Analysis and Modeling of the Natural Variability of Climate

After removing annual variability, power spectral analyses of local atmospheric temperature from hundreds of stations and ice core records have been carried out from timescales of 1 day to 200 kyr. A clear sequence of power-law behaviors is found as follows: 1) from 40 kyr to 200 kyr a flat spectrum is observed, 2) from 2 kyr to 40 kyr the spectrum is proportional to f22 where f is the frequency, and 3) below timescales of 2 kyr the power spectrum is proportional to f21/2. At timescales of less than 1 month the authors observe that the power spectra of continental stations become propotional to f23/2 while maritime stations continue to have power spectra proportional to f21/2 down to timescales of 1 day. To explain these observations, the authors model the variations in the transport of heat in the turbulent atmosphere by including a noise in the heat flux of a flux-gradient parameterization of convective transport, leading to a stochastic diffusion equation for temperature fluctuations. A correlation analysis of temperature fluctuations vertically in the atmosphere from the TIROS operational vertical sounder is carried out to verify the diffusion model and to estimate the coefficient of vertical eddy diffusivity in the atmosphere. The power spectrum of temperature fluctuations at the earth’s surface expected from this model in a two-layer geometry with thermal and eddy diffusion properties appropriate to the atmosphere and ocean and a radiation boundary condition at the top of the atmosphere exhibits the same spectral form as observed in the instrumental and ice core data.