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<br />2 <br /> <br />o NATURAL INFLOW RANDOM VARIABLES <br />CJl <br />00 The major simplification accomplished by this method is the use of <br />CO <br />only three random variables. These random variables represent monthly <br /> <br />inflows in the spring runoff, summer and winter seasons, The spring runoff <br /> <br />random variable, denoted by R, covers the months of April, May and Jtme. <br /> <br />The summer random variable (S) covers July, August and September, The <br /> <br />winter random variable (W) covers the 6 months from October through March, <br /> <br /> <br />S is dependent upon R because the melting snowpack provides IIlUch of <br /> <br />the summer inflows. However, summer rains provide considerable variation <br /> <br />in S which is not dependent upon R. W is independent of R because the <br />snowpack has melted before October. However, some correlation exists from <br />R onto W due to long tenn weather cycles, Since the winter season is <br />frequently in a frozen condition in the Rocky Motmtain region, the range of <br />W inflows is quite narrow. In the White River data, the variation in W <br /> <br />due to both R and the weather cycle correlation (which cannot easily be <br /> <br />separated) is small, <br /> <br />Year to year correlation in R exists, but it is only a small part of <br /> <br />1he total variation in R. This correlation is only significant when a <br />regulation scheme attempts to maintain carryover storage which is large <br />in comparison to annual inflows. This correlation does not affect more <br />modest regulation schemes, In this analytic method this annual correla- <br />tion is ignored (making R independent year to year). However, it should be <br />considered (requiring a large safety stock of carryover storage) whenever <br />the attempted regulation involves a high percentage of the annual inflows. <br />Simulation methods using a time series of historic inflows include the <br />correlation effect. However, it is only one short realization of this effect. <br />