Is there any way to measure of Gaussian-ness? I have some sampled data that has $1/f$ noise in it, with departures from the mean. These are long term departures. I could use something like a median filter but the window length would be longer than I would like.


Is there any way to measure its departure from a Gaussian distribution? 
Or measure how 'Gaussian-like' a time series statstical sample is?
One way to measure the similarity between two distributions is the Kullbeck-Leibler divergence. Granted, it is not a norm because it is not symmetric, but it is a way of quantifying the distance between two pdfs. 

EDIT: There is a topic called "Normality testing" or "Gaussianity testing" that is devoted to that very task. Perhaps some tools from that field will help.