3
Indicators for Characterizing Alluvial Fans and Alluvial Fan Flooding

Alluvial fans and alluvial fan floods show great variability in climate, fan history, rates and styles of tectonism, source area lithology, vegetation, and land use. For this reason, it is essential that any investigation of alluvial fan flooding include careful examination of the specific fan for which information is needed. The committee recognizes that the extent of site-specific examination will be constrained by factors such as the amount of time and money allotted to the project, the tools available to the investigator, and the investigator's experience. As discussed in this chapter, however, much information can be gleaned from topographic and soil maps, as well as aerial photographs. Nevertheless, it is essential to do at least one field inspection of the fan that involves walking across its surfaces and along its channels. In general, the more fieldwork done, the better the understanding of the processes of flooding on the fan of interest.

According to the definition presented in Chapter 1, for regulatory purposes alluvial fan flooding is a flood hazard that on active parts of alluvial fans has a 1 percent chance of occurrence, and it is identified by flow path uncertainty and deposition and erosion below the hydrographic apex. The criteria used to assess whether an area is, or is not, subject to alluvial fan flooding must determine whether the flooding occurs on an alluvial fan and whether it is characterized by deposition, erosion, and flow path uncertainty below a hydrographic apex. For these reasons, the process of determining whether or not alluvial fan flooding can occur at a given location, and of defining the spatial extent of the 100-year flood, are divided into three stages:

  1. Recognizing and characterizing alluvial fan landforms.

  2. Defining the nature of the alluvial fan environment and identifying areas of active erosion, deposition, and flooding (as well as inactive areas).

  3. Defining and characterizing areas on active parts of alluvial fans that are subject to a 1 percent chance of occurrence (the 100-year flood), the FEMA mandate.

Progression through each of these stages results in a procedure that narrows the problem to smaller and smaller areas of uncertainty (Figure 3-1). In Stage 1, the landform on which flooding occurs must be characterized. If the location of interest is an alluvial fan, then the user progresses to Stage 2, in which those parts of the alluvial fan that are active and inactive are identified. The term active means those locations where flooding, erosion, and deposition have



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3 Indicators for Characterizing Alluvial Fans and Alluvial Fan Flooding Alluvial fans and alluvial fan floods show great variability in climate, fan history, rates and styles of tectonism, source area lithology, vegetation, and land use. For this reason, it is essential that any investigation of alluvial fan flooding include careful examination of the specific fan for which information is needed. The committee recognizes that the extent of site-specific examination will be constrained by factors such as the amount of time and money allotted to the project, the tools available to the investigator, and the investigator's experience. As discussed in this chapter, however, much information can be gleaned from topographic and soil maps, as well as aerial photographs. Nevertheless, it is essential to do at least one field inspection of the fan that involves walking across its surfaces and along its channels. In general, the more fieldwork done, the better the understanding of the processes of flooding on the fan of interest. According to the definition presented in Chapter 1, for regulatory purposes alluvial fan flooding is a flood hazard that on active parts of alluvial fans has a 1 percent chance of occurrence, and it is identified by flow path uncertainty and deposition and erosion below the hydrographic apex. The criteria used to assess whether an area is, or is not, subject to alluvial fan flooding must determine whether the flooding occurs on an alluvial fan and whether it is characterized by deposition, erosion, and flow path uncertainty below a hydrographic apex. For these reasons, the process of determining whether or not alluvial fan flooding can occur at a given location, and of defining the spatial extent of the 100-year flood, are divided into three stages: Recognizing and characterizing alluvial fan landforms. Defining the nature of the alluvial fan environment and identifying areas of active erosion, deposition, and flooding (as well as inactive areas). Defining and characterizing areas on active parts of alluvial fans that are subject to a 1 percent chance of occurrence (the 100-year flood), the FEMA mandate. Progression through each of these stages results in a procedure that narrows the problem to smaller and smaller areas of uncertainty (Figure 3-1). In Stage 1, the landform on which flooding occurs must be characterized. If the location of interest is an alluvial fan, then the user progresses to Stage 2, in which those parts of the alluvial fan that are active and inactive are identified. The term active means those locations where flooding, erosion, and deposition have

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FIGURE 3-1 Three stages in the procedure to determine areas susceptible to alluvial fan flooding. occurred on the fan in relatively recent time, and probably will continue to occur on that part of the alluvial fan. Those parts of the fan that have been active in relatively recent time can be identified depending on data availability for the site and money allotted to the project. (See Box 3-1.) Each active part of the alluvial fan also is characterized based on the dominant types of processes that result in flooding and sedimentation. Finally, in Stage 3, the evaluator determines where on those parts of the fan that are active the 100-year flood is possible. Progression through each of these stages will require the investigator to refer to a variety of maps, photographs, and other information sources (Table 3-1; also see Appendix B) and to do a significant amount of fieldwork to understand and characterize the alluvial fan flooding hazard.

