FLOOD10307

• County: Statewide
• Basin: Statewide
• Title: Guidelines for Determining Flood Hazards on Alluvial Fans
• Date: 2/23/2000
• Prepared By: FEMA
• Floodplain - Doc Type: Educational/Technical/Reference Information

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14

02/23/00

Then the probability of the location being inundated by a flood above a given magnitude, say qo, is:

P[H = I nQ > qo]= JpHIQ(I,q)fQ(q)dq

q,

(I)

where Q is a random variable denoting the magnitude of the flood; PH1Q(I,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 a magnitude
between q and q+dq will occur in any given year.

Equation (I) only defines whether a location is within an SFHA and does so in terms of the
parameter qo. For riverine flooding qo represents an elevation, and P HiQ(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 floodwater (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 the stream under consideration (hence the notation qo to denote magnitude).

As in riverine analysis, the PDF 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, P HiQ(1,q) does not simplifY to 0 or I, because 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 with an * below, these
assumptions may be adjusted for observed field conditions; however, the FAN program does 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 efficient 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 that 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 /dd) is -200 (* may
be adjusted). The reasoning leads to the one-to-one relationships:

d = 0.106 q//5

(2)

v = 1,506 ql/5 (3)
where d is the specific energy in feet, v is the velocity in feet per second, and q is the discharge in
cubic feet per second (cfs).