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<br />185 <br /> <br />C) <br />CJ <br />t\:) <br />~,) Simulation estimates of average reservoir discharge and storage <br />...... <br />en are used to examine the convergence of system response in Sections <br /> <br />6.2.1 and 6.2.2 respectively. <br /> <br />Another measure of system response was taken to be the probability <br /> <br />of failure to meet target discharge. Stability of the distribution of <br /> <br />reservoir discharge is explored in Section 6.2.3. <br /> <br />6.2.1 Examination of Mean Reservoir Discharge <br /> <br />Simulations of increasing length (numbers of years) were made <br /> <br />to examine the convergence of estimates of mean reservoir discharge. <br /> <br />Simulations of equal length, but using different streamflow sequences, <br /> <br />were made to examine the variability of mean response with changes in <br /> <br />the stochastic inputs. Single simulations of 200 years of observation <br /> <br />are shown to provide good estimates of mean reservoir discharge. <br /> <br />One simulation of 1000 years was performed to provide information <br /> <br />on the convergence of estimates of average Lake Powell discharge. The <br /> <br />highest level of stream depletions was imposed, lowering the average <br />3 <br />Lake Powell inflow to 8.4 MAF/yr (10.1 km /yr) and providing a worst <br /> <br />case for the determination of simulation time. Running averages of <br /> <br />annual discharge D(N) were formed using average times of N = 50, 100, <br /> <br />200, and 500 years. The standard deviations, ~D(N)' of the N-year <br />averages are used to examine convergence of the mean. <br /> <br />The decrease of ~D(N) with increasing N is shown in Figure 6.1. <br />For an averaging period of 200 years the standard deviation, ~D(200)' <br />of the estimate of mean discharge is approximately 1% of the mean <br />