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# Debris-Flow Risk Assessment

## Summary and Keywords

Debris flows are one of the most destructive landslide processes worldwide, given their ubiquity in mountainous areas occupied by human settlement or industrial facilities around the world. Given the episodic nature of debris flows, these hazards are often un- or under-recognized.

Three fundamental components of debris-flow risk assessments include frequency-magnitude analysis, numerical scenario modeling, and consequence analysis to estimate the severity of damage and loss. Recent advances in frequency-magnitude analysis take advantage of developments in methods to estimate the age of deposits and size of past and potential future events. Notwithstanding, creating reliable frequency-magnitude relationships is often challenged by practical limitations to investigate and statistically analyze past debris-flow events that are often discontinuous, as well as temporally and spatially censored. To estimate flow runout and destructive potential, several models are used worldwide. Simple empirical models have been developed based on statistical geometric correlations, and two-dimensional and three-dimensional numerical models are commercially available. Quantitative risk assessment (QRA) methods for assessing public safety were developed for the nuclear industry in the 1970s and have been applied to landslide risk in Hong Kong starting in 1998. Debris-flow risk analyses estimate the likelihood of a variety of consequences. Quantitative approaches involve prediction of the annual probability of loss of life to individuals or groups and estimates of annualized economic losses. Recent progress in quantitative debris-flow risk analyses include improved methods to characterize elements at risk within a GIS environment and estimates of their vulnerability to impact. Improvements have also been made in how these risks are communicated to decision makers and stakeholders, including graphic display on conventional and interactive online maps. Substantial limitations remain, including the practical impossibility of estimating every direct and indirect risk associated with debris flows and a shortage of data to estimate vulnerabilities to debris-flow impact. Despite these limitations, quantitative debris-flow risk assessment is becoming a preferred framework for decision makers in some jurisdictions, to compare risks to defined risk tolerance thresholds, support decisions to reduce risk, and quantify the residual risk remaining following implementation of risk reduction measures.

# Introduction

Few months pass in which there are not newspaper reports from somewhere in the world of debris flows causing multiple fatalities and resulting in extreme economic losses where creeks interface with infrastructure along their paths or on alluvial fans.

While hydrologists are used to predicting the range of flows likely to occur in a stream channel from magnitude-frequency analyses on historical flow records, geomorphologists tasked to do the same for debris flows lack the luxury of a continuous record of events that spans the relatively large return period range of interest. In the absence of flow records for a particular channel, a number of techniques need to be combined to decipher the frequency and magnitude of debris flows. While such methods have evolved over time, much experience and judgment is still required to construct a reasonable frequency-magnitude curve.

Once frequency-magnitude relationships are established, runout analysis forms the basis for estimating debris-flow intensities on fans. Runout analysis tools range from empirical correlations between debris-flow volume and area inundated to advanced three-dimensional models that account for material entrainment and run-up along channel curves and obstacles.

Finally, once the runout intensities have been estimated and mapped for different debris-flow scenarios, risk can be estimated. In most cases this relates to loss of life and economic loss potential. Both require significant efforts in gathering and processing data and integrating such data for all hazard scenarios considered.

Debris flows and associated damages are increasingly prevalent as human, industrial, and recreational activity advances into mountain regions. Debris flows also pose a risk to pipelines, highways, rail lines, and telecommunication lines paralleling valley sides and crossing steep creeks and alluvial fans. We hope that this contribution furthers understanding and recognition of debris-flow processes and the evolving methods that are currently used to assess the associated risks.

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Figure 1. Trans-Canada Highway in Canmore, Alberta, overwhelmed by a June 2013 debris flood at Cougar Creek.

Photo: Town of Canmore.

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Figure 2. Debris flow triggered by an agricultural dam breach at Testalinden Creek, British Columbia.