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BOX 3-1 ''TIME" IN THE CONTEXT OF ALLUVIAL FAN FLOODING It is not possible to give a precise definition to the phrase "relatively recent" as used in this report. Because of the variability among fans, the complexity of single fans, and the great range of ages present on fan surfaces, as well as tremendous diversity in the climate and geologic processes operating on fans, the committee is not able to specify a single time frame to use in defining whether or not a fan is active. Instead, such a judgment must be made on a site-specific basis. At one extreme, the committee considers "recent" to be the past 10,000 years (the Holocene Epoch), which follows a particularly radical and widespread climate change at the end of the most recent Ice Age. At the other extreme, "recent" implies the time period over which there has been a relatively uniform range of environmental conditions that affect flood generation and channel behavior. Estimates of the probability of events occurring in the relevant, near-term future are based on the record of the "recent," homogeneous past. A problem exists, however, in that there often is no clear indication in most localities about how far back one should look in defining whether the record is relatively uniform, and this is in part why society is occasionally surprise by unforeseen flood hazards. For purposes of the National Flood Insurance Program (NFIP), an arbitrary but reasonable decision was made to use, as a planning tool, the flood which has a 1 percent chance of occurring in any one year ("the 100-year flood"), which is usually a generally destructive flood in most areas of human settlement. Thus, the engineering perspective involves a timescale (a century) over which structures are typically designed to survive, while the geological perspective involves a longer time period with a greater range of geologic processes and environmental variability. The engineering perspective focuses on the regulatory requirements imposed by the NFIP; the geologic perspective focuses on geologic process. Both perspectives are important to understanding alluvial fan flooding. Examples of various attempts to determine ages of fans and fan components can be explored in-depth in the following references: Bull, W. B. 1964. Geomorphology of segmented alluvial fans in western Fresno County, California. U.S. Geological Survey Professional Paper 352-E. Reston, Va.: U.S. Geological Survey. Bull, W. B. 1968. Alluvial fans. Journal of Geologic Education 17(3):101–106. Bull, W. B. 1977. The alluvial fan environment. Progress in Physical Geography 1:222–270. Kellerhals, R., and M. Church. 1990. Hazard management on fans, with examples from British Columbia. In Alluvial Fans: A Field Approach. New York: John Wiley & Sons. Lecce, S. A. 1990. The alluvial fan problem. In Alluvial Fans: A Field Approach. New York: John Wiley & Sons. Machette, M. N. 1985. Calcic soils of the southwestern United States. Geological Society of America Special Paper 203. Boulder, Colo.: The Geological Society of America. Markewich, H. W., and S. C. Cooper. 1991. One perspective on spatial variability in geologic mapping. In Spatial Variabilities of Soils and Landforms, M. J. Mausbach

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and P. J. Wilding, eds. Soil Society of America Special Publication, no. 28. Mausbach, M. J., and P. J. Wilding. 1991. Spatial Variability of Soils and Landforms. Soil Society of America Special Publication, no. 28. Rhoads, B. L. 1986. Flood hazard assessment for land use planning near desert mountains. Environmental Management 10(1):97–106. Zarn, B., and R. H. Davies. 1994. The significance of processes on alluvial fans to hazard assessment. Z. Geomorph. N. F. 38:487–500. STAGE 1: RECOGNIZING AND CHARACTERIZING ALLUVIAL FAN LANDFORMS Determining whether or not a Landform is an Alluvial Fan The committee's definition of alluvial fan flooding specifically states that it occurs on alluvial fans. As a consequence, the first step in application of the definition is analysis of the area being considered for possible alluvial fan flooding. If this area does not meet the criteria for the definition of an alluvial fan, then it does not qualify for consideration of alluvial fan flooding. The committee defines an alluvial fan as "a sedimentary deposit located at a topographic break such as the base of a mountain front, escarpment, or valley side, that is composed of streamflow and/or debris flow sediments and which has the shape of a fan, either fully or partially extended." These characteristics can be categorized as composition, morphology, and location, as follows. Composition Alluvial fans are landforms constructed from deposits of alluvial sediments or debris flow materials. To meet the criteria in the committee's definition of an alluvial fan, the landform of interest must be a sedimentary deposit, an accumulation of loose, unconsolidated to weakly consolidated sediments. In the following text, we use the term "alluvium" to refer to sediments transported by both streams and debris flows, but we emphasize that this is a grammatical convenience. On a particular fan, the distinction between these two forms of sediment transport is critical to a correct interpretation of the flood hazard. Most sediments deposited during Quaternary time (2 million years ago to the present) still are loose and unconsolidated, as the processes of diagenesis that result in compaction, cementation, and lithification require millions of years to transform sediment to sedimentary rock. As a consequence, geologic maps commonly have a unit labeled "Qal" that conventionally is mapped in yellow and represents Quaternary alluvium. Determining whether or not a landform is an alluvial sedimentary deposit might be as simple as checking a published geologic map to see if the underlying material is mapped as alluvium. If a geologic map is not available, the user can

