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I I I I I I I I I I I I I I I I I I I 15 07/16/99 Then the probability ofthe location being inundated by a flood that exceeds a given magnitude, say qo, is: P[H = I nQ > qol= J PHlQ(l,q)!Q(q)dq (I) '" where Q is a random variable denoting the magnitude of the flood; PHlQ(l,q) is the conditional probability that the location will be inundated given that a flood of magnitude q is occurring; and fQ(q) is the probability density function (PDF) defining the likelihood that a flood of magnitude between q and q+dq will occur in any given year. Equation (I) only defines whether a location is within a SPHA and does so in terms of the parameter qo. For riverine flooding qo represents an elevation and PHIQ(I,q) is I if the elevation of the location is less than qo and 0 if it is greater than qo. At a given location (point on a cross section), there is a one-to-one relationship between the discharge being conveyed by the stream and the elevation of the surface of the floodwaters (i.e., the rating curve for the cross section). For riverine flooding, solving Equation (I) reduces to defining the discharge-frequency relationship for the reach of stream under consideration (hence the notation qo to denote magnitude). As in riverine analysis, the PDP describing frequency of the magnitude of flooding for alluvial fan flooding is taken to be the discharge-frequency relationship of the contributing drainage basin. Unlike riverine analysis, PHlQ( I,q) does not simplifY to 0 or I since there is uncertainty in the flow path. The FAN program provides energy depths and velocities relating to discharge for use in defining the flood-hazard. · The FAN program uses the assumptions outlined below. Where noted below these assumptions may be adjusted for observed field conditions, however the FAN program docs not readily accommodate these adjustments. This method's assumptions are as follows. Floods on alluvial fans are at liberty to expend energy to create the most cfficient path to convey the water and sediment load. That path is shallow and approximately rectangular in cross section. Energy is expended through sediment movement until the minimum energy possible is reached. In short, the reasoning is a flood flows at critical depth and is confined to a rectangular path. The flow path would not widen indefinitely but, instead, would reach a point where it would stabilize. From empirical data, of which there is very little, that point is taken to be where the rate of change of topwidth per change in depth (dW Idd) is -200 (* may be adjusted). The reasoning leads to the one-to-one relationships: d = 0.106 qJl5 (2) v = 1.506 qJl5 (3) where d is the specific energy in feet, v is the velocity in fps, and q is the discharge in cfs.