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Earth Surface Processes and LandformsEarth Surf. Process. Landforms 30, 755–766 (2005)Published online 17 May 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/esp.1188

The significance of channel recharge rates forestimating debris-flow magnitude and frequencyMatthias Jakob,1* Michael Bovis2 and Marian Oden3

1 BGC Engineering Inc., Suite 500-1045 Howe Street, Vancouver, BC, V6Z 2A9, Canada2 Geography Department, 217-1984 West Mall, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada3 Madrone Environmental Services Ltd, 1081 Canada Avenue, Duncan, BC, V9L 1V2, Canada

AbstractThe quantification of debris-flow hazard requires estimates of debris-flow frequency andmagnitude. Several methods have been proposed to determine the probable volume of futuredebris flows from a given basin, but most have neglected to account for debris recharge ratesover time, which may lead to underestimation of debris-flow volumes in basins with raredebris flows. This paper deals with the determination of debris recharge rates in debris-flowchannels based on knowledge of debris storage and the elapsed time since the last debrisflow. Data are obtained from coastal British Columbia and a relation is obtained across asample of basins with similar terrain and climatic conditions. For Rennell Sound on the westcoast of the Queen Charlotte Islands, the power-law relation for area-normalized rechargerate, Rt, versus elapsed time, te was Rt ===== 0·23te

−−−−−0·58 with an explained variance of 75 per cent.A difference in recharge rates may exist between creeks in logged and unlogged forestedterrain. The power function for undisturbed terrain was Rt ===== 0·20te

−−−−−0·49, while the functionfor logged areas was Rt ===== 0·30te

−−−−−0·77. This result suggests that for the same elapsed time sincethe last debris flow, clearcut gullies tend to recharge at a slower rate than creeks in oldgrowth forest. This finding requires verification, particularly for longer elapsed times sincedebris flow, but would have important implications for forest resource management in steepcoastal terrain. This study demonstrates that commonly used encounter probability equationsare inappropriate for recharge-limited debris flow channels. Copyright © 2005 John Wiley& Sons, Ltd.

Keywords: debris flows; magnitude; frequency; channel recharge

*Correspondence to: M. Jakob,BGC Engineering Inc., Suite 500-1045 Howe Street, Vancouver,BC V6Z 2A9, Canada. E-mail:mjakob@bgcengineering.ca

Received 9 January 2004;Revised 16 August 2004;Accepted 29 September 2004

Introduction

Debris flow is a dominant mass movement process in the Coast Mountains of British Columbia, and constitutes asignificant natural hazard. Consequently, knowledge of the frequency and magnitude of debris flows is important inapplied geomorphology and geotechnical engineering for hazard and risk assessments (Rickenmann, 1999). It alsoallows estimates of geomorphic work done by debris flows, which is of interest in sediment budget estimation andmodels of landscape evolution.

Very few debris flow creeks have been monitored over sufficiently long periods to allow construction of usablefrequency–magnitude relationships. Exceptions exist in densely populated areas, where debris-flow monitoring andmitigation have been more urgent to prevent loss of life and property (e.g. Johnson et al., 1991). A variety of methodshave been proposed to allow estimates of debris-flow volumes and return periods, despite the general lack of data.These include: stratigraphic methods; volume estimates from aerial photography (Jakob and Podor, 1995; Jordan1994); determination of source area volume and debris entrained along the path (Eaton et al., 2003a,b, Hungret al., 2005); and tree-ring records, combined with ground surveys for both volume and event frequency estimates(Shroder, 1980; Osterkamp et al., 1986; Strunk, 1991; Jakob and Bovis, 1996, Stefanini and Ribolini, 2003). Wherepossible, historical accounts of debris-flow events are also used for more precise dating control (Couture and Evans,2000; Jakob et al., 2000, Carrara et al., 2003). Since much of the field evidence typically resides on debris-flowfans, such studies are referred to hereafter as ‘fan-based studies’. One of the major problems encountered in thelatter studies is that relatively small, high-frequency events are usually eroded or overprinted by subsequent higher

