I think there are a number of ways to see the transition between dry and wet seasons. You can choose one of the three variables or choose all three of them namely, Rainfall, NDVI, Surface Temperature for the time period which you are interested in and create a time series like the ones shown in the examples (Check attached links). The aim with a time series remote sensing satellite data analysis would be to monitor the temporal changes occurring in and around the area of interest with respect to the amount of rainfall, surface temperature and the amount of greenness and correlate them with ground conditions. The links which I have attached are from NASA Earth Observatory which shows global time series maps of various variables. I can imagine if you make a similar time series map for south of Amazon region the picture would become much clearer and you will be able to draw relevant conclusions to ascertain the transition between dry/wet seasons based on the variables. This is just one of the ways to answer the question. May be there are better ways.

http://earthobservatory.nasa.gov/GlobalMaps/view.php?d1=TRMM_3B43M

http://earthobservatory.nasa.gov/GlobalMaps/view.php?d1=MOD13A2_M_NDVI

http://earthobservatory.nasa.gov/GlobalMaps/view.php?d1=MOD11C1_M_LSTDA

Hi,

 You can use NDWI if you are looking for wetness index of soil. As the concerned region is quite complicated, it would be better if you can conduct field - survey and collect the MODIS imageries. I think that might help you. Also, follow Varghese.

Good luck!!

For the identification of the transition between dry and wet spell, you may use climatological rainfall of the particular region. 

if you get positive anomalies- i.e. the rainfall is above than the climatological mean, it will be an indicator of the wet spell, like wise you can find out the dry spells.. 

once you get dry and wet spells estimated in terms of the rainfall anomalies, try to relate them with other meteorological parameters. 

The transition period between dry and humid seasons is not my topic. I am working on the regulation of insect development/reproduction by day-length; particularly on the resumption of photoperiodic response after completion of diapause of adults - recurrent photoperiodic response (e.g. Carabus yaconinus [Psyche 2012: Adult diapause in Coleoptera].

Thanks a lot!

All of you gave me great ideas for my work.

Regards! :)