Time-Reversibility in Atmospheric Dispersion

Due to the chaotic nature of atmospheric dispersion, small deviations, e.g., numerical errors in dispersion simulations, increase rapidly over time. Therefore, the accuracy of backward simulations is limited. In the paper, the degree of the fulfillment of time-reversibility over different time periods is investigated by a Lagrangian dispersion model at a global scale using pollutant clouds consisting of a large number of particles. The characteristics of the pollutant clouds in the backward simulation are compared to those in the forward simulation. In order to characterize the degree of time-reversibility, Lagrangian quantities, such as the fraction of particles that return to the initial volume, the center of mass and the standard deviation of the pollutant clouds, are determined. Furthermore, the overlap and the Pearson’s correlation coefficient between the forward and backward clouds are also investigated. Both a case study and global results are presented. Simulations reveal that the accuracy of time-reversibility decreases in general exponentially in time. We find that after the Lyapunov time of the dispersion (in our case three to four days), the results of the backward tracking become unreliable, and any sign of time-reversibility is lost.