On the temporal variance of stratospheric trace gas concentrations

The relative variances in stratospheric observations of longlived trace gases, CH$_{4}$, N$_{2}$, CF$_{2}$Cl$_{2}$, CFCl$_{3}$, show large differences. These differences are greatly reduced when the local me an standard deviation is normalized to the local vertical gradient. This ratio, called "equivalent displacement height" exhibits a characteristic vertical profile which is very similar for all the longlivedtrace gases as well as for O$_{3}$. With the help of this ratio it is demonstrated that the variances are essentially due to natural causes, i.e. transport. Using the mixing length hypothesis a theoretical expression for the equivalent displacement height is derived. From it the meridional slope of the mixing surfaces and the mixing length can be calculated as function of the altitude. Additional information is obtained on the variance of that slope. The uncertainty of the measured mean trace gas profiles is defined