10⁶ yr

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.