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magnitude events. Such gaps in the debris-flow record may be bridged by air photographs or historical accounts, butin remote mountain areas such data are usually not available (Carrara et al., 2003). Test trenching or drilling mayprovide stratigraphic information from which volumes of past events may be extrapolated (Thurber EngineeringConsultants and Golder Associates, 1995; Jakob et al., 2003), but this is possible only where considerable funds areavailable, typically where a new development requires a detailed investigation of geological hazards prior to itsapproval. In such cases it could be argued that overprinting of small events by larger ones is not a significant obstacle,since the hazard posed by the largest events is more important. However, since the return periods of design flows usedin the design of mitigative structures typically range between 100 and 1000 years, frequency–magnitude relations aresometimes required which cannot rely solely on the largest reconstructed events (e.g. Thurber Engineering Consultants,1983; Kerr Wood Leidal Associates, 2003).

Other empirical methods to predict debris-flow volume and travel distances include those of Benda and Cundy(1990), who used channel slope and tributary junction angle; Cannon (1993), who used regression analysis incorporat-ing slope angle and the transverse radius of channel curvature for volume prediction; Iverson et al. (1998), who usedan empirical correlation between lahar volume and area inundated by debris for runout determination; and Fannin andWise (2001), who used reach length, material entrainment, and slope angle to predict volume changes along debris-flow paths. However, the most significant neglect of these studies is that no allowance is made for channel rechargerates. In Fannin and Wise’s (2001) work, for example, a debris flow occurring one year after the most recent eventwould have had the same predicted volume as its predecessor. Clearly, actual volumes will be significantly lower sincethe channel will likely have been scoured clear of debris by the earlier event. Their model therefore is applicable onlywhere debris-flow channels are in approximately the same state of recharge as the sample of channels used to developthe predictive model.

A different approach to predicting debris-flow frequency uses magnitude and frequency of rainstorms capableof triggering events. There is a substantial literature on this topic (e.g. Caine, 1980; Church and Miles, 1987; Keeferet al., 1987, Wilson and Wieczorek, 1995; Deganutti et al., 2000; Wieczorek et al., 2000; Jakob and Weatherly, 2003).However, a common failing of such studies is that climatic thresholds are difficult to establish for the all-importanthigh-magnitude, low-frequency events because of temporal changes in sediment availability (Church and Miles, 1987;Jakob and Weatherly, 2003). In this study, we emphasize the importance of channel recharge mechanisms and theireffect on debris-flow volume, since channels insufficiently recharged with debris might register high water and fluvialsediment mobilization during a given storm, but would lack adequate debris storage to permit debris-flow develop-ment. Exceedence of a climatic threshold is thus a necessary, but not a sufficient, condition for debris flow occurrence.In this context it is important to differentiate between weathering-limited and transport-limited basins (Bovis andJakob, 1999). Channels in weathering-limited basins typically recharge at rates controlled by rock weathering anddisintegration, whereas transport-limited basins typically contain large volumes of readily mobilizable glacial, colluvial,or volcanic materials. Consequently, transport-limited basins tend to produce debris flows more readily whenever aclimatic threshold is exceeded. This paper focuses primarily on weathering-limited, or supply-limited debris-flowbasins, which occur most frequently in the more competent igneous, meta-sedimentary and meta-volcanic rocks ofcoastal British Columbia. The objective of this paper is to predict future debris-flow volumes based on a relationbetween expected event volume and the time elapsed since the last debris flow. It is also demonstrated that encounterprobabilities in weathering-limited basins cannot be calculated using traditional methods and may have to be adjusteddepending on recharge–time correlations.

Study Areas: Physiography and Climate

Queen Charlotte IslandsThe Queen Charlotte Islands (Haida Gwaii) are located 130 km off the coast of central British Columbia and form partof the Insular Belt of the Canadian Cordillera. The study area is located on the western slope of the Queen CharlotteRanges, where steep basins descend 800 to 1100 m to Rennell Sound (Figure 1). Headwater slopes are typically steep,up to 60°, and are deeply dissected by gullies entrenched in bedrock, colluvium and till. The area is dominated by theJurassic Yakoun Formation, consisting of weak volcanic and sedimentary rocks including shale, siltstone, sandstone,and andesite characterized by a moderate to high degree of fracturing. Other rocks include argillite, sandstone andlimestone of the Kunga Group and minor outcrops of post-tectonic plutons, consisting primarily of quartz diorite andquartz monzodiorite of Jurassic age (Sutherland-Brown, 1968; Hesthammer et al., 1991). Most of these rocks weatherrapidly and have low resistance to surface erosion (Alley and Thomson, 1978; Lewis, 1985). Consequently, naturalrates of debris supply to steep channels tend to be high.

