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. I I I I I I I I I I I I I I I I I I 16 07/16/99 The conditional probability in Equation (I) accounts for the uncertainty in the path of a flood with a given magnitude. Even if the path of the flood can be predicted with reasonable certainty, the magnitude of the flood at a particular location may not be so certain as deposition or scour in shallow channels may greatly affect the direction of flow at channel splits. Many alluvial fans exhibit a channel network. The capacities of the individual channels as well as the capacities of the networks in aggregate vary from almost negligible to more than the lOO-year flood discharge. The treatment of the uncertainty in a given discharge being exceeded at a particular location given the discharge somewhere else [PHIQ( I,q)] varies. The least complex treatment (used in FAN program) follows from the reasoning that the topography of the area is the result of deposition occurring during past. If that process continues, then, over the long term, the probability of every point on a contour being inundated is the same. That is, PIIIQ(I,q) is uniformly distributed and, for a given point, is approximately the width of the flood path divided by the width (the "contour width") of the area subjectto flooding at the elevation of that point (* may be adjusted). This method assumes that all areas of the alluvial fan are subject to flooding and that there is a fixed relationship between flooding depth and discharge. In general, these assumptions apply when there is absolute uncertainty regarding how floods will occur. Thus, for the FAN program, under the simple conditions, (I ) _ w(q) _ 9.408 q2lS PHIQ ,q --- Wfall Wfun (4) where w( q) is the width ofthe path conveying q cfs and W fan is the contour width seen in Figure 3. The resulting flood insurance rate zones are depicted in Figure 4 for this example. The functional form of Equation (4) is a consequence of the reasoning leading to Equations (2) and (3) and is presented here for demonstrative purposes, not as the only form possible. The FAN program provides for the situation where flows are near normal depth in multiple channels. Program output includes results for this situation in addition to the single channel at critical depth. The results are then applied based on observed field conditions. Please refer ro FAN An Alluvial Fan Flooding Computer Program User's Manual and Program Disk for more information.