Laserfiche WebLink
<br />EXHIBIT 2 <br />DAMAGE-FREQUENCY INTEGRATION PROCEDURE <br /> <br />. INTRODUCTION <br /> <br />An accurate computation of expected annual damage requires good <br />input data and a good integration method. The user is responsible for <br />preparing good input data. Since linear interpolation is used to define <br />most of the relations, the input data points must be selected to ade- <br />quately represent each relation by a series of straight lines. Past <br />experience has shown that integration by the usual summation of rectangu- <br />lar areas can result in significant errors because of the nonlinearity <br />of the damage-frequency function. An integration procedure has been <br />developed for expected annual damage which will yield accurate results <br />and is computationally efficient. <br /> <br />EXCEEDANCE FREQUENCY RELATIONS <br /> <br />To obtain expected annual damage, a damage-frequency relation is <br />necessary. Therefore, depending on input, several levels of interpolation <br />may be necessary to obtain the necessary relationship. If the input <br />relations are already damage-frequency, the interpolation routines are bypassed <br />and the process goes directly to the integration step. As the interpolation <br />process keys on the input exceedance frequency values, additional exceedance <br />frequency points are internally inserted between the input values to better <br />define the nonlinear relation as well as to more accurately define the <br />beginning of damage. Three exceedance frequency values are added that are <br />1/4, 1/2 and 3/4 of the interval between each pair of input exceedance <br />frequency values. Therefore, if the first two input values are 90.0 and <br />80.0, the three values added between this interval would be 87.5, 85.0 and <br />82.5. <br /> <br />If flows (or stages) corresponding to exceedance frequencies are <br />provided for several input data years, then the flow (or stage) corresponding <br />to the frequency is found by linear interpolation between input data years <br />for the year that expected annual damage is being computed. <br /> <br />The exceedance frequency-stage or exceedance frequency-flow relation <br />is highly nonlinear. To obtain reasonable interpolated values, the input <br />frequency relations are fit by a cubic spline procedure developed by Akima <br />(1970). The cubic.spline procedure fitsca smooth curve through the data <br />points. Then, either stage or flow values, depending on input, are found <br />for each inserted frequency value (the 1/4, 1/2 and 3/4 points). <br /> <br />Akima, H., "A New Method of Interpolation and Smooth Curve Fitting <br />Based on Local Procedures," Jour of the Association for Computing Machinery, <br />v. 17, 1970, pp. 589-682. <br /> <br />EXHIBIT 2 <br />1 of 6 <br />