Statistics Colloquium

Drought and dry spells are a recurrent feature of the natural climate in the dry zone of Sri Lanka.  The unpredictable pattern of dry spells has already caused significant damages to the agricultural system, livelihood of people and the economy of the country.  An extensive review of statistical anlysis on dry spells  revealed  that no studies were reported to predict the starting date or length of dry spells. Thus there are various directions in climate analysis, where applied statisticians can contribute a major role. In my presentation most recent work carried out by us in modeling starting time and length of critical dry spell is presented along with the problems we faced. Furthermore, some problems in climate analysis which need attention are highlighted. 

Data for this study are daily rainfall from 1950 to 2005 in 11 locations in dry zone (DZ) of Sri Lanka. It was found that the mean number of dry spells (> 7 dry days) per year, irrespective of locations, was 12whilelength of dry spells varied from 15 to 23 days with a mean of 19 days.  The four longest dry spells according to the time of occurence were considered as 'critical dry spells' and were denoted by CDS1-CDS4.The period of onset of critical dry spells is location specific.The mean lengths of four critical dry spells in dry zone were 31, 33, 38 and 33, days respectively.  The length of critical dry spell increased from one  to four  in some locations while decreased in some locations.Based on the results obtained on the temporal and spatial varaibility of critical dry spells, climate charts were developed  to be used by the decision makers in the respective locations. 

Linear and non linear regression  with or without autoregressive error models  were developed to forecast the starting dates of second,  third and fourth critical dry spells separately for all locations using 1950 to 1999 data.  Validty of models were confirmed using various statistical indicators  and alsovalidated for an independant data from  2000 to 2005.These models have admitted some drawbacks.  Neverthless, it was not possible to develop standard models for the four critical dry spell length  series separately.  Thus one critical length series was formed by pooling all four series for a given location.  New types of models known as   non linear bilinear type time series models with one, two or three locational specific input variables were developed to forecast length of a given critical dry spell for each location separately. A new approach was developed to identify location specific input variables using the same series. The prediction performance of the proposed models was demonstrated using a real dataset of 12 individual points. 

The results obtained in this study will be helpful to minimize unexpected damage due to droughts and will   help effective and efficient planning for farmers, irrigation engineers, coconut growers, policy makers and researchers.  One major difficulty is that neither individual critical dry spell series nor pooled series are not equally spaced. The time difference between two consecutive dry spells varies at random. Therefore investigation of use of autoregressive conditional duration (ACD) models is recommended. The major difficulty faced in modeling dry spell properties is that identification of robust models which will a challenging problem to the applied statisticians. Furthermore, forecasting weekly moving total rainfall as well as weekly running total during two inter monsoon periods is another challenging problem in climate analysis in Sri Lanka.