The use of chaos metrics to analyze Lagrangian particle diffusion models

Abstract

Chaos metrics are examined as a tool to analyze atmospheric three-dimensional dispersion models at the individual particle rather than the aggregate level. These include the self-affine fractal dimension, D (^), Shannon entropy, S, and Lyapunov exponent, (^). Intercomparison of these metrics is first performed with the one-dimensional logistics difference and the two-dimensional Henon systems of equations. The fractal dimension and Shannon entropy are then measured as a function of the inverse Monin-Obuhkov length (1/L) for two three-dimensional Lagrangian particle dispersion models, the McNider particle dispersion model and the NPS particle dispersion model now under development. The fractal dimension and Shannon entropy uncover weaknesses in both models which are not obvious with standard geophysical measures. They also reveal similarities and difference between the atmospheric models and simple chaos systems. Combined, these chaos measures may lend detailed insight into the behavior of Lagrangian Monte Carlo dispersion models in general. .