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<br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />I. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br /> <br />15 <br /> <br />02/23/00 <br /> <br />The conditional probability in Equation (I) accounts for the uncertainty in the path of a flood with <br />a given magnitude. Even if the path of the flood can be predicted with reasonable certainty, the <br />magnitude of the flood at a particular location may not be so certain, as deposition or scour in <br />shallow channels may greatly affect the direction of flow at channel splits. Many alluvial fans <br />exhibit a channel network. The capacities of the individual channels as well as the capacities of the <br />networks in aggregate vary from almost negligible to more than the 100-year flood discharge. The <br />treatment of the uncertainty in a given discharge being exceeded at a particular location given the <br />discharge somewhere else [p HIQ(1,q)] varies. <br /> <br />The least complex treatment (used in the FAN program) follows from the reasoning that the <br />topography of the area is the result of deposition that occurred during the past. If that process <br />continues, then, over the long term, the probability of every point on a contour being inundated is <br />the same. That is, PH1Q(1,q) is uniformly distributed and, for a given point, is approximately the <br />width of the flood path divided by the width (the "contour width") of the area subject to flooding at <br />the elevation of that point (* may be adjusted). This method assumes that all areas of the alluvial <br />fan are subject to flooding and that there is a fixed relationship between flooding depth and <br />discharge. In general, these assumptions apply when there is absolute uncertainty regarding how <br />floods will occur. Thus, for the FAN program, under the simple conditions, <br /> <br />2/5 <br />(I q) - w(q) _ 9.408q <br />PH1Q , --- <br />Wr", Wr", <br /> <br />(4) <br /> <br />where w(q) is the width of the path conveying q cfs and Wr.. is the contour width seen in Figure 3. <br />The resulting flood insurance rate zones are depicted in Figure 4 for this example. The functional <br />form of Equation (4) is a consequence of the reasoning leading to Equations (2) and (3) and is <br />presented here for demonstrative purposes, not as the only form possible. <br /> <br />The FAN program provides for the situation where flows are near normal depth in multiple channels. <br />Program output includes results for this situation in addition to the single channel at critical depth. <br />The results are then applied based on observed field conditions, Please refer to FAN An Alluvial Fan <br />Flooding Computer Program User's Manual and Program Disk for more information. <br />