## Debris-Flow Phenomenon

Debris flows are defined as very rapid to extremely rapid surging flows of saturated debris in a steep channel (Hungr, Picarelli, & Leroueil, 2014). Debris flows typically occur in creeks with slopes between 15 and 35°, with watershed areas between 0.1 and 10 km2, Melton ratios of greater than 0.6, and a straight line watershed length of < 2.6 km (i.e., Jakob, 2005, Wilford, Sakals, Innes, Sidle, & Bergerud, 2004). Some regional variation exists: Holm et al. (2016) examined 710 debris-flow and debris-flood creeks in the Canadian Rockies and found debris-flows typically occurring in basins with Melton rations greater than 0.5, a maximum channel length upstream of the fan apex of less than 0.3 km, and with an average fan gradient exceeding 5°. The most significant contributor to debris-flow occurrence is a supply of readily erodible material, often created by rock falls and landslides. If a steep creek system (as defined by Church, 2013) with gradients exceeding approximately 25% has a supply of erodible material (Bovis & Jakob, 1999), a debris flow may occur once a hydroclimatic threshold (e.g., specific antecedent rainfall) has been reached. If a system has a limited supply of erodible material, the creek bed must gradually recharge with debris until there is sufficient material for a debris flow to re-occur (Jakob, 1996). The process of gradual recharge helps explain why debris-flow occurrence can be intermittent, and is not always correlated with significant rainfall events (Jakob et al., 2005).

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Figure 3. Spectrum from floods to debris avalanches structured by sediment concentration, slope and movement velocity.

Artwork: BGC Engineering.

Debris flows are characterized by three general formative stages: initiation, transportation, and deposition. However, transport reaches can also be subject to some deposition, while deposition zones can, under some circumstances, be subject to additional debris entrainment. Entrainment will occur especially when the channel bed materials are at least partially saturated and when the water content of the debris flow is high. Channel banks can be eroded and then topple into the debris flow, thus adding more material and widening the channel. With all other conditions being equal, larger and thus rarer debris flows are likely to cause more entrainment than smaller, more frequent, debris flows.

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Figure 4. Typical low gradient and steep fans feeding into a broader floodplain. On the left, a small watershed prone to debris flows has created a steep fan that may also be subject to rock fall processes. Development and infrastructure are shown to illustrate their interaction with hydrogeomorphic events.

Artwork: Derrill Shuttleworth.

Once initiated, debris flows travel down a confined channel, over-running stream flow, further eroding saturated channel bank sediments, both of which sustains mobility and momentum. Debris flows often scour to bedrock in the transportation zone. Scoured materials are entrained in the debris flow, increasing its volume and flow velocity where sufficient water is available. Flow velocity is dependent on channel gradient, debris-flow volume, water content, and the grain size and composition of the transported materials, but it will not increase indefinitely due to flow resistance inherent in its flow mechanics. Debris flows have flow velocities exceeding several meters per second, and maximum velocity is reached in steep and confined sections of the transport zone.

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Figure 5. Schematic diagram of a drainage basin that shows the principal zones of distinctive sediment behavior. The alluvial fan is thought of as the long-term storage landform with a time scale of thousands to tens of thousands of years.

Debris deposition occurs either when the channel becomes unconfined or when the channel gradient becomes too shallow to sustain continued flow. Debris flows typically deposit on a fan, which is often formed over thousands of years from multiple debris-flow deposits, sometimes overprinted or interfingered by fluvial or other colluvial processes. The extent of debris-flow runout on a fan primarily depends on the debris-flow magnitude and velocity, with fine-grained clay-rich debris flows without frictional bouldery front travelling further than coarse-grained debris flows with such fronts. For bouldery debris flows, Hungr et al. (1984) reported for southern British Columbia that most debris will begin to deposit in confined channels on slopes less than about 8 to 12˚ and in unconfined channels on slopes of 10 to 14˚. Similar slope ranges have been observed elsewhere. In contrast, volcanic debris flows or those originating in weak sedimentary rock can run out on much lower slope angles (i.e., Pierson, 2005).

Avulsions are possible in poorly confined channel sections, particularly on the outside of channel bends where debris flows tend to super-elevate. Sudden loss of confinement and decrease in channel slope cause debris flows to decelerate, drain their inter-granular water, and increase shearing resistance, which slow the advancing bouldery flow front and block the channel. The more fluid afterflow (hyperconcentrated flow) is then often deflected by the slowing front, leading to secondary avulsions and the creation of distributary channels on the fan. Since debris flows often display surging behavior, in which bouldery fronts alternate with hyperconcentrated afterflows, the cycle of coarse bouldery lobe and levee formation and afterflow deflection can be repeated several times during a single debris-flow event. These flow aberrations and varying rheological characteristics pose a particular challenge to numerical modelers seeking to simulate debris flow behavior using an equivalent fluid approach (Iverson, 2014).

