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<br />COMPUTATION OF DAMAGE <br /> <br />A damage value must be computed for each input and inserted exceedance <br />frequency value. The exact steps that are taken depend upon the input <br />data. The usual input relations of f10w-exceedance frequency, stage-flow <br />and stage-damage will be used to illustrate the process. <br /> <br />After the flows have been interpolated for each exceedance frequency <br />as described above, the stages for each of the flows must be found from <br />the stage-flow relation (rating curve). The appropriate stage-flow <br />relation for the year for which expected annual damage is being computed <br />would be found by linear interpolation if the rating curve was expected <br />to change with time. Completion of this step provides a stage-frequency <br />relation. <br /> <br />Next, the damage values corresponding to the interpolated stages <br />from the previous step are computed for each damage category. If the <br />damage values change with time, the appropriate stage-damage relation <br />would be computed first for the year for which expected annual damage <br />is being computed. Completion of this step provides a damage-frequency <br />relation for each damage category. <br /> <br />INTEGRATION <br /> <br />The remaining task is to integrate the damage-frequency relation to <br />obtain the expected annual damage. The relation is well defined at this <br />stage because of the insertion of the additional exceedance frequency points. <br />This relation can be quite nonlinear in nature so it is also fit by the cubic <br />spline procedure mentioned earlier. <br /> <br />The exceedance frequency values are converted to exceedance probability <br />values by dividing by 100. Then the area between each pair of points is <br />found by the three-point Gaussian quadrature method. This method computes <br />three points between a pair of points for the X variable (exceedance probability <br />in this case) and then finds the corresponding Y value (damage) by the cubic- <br />spline fit. These three Y values are given mathematically derived weights, <br />summed, and multiplied by the X interval. Repeating this process for each <br />successive pair of exceedance probability points and summing the results <br />yields the expected annual damage between the limits of the input exceedance <br />frequency values. <br /> <br />Care must be exercised in beginning with a frequency value that is <br />below the nondamaging stage since there is no extrapolation to zero damage. <br /> <br />EXHIBIT 2 <br />2 of 6 <br />