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The Queen Charlotte Islands are characterized by a perhumid, cool-temperate climate, with mild wet winters andcool summers. Most precipitation falls between October and April with annual totals ranging from 1200 mm on thedrier, leeward east side of the islands to more than 4200 mm on the more rugged, windward side of the archipelago(Williams, 1968; Wilford and Schwab, 1982; Schwab, 1988). Given the steep terrain and heavy precipitation, land-slides and debris flows are very frequent events (Rood, 1984; Gimbarzevsky, 1988). The Rennell Sound area wasselected for this study because of easy access to numerous debris-flow channels located in both old-growth and clear-cut terrain, and because the approximate dates of many debris flows had previously been determined by Hogan andSchwab (1991).

Previous work has shown that the spatial frequency of slope failures in the Rennell Sound area is up to 55 timeshigher in clear-cut terrain (22·1 km2 a−1) relative to unlogged, old-growth forested terrain (0·4 km2 a−1), with failurevolumes up to 90 times higher in clear-cut terrain (1·8 m3 ha−1 a−1 versus 0·02 m3 ha−1 a−1; Rood, 1984). These observa-tions stress the importance of land use changes on sediment supply to debris-flow channels, and corroborate similarfindings by geomorphologists working in Alaska, Washington, and Oregon (Fredriksen, 1970; Swanson et al., 1977;Swanson and Dyrness, 1975; Swanson and Grant, 1982).

Coast Mountains of southwestern British ColumbiaThirty-five basins were selected from within a 25 000 km2 segment of the rugged southern Coast Mountains ofsouthwestern British Columbia (Figure 1). The area spans the basins of the Squamish, Lillooet, Bridge, and Fraserrivers. Within this area there occur thousands of small creeks capable of delivering debris flows. Debris-flow basinswere selected for detailed study primarily on the basis of their accessibility, and the quality of their records of debris-flow frequency and event volume. Basins affected by both snow avalanches and debris flows were avoided because ofthe problems encountered in interpreting tree scars that could have resulted from either process.

The study area encompasses an area of pronounced geological diversity: it lies mostly within the granitic andgneissic Coast Plutonic Complex, but several study basins were located within the Plio-Quaternary volcanoes at

Figure 1. Map of British Columbia, showing the two study areas used for this investigation.

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Mount Cayley and Mount Meager, and others within a weak assemblage of Cretaceous sedimentary rocks located justeast of the Fraser River. The bedrock of the study basins is thus representative of most rock types found on thesouthwestern mainland of British Columbia.

Quaternary glaciations have profoundly influenced geomorphic conditions in the Coast Mountains (Ryder, 1981)both in terms of bedrock landforms and blankets of Quaternary till. High-relief, alpine, glacial landforms exhibit arange of large-scale mass-movement processes including rock avalanches, debris avalanches and debris flows. Inmany cases, rock-slope instability directly feeds steep channels and sometimes triggers debris flows. Pleistoceneglacial till deposits and Neoglacial moraines also serve as source materials for many debris flows (Jackson et al.,1989; Haeberli et al., 1997; Holm et al., 2003).

Climate and hydrologic conditions vary greatly between the perhumid western and the subhumid eastern flankof the Coast Mountains. Precipitation in the Howe Sound–Whistler–Pemberton corridor has a winter maximumwith annual totals ranging from 1100 mm at sea level to over 3000 mm at 2000 m elevation. Most debris flows aretriggered by cyclonic rainfall in autumn and early winter, often combined with rain-on-snow events and strongsoutheasterly to southwesterly winds (Church and Miles, 1987; Jakob and Weatherly, 2003).

