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<br />., <br />, <br /> <br />INTRODUCTION <br /> <br />11 <br /> <br />that their behavior is completely uncertain). The procedure ignores possible incision or stability of <br />channels on alluvial fans. At any distance down the fan, the channel has an equal probability, over <br />the long term, of intersecting any part of a contour in a flood, and this probability is proportional <br />to the ratio between the widths of the channel and the total width of the fan at that radial distance. <br />· That individual floods remain in single channels in which the flow occurs at critical depth <br />and velocity (i.e" velocity is proportional to the square root of depth) and has a width-to-depth <br />ratio of200. <br /> <br />Although the original outline of the procedure was based on the assumption of complete <br />uncertainty about the behavior of channels, the recommendations for application were quite <br />flexible (Dawdy, 1979) and left open the importation of other concepts and data to constrain the <br />generally applicable probability theory (e,g., Miffiin, 1990). FEMA adopted this method in an <br />appendix to its Guidelil/es and Specifications for Study Contractors, calling it, in early versions, <br />"Alluvial Fan Studies" (FEMA, 1985), and, in the latest version, "Studies of Alluvial Fan <br />Flooding" (FEMA, 1995). The simplest form of this method was eventually codified into a <br />computer program called FAN (FEMA, 1990), which likened alluvial fan flooding to rolling balls <br />down a cone. In this form, the procedure can be followed by anyone, even with little or no <br />knowledge of alluvial fans and their flooding characteristics, The FAN manual leads the <br />practitioner through the procedure required to map zones of flood risk on the basis of only (I) a <br />cursory identification that the site of interest lies on an alluvial fan, (2) measurement of the apical <br />angle of the fan for computing its width at any radial distance, and (3) choice of a peak flow- <br />frequency curve from regional data or a similar source. <br />When delineating flood hazard boundaries, the assumption of complete randomness in <br />channel behavior may be relaxed if some field information is available that will allow the <br />conditional probability equation to be solved with other constraints. But there does not appear to <br />be any practical process, other than the review by consultants to FEMA, for deciding whether or <br />which modifications should be applied in a particular circumstance. <br />Despite the elegance of its formulation, the FEMA procedure has been resisted in an <br />important number of locations where it has been applied, particularly in those communities with <br />the financial and technical resources to mount a challenge. The resistance arose for a number of <br />reasons: <br /> <br /> <br />· Misapplication of the procedure to locations that were not alluvial fans or to fans or <br />portions of fans that are not subject to flooding. <br />· Disparities between how floods occur on a particular fan and the assumptions of complete <br />randomness. <br />· Assumption that the hazard is dominated by rainfall-runoff without recognition of the <br />debris flow hazard in flood insurance studies, <br />· Too little investment being made in field identification of the conditions of flooding, <br />leading to later huge expenditures for litigation and field surveys. <br />· The mismatch between the rather inclusive actuarial goals of the original procedure and <br />other traditional uses of the resulting FIRM, such as floodplain management or hazard mitigation. <br />