Temperature fluctuations at various time scales fit better to Levy distributions than to Gaussian distributions
Temperature fluctuations show scale-free power spectra. This allows a single number to characterize the correlation structure.
Stochastic Processes
I am working on a rigorous method to perform Monte Carlo simulations of nonequilibrium systems in which both transition probabilities and the time scale are specified for any energy-based kinetic Monte Carlo simulation. My nonequilibrium method recaptures detailed balance and Boltzmann statistics in the equilibrium limit. I have observed that temperature distributions on the scale of one day or less fit Levy distributions after appropriate filtering. Verification will strongly impact the results of stochastic climate models since Levy distributions predict more extreme events (Balter, et al. in prep).
Rigorous methods for evolving Monte Carlo simulations of nonequilibrium systems are of great value to the computational physics community. Monte Carlo methods are finding new applications for systems that are strictly kinetic, including but not limited to my CPM simulations of biological systems and foams. Methods exist for mapping Monte Carlo time to real time in kinetic systems, but these are not rigorous because they are based on Boltzmann transition probabilities, which do not apply out of equilibrium. In my method the transition probabilities are still derived from an energy function, but in a slightly different way.
This work reflects my general interest in stochastic processes which began with nonlinear time series in climate. I have observed that temperature distributions on the scale of one day or less appear to fit well to Levy distributions after appropriate filtering. Verification will stongly impact the results of stochastic climate models since the Levy distributions predict more extreme events (Balter, Brabson, Robeson, in prep). We have a provisional model for how these distributions might be arise in climate through nonlinear feedback.
In the theory of extreme values one can use the generalized extreme value (GEV) distribution, which has a power law decay, to model the behavior of tails. If the temperatures are actually following a Levy distribution, then the entire distribution can be characterized by a power law exponent rather than just the extreme tails. We have a provisional model for how these distributions might be generated through a nonlinear stochastic process. In collaboration with Profs. Ben Brabson and Scott Robeson I am considering the power law decay of the power spectrum as an efficient measure of the correlation structure of temperature time series. By graphing these spatially across large land masses (such as the United States) we hope to discover significant patterns that will inspire further study.