Drought prediction can be done from simple data analysis or using ANN or by simple ITK whatever it may be the best way to predict for tropical conditions is?
I guess, as first you should try to define better what is "drought" for you. Then you can try to identify the main drivers and therefore the best predictor(s) to use. In any case the "quality" of your predictions will depend from the reliability of the prediction of the selected predictor(s)
Drought is a multifarious hazard. From my point of view you first have to decide what kind of drought should be assessed. More interestingly, the underlying processes in drought generation and propagation should be understand to develop a reliable drought prediction approach.
A few of categories of droughts have been identified. It is also known that meteorological and hydro droughts occur on varied time scales. Prediction of drought therefore depends on what kind of droughts and the time scales you concern with. In any case, long-term historical data of relative variables and the understanding of mechanism of droughts are necessary.
When you want to predict agricultural drought you should analyze the amount of available water and ET that these parameters are related to precipitation, ETO, soil water, temrature and source of water supply.
thre are many indices for this aim: pdsi, phdi, ......