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because tributary inputs cannot be forecasted accurately. Also, Wright and others (in press) showed that the sand routing <br />model is not particularly sensitive to the initial bed conditions for the sensitivity range studied therein. <br />Uncertainties in the model results were evaluated by conducting simulations with estimated errors incorporated into the <br />boundary conditions (tributary inputs) and model calculations (sand transport rates). Following the methods used by Topping <br />and others (2010) for constructing error bars for sand budgets based on high - resolution monitoring data, the tributary inputs <br />were varied by t10 percent and the sand transport rates were varied by t5 percent. That is, for each scenario, two additional <br />simulations were performed: 1) tributary inputs increased by 10 percent and sand transport rates decreased by 5 percent, <br />providing an upper uncertainty bound; and 2) tributary inputs decreased by 10 percent and sand transport rates increased by 5 <br />percent, providing a lower uncertainty bound. This technique is particularly appropriate here because the sand routing model <br />was calibrated to sand transport measurements with comparable error estimates. It is noted that these uncertainty bounds are <br />most useful for evaluating whether there is net accumulation or erosion for a given scenario. For comparing scenarios to each <br />other, it is important to only compare simulations with the same boundary conditions and model parameters. For example, it <br />would not be appropriate to compare one operating scenario with tributary inputs increased by 10% with a different <br />operating scenario with tributary inputs decreased by 10 %. <br />Results <br />The sand routing model predicts sand concentrations at the three computational nodes shown in figure 1 (RM 30, RM <br />61, RM 87). The sand concentrations were combined with the flows at these locations to compute sand fluxes, and the sand <br />fluxes were then used to construct sand budgets for the three reaches bounded by the computational nodes (flux is assumed <br />to be zero past Lees Ferry). For this report, the two Marble Canyon reaches were combined for sand budgeting purposes. The <br />sand budgets are simply a cumulative accounting of sand inputs to a reach minus sand export from a reach; thus, a positive <br />sand budget indicates net sand accumulation within the reach and a negative sand budget indicates net sand erosion within <br />the reach. <br />The primary results of the simulations are shown in the series of figures 3 -8. Each figure represents a different <br />operational scenario and consists of three panels. The top panel shows the hourly release hydrographs for the given <br />operational scenario for both the 8.23 and the 11.0 MAF annual volumes. The middle panel shows the modeled cumulative <br />sand budgets for Marble Canyon, again for 8.23 and 11.0 MAF, including the uncertainty envelopes. The bottom panel <br />shows the simulated sand budgets for the eastern Grand Canyon reach. <br />The model results show some expected trends that are common to most of the operational scenarios. First, the higher <br />annual release volume (11.0 MAF) consistently leads to more sand export and thus less sand in the reaches projected at the <br />end of WY 2011. The sand budgets are also seen to reflect variations in flow releases (patterns and volumes) and tributary <br />inputs throughout the year. For example, the Marble Canyon sand budgets tend toward accumulation during August and <br />September when Paria sand inputs are greatest (fig. 2Q. An example of the impact of flow volume on the sand budgets is <br />apparent in the results for SAS (fig. 7), where it is seen that extended periods of relatively high flows in the spring drive the <br />sand budgets substantially in the negative direction (that is, erosion). The dashed lines define the modeling uncertainty <br />envelopes and allow for determination of the sign of the sand budget for each scenario at the end of WY 2011 (that is, for <br />determination of a positive or negative sand budget, the uncertainty envelope must not span zero). <br />In order to compare the scenarios more directly, annual sand budgets, including the uncertainty envelopes, were <br />computed for each simulation. The annual sand budgets are equivalent to the cumulative sand budgets shown in figures 3 -8 <br />at the end of WY 2011. These results are shown in figures 9 and 10; in these figures, the horizontal lines represent the "base" <br />simulations (that is, without uncertainty estimates) and the vertical lines denote the range based on the uncertainty <br />simulations. <br />13 <br />