Given the terrain complexity, a wide range of natural debris-flow terrain conditions occurs within the sample of35 study basins. For this reason, basins previously subjected to logging, mining and other significant human impactswere avoided. Thirteen basins are classed as transport-limited, and 22 as weathering-limited, based on air photographinterpretation and detailed field checking and criteria previously developed by Jakob and Bovis (1996).

Methods

Determination of debris-flow volumesDebris-flow channels were surveyed to determine the total volume of debris accumulation during the time intervalsince the last debris flow. The important assumption is that the channel was scoured clear by the last flow, leavingnegligible debris in the channel. Field evidence from both study areas has demonstrated that this assumption is validfor bedrock-based channels due to the very high erosivity of bouldery debris flow in steep mountain creeks (Figure 2).In carved deep colluvial deposits, this assumption is not necessarily valid because the debris flow may undercut thechannel banks, which will then destabilize and deliver debris to the channel (Hungr et al., 2005).

Estimating the total volume of stored sediment in a channel is dependent on locating the underlying channel base.A sediment wedge upstream of an obstruction can be characterized as a rectangular prism (Megahan, 1982; Hogan,1987; Nakamura and Swanson, 1993). Within the study areas, widths and depths of sediment accumulations are highlyvariable, the slope of the sidewalls varies non-systematically, and the gully base is often irregular. As a result, simple

Figure 2. Bedrock channel completely scoured by a debris flow, Gregory Creek, Rennell Sound, Queen Charlotte Islands.

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shape approximations were considered inappropriate, and sediment volume was determined using multiple measure-ments and estimates of the cross-sectional area of the sediment fill, along with measurements of the bedrock longitu-dinal profile.

The cross-sectional area of each of the excavation sites was determined from an overlay of the sediment andbedrock surface profiles, and the resulting sediment polygon was divided into trapezoids with each trapezoid areaAt being calculated as:

At = [(a + b)/2]c (1)

where a is the width of the fill surface, b is the estimated width of the prism base, and c is the thickness of the debrisfill. Trapezoidal volumes were then computed from the known length of a debris prism.

In cases where direct measurement by excavation was not feasible (for example, boulders were too large orsediment fill was beyond what could reasonably be excavated by hand), alternative methods were used to estimatesediment cross-sectional area. Examples of such methods were: (1) the cross-profiles of sediment wedges were plottedfrom known gully sidewall angles and prism widths; (2) polygons of sediment were identified on plotted cross-sections by extrapolating bedrock profile trends, and these polygons were graphically integrated; (3) bedrock cross-sections in the channel were identified as sites of zero sediment storage; and (4) linear regression analysis was used topredict the area of sediment at the start of channelization of the gully and the start of the deposition zone of the mostrecent debris flow. Methods (1), (2) and (3) were applied at as many sites within each gully or creek as possible, whilemethod (4) was applied to the entire data set to identify cross-sectional area at the end-points of the longitudinalprofile. Each method is described in detail in Oden (1994).

Sediment sources and sidewall materials were recorded. Deposits from recent debris flows were surveyed to obtainestimates of total event volume, being defined by the amount of material delivered to the terminal debris fan. Inseveral cases, debris flow deposits had been significantly eroded by the stream traversing the fan, or by the higherorder stream into which the debris flow had discharged. Reliable volume estimates could not be obtained in thesecases.

Debris recharge rates were estimated by dividing the total volume of clastic and large organic debris (logs, treestumps) by the elapsed time since last debris flow, the latter determined by dating impact scars on nearby trees. Debrisvolume was determined by detailed surveys of debris prisms along each channel. In many smaller bedrock gullies inthe Queen Charlotte Islands, the depth of debris fill was determined directly by excavation to bedrock. Elsewhere,reasonable estimates of depth were made from numerous surveyed cross-profiles of gully sidewalls and channel fills.

