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<br />. <br /> <br />. <br /> <br />. <br /> <br />(l u t ~jl) J <br /> <br />. <br /> <br />. <br /> <br />5. <br /> <br />study based on this approach. We have gone over his study carefully, expanded on <br /> <br /> <br />it, and fully explored the use of such techniques. Al though these represent a <br /> <br /> <br />great advance, it has become clear from the results of our second phase that the <br /> <br /> <br />assumption of random stream flovis through time does not hold. <br /> <br /> <br />In the second phase of the statistical analysis we have applied a new <br /> <br /> <br />and powerful statistical procedure, spectrum analysis, to tlle examination of <br /> <br /> <br />stream-flow records of the main stem and the major tributaries. To the best of <br /> <br /> <br />our knowledge this is the first time that this method has been applied to stream- <br /> <br /> <br />flow data. <br /> <br /> <br />The results of the spectrum analysis are: at the higher altitudes there <br /> <br /> <br />is no significant year to year connection in the run-offs; but at the lower <br /> <br /> <br />altitudes (Lees Ferry, Cisco, Bluff, Green River) there is a definite and <br /> <br /> <br />significant relation of the run-offs from one year to the next. This influence <br /> <br /> <br />of the run-off of any given year on the next year's run-off is called by statis- <br /> <br /> <br />ticians autocorrelation or serial correlation -- that is, the nun-off in any <br /> <br /> <br />given year is related to the~-off of the preceding year or years. The relation- <br /> <br /> <br />ship in the case of Lees Ferry is not high, but it is statistically significant. <br /> <br /> <br />Thus, instead of having to depend upon random selection in our attempts to <br /> <br /> <br />re-create the river flows at Lees Ferry, we now Imow that Vie should simulate <br /> <br /> <br />these past flows with a built-in relationship between one year and tlle next. Be- <br /> <br /> <br />cause of the 10\v o~der of magnitude of the serial correlation, the improve- <br /> <br /> <br />ment in our predictive ability is not great. But it is a beginning. Moreover, <br /> <br /> <br />this permits us to start creating mathematical models that describe or fit the <br /> <br /> <br />river basin. We have found from statistical tests that the precipitation at the <br /> <br /> <br />high altitudes is random. We know that the run-off at Lees Ferry exhibits serial <br /> <br /> <br />correlation. We can now try to describe what happens to a random series to make <br /> <br /> <br />it become serially correlated, and thus try to describe what is actually taking <br /> <br /> <br />place in the river basin. <br />