i guess Pm concentrations are more due to regional influence and certainly are indicative of desertification but direct correlation of Pm and desertification will not be very realistic.

What do you mean by desertification area "spatial extent"? there will be no direct correlation possibile. Also i will suggest use aridity rather than term desertification. Certainly NDVI can be related to vegetation presence or absense which might be due to aridity or loss of soil moisture, try correlating SAVI as well. But PM counts I doubt have any direct bearing as much of it is due to long range transport.

I think you can try restrend method which involve controlling climate components of NDVI due to precipitation and or soil moisture and then examine the trend of the remaining fraction. The method assumed trend of the fraction of NDVI independent of climate is an indication of either greening (postive) or desertification (browning).

I agree with Mr. Yahya Ibrahim that the long term monitoring of NDVI can help us to identify hot spots of land degradation area. I suggest you look over the recent working paper published at ZEF university of Bonn  in the following link. http://www.zef.de/uploads/tx_zefnews/zef_dp_193.pdf

good luck

I think you have combined all of the important desertification issues into one complete package, with one exception.  

Instead of using PM 10 and PM 2.5 I would use the NAAPS micrograms per cubic meter at http://www.nrlmry.navy.mil/shared-bin/display_image.cgi?URL=/aerosol_web/globaer/ops_01/india/current.gif.  

The atmospheric dust contributes at least two things, it warms the air so that the dew point changes and rain clouds cannot form, and has a blocking effect when moisture is trying to move into an area, can form a wall against it, or can form a pocket that stalls the moisture, causing floods where the pocket is located.

The range of measurements that NAPPS have mapped is between 20 micrograms to >10,240 but I am seeing drought conditions starting at the lowest levels between 20-40 micrograms, like at http://www.ecoseeds.com/2012drought.html.