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<br /> <br />N <br />I-" <br />00 <br />W <br /> <br />Similarly to averages of flows, the variance of flow records must be <br />adjusted to the common period. Actually, this adjustment is very <br />complex since the variance of a sum of flows, such as two tributaries, <br />depends on the covariance between them as well as sampling differ- <br />ences due to varying periods of record. Additionally, since the <br />flow at the lower locations results from adding upstream tributaries <br />and intervening flows, the variance at the downstream station is <br />composed of many covariance terms, The data generation model cannot <br />preserve all the needed properties since to do so would require a <br />multiple regression equation containing all possible independent <br />stations. Also, the analysis would have to be done for the entire <br />common period of record to account for all variance of the data, To <br />maintain the correlation structure of the Basin as well as approxi- <br />mate the variance at downstream locations as well as possible, many <br />attempts at adjusting the variance at each inflow point were tried. <br />Unfortunately, time did not permit a rigorous analysis of all avail- <br />able data and techniques for maintaining variance. <br /> <br />One method of adjustment commonly used was taken from Yevjevich,2/ <br />Given flow records at two stations, y having record length of k - <br />periods and x of n periods, the problem is to estimate the variance <br />of the y-series for the long period, <br /> <br />y I <br /> <br />----I <br /> <br />k <br /> <br />x I <br /> <br />n <br /> <br />Figure 4. Schematic representation of <br />two time series with different <br />record lengths <br /> <br />If Y and x are related by the regression relationship y = a + bx, <br />Yevjevich ~gives the following equation to estimate the long term <br />variance of y: <br /> <br />S~ = S~k - rk <br /> <br />SYk <br />Sxk <br /> <br />(13) <br /> <br />(S~k - S~n) <br /> <br />2/ Yevjevich,-V., Probability and Statistics in Hydrology, pg. 260, <br />Water Resources Publications, Fort Collins, Colorado, 1972, <br /> <br />20 <br />