Diagnosing mixing properties in model simulations for CH4 in the stratosphere

Isentropic mixing properties in the stratosphere modeled by the forward calculation of an inverse model (TM5-4DVAR) are evaluated against Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) and Microwave Limb Sounder (MLS) observations. The isentropic mixing processes are separated into large-scale stirring described by the "equivalent length" and small-scale diffusion described by the diffusivity. Compared to the measurements, we find that the modeled stirring is not strong enough and that the small-scale diffusivity is too large. TM5-4DVAR produces excessive mixing-induced poleward flux for stratospheric CH4. The flux convergence presents negative biases in the tropics and positive biases in the polar regions. The biases cannot be reduced by improving the horizontal resolution only. Modeled isentropic mixing depends on the horizontal as well as the vertical resolution of the model. An increase in vertical resolution reduces numerical diffusion of the model in the vertical. The decreased vertical diffusion leads to reduction in the modeled isentropic diffusivity. Biases in modeled total column-averaged mixing ratios of CH4 are significant for both models with a coarse vertical resolution of 4 degrees x 6 degrees x 25 (and 2 degrees x 3 degrees x 25, 1 degrees x 1 degrees x 25) and an improved one of 1 degrees x 1 degrees x 40. They are estimated to be 7-14 and 3-7 ppb in the winter extratropics under the assumption that isentropic mixing is dominant over vertical transport on a time scale of 3 days. Correspondingly, resulted biases in inverted CH4 surface emissions are estimated to be 0.5-1 and 0.2-0.5 mg/m(2)/hr, respectively, in the extratropics.