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check Natural Resources Conservation Service (NRCS) soil maps or drilling and logging records from water wells. If none of these sources is available, field reconnaissance can be done to determine whether or not the landform consists of alluvial sediments. Morphology Alluvial fans are landforms that have the shape of a fan, either partly or fully extended. To meet the criteria in the committee's definition of an alluvial fan, the landform of interest must have the shape of a fan, either partly or fully extended. Flow paths radiate outward to the perimeter of the fan. This criterion can be assessed with topographic maps. For example, in Figure 3-2a the landform downstream from the Lawton Ranch, Montana, has the shape of a fan that is nearly fully extended. This landform is known as the Cedar Creek alluvial fan and is a classic example of a fan with nearly ideal morphology. Location Alluvial fan landforms are located at a topographic break. To meet the criteria in the committee's definition of an alluvial fan, the landform of interest must be located at a topographic break where long-term channel migration and sediment accumulation become markedly less confined than upstream of the break. This locus of increased channel migration and sedimentation is referred to as the alluvial fan topographic apex. Figure 3-2 shows that the Cedar Creek alluvial fan begins at a topographic break, which in this case is a slightly embayed mountain front. As Cedar Creek exits its narrow bedrock canyon, it becomes less confined and is able to migrate more freely. Less confinement can lead to greater channel widths and smaller channel depths. As a result, the occurrence of deposition increases, and flow paths become more unstable. Defining the Boundaries of an Alluvial Fan Where are the toe and lateral boundaries of the alluvial fan? Toe The distal terminus, or toe, of an alluvial fan commonly is defined by a stream that intersects the fan and transports deposits away from the fan, a playa lake, an alluvial plain, or smoother, gentler slopes of the piedmont plain.

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TABLE 3-1 Data Sources for Information on Alluvial Fans Agency or Source Source Numbera Topography Surface Features Land Cover Land Use Remotely Sensed Aerial Photography U.S. Department of the Interior Bureau of Land Management 1             National Park Service 2             U.S. Geological Survey 3             U.S. Department of Agriculture Agricultural Stabilization and Conservation Service 4             Forest Service 5             Natural Resources Conservation Service 6             U.S. Department of Commerce National Ocean Service 7             U.S. Army Corps of Engineers 8             Independent Federal Agencies Federal Emergency Management Agency 9             Tennessee Valley Authority 10             National Archives and Records Administration 11             Library of Congress 12             Other agencies or sources: State geologists 13             State floodplain management agencies 14             University libraries 15             County floodplain management agencies 16             Long-time residents 17             Newspapers 18             Technical journals 19             University theses 20             a See Appendix B.

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Orthophotoquads Satellite Hydrologic Flood Hydrography Water data Floodplain Subsurface Geology Soils Other                                                                                                                                                                                                                                                                                                                                                                                                                                          

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FIGURE 3-2 (a) Shaded relief map and (b) geologic map of Cedar Creek alluvial fan in Montana. SOURCE: Reprinted with permission from Ritter et al. (1993).

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Such boundaries often can be identified on the basis of changes in the shapes of contour lines on topographic maps. For example, at the toe of a fan contour lines may become straighter or less concave when viewed downslope, although in the case of deeply dissected fans, contour lines may become more irregular and crenulated because of channel incision. The toe of the Cedar Creek1 alluvial fan (Figure 3-2a) is defined by Bear Creek along the fan's western margin, and by the much larger valley floor of the Madison River into which Bear Creek flows along the fan's northwestern margin. Streams draining the northern part of the fan are more deeply incised because the Madison River valley floor forms a lower base level for erosion than its tributary valley floor along Bear Creek. The toe of some alluvial fans in arid regions is indicated by a relative increase in the amount, size, and type of vegetation because ground water is closer to the surface there than on the upper parts of the fan. The toe of some alluvial fans in humid regions may be indicated by relatively less vegetation because the recent deposits are less fertile than older sediments. A general sense of vegetation types often is indicated on topographic maps. Lateral Boundaries Lateral boundaries of alluvial fans are the edges of deposited and reworked alluvial materials. The lateral boundary of a single alluvial fan typically is a trough, channel, or swale formed at the lateral limits of deposition. Crenulations in contour lines at fan boundary troughs can be observed along the margins of the Cedar Creek alluvial fan (Figure 3-2a). Lateral boundaries of single alluvial fans commonly are distinct contacts between light-colored, freshly abraded, alluvial deposits and darker-colored, weathered deposits with well-developed soils on piedmont plains. Soils of active alluvial fans typically are less oxidized and lower in clay content than soils on older landforms. As a consequence, the younger soils generally are lighter colored and more friable. Color and texture changes often are pronounced on aerial photos or infrared remote sensing imagery. In areas with rock varnish formation,2 the lighter surfaces of recent alluvial fan deposits in contact with undisturbed varnished surfaces of older deposits form a distinct boundary or contact that readily is distinguished by the relative darkness of the ground on aerial photographs and by on-the-ground inspection. Dark, undisturbed surfaces of rock varnish are found on old piedmont and valley deposits throughout the Basin and Range province of the western United States. In the case of multiple fans that coalesce to form bajadas, where deposits and reworked material of adjacent alluvial fans merge, the boundaries between adjacent fans may be less distinct than those of individual fans adjacent to streams, rivers, or smooth piedmonts, but generally are 1   The committee has not visited the Cedar Creek fan and inspected its surface and deposits. It is used as an example here because it has been studied intensively by prominent geomorphologists, and thus much information is available regarding it. In addition, it is a classic alluvial fan in shape and history. 2   Rock varnish is a dark coating (from 2 to 500 microns thick) that forms on rocks at and near the Earth's surface as a result of mineral precipitation and eolian influx. The chemical composition of rock varnish typically is dominated by clay minerals and iron and/or manganese oxides and hydroxides, forming red and black varnishes, respectively. With time, the thickness of the coating increases if abrasion and burial of the rock surface do not occur. As a result, clastic sediments on alluvial fan surfaces that have been abandoned for long periods of time have much darker and thicker coatings of varnish than do younger deposits.

