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We define the standardized runoff index (SRI) as the unit standard normal deviate associated with the percentile of hydrologic runoff. Calculation of SRI follows the general approach employed by Mckee et al. (1993) to estimate the SPI.
Like the SPI, the SRI can be calculated for runoff totals accumulated over different durations (e.g., 1-month, 9-month), and for different spatial aggregations depending on source runoff data resolution and desired application. SPIs, for instance, are calculated by NOAA on a climate division basis and by state agencies on a county level basis. The procedure for calculating the SRI includes the following steps:
1. A retrospective time series of runoff at the desired temporal and spatial level of aggregation is obtained by simulation, and a probability distribution is fit to the sample represented by the time series values.
2. The distribution is used to estimate the cumulative probability of the accumulated runoff value of interest (either the current value or one from a retrospective date).
3. The cumulative probability is converted to a standard normal deviate (with zero mean and unit variance), which can either be calculated from a numerical approximation to the normal cumulative distribution function (CDF) or extracted from a table of values for the normal CDF that is readily available in statistics textbooks or on the World Wide Web.
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