While most debris flows deposit material on fans, it is also possible for debris flows to scour material from the fan and increase in size. A debris flow in 1995, on Hope Creek, British Columbia (Canada), obtained 90% of its material through entrainment of fan sediments (Jakob, Hungr, & Thomson, 1997). This may occur during times with elevated phreatic (ground water level) surfaces and preferentially in pre-existing (paleo) channels. Channel entrainment has further been studied by Hussin et al. (2012). Those workers allow for erosion of one or more layers when a user-specified critical shear stress is exceeded. In a recent paper by Frank, McArdell, Huggel, and Vieli (2015), the relationship between maximum shear stress and measured erosion was used to determine the maximum potential erosion depth of a debris-flow prone channel in Switzerland (Illgraben) without the necessity of specifying the depth of erodible material. Despite these recent advances, debris-flow science has not advanced to a point where the likelihood, magnitude or location of fan scour can be predicted with confidence.

Due to their high flow velocities, peak discharges at least one order of magnitude larger than those of comparable return-period floods, and the large caliber of transported sediment and wood, debris flows are highly destructive along their channels and on fans. Channel banks can be severely eroded during debris flows, although lateral erosion is often associated with the trailing hyperconcentrated flow phase that is characterized by lower volumetric sediment concentrations. The most severe damage may result from direct impact of large clasts or coarse woody debris against structures that are not designed for the impact forces. Even where supporting walls on buildings may be able to withstand the loads associated with debris flows, windows and doors can be crushed and debris may enter the building, leading to extensive damage to the interior of the structure (Jakob, Stein, & Ulmi, 2011). Debris deposition can also block or divert existing creek channels, causing localized flooding, scour, erosion and debris re-deposition that is difficult to predict, preventing accurate delineation of potential impact zones.

## Evolution of Debris-Flow Risk Assessments

Debris flow risk assessments, by definition, need to be based on a hazard assessment. The latter have a long history, particularly in Austria and Japan. For example, in Austria, a commission to investigate the reasons for disasters was inaugurated in 1882, which also led to the formation of the WLV (federal torrent and avalanche control) in the same year. The first physical models in Austria were developed in 1954, and hazard zonation began in 1965. Systematic documentation of disasters including debris flows was instituted in 1987 (H. Hübl, personal communication, 2015).

In Japan, scientific investigations of debris flows began in the 1950s and included qualitative discussions of the definition of debris flow. According to Takahashi (2009), full investigations were not undertaken until the 1970s, by which time mitigation measures had lowered the risk of debris flows on larger rivers. Japan also spearheaded some of the earliest direct debris flow measurements. In the early 1970s, the Kamikamihori and Ashiaraidani ravines on the mountainside of Yakedake volcano were instrumented, with the first debris flow being documented scientifically in 1976, by Okuda and colleagues of the Disaster Prevention Research Institute (DPRI, Kyoto University). Takahashi (2009) provides a good summary of Japanese debris flow research. Similar to Austria, there is a long history of mitigation works, which, according to Mizuyama (2008), began some 200 years ago. Erosion and sediment control works in Japan are administered and conducted under the authority of the erosion department of the Ministry of Land, Infrastructure and Transport and the Forestry Agency of The Ministry of Agriculture, Forestry and Fisheries. The former is responsible for erosion and sediment control mainly related to rivers, while the latter agency focuses on erosion control to conserve forest lands (Mizuyama, 2008).

The advances of Austria and Japan towards hazard recognition and mitigation are clearly related to the fact that those countries are mountainous and urban development has interfaced with mountainous terrain for a long time. Assessments in previous time were mostly empirical and based on observations of debris flow events at a given site or nearby sites. Development shunned particularly hazardous areas but with increasing development pressure, and the perception that floodplains are more dangerous than fans, development on alluvial fans became the norm. Episodic destructive events then led to the inauguration of state-run organizations to protect its citizens from debris-flow impact and destruction. SABO works in Japan and the Wildbachverbauung (Torrent Control) in Austria are examples. Over time, debris flow assessments became more sophisticated, and hazard maps were created to aid planning. Interestingly, some nations have, and are continuing to rely on fixed return periods to plan for mitigation and zone fans for construction. For example, Austria calls for examination of return periods of up to 150 years (H. Hübel, personal communication, 2015), while in Switzerland return periods of up to 300 years are considered, including the assessment of residual risk associated with return periods exceeding 300 years. In Switzerland, hazard maps are then based on a combination of debris-flow intensity and the occurrence probability, and thus have a measure of risk implicit in their assessment. Rudolf-Miklau, Bak, Skolaut, and Schmid (2011) provide a comprehensive overview of the hazard and risk assessment guidelines in various European nations.