Dating debris flowsThe elapsed time since the last debris flow event was most reliably determined by dendrochronology, with the mostprecise dates obtained from scarred trees and the time of onset of reaction wood related to debris-flow deposition.Approximately 850 wood samples were examined, including more than 100 complete discs cut from trees damagedor toppled by debris-flow impacts. Cores and discs were mounted, sanded with increasingly finer sand paper andexamined by a hand lens or microscope. A detailed description of this work is given by Jakob (1996). These data weresupplemented by air photograph records of recent debris flows and eyewitness reports, principally from forestryworkers. Approximately 400 debris flow events were documented over the period AD 1770–2000.

Debris-flow recharge ratesBecause of differences in basin size, normalized debris recharge rates were computed by dividing total debris storageover the elapsed period by the length of active channel surveyed. An average, normalized rate of debris recharge(m3 m−1 a−1) was then computed. For channels of a given terrain type, this measure provides a basis for calculatingexpected magnitudes of debris flows for various return periods. Thus, at elapsed time te following a previous debrisflow, magnitude M is expected assuming that all stored debris is scoured away by the next flow. Channels in a givenarea will be at varying stages of debris recharge at a given channel survey time, because not all channels experiencedebris flows at the same time, and thus have differing elapsed times at the time of survey. This variation allows a timeversus recharge curve to be constructed (Figure 3). The data for the graphs from southwestern British Columbia aresummarized in Table I, and the data from the Queen Charlotte Islands are listed in Table II. In years when severalchannels experienced debris flows more or less simultaneously, error bars for mean recharge rate can be constructed ata given elapsed time. Errors are least well constrained for events in the distant past because of the problems of eventoverprinting discussed previously. Thus the magnitudes of large, low-frequency events are the most poorly constrained.

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Figure 3. Area-normalized channel recharge rates for debris-flow basins in the southern Coast Mountains and the QueenCharlotte Islands of British Columbia.

Table I. Summary data for Southwestern British Columbia

Surveyed Total material Specific material Time since last Specificchannel length storage storage debris flow recharge rate

Creek name (m) (m3) (m3 m−−−−−1) (years) (m3 m−−−−−1 a−−−−−1)

Turbid 2430 210 000 86 9 9·6Boundary 1700 330 000 194 2 97·1Capricorn 1300 425 000 327 5 65·4Fools Gold 1200 52 000 43 12 3·6Clearwater 1400 44 000 31 5 6·3Deepa 1200 59 000 49 2 24·6Fergusson 1400 55 000 39 3 13·1Gunbarrel I 920 36 000 39 3 13·0Gunbarrel II 1300 100 000 77 6 12·8Gunbarrel III 1250 150 000 120 5 24·0Hotsprings 3300 240 000 73 5 14·5Kaboose 1500 15 000 10 4 2·5McLeod 2100 73 000 35 4 8·7Mt. Currie 1300 190 000 146 5 29·2No Good 1800 280 000 156 6 25·9Pothole 1000 66 000 66 11 6·0Snake 1850 60 000 32 7 4·6Wildcat 1300 30 000 23 11 4·0Terminal 1850 77 000 42 15 2·8Holmden 1500 25 000 17 4 4·2Percy 800 30 000 38 100 0·4

Results

The normalized recharge rate curves in Figure 3 show that there is a significant difference between the two studyareas, due possibly to both geological differences (granitic versus volcanic and sedimentary), and catchment size –

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Table II. Summary data for Rennell Sound

Surveyed Total material Specific material Time since last Specific rechargeCreek name* channel length (m) storage (m3) storage (m3 m−−−−−1) debris flow (years) rate (m3 m−−−−−1 a−−−−−1)

