Standardized Precipitation Index (SPI)

The following was contributed by Dr. John Keyantash, California State University, Dominguez Hills, January, 2014:

The Standardized Precipitation Index (SPI) is a widely accepted index for the quantification of drought. In fact, the SPI was recommended through the Lincoln Declaration on Drought as the internationally preferred index for meteorological drought (Hayes et al., 2011). The SPI specifically addresses the intensity of meteorological drought, or precipitation deficit. The shortage of precipitation is a fundamental, intuitive metric for drought—perhaps the most basic description possible. However, interpreting the magnitude of the precipitation deficit can be challenging, because precipitation climatology varies widely over geographical regions as well as temporal scales. For example, when an unusually wet month is embedded within a period of extended drought, should the month be considered droughty or not? Furthermore, the level of the precipitation deficit/excess should be judged relative to some climatological norm for the location. Thus the challenge of drought definition lies not in the raw measurement of hydrometeorological data, but instead the objective assessment of the observations.

The SPI addresses this challenge by comparing the precipitation total for the chosen interval against a cumulative probability distribution for the precipitation data (for the identical interval). For example, what is statistical interpretation of the one-month precipitation total (e.g., 29 mm), compared to all known one-month totals? Obviously, the geographic location and time of year are important restrictions; if the precipitation was during April 2005 in southwestern Idaho, its magnitude should only be judged against April data from other years, in southwestern Idaho. Thus, it is necessary to view the drought according to the climatological norms for the location and season.

The SPI can compute drought intensity over any desired interval, e.g., one month, five months or 200 days. However, one of the most powerful features of the SPI is its intrinsic ability to simultaneously assess drought over a suite of timescales. For example, the precipitation totals for one, three, six, 12, 18, 24, 36, 48, and 60 month durations are routinely used by researchers to compute the SPI for the same respective intervals. A plot of SPI values from southwestern Idaho, for two different timescales, is shown in the first figure.

The SPI can accomplish the simultaneous assessment of drought because the observed precipitation during each time period is considered a statistical sample from a larger parent population. That is, each precipitation observation can be considered as a single datum—a random sample—from the broader precipitation probability distribution. For computational accuracy, Guttman (1999) recommends a minimum of 50 years of precipitation data. Observational data need not be preprocessed into the desired aggregations; available software codes (such as available from the National Drought Mitigation Center [NDMC]) accept monthly input data (which is usually the minimum interval frequency used to study drought [i.e., the one-month SPI]) and aggregate it to desired intervals (e.g., six month precipitation, for the six month SPI).

Precipitation is known to follow an asymmetric frequency distribution, with the bulk of the occurrences at low values, and a rapidly decreasing likelihood of larger precipitation totals. There are a number of such positively-skewed analytical distributions, six of which were analyzed for SPI computations by Guttman (1999). The distribution for the SPI adopted by McKee et al. (1993), as well as the NDMC, is the incomplete gamma distribution. SPI algorithms analyze the input data to optimally estimate two key coefficients which govern the transformation, and the observed precipitation data are transformed to Gaussian (normal) equivalents. The transformed precipitation data are then used to compute the dimensionless SPI value, defined as the standardized anomaly of the precipitation:

 SPI = (P-P*) /  σ_p

where P = precipitation

p* = mean precipitation

σ_{p = standard deviation of precipitation}

The dimensionless SPI values are typically associated with the drought descriptions of “dry”, “moderately dry”, or “extremely dry”, as well as other labels for near-normal conditions or precipitation excesses. The occurrence of these along the normal distribution is shown in the second figure.##