At the time of this publication, quantitative assessments of safety and economic risk have been completed in Canada for over 30 creeks prone to debris-flow or debris-floods. Compared to qualitative or semi-quantitative methods, a quantitative approach provides a more powerful way to assess a wide range of hazard scenarios and elements at risk, describe uncertainties, and optimize the design of risk reduction measures. Moreover, it allows for more detailed quantification of residual risk than where a fixed return period is chosen for mitigation design.

# Frequency-Magnitude Analysis

Frequency-magnitude (F-M) relations relate the volumes or peak discharges of landslides to specific return periods (or annual frequencies) of their occurrence. This relation forms the core of any hazard assessment because it combines the findings from frequency and magnitude analyses in a logical format suitable for numerical analysis.

Any frequency-magnitude calculation that spans time scales of centuries and millennia necessarily includes significant judgment and assumptions, both of which are subject to uncertainty. Multiple approaches are available to characterize hazards and estimate their magnitude and frequency of occurrence. Each approach provides partial insight that, taken together, yields the best possible estimate with the data available.

This section uses the terms frequency, hazard probability, and return period interchangeably, depending on the context. Frequency is numerically equivalent to hazard probability and is defined as the annual probability of occurrence of a hazard scenario. Return period is the inverse of annual frequency and is defined as the average recurrence interval (in years) of a hazard scenario. For example, an annual frequency of 0.01 corresponds to a 100-year return period.

## Principles

There are no commonly applicable rules to define the range of hazard event frequencies or return periods that should be considered in a debris-flow risk assessment. Regulatory guidance and/or legislation worldwide mandate a return period range from several tens of years up to 10,000 years. As noted above, in Austria and Switzerland, return periods from 150 years to 300 years are considered, with Switzerland allowing for residual risk for return periods exceeding 300 years (H. Hübel, personal communication, 2015). The other bookend is British Columbia, Canada, where the current guidance to Ministry of Transportation approving officers is that a 10,000-year return period be considered for all life threatening landslide processes (APEGBC, 2010).

The two order of magnitude ranges described above give rise to a critical consideration: If only a limited range of return periods is considered in a risk assessment, the residual risk is implicitly accepted. For example, if a risk assessment entails consideration of 10–30 year, 30–100 year, and 100–300 year return periods only, the risks of >300 year return period events do not factor into the risk assessment. In supply-limited debris flow watersheds, this may not be a problem because the volume of debris flows may asymptotically reach some maximum limited by the availability of sediment. In contrast, watersheds subject to rare but large and destructive debris flow triggers, such as outburst floods or large rock slope failures, can dominate a risk profile due to the high level of consequences. These processes can introduce a bimodal distribution, which when neglecting such rare, but high consequence events, can result in significant underestimation of risk.

Once events have been documented, and their age and volume estimated, return periods need to be assigned to individual events that allow extrapolation and interpolation into annual probabilities beyond those extracted from the physical record. Such record extension is necessary to develop scenarios across the return period range under consideration. These scenarios then form the basis for debris-flow modeling and risk analysis.

In this context, judgement is required to assign magnitudes for very long return periods (thousands of years) in jurisdictions where inclusion of such long return periods is mandated, and the degree of error increases with the length of the return period.

## Frequency Analysis

Frequency analysis assesses how often hydrogeomorphic events such as debris flows occur on average. Frequency and magnitude of debris flows are inversely related, where magnitude refers to both the volume and the peak discharge.1 The higher the frequency, the lower the debris-flow magnitude and vice versa. In short, the larger an event, the rarer it will be. A frequency analysis alone does not inform on the relationship between magnitudes and frequencies. This relationship is the subject of the section Magnitude Analysis.

The frequency principle is complicated by several factors:

1. 1. A continuum exists between flooding and debris flooding and sometimes even debris flows. Exact differentiation of these processes can only be achieved through direct sampling of the sediment-water slurry and subsequent measurement of the water-sediment ratio. Furthermore, it is often difficult to detect when bedload transport of individual particles ends, and mass mobilization of the channel bed begins.

