I dont know if this paper or the cited references would be of help.  Often in prediction, areas with long term data richness are used to develop maps that predict conditions on larger scales.  But also to do this, a variety of smaller short term or local data bases may be used to help fill in the large blanks and areas with inadequate data, with the understanding that short term data has less reliability and precision.  

In addition, we must consider that areas can have cycles of wet and dry years, so with only 16 years of data and nothing else, you dont have much to go on relative to long term cycles.  My suggestion would be to take what you have, and try to find as many other stations with more long term data of perhaps 50 years plus for adjacent areas or bordering countries to help.  How does your 16 years of data compare to their data for the 16 years relative to their long term data.  In addition, you may want to consider any historic records relative to drought, crop losses, etc. and the frequency and severity of these reports, even if not the actual rainfall and temperature data you seek.

When comparing to conditions of adjacent areas, atmospheric, geology/soils and topographic patterns or differences can also affect rainfall, temperature and availability of moisture for plants that may be adjustments to consider.  One caveat also to consider, if you live in an arid area, where aridity is common occurrence, you may be able to use shorter periods of record and see if you can find other supportive data such as streamflow, water table (well) or other supportive or surrogate long term records you can correlate the existing data to.  

Concerning the attachment, Dr. Motmot, 2010 authored and no mention of being published, but you may want to check further if cited. 

Since there are several methods that can estimate aridity index, some may be able to use annual data.  It has been years since I used the Thornthewaite-Mather approach to estimate monthly ET, and use the calculations to help evaluate a water balance on a small gauged catchment in Missouri.  

Most of the methods I have considered would be more of a monthly frequency of data, as a help to evaluate stress on plants, streamflow, water tables or wells, aquatic organisms, etc. Alot may depend on how you might want to apply the annual data, and does it meet your intent.  

http://www.cgiar-csi.org/wp-content/uploads/2012/11/Global-Aridity-and-Global-PET-Methodology.pdf

http://www.cgiar-csi.org/data/global-aridity-and-pet-database

http://www.droughtmanagement.info/aridity-index-ai/

http://webcache.googleusercontent.com/search?q=cache:qvi3vb8TTVAJ:www.springer.com/cda/content/document/cda_downloaddocument/9783642291036-c2.pdf%3FSGWID%3D0-0-45-1336215-p174311469+&cd=17&hl=en&ct=clnk&gl=sa

Thank you all

minimum 30 years data is required

Dear Nawbahar

As usual minimum of 30 years of data is required in climatic studies and it seems that it is valid for your research...it is my opinion...Good Luck

Thank you 

Dear Dr. Nawbahar, it might be useful to use the forcasting equation in Ms Excel, you can predict you time seies from 15 to be 30 years. On other hand please read these researches.

https://www.researchgate.net/publication/311487075_Monitoring_drought_trends_induced_climate_variability_over_Egypt_using_MODIS_NDVI_satellite_data_and_Drought_Indices?ev=prf_pub

https://www.researchgate.net/publication/283537262_Evaluation_Of_Present-Day_Climate-Induced_Desertification_In_El-Dakhla_Oasis_Western_Desert_Of_Egypt_Based_On_Integration_Of_MEDALUS_Method_GIS_And_RS_Techniques?ev=prf_pub

Article Monitoring Drought Trends Induced Climate Variability over E...

Article Evaluation Of Present-Day Climate-Induced Desertification In...

Thank you

Dear Nawbahar,

Aridity may be counted for one month, for one season, for one year, for several years or several decades. See link:

https://www.researchgate.net/publication/257449375_Aridity_in_Vojvodina_Serbia

Regards,

Milivoj B. Gavrilov

Article Aridity in Vojvodina, Serbia

If you have daily data it is possible 

Thank you all

i agree with Hansen