I know that some people used a simple index to define the Hadley cell intensity, which is the maximum value in the meridional mass streamfunction within the Hadley cell. However I am wondering whether this definition is too simple, if the meridional span of Hadley cell shrinks due to some reason, could we say that the intensity increases at the same time? Any alternative definitions?
Enclosed is a paper/report (31 pages) that presents consistent evidence for an
intensification of the Northern Hemisphere winter Hadley cell since 1950. This may provide some clues for you.
http://www.esrl.noaa.gov/psd/people/quan.xiaowei/PDF/HCpaper.pdf
I don't know if this will help, but I wrote two chapters about the Hadley cell:
1. how it works:
http://www.climatetheory.net/10-the-standard-greenhouse-theory-reconsidered-the-hadley-cycle/
2. How it moves the imfamous missing hot spot to the subtropics:
http://www.climatetheory.net/11-analysing-the-missing-tropical-hot-spot/
This is not accepted science (yet), but it may inspire you!
I've been thinking about diagnostics for the Hadley circulation lately as well. I think you need at least two numbers for the description you are looking for: strength and size. For strength, I find that using the maximum meridional streamfunction works well. For size/width you can use any of several measures that are all pretty similar. Two easy ones are:
A. the latitude where the meridional streamfunction crosses zero.
B. the latitude where the direction of the surface zonal wind switches sign.
A good recent reference:
G. Gastineau, L. Li, and H. Le Treut. Some atmospheric processes governing the large-scale tropical circulation in idealized aquaplanet simulations. Journal of the Atmospheric Sciences, 68(3):553–575, 2011.
Note that zonal asymmetries and seasonal effects are sources of noise in these calculations, so you might need to focus on particular sectors and/or seasons to get a clean/significant signal.
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