Mixing entropy analysis of dispersal of aircraft emissions in the lower stratosphere

A trajectory calculation is used to compare the characteristic time for northern midlatitude aircraft emissions to disperse during both summer and winter. The mixing process is summarized by the time evolution of the “mixing entropy,” which is proportional to the number of ways of partitioning N parcels over M equal area subregions of the hemisphere. The mixing entropy is a measure of the disorder in the parcel distribution and quantifies the approach to a spatially uniform state as time increases. We show that the time for a single release of exhaust to become mixed down to length scales of the order of 800 km is about 2 months in winter and at least 4 months in summer. We also examine the time evolution of the mixing entropy of emissions from a continuous source over two 6-month periods starting in January and June. For a single continuous source, which represents a persistent and highly asymmetric perturbation, we find that the horizontal distribution of the total emissions reaches a mixing steady state in 6–8 months. On this timescale the mixing entropy is close to the maximum value, and the likelihood of large temporal fluctuations becomes small. The dependence of the mixing on the location of the source and the effect of multiple flight paths on the overall uniformity of the spatial distribution is also considered.

[1]  Mark R. Schoeberl,et al.  Reconstruction of the constituent distribution and trends in the Antarctic polar vortex from ER‐2 flight observations , 1989 .

[2]  M. McIntyre.  On the Antarctic ozone hole , 1989 .

[3]  Mark R. Schoeberl,et al.  A computation of the stratospheric diabatic circulation using an accurate radiative transfer model , 1987 .

[4]  J. Gille,et al.  Stratospheric transport from the tropics to middle latitudes by planetary-wave mixing , 1993, Nature.

[5]  W. Baker,et al.  Meteorological atlas of the Southern Hemisphere lower stratosphere for August and September 1987 , 1988 .

[6]  A. Douglass,et al.  Tracer exchange between tropics and middle latitudes , 1992 .

[7]  P. Mote,et al.  Simulation of the Pinatubo aerosol cloud in general circulation model , 1991 .

[8]  A. J. Miller,et al.  The anomalous arctic lower stratospheric polar vortex of 1992-1993 , 1994 .

[9]  Tim Palmer,et al.  The «surf zone» in the stratosphere , 1984 .

[10]  J. Ottino.  The Kinematics of Mixing: Stretching, Chaos, and Transport , 1989 .

[11]  Anna Jones,et al.  Ozone Response to Aircraft Emissions: Sensitivity Studies with Two-dimensional Models , 1992 .

[12]  Charles R. Trepte,et al.  Tropical stratospheric circulation deduced from satellite aerosol data , 1992, Nature.

[13]  P. Newman,et al.  Trajectory modeling of emissions from lower stratospheric aircraft , 1995 .

[14]  Richard B. Rood,et al.  Tracer transport for realistic aircraft emission scenarios calculated using a three-dimensional model , 1995 .

[15]  J. R. Holton,et al.  The atmospheric effects of stratospheric aircraft: A current consensus , 1991 .

[16]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[17]  M. Schoeberl,et al.  Conservative-coordinate transformations for atmospheric measurements , 1992 .

[18]  Malcolm K. W. Ko,et al.  Interrelationships between mixing ratios of long‐lived stratospheric constituents , 1992 .

[19]  Mark R. Schoeberl,et al.  The structure of the polar vortex , 1992 .