2. 2. Just like debris floods,2 clear water floods in steep mountain creeks transport large amounts of debris as bedload, which is being differentially deposited. Characteristic flood deposits with normal grading (finer particles on top) may be observed along the fan fringes but are rare on alluvial fans in mountainous environments. With respect to frequency analysis, this implies that mixed (debris flood/clear water flood) populations can be expected in the stratigraphic column and that some judgment needs to be applied to assign the observed deposits to either process.

3. 3. Frequency analysis assumes that the occurrence of debris floods is stationary over time, and that there is no upward or downward trend in the temporal occurrence of debris flows. While one can still average return periods over time series in the past, an observed trend would not allow one to extrapolate the long-term average into the future as such an average may over or underestimate future debris-flood frequencies. This is especially important in light of climate change, which increasingly challenges the stationarity assumption (Milly et al., 2008). Thus, deciphering frequencies of the past may no longer be sufficient on its own to predict frequencies of the future.

4. 4. Frequency analysis assumes data independence. Data independence implies that one climatic event leading to a debris flood does not influence the occurrence of the next one.

Numerous techniques have developed and been refined over time to reconstruct the frequency of debris flows and are listed in the following sections.

### Historical Accounts

Historical accounts are defined as debris flow records outside those collected as part of a more formal event-monitoring program. Such accounts can be very valuable, particularly in regions where hazardous events have been documented meticulously by journalists, naturalists, clerics, or sometimes even town doctors following a disaster. Many major newspapers facilitate online keyword searches, and most of their archives are now digital. This has been very useful for frequency estimates for debris flows, though detailed information on the flow thickness, velocity, or inundation area is rare. Accounts for memory alone have shown to be less valuable, as people tend to quickly forget unless events were cataclysmic and loved-ones perished. After more than 10 years, collective memory fades quickly (H. Hübl, personal communication, 2015).

### Air Photograph Interpretation

Stereo air photographs exist in many places of the world at least since the Second World War, and in some places reach back to the late 1920s. The amount of overlap is not consistent, nor is the scale at which they are taken, ranging typically between 1:10,000 and 1:60,000, with odd scales. Air photos are widely available in most Western nations and can nowadays be ordered digitally at very high resolution. Ortho-rectified air photos are rarer and typically associated with targeted flight missions for special projects.

Air photos can be examined for evidence of debris flows. Debris flows on mountain creeks typically strip the affected area of vegetation or obliterate it. If such events are large enough, they leave a cover of debris-flow deposits that show up as light grey or white on the air photographs. The air photograph chrono-sequence can also be used to map changes in channel flow direction and avulsions, and to examine the channel systems upstream of the fan apex as well as the watershed.

The air photos can be used in conjunction with the historical accounts to estimate a frequency of debris floods for the duration of the air photo record. Photos can be ortho-rectified for later measurement of debris area.

### Dendrochronology

Dendrochronology is an absolute dating method in which annually distinct tree rings are used to determine the age of a tree. Dendrogeomorphology, a sub discipline of dendrochronology, focuses on geomorphological processes that influence tree growth. It is used to accurately date geomorphic events such as debris flows and debris floods.

Depending on the ages of trees along the mainstem channel of a creek, dendrogeomorphology can extend the frequency record of debris floods well past the air photograph record, and it may close the time gap between air photograph interpretation (several decades) and radiocarbon dating (century to millennia). Unlike the other two methods, dendrogeomorphology can also be precise to the nearest year in dating growth disturbances, and in some cases, even the seasonal timing of growth disturbance can be deciphered (Stoffel & Bollschweiler, 2008).

In contrast to historical accounts, air photographs, and dendrochronology, radiocarbon dating potentially extends the record of debris-flood frequency to include the entire history of fan development, depending on the availability of datable material and the depth of test trenches with respect to the total fan thickness.

Radiocarbon dating involves measuring the amount of the radioisotope 14C preserved in fossil organic materials and using the rate of radioactive decay to calculate the age of a sample. This method requires the deposition and preservation of organic materials within the sedimentary stratigraphy of the fan. The age range of this method is from approximately 45,000 years to several decades. As such, the method is applicable to the time scale of post-glacial fan formation in the Rocky Mountains and Cordillera.

## Magnitude Analysis

Magnitude analysis involves remote-sensed and field interpretations of landslide source zones, estimation of the potential range of debris-flow volumes and peak discharges that could be generated by entrainment of debris within the channel, and estimation of the volume of deposits identified on the fan.