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marked by a topographic trough or ridge. Although it is difficult to separate young deposits on one fan from similar age deposits on a coalescing fan, it sometimes is possible to distinguish them based on different source basin rock types. For example, Bull (1963, 1964) defined fan boundaries in central California using contour maps, aerial photographs, and tests of the gypsum content of core hole samples. Bull found that the gypsum content of fan deposits derived from drainage basins underlain predominantly by clay-rich rocks was about five times that of fan deposits from drainage basins underlain predominantly by sandstone. Boundaries of many alluvial fans are defined on 7.5-minute series orthophoto base maps by the NRCS. In the U.S. Southwest, typical NRCS soil series for alluvial fans include the Ramona, Soboba, Kinburn, and Anthony. Large areas where material from stream banks is freshly deposited and partly reworked during floods also are mapped, and smaller areas are identified as part of a particular series where the reworked material is located. For small alluvial fans less than about .8 km2 (.3 mi2), the detail of the mapped soil units on the 7.5-minute soil map series may not be sufficient to show many distributary channels and the fan boundaries. Soil maps used in conjunction with aerial photographs are an excellent means to define fan boundaries. The nature and extent of alluvial fan flooding can be partially determined from published topographic, soils, and geologic maps and other sources of data. However, the committee emphasizes the importance of a field inspection by a qualified professional with experience and technical knowledge of geomorphology, slope stability, avalanche potential, flood hydraulics, flood hydrology, sedimentary facies, and alluvial fan processes. The general use of secondary information and the importance of field information is described in this chapter and in the examples described in Chapter 4. STAGE 2: DEFINING THE NATURE OF THE ALLUVIAL FAN ENVIRONMENT AND IDENTIFYING THE LOCATION OF ACTIVE EROSION AND DEPOSITION Most alluvial fans have parts that are active and parts that are inactive. Alluvial fan flooding occurs on active parts of alluvial fans. In Stage 2, evidence is obtained that identifies areas of potential flooding. This step narrows the area of concern for Stage 3, which is the specification identification of the extent of the 100-year flood. Although alluvial fan flooding has occurred on all parts of an alluvial fan at some time in the geologic past in order to construct the landform itself, this does not mean that all parts are equally susceptible to alluvial fan flooding now. In fact, in most of the United States it is possible to identify parts of alluvial fans that were actively constructed during Pleistocene time (about 2 million to 10,000 years ago) and parts that have been active (i.e., flooded) in the Halocene (the past 10,000 years). The reason that this broad distinction generally is straightforward and simple in practice is that the two time periods were identified and defined on the basis of different climatic conditions. The Halocene epoch is a time of interglacial warm conditions, whereas the Pleistocene epoch was marked by repeated full glacial, cool conditions alternating with warm interglacials like that of the Halocene (Figure 3-3). During glacial times, ice masses expanded and advanced, evaporation was low, and in the dry western U.S. ground water tables and stream discharges were high relative to interglacial times. As a result of these climatic differences, flooding and sedimentation occurred at different rates and magnitudes during the

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FIGURE 3-3 Quaternary period timescale illustrating oscillating climatic conditions from full glacial (cool) to interglacial (warm). SOURCE: Reprinted with permission from Skinner and Porter (1995). Pleistocene and Holocene epochs. In many regions, the post-Pleistocene change of climate resulted in a reduction in the rate of sediment supply to fans, whether by streams or debris flows. As a result, the discharges presently available are able to move the sediment supplied on a lower slope than that formed during the Pleistocene, so fanhead incision is occurring on some fans. One of the most common causes of the abandonment of large parts of an alluvial fan is a change in elevation of local streams. Elevation change can result from a change in climatic conditions or in rates of tectonism. Climatic change might result in a decrease in the size of large streams and/or lakes at the toe of the fan, as in the case of a change from braided, postglacial meltwater streams to smaller, meandering streams incised into the braided gravel deposits.

