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.

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Analysis and Modeling of the Natural Variability of Climate

Publisher Summary This chapter focuses on the applications and models of self-affine time series. The chapter presents the stochastic component of time series associated with complex phenomena that can have considerable order and, in particular, exhibit self-affine behavior. One of the applications considered is the natural variability of climate. On short time scales, atmospheric temperature observations exhibit deterministic daily and yearly periodicities. The studies of the stochastic variability of climate are important in a variety of ways. They provide an important test of the validity of global circulation models (GCMs). The second application considered is porosity variations in sedimentary basins. A model developed for the growth of atomic surface layers is modified so that it is applicable to the spatial and temporal variations in deposition and erosion. The third application considered is the variability of the earth's magnetic field. The field exhibits a binormal behavior and when a fluctuation crosses the zero intensity value a reversal occurs.

Self-Affine Time Series: II. Applications and Models

http://geomorphology.geo.arizona.edu/PAPERS/pelletier_98.pdf

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

The problem of low-frequency current noise with a 1/f spectrum in solids (flicker noise) is reviewed. The fundamental general properties of this noise are described: frequency-dependence of the spectral density, time-dependence of the correlation function, form of the distribution function of the fluctuations, dependence of the spectral density on the potential applied to the specimen, anisotropy of the fluctuations of the resistivity tensor, correlation length of the fluctuations, dependence of the noise on the dimensions of the specimen and on the concentration of current carriers, the empirical Hooge relationship, etc. A model of 1/f noise is presented and discussed that associates its spectrum with the presence in solids of an extensive hierarchy of relaxation times. Concrete models of systems having an exponentially broad spectrum of relaxation times are described (the McWhorter model, two-level tunneling systems, the disordered Ising kinetic model). The theory and experimental data on current noise caused by temperature fluctuations are analyzed. The problem is treated of surface noise in semiconductors and 1/f noise in metal films.

https://iopscience.iop.org/article/10.1070/PU1985v028n02ABEH003853/pdf

Low-frequency current noise with a 1/ f spectrum in solids

The 1/f spectrum of the ocean surface temperature in the Atlantic and Pacific midlatitudes is explained by a simple vertical diffusion model with a shallow mixed layer on top of a deep ocean The model is forced at the air-sea interface with the total surface heat flux from a 1000 year climate simulation The analysis reveals the role of ocean advection and substantiates estimates of internal thermal diffusivities

1/f model for long-time memory of the ocean surface temperature.

A computation is given of the fluctuations in average temperature of an isolated thin film on a substrate, the noise being due to two causes: (i) fluctuations in blackbody radiation absorbed and emitted by the front surface; (ii) thermal diffusion in the sample and the substrate. The surface source results in a large 1/f range, the level of which decreases with increasing heat conductivity of the substrate; the noise goes over into a 1/f2 spectrum at high frequencies. The noise due to the volume source results in a 1/f1/2 spectrum, going over into a 1/f3/2 spectrum at higher frequencies; the noise also decreases with increasing heat conductivity of the substrate. The integrated total noise is of the order kT20/C . Under most circumstances the spectrum due to the volume source dominates.

Temperature‐fluctuation noise of thin films supported by a substrate

It is shown that the presence of the zero point energy noise term in thermal noise can be detected at 100 GHz, when noise measurements at that frequency can be made with an accuracy of 0.3%.

R. R. Schmidt

Papers

Temperature‐fluctuation noise of thin films supported by a substrate

On the presence of the zero point energy noise term in thermal noise