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<br />standard deviation of one with a cumulative probability defined as N(z) or a particular G(x;) as <br /> <br />N(z,). Both G(x;) and N(Zi) have the same probability. The advantage of the transformation is <br /> <br />that N is normally distributed so it can be used to define wet periods as well as dry periods and <br /> <br />the values of z are in units of standard deviations. Thus the values of z are the values of the <br /> <br /> <br />SPI. An example is given for Fort Collins, CO, in Figure 5 for its period of precipitation <br /> <br /> <br />observation. Figure Sc is 12 month values of precipitation which are the previous 12 months from <br /> <br /> <br />the point on the graph where the value is plotted. The SPI values on the ordinate are uniquely <br /> <br />connected to cumulative probability as given in Table 3 so -1, 0, 1 are associated with cumulative <br /> <br /> <br />probability of 16%,50% and 84%. Values ofSPI are linear with precipitation difference from the <br /> <br /> <br />mean but they do not have a unique relationship to probability. Since the mean value of <br /> <br /> <br />precipitation from the Gamma /3r, the fraction of average precipitation is just Xi / /3r. This can <br /> <br />also be normalized as the precipitation deficit as a fraction of average values as (YI - /3r) / /3r. <br /> <br />The actual annual water-year precipitation (October through September') for Fort Collins, CO, is <br /> <br />shown in Figure 6. Figure 6 has one point per year and Figure 5 has one point per month but <br /> <br />Figure 6 and Figure 5c are both 12 month values. Water year 1961 ended in September 1961 in <br /> <br /> <br />Figure 6 for the single wettest year in the graph. In Figure 5c the montWy data points reach a <br /> <br /> <br />peak in later 1961 and continue into 1962. The SPI values in Figure 6 give a better picture of the <br /> <br /> <br />duration of a wet or dry period. Some of the advantages of the SPI as a monitoring tool are that <br /> <br /> <br />it has a straightforward interpretation as probability, percent of average, precipitation deficit and it <br />show duration clearly. <br /> <br />Another useful application of the SPI is that any accumulation period of a number of <br /> <br /> <br />months can be used. Figure 5 shows the history of Fort Collins precipitation for periods of <br /> <br />13 <br />