CEE Paper Published in Physical Review Letters
Veronica Nieves, Ph.D., a physicist postdoctoral scholar who was awarded a Balsells Fellowship in 2009, had her paper “Maximum Entropy Distributions of Scale-Invariant Processes” published in Physical Review Letters (PRL), Vol. 105, Issue 11. Nieves’ research for the paper is in the research group of Visiting Professor Rafael L. Bras in the Department of Civil and Environmental Engineering (CEE) at The Henry Samueli School of Engineering at UC Irvine.
Nieves, who defended her Ph.D. in 2008 at the Universitat Politecnica de Catalunya, has been working with Bras and Jingfeng Wang, Ph.D., an associate researcher, for almost a year on an Army Research Office-sponsored project entitled “Using the Maximum Entropy Principle as a Unifying Theory for Characterization and Sampling of Multi-scaling Processes in Hydrometeorology”.
Many variables in nature such as soil moisture and topography exhibit patterns that look similar at different resolutions. The Principle of Maximum Entropy (MaxEnt) is proposed to show how these variables can be statistically described using their scale-invariant properties and geometric mean. MaxEnt predicts with great simplicity the probability distribution of a scale-invariant process in terms of macroscopic observables and offers a universal and unified framework for characterizing such multiscaling processes.
The original goal of the project was to design an optimal data-sampling network using the concept of entropy as a measure of information so that the maximum amount of information is gathered under certain physical and financial constraints. The first step towards that goal is to characterize the statistical properties of the hydrological, meteorological and geographical variables to be sampled through their probability distributions.
The group applied MaxEnt to derive the probability distributions, as one major advantage of this approach is that the parameters of the MaxEnt distributions are related to a small number of observable quantities without computing histograms using a large number of data points. These MaxEnt distributions may be directly tested with those obtained through histograms.
The project led to another major step in developing an innovative model of surface heat fluxes also using the concept of entropy through the Principle of Maximum Entropy Production (MEP) as a special case of the general MaxEnt applied to non-equilibrium thermodynamic systems. Part of Nieves’ upcoming research is to further test the MEP model for producing global maps of heat fluxes over landmasses, oceans and snow/ice caps, which play important roles in modeling and monitoring global climate change and its impacts on the environment.
The paper, co-authored by Nieves, Elizabeth Wood, Wang and Bras, can be found online at http://prl.aps.org/abstract/PRL/v105/i11/e118701.