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deposits by differences in morphology, depositional relief, stratigraphy, and clast fabric (Figure 3-8; Table 3-4). Exposures in channel banks can be examined and can be supplemented with shallow trenches in different deposits. In an example of a channel bank exposure described by Hereford et al. (1995) in the eastern Grand Canyon, debris flow deposits are interbedded with streamflow gravels, but can be distinguished by the differences in stratigraphy and clast fabric (Figure 3-9). STAGE 3: DEFINING AND CHARACTERIZING AREAS OF 100-YEAR ALLUVIAL FAN FLOODING For FEMA to carry out the mandates of the National Flood Insurance Program (NFIP), areas that are subject to flooding during a 100-year flood—that is, areas subject to a 1 percent chance of flooding in any year—must be identified. The two previous sections described methods of identifying landforms subject to alluvial fan flooding and the active portions of the fan that are subject to flooding. But identification of possible hazard areas is only the first step. The third step, one that is critical for floodplain managers and regulators, is to determine the severity and to delineate the extent of the 100-year flood, that is, the area exposed to a 1 percent risk of flooding in any given year. Although field work and study of aerial photographs and topographic maps are essential for carrying out the three stages necessary to identify alluvial fans and stable and unstable components of fans, the three-stage analysis can be quantified by the use of hydrologic methods. Although it is beyond this committee's scope and resources to explore in detail the numerous methods that have been developed to evaluate flood hazards, it is appropriate to give a general overview of the methods available to delineate the actual flood hazards on a fan. Thus this section briefly addresses the techniques, the types of analysis, and the appropriate perspectives that may be of assistance in the delineation of the hazards on alluvial fans and explores their potential for assisting FEMA in its mapping responsibilities. This discussion is not intended to be a complete exploration of all the methodologies that have been developed for hydraulic analyses, but rather it is a general introduction to several methods currently in use. In the future FEMA might consider conducting a detailed review of these methods and how they are applied The mapping of flood risks for purposes of the NFIP is based on the flooding that is likely to result from an event that has the probability of occurrence of 1 percent in any given year, an event more commonly known as the 100-year flood. Within relatively stable river systems, it has been a standard practice to delineate the 100-year floodplain using a modeling technique based on the assumption that the flow is clear water and the hydraulic conditions are such that flow is gradually varied. In many instances, this technique also is used to model more dynamic systems with some acknowledgment of its limitations, because the areas of hazard within a river valley are usually apparent and confined to a geologic floodplain. Areas subject to alluvial fan flooding often are not as readily apparent as those subject to riverine-type flooding. The physical characteristics of the fan-shape also make the use of simplifying assumptions seem less logical and therefore less acceptable. Active alluvial fans are changeable, and erosion and deposition occur to some degree with most events. Inactive fans may also have flow paths that are unconfined and subject to uncertainty largely because of the numerous channel forks and joins.

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FIGURE 3-8 Morphologic and stratigraphic characteristics of different flow types developed from an example fan in England. SOURCE: Reprinted with permission from Wells and Harvey (1987). When floodwater contains a significant amount of sediment or the flooded area is subject to scour and deposition, the flow behavior becomes less predictable. High concentrations of sediment and debris in flowing water can cause it to behave differently than clear water flows. Some of these differences, such as the unit weight, are quantitative in nature. Other differences, such as the vertical velocity distribution for a debris flow, display qualitative differences when compared to clear water.

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TABLE 3-4 Summary of Morphologic and Sedimentologic Field Criteria for Distinguishing Facies Types Facies Type Morphology Depositional Relief (m) Texture and Stratification Characteristics of Clast Fabric Debris flow (D1) Lobate to digitate; narrow; steep front and flanks; flat tops with low relief pressure ridges High (0.8–1.5) Matrix-rich (muddy); matrix-supported clasts; poorly sorted; bmax range 80–210 mm; stratification absent Elongate clasts oriented parallel to flow boundary forming a push fabric Dilute debris flow (D2) Thin lobate; broad, flat top; gentle lobe fronts and flanks Moderate (0.3–0.5) Matrix-rich; matrix-supported clasts; poorly sorted; bmax range 60–230 mm; stratification absent None observed Transitional flow deposits (T1) Stacked lobes; broad small superimposed mounds; small collapse depressions High (0.5–1.5) Clast support with no matrix in upper few centimeters; matrix (sandy) increases with depth bmax typically <180 m; moderately sorted; stratification present Collapse packing Fluvial boulder bar and lobes (S1) Linear bars to transverse lobes Moderate to high (0.5–0.8) No matrix; clast support; front-to-tail sorting; bmax typically >200 mm Imbrication Fluvial longitudinal bar (S2) Linear bars Moderate (0.2–0.5) Clast support; matrix (sandy) increases with depth; market front-to-tail sorting; more poorly sorted than type S1; bmax typically <120 mm Strong imbrication Fluvial sheet deposits (S3) Broad and flat; some fan-shaped; subdued bar and swale forms Low (–0.1) Clast support; little matrix (sandy); well stratified; normal grading in some strata; moderate sorting in each stratum; bmax typically <100 mm Weak imbrication   SOURCE: Reprinted with permission from Wells and Harvey (1987).