Determining debris-flow magnitudes is fraught with difficulty because older deposits can be eroded or reworked and are therefore often difficult to distinguish unambiguously from one another. Given the spatially limited extent of test trenching, it is also questionable if the full extent of individual events has been documented, or if the originally deposited material has been preserved. Moreover, it is problematic to differentiate between the amount of debris that is introduced to the fan from upstream past the fan apex, and debris that is recruited from bank erosion or channel bed scour from the fan reaches.

Trenching, radiocarbon dating of organic materials and extrapolation of layers of known age from one trench to another is still the most reliable method to decipher the volume of past debris flows (e.g., Chiverrell & Jakob, 2011). Additional methods that, when used in combination, can increase the accuracy of magnitude estimation include:

• Volume estimate for specific debris flows through the comparison of pre- and post-event LiDAR, though this only applies to few cases where pre-event LiDAR exists.

• Direct surveys of deposit volumes on the ground.

• Measurements of debris deposition areas on historical air photographs.

• Using dendrochronology to estimate debris flow magnitudes (e.g., Stoffel & Bollschweiler, 2008).

• Volume estimations from stratigraphic analysis and radiocarbon dating.

Significant advances have also been made in the use of traditional extreme value statistics (summarized in Jakob, 2012) and Bayesian statistics (Nolde & Joe, 2013).

## Frequency-Magnitude Relationship

There are no commonly applicable standards worldwide to construct debris-flow frequency-magnitude relationships. Once events have been documented and their age and volume estimated, return periods need to be assigned to individual events that allow extrapolation and interpolation into annual probabilities beyond those extracted from the physical record. Such record extension is necessary to develop quasi-continuous event scenarios that then form the basis of numerical runout modeling and finally, the consequence analysis that forms part of the risk assessment.

For one, extrapolation into high return periods that are a multiple of the initial record length increases the uncertainty significantly in absence of information on how climatic or geomorphic watershed conditions may have changed.

Source material depletion, vegetation changes, wildfire suppression, changes in the frequency and/or magnitude of hydroclimatic events and the occurrence of cataclysmic events such as large landslides in the watershed can all alter the stationary assumption at different temporal scales. Ergodicity, which describes a random process for which the time average of one sequence of events is the same as the population average, demands that the geophysical process can be viewed as an infinite number of equally likely stochastic events. This assumption may be challenged if an upward trend in multi-day rainfall is observed, one notice a temporal clustering of debris flow or debris flood initiating storms for meteorological reasons, or if there is progressive exhaustion of potentially mobile material in the drainage basin.

These considerations point towards the possible fallacies of applying traditional flood frequency assessments to debris-flow frequency analysis. A promising method that avoids some of the fallacies or traditional flood frequency analysis is cumulative frequency-magnitude analysis that is discussed below:

### Magnitude-Cumulative Frequency Analysis (MCF)

Seismology has been the precursor to the use of regional magnitude-cumulative frequency curves (MCF) (Gutenberg & Richter, 1954). An inventory of debris-flow volumes of known dates in a given time interval Ti is ranked from largest to smallest. The incremental debris-flow frequency of rank i is determined as 1/Ti, and the MCF then states the cumulative incremental frequencies as:

$Display mathematics$
[2-1]

where fi is the incremental frequency of an event of rank i and Fi is the annual debris-flow frequency of an event of greater than volume Vi. The MCF curve is then produced by plotting Fi against Vi.

The use of MCF assumes that all events are known, and volumes can be combined in reasonable volume classes, or that the dataset is stratified into classes where confidence exists that all such events have been included. Furthermore, the selection of different plotting methods (cumulative vs. non-cumulative, linear and logarithmic binning, different bin sizes, and choice of trendlines for extrapolations) can bias the results (Brardinoni & Church, 2004). A major limitation of the MCF technique is its demand on data, as all events are assumed to be known. The MCF technique is very sensitive to the number of events, as adding events will invariably decrease the individual return periods for events smaller than those newly added.

## Uncertainties

While based on the best available data, estimates of debris-flow frequency and magnitude span time scales of millennia and require judgment and assumptions that are subject to uncertainty.

Typical uncertainties and limitations of a debris flow risk assessment include:

• Older events are covered by new ones, thus obliterating evidence.