R4 (og) 350 230 0·66 6 0·110S1 (og) 120 50 0·42 8 0·052R5 (og) 295 120 0·41 10 0·041G1 (og) 220 390 1·77 14 0·127G2 (og) 340 575 1·69 14 0·121G3 (og) 230 340 1·48 14 0·106G4 (og) 235 385 1·64 14 0·117G9 (og) 410 230 0·56 14 0·040G10 (og) 180 308 1·71 14 0·122G11 (og) 280 465 1·66 14 0·119G12 (og) 50 50 1·00 14 0·071G6 (og) 510 745 1·46 57 0·026G5 (og) 245 435 1·78 75 0·024B1 (cc) 895 365 0·41 1 0·408R12 (cc) 285 110 0·39 1 0·386R7 (cc) 340 70 0·21 2 0·103R2 (cc) 160 70 0·44 3 0·146B4 (cc) 275 95 0·35 6 0·058R8 (cc) 320 70 0·22 7 0·031R10 (cc) 310 380 1·23 7 0·175B2 (cc) 230 310 1·35 8 0·168R13 (cc) 245 95 0·39 8 0·048S1cc (cc) 180 170 0·94 8 0·118SB1 (cc) 135 35 0·26 8 0·032SB2 (cc) 190 15 0·08 8 0·010B3 (cc) 780 345 0·44 10 0·044R3 (cc) 255 155 0·61 11 0·055R9 (cc) 330 175 0·53 14 0·038R14 (cc) 150 55 0·37 14 0·026

* og, Old-growth forest; cc, clear-cut areas.

Coast Mountains basins are in general larger than those in the Queen Charlotte sample. Larger catchments and deeperand wider creeks will generally produce higher amounts of debris per unit length of the stream channel because of thelarger contributing areas of channel sidewalls. Of the 35 creeks from the Coast Mountains, 17 had to be excluded fromthe analysis because part of the creek traversed colluvial blanket sections, which had likely added significantly tomeasured debris-flow volumes. The remaining 18 data points show significant scatter, and reflect the highly variablegeological, geomorphological and climatic conditions encountered in this area. Figure 4 shows that predicted rechargerates in both study areas may be up to five times higher than observed rates. Using the relationship shown in Figure 3for debris-flow hazard assessments could lead to overdesign of debris-flow mitigation measures. This demonstratesthat recharge curves are likely only achievable where climatic, geological and geomorphological conditions arecomparable, which is the case in the Queen Charlotte Islands. Here, the knowledge of the time elapsed since the lastdebris flow, te, can then be used to determine the normalized recharge rate, Rt, for undisturbed gullies via therelationship:

Rt = 0·23te−0·58 (2)

The Queen Charlotte data set also shows significant scatter, but the results are more coherent when divided intounlogged and logged subgroups. The unlogged group yields:

Rt = 0·20te−0·49 (3)

and for logged gullies:

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Figure 4. Observed area-normalized channel recharge rates versus predicted channel recharge rates. Line of equal values isincluded.

Rt = 0·30te−0·77 (4)

Figure 3 and Equations 3 and 4 suggest that, for the same elapsed time, normalized recharge rates are perhapshigher in unlogged basins, which retain their old-growth forest cover. This anomaly may be explained by the fact thatmany logged gullies lack an adequate input of large organic debris (LOD), after the first post-logging debris flows,since LOD is usually required for the accumulation of sediment wedges in steep, confined channels (Bovis et al.,1998). The differentiation between old growth and clearcut gullies according to Figure 3 requires further confirmation,particularly for clearcut gullies with longer elapsed times since last debris flow, for which there are currently no data.The difference in recharge rates between logged and unlogged terrain was also confirmed in a study carried out in theCoquitlam Watershed 50 km north of Vancouver (Figure 1; Pellerin, 2001). This study showed that in the five yearsfollowing debris-flow scour, average sediment yields from logged gully sidewalls were more than double those fromunlogged sidewalls. However, over a 15–20 year period following the debris flow, sediment yields in both environ-ments declined, but at a slightly higher rate on logged sidewalls. This is associated with more rapid growth of fastcolonizer species which cause sharp reductions in bare soil area over time (Pellerin, 2001).

Figure 5 shows the development of gully recharge over time in creeks in logged and unlogged terrain. Figure 6translates Figure 5 into a conceptual model of debris-flow volume changes for both land-use types. According to thesefigures, creeks in recently logged terrain will initially produce high-frequency, low-magnitude debris flows, whilecreeks through unlogged, old-growth terrain will likely produce lower-frequency, higher-magnitude flows. This impliesthat creeks in clearcut areas initially deliver finer sediment to higher order stream channels more frequently thancreeks through unlogged areas, until channel sidewalls have been stabilized by regrowth and slope angle adjustment.