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FIGURE 3-9 Interbedded debris flow and streamflow gravel, eastern Grand Canyon. SOURCE: Hereford et al. (1995). AVAILABLE METHODS OF ANALYSIS To investigate flood hazards, there are three general categories of interest: clear water flows that can be analyzed with traditional hydraulic methods, hyperconcentrated sediment flows that can be analyzed to a great extent by sediment transport theory, and debris flows that can be assessed by various empirical methods such as the bulking factor, the Bingham model, and other methods. Appendix 5 of FEMA 37, Guidelines and Specifications for Study Contractors (1995), describes a method for delineating the boundaries of flood hazards on a fan-shaped surface. This method, however, is the cause of some confusion. The method considers the conditional probability of the occurrence of a flood with a given magnitude, taking a certain path through the spatial domain, and inundating a point of interest. The equation that allows one to apply this method is called the total probability equation. Its purpose is to compute, for example, when the combined probability of two events is equal to 0.01. The events can be the occurrence of a flood, the failure of a levee, the coincidence with a different flood, the chance that floodwaters take a certain flow path, and so on. The purpose of using this method is to account for uncertainty when it cannot be easily set aside.

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The use of the total probability equation is not limited to alluvial fans, and it is used by other federal agencies in addition to FEMA (NRC, 1995). The method of solving the total probability equation proposed by Dawdy (1979) has been used in the preparation of several FIRMs in the western United States. This method assumes that all areas of the fan are subject to flooding and that there is a fixed relationship between flooding depth and discharge. These assumptions apply when there is absolute uncertainty regarding how floods will occur. The advantages of these assumptions are that they are reproducible, they lend themselves to uncomplicated regulatory implementation, and, in certain situations, they are the easiest assumptions to defend. FEMA has developed a computer program called FAN (FEMA, 1990) that incorporates these assumptions, and it provides this program to contractors charged to delineate alluvial fan flooding. When it comes to mitigation and the implementation of floodplain management regulations, however, it may be appropriate to review the assumption of complete uncertainty. There may be historical flow paths that are preferred during small floods. From a mitigation perspective, it would make sense to reinforce these paths rather than ignore them. The current Flood Insurance Rate Maps (FIRMs) that have been prepared using the procedure recommended by FEMA are a statement of complete uncertainty. These FIRMs then are not necessarily useful to floodplain mangers and regulators (who are often unaware of the procedures followed to identify the hazard) to assist them in determining the hazards on a particular fan area. Since the decision on how or whether to solve the total probability equation is usually made by the flood insurance study contractor, the safe, default assumption of complete uncertainty is typically embraced to save, among other things, time. Most of the alluvial fan areas examined by the committee, however, show obvious, preferred flow directions. Alternative solutions to the total probability equation can be applied to these areas, but the guidelines in FEMA 37 (1995) are not clear about this and suggest only that the default assumption should be a starting point. Furthermore, permission to deviate from this assumption must be obtained in writing from FEMA. All flooding sources have uncertainty. There is an apparent contradiction between the existing definition of alluvial fan flooding, which is very inclusive, and the actual method being used to delineate the hazard, which is limited to fan-shaped landforms. Flood behavior is predictable within the expected range of uncertainty. When the uncertainty can no longer be set aside but must be dealt with directly to achieve a reasonable result, then the total probability equation becomes a useful method for delineating flood hazards. The applicability of the method, however, does not mean that an area is subject to alluvial fan flooding. It is merely a way of expressing uncertainty. FEMA has not developed guidelines on the general solution of the total probability equation. The committee recommends consideration of the use of Guidelines for Risk and Uncertainty Analysis in Water Resources Planning (USACE, 1992) for specific guidelines on how to apply the method. The principles of risk-based analysis (USACE, 1992) provide a framework for a more general and realistic way to identify areas subject to flooding with an annual probability of 1 percent. The degree of uncertainty associated with a prediction of a given flood scenario is assessed by bringing to bear evidence derived from geomorphologic and other studies (for example, an alluvial fan with a series of branching channels). Figure 3-10 shows a flow diagram for conducting an analysis of diverging channels by considering various scenarios. Figure 3-11

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FIGURE 3-10 Analysis of flow path uncertainty considering possible scenarios.

