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Drought Triggers and Indices <br />Index Documentation <br />Standardized Precipitation Index (SPI) — Please refer to Edwards and McKee, 1997 for a <br />complete description of the SPI methodology. <br />The SPI was developed at the Colorado Climate Center (McKee et al. 1993) as a tool for <br />defining and monitoring drought. This is a relatively simple index that can be used in <br />any location or region to compare wet and dry periods as long as there are weather <br />stations with a reasonably long (ideally 30 years or longer) period of consistent data. <br />The SPI is ideally suited for examining dryness on a variety of different time scales such <br />as the past month, the past 3 months, the past year or even longer periods. Precipitation <br />is the only input data requirement for the SPI method. First, a time series of running <br />precipitation sums of length n are calculated. This distribution of empirical data, <br />depending on the selected time scale, may not be normally distributed. To simplify the <br />statistical analysis of the data, the distribution of raw data is fit with a smooth curve. <br />Gamma distributions (Thom, 1966) are well suited for describing the shapes of the <br />distributions of monthly and seasonal precipitation totals. The shape and scale parameters <br />of the gamma distribution are estimated for each individual station, for each time scale <br />for each month of the year using the empirical probabilities of the precipitation data <br />(Thom, 1966). The running precipitation sums are converted to non - exceedance <br />probabilities using the incomplete gamma function (Figure 1). The non - exceedance <br />probabilities are then converted to an index value using the inverse normal function <br />shown in the equations below. This transforms the data from a skewed distribution to a <br />standard normal distribution with a mean of zero and variance of 1 (i.e. the bell- shaped <br />curve) using the methodology of Abramowitz and Stegun (1965). The SPI is essentially <br />the number of standard deviations an event is above or below the mean value. Table 1 <br />provides the relationship of the SPI values to condition descriptors and percentile <br />rankings. <br />Z = SPI = —( c + c,t + c2t2 for 0 < H(x) < 0.5 <br />1 +d,t +d +d <br />Z = SPI = + t— co +c,t +c2t2 for 0.5 <H(x) <1.0 <br />1 +d,t +d +d <br />where: <br />H(x) = non - exceedance probabilities from the incomplete gamma function. <br />t = In ( x )) 2 for 0 < H(x) <_ 0.5 <br />H <br />