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Methodology <br />Since there are gaps in the indicator gage data, and an empirical frequency analysis may not <br />provide a true representation of the population and population quantiles, the data were fit with a <br />known distribution. Cutoff quantiles of 25% and 75% are recommended for two reasons. The <br />first is that these cutoffs seem to characterize the data in a hydrologically realistic manner, i.e. <br />historic years that were generally wet or dry appear to be characterized correctly. Second, these <br />cutoff limits are consistent with those used by the USBR. <br />Two well-known distributions were evaluated against the empirical frequency distributions of <br />both annual and monthly data for several of the indicator gages. These are the nornlal and two- <br />parameter lognorn~al distributions. The normal distribution was chosen because "...it is widely <br />used for fitting empirical distributions with symmetrical histograms or with skewness <br />coefficients close to zero..." (Salas et al. 1995). The lognornal distribution was chosen because <br />it has been shown "that [it] can be applied to a wide variety of hydrologic events especially when <br />the corresponding variable has a lower bound, the empirical distribution is not symmetric, and <br />the factors causing those events are independent and multiplicative (Chow, 1954; Markovic, <br />1965; Sangal and Biswas, 1970; Yevjevich, 1972)...Likewise, Markovic (1965) studied the <br />distribution of annual precipitation and runoff series of 2060 stations in the continental U.S.A. <br />and found that the two-parameter lognormal distribution gave an excellent fit" (Salas et al. <br />1995). The parameters for these two distributions are the mean and standard deviation of the <br />actual data, and the mean and standard deviation of the natural log of the data, respectively. <br />Exhibit 3 shows the annual discharge distributions for the seventeen indicator gages. The normal <br />distribution generally appears to provide a better fit than the lognormal. Although the goodness <br />of fit of the entire curve is taken into account, the 25% and 75% quantile marks are given <br />particular consideration. The normal distribution was chosen to model the empirical data. <br />Before analysis could begin, the issue of missing streamflow data within the indicator gage <br />periods of record had to be addressed. Two options considered were translating characterizations <br />from a nearby indicator gage, and characterizing data that had been filled through regression <br />analysis. Simple linear regression, in effect, takes the statistical properties of one data set and <br />applies them to another set. This means that as long as the characterization is translated from the <br />gage with the highest correlation, results from translated, verses filling and characterizing, will <br />be the same. Since characterizing a complete data set reduces the level of complexity of the <br />analysis, and the Mixed Station Method has been approved for filling naturalized flows in <br />Subtask 11.10, this method was used to fill in missing data before the entire record was <br />characterized. <br />Streafnflow Characterization <br />The general approach to completing the streamflow characterization encompasses selecting the <br />gage, accessing the monthly streamflow data, filling in missing data, and then characterizing the <br />monthly data. The streamflow characterization is accomplished by selecting the data from the <br />CRDSS database using the Time Series Tool (tstool). The data is then filled using the Mixed <br />Station Method (MSM). The data from each source is input to the streamflow characterization <br />tool (SCT), a Microsoft Excel workbook that calculates the cutoff criteria and creates an output <br />Appendix E E-70 <br />