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FIGURE 3-11 Conditional nonexceedance probability estimation with event sampling.

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shows an example of estimating conditional nonexceedance probability using event sampling. The broad spectrum of types of flooding that can occur and that have been observed on alluvial fans illustrates the futility of developing a ''cookbook" method to apply to all fans in all geographic areas. Reviews of current research and discussions with local officials charged with regulating development in alluvial fan flooding areas indicate a prevailing preference for analysis of the flood hazards based on site-specific evaluations. The types of information that should be gathered include both geomorphic and process considerations. For example, some flow associated with channels meets the criteria for alluvial fan flooding, even though it occurs in channels in much the same way that riverine flow occurs in channels. The difference between the two is that in alluvial fan flooding the channels are likely to shift position with time and flows often abandon one channel to form another, resulting in much unpredictability regarding the locations of future flow paths. The following questions can provide guidelines to identify areas where flow paths are uncertain and flow is likely to leave confined channels to move in unpredictable directions: Where is there evidence of recent channel shifting? Where is there evidence of recent channel avulsion? Where is there evidence of the potential for channel avulsion? Where has channel geometry changed markedly in recent time? Because alluvial fan flooding is associated with high rates of erosion, sediment transport, and deposition, it is common for such flows to shift position as sediment is dropped and forms obstructions to the flow. In some events, previous channels are completely blocked by deposits, and a new channel is formed. This process is known as avulsion and can be identified from aerial photos or field mapping by the presence of topographic lows (abandoned channels), the upstream parts of which filled with sediment. Areas of potential channel avulsion sometimes can be identified from construction of longitudinal and cross-fan profiles, because avulsion is likely to occur in places where sedimentation has raised the channel floor surface to a level that is nearly as high as the surrounding surface of the alluvial fan. In addition, human modification of alluvial fan surfaces and urban development on alluvial fans have resulted in cases where human-made obstructions themselves have been the cause of alluvial fan flooding. For example, construction of culverts to divert water from one part of a fan to another sometimes results in rapid sedimentation downstream from the mouth of the culvert. The result can be that alluvial fan flooding then occurs in an area that might not have been mapped as susceptible to this type of flooding before human alteration of the landscape. Special attention is needed to identify areas where engineered works might aggravate or cause alluvial fan flooding during the time period designated as active by the investigator. Specific steps that should be followed before undertaking any final delineation of alluvial fan flooding hazards include detailed office and field reviews of historical information and the evaluation of the present landform. Initial office procedures include the review of topographic maps and aerial photographs to determine the location and the morphology of the landform to determine whether it is a true alluvial fan. Other data that should be gathered early include historical maps and old photographs to document channel changes, changes in channel morphology, and the areas of the fan that may be classified as either active or inactive. Soil and geologic mappings should be examined to confirm the relative geologic age of fan deposits. Climatologic data and appropriate hydrologic analyses will be needed to determine the magnitude

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and frequency of flooding to be addressed. Aerial photographs and geologic information of the catchment area will provide indications of the amount of sediment and debris that can be delivered to the fan. Field investigations by a trained observer should include gathering information on elevation differences across the fan and in a transverse direction if detailed topographic maps are not available. Vegetation types, soil characteristics, and the presence of desert varnish should be added to the office maps to confirm the active or inactive portions of the fan. Observations and measurements of channel conditions should be made to determine areas of possible avulsion. Detailed inspection of diffluences or abandoned channels should indicate the most likely flow paths. The results of the initial office and field investigations should provide sufficient information to direct the final analysis. SUMMARY The previous three stages demonstrate that flood risk on alluvial fans is not unpredictable, but rather that it is predictable with varying degrees of uncertainty. The assumption of a uniform risk (FEMA, 1995) or complete uncertainty across an alluvial fan can be used as a formalized guess that allows one to delineate risk on the FIRM using a straightforward technique. This technique may be reasonable for the delineation of hazards on certain alluvial fans. The method proposed by Dawdy (1979) is an insightful application of the total probability equation. Although the assumptions used to solve the equation may vary for each situation, the method itself is sound and quite general. A FIRM showing alluvial fan flooding hazards mapped considering complete uncertainty is of little use for floodplain management. By making a conservative trade-off in favor of all possibilities, this type of FIRM ignores the importance and the more threatening hazard of flow in existing channels and historical flow paths and conversely penalizes safer areas. The FEMA Guidelines and Specification for Study Contractors (1995) asserts that flow paths for alluvial fan flooding are unpredictable and the assumption of uniform uncertainty must be used in the hazard delineation unless written approval is sought. Approaching the wide range of alluvial fan flooding conditions from the inflexible perspective of this special case is part of the reason for the conflict surrounding this matter. The committee recommends that all efforts at mapping start with the existing channel. For situations where there is an entrenched channel on an alluvial fan, the uncertainty may be set aside. However, elsewhere the uncertainty associated with flow path direction might cause one to select FEMA's uniform risk method. For the majority of the cases, however, consideration of specific, foreseeable scenarios based on stages 1 and 2 make the most sense. For some undissected fans, the assumption of uniform flow path uncertainty may apply. Such cases are not in the majority, and yet they are the only cases where the computer program FAN (FEMA, 1990) might be applicable.

