Standardized Precipitation Index (SPI)

Standardized Precipitation Index (SPI): The SPI is a drought index first developed by T. B. McKee, N.J. Doesken, and J. Kleist and in 1993 (McKee et al. 1993). The SPI is used for estimating wet or dry condition based on precipitation variable. This wet or dry condition can be monitored by the SPI on a variety of time scales from subseasonal to interannual scales. The SPI is expressed as standard deviations that the observed precipitation would deviate from the long-term mean, for a normal distribution and fitted probability distribution for the actual precipitation record. Since precipitation is not normally distributed, a transformation is first applied, followed by fitting to a normal distribution.

Calculation: The SPI calculation is based on the long-term precipitation record for a particular location and long-term period (longer than 30 years is desirable). The calculation method is comprised of a transformation of one frequency distribution (e.g., gamma) to another frequency distribution (normal, or Gaussian). The first step to calculate SPI is to adequately choose a particular probability distribution (e.g., gamma distribution, incomplete beta distribution (McKee et al. (1993, 1995)), and Pearson III distribution (Guttman (1998, 1999))) that reliably fits the long-term precipitation time series and conduct fitting to that distribution. Gamma distribution has been widely used, as the gamma distribution has been understood as the reliable fit to the precipitation distribution. The fitting can be achieved through the maximum likelihood estimation of the gamma distribution parameters. The percentile value from this probability distribution is then transformed to the corresponding value in the new probability distribution. As a result, the probability that the rainfall is less than or equal to any rainfall amount will be the same as the probability that the new variate is less than or equal to the corresponding value of that rainfall amount. The normal distribution is usually used for this another transformation so that the mean and standard deviation of the SPI for a certain station and long-term period is zero and one, respectively (Edwards and McKee 1997). Positive SPI values indicate wet condition greater than median precipitation, whereas negative values the dry condition less than median precipitation. More detailed description of the steps required to calculate the SPI is provided in Lloyd-Hughes and Saunders (2002).

Interpretation: Since the SPI values are obtained from the standard normal distribution, the unit of the SPI can be “standard deviations”. The following table summarizes the cumulative probabilities for various SPI values and possible interpretation of wet (or dry) conditions using the resulting SPI values.

 SPI Cumulative Probability Interpretation -3.0 0.0014 extremely dry -2.5 0.0062 extremely dry -2.0 0.0228 extremely dry (SPI < -2.0) -1.5 0.0668 severely dry (-2.0 < SPI < -1.5) -1.0 0.1587 moderately dry (-1.5 < SPI < -1.0) -0.5 0.3085 near normal 0.0 0.5000 near normal 0.5 0.6915 near normal 1.0 0.8413 moderately wet (1.0 < SPI < 1.5) 1.5 0.9332 very wet (1.5 < SPI < 2.0) 2.0 0.9772 extremely wet (2.0 < SPI) 2.5 0.9938 extremely wet 3.0 0.9986 extremely wet
The SPI maps can be interpreted at various time scales. This in turn indicates that the SPI is useful in both short-term and long-term applications. These time scales reflect the impact of drought on the availability of the different water resources. For instance, soil moisture conditions respond to precipitation anomalies on a relatively short scale. Groundwater, streamflow, and reservoir storage reflect the longer-term precipitation anomalies. For these reasons, SPI was originally calculated for 3–, 6–,12–, 24–, and 48–month time scales (McKee et al. (1993)). A separate SPI value can be calculated for a selection of time scales, covering the last months (e.g., 3, 6, 12, 24, and 48 months), and ending on the last day of the latest month.