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Modeling Results for <br />Colorado River Basin States' Modeling of <br />Colorado River and Reservoir Management Strategies <br />In addition to the percentile lines, three distinct traces were added to Figure A -1 <br />to illustrate what was actually simulated under those traces and respective <br />hydrologic sequences: <br />• Trace 1 representing hydrology start year 1907 <br />• Trace 20 representing hydrology start year 1926 <br />• Trace 47 representing hydrology start year 1953 <br />This figure highlights the fact that percentiles do not represent single traces, but <br />rather the ranking of the data from all traces for the conditions modeled. The <br />single traces illustrate the variability among traces and the potential that reservoir <br />levels could decline below the 10th percentile line (Trace 47), or above the 90th <br />percentile line (Trace 1). <br />At the 10th percentile, you can make the following statement: In any given year, <br />there is a 10% chance Mead would be at or below a certain elevation. This does <br />not imply that Mead will be below this elevation year after year. Computing a <br />percentile is not conditional on the previous year, nor is it the result of repeating <br />any particular hydrology. Percentile analysis should not be confused with ranking <br />the input hydrology, then repeating a specific hydrology year after year. <br />The general method to compute percentiles is to rank the total number of values <br />(N), in this case N = 90, and to determine the index (n) that corresponds to a <br />percentile of interest. The value that corresponds to index (n) represents the value <br />at which a certain percent of values fall below. The method used in GPAT was <br />chosen by developers because it works well for small sample sizes. To compute <br />the index (n), the method can sometimes result in an index that is not a whole <br />number. In this case, the percentile value becomes a weighted average of the next <br />highest and lowest values, i.e. the percentile value was not directly produced in <br />the model simulation. Below is an example of the GPAT calculation of Powell's <br />10th percentile elevation. <br />Total number of values N= 90 <br />Percentile of interest %tile =10 <br />Index for percentile n = N* %tile +50 _ 90 *10 +50 = 9.5 <br />100 100 <br />Powell elevations N9 = 3573 and Nio = 3580 <br />h N9 + Nto _ 3573 + 3580 <br />10` Percentile elevation = = 3576.5 <br />2 2 <br />34 <br />