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Jon D. Pelletier

Publications and source records attributed to Jon D. Pelletier.

8 recordsLinked to original sources
arXiv1997

Why is topography fractal?

The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to -2: S(k) is proportional to k^-2. In addition, river networks are fractal trees that satisfy many power-law or fractal relationships between their morphologic components. A model equation for the evolution of the earth's topography by erosional processes which produces fractal topography and fractal river networks is presented and its solutions compared in detail to real topography. The model is the diffusion equation for sediment transport on hillslopes and channels with the local diffusivity proportional to the square of the discharge. The dependence of diffusivity on discharge follows from fundamental equations of sediment transport. We study the model in two ways. In the first analysis the diffusivity is parameterized as a function of relief and a Taylor expansion procedure is carried out to obtain a differential equation for the landform elevation which includes the spatially-variable diffusivity to first order in the elevation. The solution to this equation is a self-affine or fractal surface with linear transects that have power spectra S(k) is proportional to k^-1.8, independent of the age of the topography, consistent with observations. The hypsometry produced by the model is skewed such that lowlands make up a larger area than highlands as in real topography. In the second analysis we include river networks explicitly in a numerical simulation by calculating... Abstract continued in paper.

physics.geo-ph↗
arXiv1997

Statistical analysis and modeling of variations of the earth's magnetic field

Power spectral analyses of the dipole moment of the earth's magnetic field inferred from ocean sediment cores and archeomagnetic data from time scales of 100 yr to 4 Myr have been carried out. The power spectrum is proportional to 1/f where f is the frequency. These analyses compliment previous work which has established a 1/f^2 spectrum for variations at time scales less than 100 yr. Power spectral analyses of inclination and declination inferred from lake sediments from time scales of 10 yr to 30 kyr have also been performed. The spectra are constant above time scales of 3 kyr, proportional to 1/f^2 from time scales of 500 yr to 3 kyr, and constant again below time scales of 500 yr. The 3 kyr time scale is associated with the decay time of the quadrupole moment. We test the hypothesis that reversals are the result of variations in dipole intensity with a 1/f spectrum which occasionally are large enough to cross the zero intensity value. Synthetic binormal time series with a 1/f power spectrum representing variations in the earth's dipole moment are constructed. Synthetic reversals from these time series exhibit statistics in good agreement with the reversal record. 1/f noise behavior is reproduced with a model of magnetic diffusion in the earth's core driven by dynamo action modeled as a random amplification or destruction of the local magnetic field.

physics.geo-ph↗
arXiv1997

Scale-invariance of soil moisture variability and its implications for the frequency-size distribution of landslides

Power spectral analyses of soil moisture variability are carried out from scales of 100 m to 10 km on the microwave remotely-sensed data from the Washita experimental watershed during 1992. The power spectrum S(k) has an approximately power-law dependence on wave number k with exponent -1.8. This behavior is consistent with the behavior of a stochastic differential equation for soil moisture at a point. This behavior has important consequences for the frequency-size distribution of landslides. We present the cumulative frequency-size distributions of landslides induced by precipitation in Japan and Bolivia as well as landslides triggered by the 1994 Northridge, California earthquake. Large landslides in these regions, despite being triggered by different mechanisms, have a cumulative frequency-size distribution with a power-law dependence on area with an exponent ranging from -1.5 to -2. We use a soil moisture field with the above statistics in conjunction with a slope stability analysis to model the frequency-size distribution of landslides. In our model landslides occur when a threshold shear stress dependent on cohesion, pore pressure, internal friction and slope angle is exceeded. This implies a threshold dependence on soil moisture and slope angle since these factors are primarily dependent on soil moisture. Abstract continued in paper.

physics.geo-ph↗
arXiv1996

Analysis and modeling of scale-invariance in plankton abundance

The power spectrum, $S$, of horizontal transects of plankton abundance are often observed to have a power-law dependence on wavenumber, $k$, with exponent close to -2: $S(k)\propto k^{-2}$ over a wide range of scales. I present power spectral analyses of aircraft lidar measurements of phytoplankton abundance from scales of 1 to 100 km. A power spectrum $S(k)\propto k^{-2}$ is obtained. As a model for this observation, I consider a stochastic growth equation where the rate of change of plankton abundance is determined by turbulent mixing, modeled as a diffusion process in two dimensions, and exponential growth with a stochastically variable net growth rate representing a fluctuating environment. The model predicts a lognormal distribution of abundance and a power spectrum of horizontal transects $S(k)\propto k^{-1.8}$, close to the observed spectrum. The model equation predicts that the power spectrum of variations in abundance in time at a point in space is $S(f)\propto f^{-1.5}$ (where $f$ is the frequency). Time series analysis of local variations of phytoplankton and zooplankton yield a power-law power spectrum with exponents -1.3 and -1.2, respectively from time scales of one hour to one year. These values are roughly consistent with the model prediction of -1.5. The distribution of abundances is nearly lognormal as predicted. The model may be more generally applicable than for the spatial distribution of plankton. I relate the model predictions to observations of spatial patchiness in vegetation.

ao-sci↗
arXiv1996

Kardar-Parisi-Zhang model for the fractal structure of cumulus cloud fields

We model the ascent of warm, moist air in the Earth's atmosphere by turbulent convection and expansion with the KPZ equation, familiar in the physics literature on surface growth. Clouds form in domains where the interface between the rising air and its surrounding air achieves an elevation higher than that necessary for condensation. The model predictions are consistent with the perimeter fractal dimension and the cumulative frequency-size distribution of cumulus cloud fields observed from space.

ao-sci↗
arXiv1995

A Stochastic Diffusion Model of Climate Change

We present a model for variations in atmospheric temperature from time scales of one day to one million years based on a stochastic diffusion (random walk) model of the turbulent transport of heat energy vertically in a coupled atmosphere-ocean model. The predictions of the model are supported by station records and paleoclimatic proxy data of temperature variations.

ao-sci↗
arXiv1995

Variations in Solar Luminosity from Time Scales of Minutes to Months

We present the power spectrum of solar irradiance during 1985 and 1987 obtained from the ACRIM project from time scales of minutes to months. At low frequency the spectra are Lorentzian. At higher frequencies they are proportional to $f^{-{1/2}}$. A linear, stochastic model of the turbulent heat transfer between the granulation layer (modeled as a homogeneous thin layer with a radiative boundary condition) and the rest of the convection zone (modeled as a homogeneous thick layer with thermal and diffusion constants appropriate the lower convection zone) predicts the observed spectrum.

astro-ph↗