At the moment only two easy usable norms are available: the standard norm and the LogNorm.
More different normalization would be a nice and easy way to modifiy the colormap useage.
(In #875 it was discussed to add a symmetric norm for diverging colormaps. See the comment by @pelson , for instance #875 (comment) )
The code for the symmetric norm is available here: https://github.com/SciTools/iris/blob/master/lib/iris/palette.py#L144
Its standalone in that file, and it would be great to get it into mpl. Unfortunately I am pretty tight for time for the next couple of weeks so wont be able to turn this into a PR. Feel free to do so if you wish.
Also @efiring was working on a vmid argument that would create a symmetric norm