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REFERENCES Bull, W. B. 1963. Alluvial fan deposits in western Fresno County, California. Journal of Geology 71:243–351. Bull, W. B. 1964. Alluvial fans and near surface subsidence in western Fresno County, California. U.S. Geological Survey Professional Paper 437-A. Reston, Va.: U.S. Geological Survey. Bull, W. B. 1977. The alluvial fan environment. Progress in Physical Geography 1(2):222–270. Bull, W. B. 1991. Geomorphic Response to Climatic Change. New York: Oxford University Press. Christenson, G. E., and C. Purcell. 1985. Correlation and age of Quaternary alluvial fan sequences, Basin and Range province, southwestern United States. Pp. 115–122 in Soils and Quaternary Geology of the Southwestern United States. GSA Special Paper 203. Boulder, Colo.: The Geological Society of America. Cooke, R., A. Warren, and A. Goudie. 1993. Desert Geomorphology. London, England: University College London Press. Dawdy, D. R. 1979. Flood frequency estimates on alluvial fans. American Society of Civil Engineers Journal of the Hydraulics Division 105(HY11):407–1413. Dorn, R. I. 1994. The role of climatic change in alluvial fan development. Pp. 593–615 in Geomorphology of Desert Environments, A. D. Abrahams and A. J. Parsons, eds. London, England: Chapman and Hall. Federal Emergency Management Agency (FEMA). 1990. FAN: An Alluvial Fan Flooding Computer Program, User's Manual and Program Disk. Washington, D.C.: FEMA. Federal Emergency Management Agency (FEMA). 1995. Guidelines and specifications for study contractors. Document no. 37, Appendix 5: Studies of alluvial fan flooding, Washington, D.C.: FEMA. Hereford, R., K. S. Thompson, K. J. Burke, and H. C. Fairley. 1995. Late Holocene debris fans and alluvial chronology of the Colorado River, Eastern Grand Canyon, Arizona. U.S. Geological Survey Open-File Report 95-97. Reston, Va.: U.S. Geological Survey. Hydrologic Engineering Center (HEC). 1990 HEC-2 Water Surface Profiles, User's Manual. Davis, Calif.: U.S. Army Corps of Engineers Water Resources Support Center. Keaton, J. R. 1988. A Probabilistic Model for Hazards-Related Sedimentation Processes on Alluvial Fans in Davis County. Ph.D. dissertation. Texas A&M University, College Station. Kellerhals, R., and M. Church. 1990. Hazard management on fans, with examples from British Columbia. In Alluvial Fans: A Field Approach, A. H. Rachocki and M. Church, eds. New York: John Wiley & Sons. MacArthur, R. C. 1983. Evaluation of the effects of fire on sediment delivery rates in a southern California watershed. In Proceedings of the D. B. Simons Symposium on Erosion and Sedimentation, Colorado State University, Fort Collins. July 27–29, 1983. National Research Council. 1995. Flood Risk Management and the American River Basin: An Evaluation. Washington, D.C.: National Academy Press. Pearthree, P. A., K. A. Demsey, J. Onken, K. R. Vincent, and P. K. House. 1992. Geomorphic Assessment of Flood-Prone Areas on the Southern Piedmont of the Tortolita Mountains, Pima County, Arizona . Arizona Geological Survey Open-File Report 91-11. Tucson, Ariz.: Arizona Geological Survey.

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Ritter, J. B., J. R. Miller, Y. Enzel, S. D. Howes, G. Nadon, M. D. Grubb, K. A. Hoover, T. Olsen, S. L. Reneau, D. Sack, C. L. Summa, I. Taylor, K. C. N. Touysinhthiphonexay, E. G. Yodis, N. P. Schneider, D. F. Ritter, and S. G. Wells. 1993. Quaternary evolution of Cedar Creek alluvial fan, Montana. Geomorphology 8:287–304. Ritter, D. F., R. C. Kochel, and J. Miller. 1995. Process Geomorphology, 3rd Ed. Dubuque, Iowa: Times Mirror Higher Education Group. Skinner, B. J., and S. C. Porter. 1995. The Blue Planet. New York: John Wiley & Sons. U.S. Army Corps of Engineers (USACE). 1992. Guidelines for Risk and Uncertainty Analysis in Water Resources Planning. Report 92-R-1. Fort Belvoir, Va.: USACE Water Resources Support. Wells, S. G., and A. M. Harvey. 1987. Sedimentologic and geomorphic variations in storm-generated alluvial fans, Howgill Fells, northwest England. The Geological Society of America Bulletin 98:182–198.