To estimate the dry spells in the future, you might use different statistical methods e.g. probability analysis pointed by Kenneth M Towe, or you may use Global Climate models (GCMs). GCMs provide geographical and physical estimates of regional climate and climate change using three dimensional grids over the globe. The newest generation GCMs are used in the CMIP5 to understand the past and future climate changes.

Wet spell defined as the number of consecutive days with greater than zero precipitation and dry spell length refers to the number of consecutive days with an absence of precipitation for that particular area. Statistical Down Scaling Model SDSM, can easily be used to estimate the length of Dry/wet days from GCMs.

http://co-public.lboro.ac.uk/cocwd/SDSM/

Best!

Thank you, Sir Towe! Uncertainty in replicating the observed series specially precipitation is the big issue of GCM models, however, the confidence in model prediction can be enhanced by calibrating model predictor variable and correcting the bias on the basis of observed data.

Most of these climate models currently running provides precipitation and temperature, which are enough for the aforementioned question.

All the best! 

Dear Muhamad,

You can find various methods and studies. Please check the attached paper for inspiration.

Best!

In California we are having the worst "dry spell" according to tree ring studies, in the last 500 years, and after four years, many of our water supply reservoirs will be at zero in the next six months, for the 38 million people and the millions of acres of farmland that depend on them. 

All the climatologists and meteorologists have not yet invented any reliable method to estimate the duration of this dry spell, and a picture that I took this week of the Folsom Lake above Sacramento is a reminder how vulnerable we are, when we have no science to predict the length of dry spells.  That photo was taken from the edge of the lower boat ramp at what would be normally the lowest lake level in late summer.