Standardised Precipitation Index

To compute standard precipitation index (SPI), IMDs high resolution (0.250 x 0.250) daily gridded rainfall data (Pai et al. 2014) has been used.

The SPI is an index developed by McKee et al. (1993) based on the probability of rainfall for the time scale of interest and is relatively less complex to compute. The time scale reflects the impact of drought on the availability of the different water resources. Soil moisture conditions respond to rainfall anomalies on a relatively short scale. Groundwater, stream flow, and reservoir storage reflect the longer-term rainfall anomalies. For the calculation of SPI for any location, long time series of rainfall for the desired period (here daily rainfall data for the period 1901-2010) is used. This long time series of rainfall is fitted to a probability distribution, which is then transformed into a standardized normal distribution so that the mean SPI for the location and desired period is zero. Positive SPI values indicate greater than median rainfall and negative values indicate less than median rainfall. The classification of the dry/wet spell intensities based on the SPI value is as follows;

It is called mildly dry for SPI value from -0.99 to 0, moderately dry for SPI value from -1.0 to -1.49, severely dry for SPI value from -1.5 to -1.99 and extremely dry for SPI value of -2 and less.

It is called mildly wet for SPI value from 0 to 0.99, moderately wet for SPI value from 1.0 to 1.49, severely wet for SPI value from 1.5 to 1.99 and extremely wet for SPI value of 2 and more.

The gridded daily rainfall data series was fitted to the gamma distribution. The gamma probability distribution function (pdf) is given as.

f (x) = (1 / baΓ(a) )xa-1e-x/b

for x >0, where a>0 & b>0 are the shape and scale parameters respectively, x>0 is the rainfall and Γ(a) is the gamma function.

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The aim of fitting the distribution to the data is to compute a and b. Integrating pdf with respect and inserting the estimated values of parameters a and b, the gamma cumulative distribution function (cdf) is computed at each value of x. The cdf is then transformed into the standard normal distribution to yield SPI. More details regarding computing SPI are available in (Pai et al. 2011) .

References:

1. McKee T.B., Doesken N.J., Kliest J. 1993: The relationship of drought frequency and duration to time scales, In proceedings of the 8th Conference on Applied Climatology, 17-22 January, Anaheim, CA, American Meteorological Society: Boston, MA; 179-184.

2. Pai. D.S., Latha Sridhar, Pulak Guhathakurta and H. R. Hatwar. 2011: District-Wise Drought Climatology Of The Southwest Monsoon Season over India Based on Standardized Precipitation Index (SPI), Nat. Hazards, I DOI10.1007/s11069-011-9867-8.

3. Pai. D.S., Latha Sridhar, M. Rajeevan, O.P. Sreejith, N.S. Satbhai and B. Mukhopadhyay. 2014: Development of a very high spatial resolution (0.250 x 0.250) Long period (1901-2010) daily gridded rainfall data set over the Indian region”, Mausam, 65, 1, PP 1-18.