Discussion

The results presented above suggest that under similar geological, climatic, and geomorphological conditions, debrisrecharge rate may be estimated if the elapsed time since the last debris flow is known. This knowledge is valuable formany hazard studies in which the total volume of the debris flow is of paramount importance in delineating hazardzones and in designing debris-flow mitigation measures. In many cases, assessment of the consequences of debris-flow occurrence is included to arrive at a risk assessment that is used for land-use decisions and is integrated intocost–benefit analyses. Debris-flow risk analysis often requires the calculation of encounter probabilities, defined by theprobability of persons, facilities or vehicles being impacted at least once during a finite time period with events of

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Figure 5. Conceptual sketch of gully recharge in logged and unlogged terrain after debris flow occurrence. At time T-1, soon aftera debris flow during which the channel is just beginning to fill with materials from the side slopes. Due to logging-related grounddisturbance the recharge rate in a logged gully may exceed that of the old-growth gully. At time T-2, the gully in old-growth foresthas recharged with debris at a higher rate than its logged counterpart, which is due to the lack of large organic debris that formsstable log jams and sizable sediment wedges. This trend is continued over longer (decadal) time periods (T-3) at which time adebris flow occurs and completely scours both creek channels (T-4).

specified return period at a given location. Encounter probabilities can be calculated interchangably by using thebinominal or Poisson models (McClung, 1999). The assumption in calculating encounter probabilities is that debrisflows are rare and independent events. Given the findings of this study, the assumption of independence is fulfilledonly in supply-unlimited basins. In supply-limited basins, both the timing and magnitude of debris flows depend onelapsed time, which in turn determines recurrence interval for a given magnitude of event. This implies that encounterprobabilities calculated as described by McClung (1999) will lead to overestimates, especially where a debris flow hasrecently occurred in a supply-limited basin.

Conclusions

Accurate debris-flow volume estimates are the most important prerequisite in most debris-flow hazard assessments.Debris-flow volumes are often not reliable from the record of previous deposits because of subsequent erosion or thecomplex superposing of events on debris fans. This paper has demonstrated that, at least for some debris-flow

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Figure 6. Conceptual model of debris-flow volume changes over time for logged and unlogged terrain. This model relates to thefour time periods shown in Figure 5. Gullies in logged terrain are likely to recharge quicker in the first few years after loggingdisturbance than gullies in old-growth forest, but this effect diminishes and finally reverses over time due to stable log-jamformation in old-growth forest. The likelihood of low-frequency (high return period) debris flows increases linearly with anincrease in the probability of a high-intensity rainstorm triggering sufficiently recharged gullies or creeks.

channels, knowledge of the time elapsed since the last debris flow can yield estimates of average rates of channelrecharge, provided that a normalized relation between debris recharge and elapsed time is available. Traditionaldebris-flow hazard assessments estimate the amount of debris stored in the channel at the time of the investigation andadd those to the volume of discrete point sources in the watershed (Hungr et al., 1984). Channel recharge curves canimprove estimates of total debris-flow volume by considering the volume–time dependency. For the calculation of adesign debris-flow magnitude, associated with a fixed return period, it is necessary to estimate the maximum time thatmay elapse before debris-flow recurrence. This will allow an estimation of the amount of debris stored in a debris-flowchannel and hence will yield a corresponding magnitude. It is cautioned, however, that the use of encounter probabil-ities may lead to false results since observed encounter probabilities shortly after a debris-flow occurrence will bemuch lower than predicted for truly independent events.

Acknowledgements

Funding for the field work was provided by grants to M.J. Bovis from the Natural Sciences and Engineering Councilof Canada. Living expenses for M. Jakob were covered by a scholarship from the Gottlieb-Daimler und Karl-BenzStiftung, Germany. Field assistance for Marian Oden and Matthias Jakob was provided by Drew Brayshaw, ElizabethBronson, Noel Castree, Scott Davidson, Ernst Jakob, Katherine McLeod, Steve Rice, Deepa Spaeth, Lars Uunila, andScott Weston. Steve Chatwin and Dan Hogan aided during parts of the Queen Charlotte work. Two anonymousreviewers improved an earlier draft of this paper.

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