• For very old events, dateable organic material is often not found in test trenches.

• Trees are not always scarred or otherwise affected by debris flows, leaving insufficient evidence for dendrochronologic dating.

• Tree scars can be misleading, as scars are also formed by trees falling on trees, animal scratching, frost scars, fire scars, and scars from trail blazing.

• Debris-flow layers discovered in only one or two test pits cannot be correlated across the entire fan to yield reliable volumes.

• Test trench soil stratigraphic information may be ambiguous.

• Airphotos may not show small debris flows that flow through forested areas without creating visible swaths of damaged vegetation and deposits.

• Access restrictions (e.g., housing development) or budget limitations do not allow test trenching equally distributed over the fan.

Typical assumptions of a debris flow risk assessment include:

• The probability of two or more simultaneous events is negligible in the same main channel (see McClung, 1999, who describes a similar assumption for snow avalanche assessments).

• The premise of stationarity over time (no long-term trend in the frequency of debris flows), and that they are independent from initial conditions.

Both of the above assumptions can be questioned. For example, extrapolation of high return periods from the initial record length is done with only limited information on how climatic or geomorphic watershed conditions may have changed during this time. Changes in vegetation cover, wildfire suppression, changes in the frequency and/or magnitude of hydroclimatic events and the occurrence of cataclysmic events such as large landslides will influence levels of hazard and associated risk.

Despite these limitations, a combination of field and analytical techniques, as well as geomorphic reasoning, can reduce uncertainty and allow the derivation of a plausible debris-flow frequency-volume relationship. The key is to view frequency–volume estimates as credible proxies for true events rather than precise estimates. These estimates are then used to determine key consequences and risks that support risk reduction decision making.

## Hazard Scenarios

Once a frequency-magnitude relationship has been established, the next step is to select events representing the range of return periods under consideration for modeling and risk analysis. These are termed hazard scenarios.

For example, a frequency-magnitude relationship, for events ranging from 10 to 10,000 year return period, might be broken into the 10–100 year, 100–1,000 year, and 1,000–10,000 year hazard scenarios. The 10–100 year scenario includes all sub-scenarios in which the event is larger than the 10-year event but not larger than the 100-year event.

Given a scenario with the annual exceedance probability range Pmin to Pmax, the probability of events within this range corresponds to:

$Display mathematics$
[1a]

For example, for the 1:10–1:100 year range, this would correspond to:

$Display mathematics$
[1b]

Once hazard scenarios are established, the next step is to assign a representative magnitude for each hazard scenario as input to debris flow modeling. While the most conservative approach would be to choose the maximum estimated magnitude for each range, most commonly an event magnitude towards the mid-point of the range is chosen.

# Debris-Flow Modeling

A number of methods are available to estimate debris-flow inundation limits and intensity parameters, such as flow depths and velocities that are required for a debris-flow risk assessment. Empirical methods based on statistical correlations between commonly-reported geometric parameters, including flow volume and travel angle (e.g., Corominas, 1996) or flow volume and deposit area (e.g., Iverson, Schilling, & Vallance, 1998; Griswold, 2004), can be used to estimate inundation limits. Calibrated methods based on the volume balance of material entrained and deposited along the path can also be used (e.g., Fannin & Wise, 2001). Other statistical correlations have also been developed to estimate peak velocities and discharges (e.g., Rickenmann, 1999).

Numerical models that simulate debris flow motion are increasingly favored for risk assessment purposes because they can be used to estimate inundation limits as well as the spatial distribution of flow intensities within those limits. This section describes these types of models and their current main limitations.

## Current Modeling Approaches and Challenges

Most numerical debris-flow models are based on shallow flow theory, with modifications to account for the effects of entrainment, internal stresses, and spatial variations in rheology that are important characteristics of debris flows. An overview of the evolution of landslide runout models was provided by McDougall, Pirulli, Hungr, and Scavia (2008).

Two main modeling approaches have been proposed: first, using physical material properties that are measured in the field or laboratory (e.g., Iverson & George, 2014), and second, using calibrated parameters that are estimated through back-analysis of previous debris flow case studies (e.g., Hungr, 1995). Hybrids of these two main modeling approaches are also possible. The first modeling approach typically involves more input parameters and requires the use of material sampling and testing methods that are appropriate for the scale and velocity of real debris flows, which can be a significant challenge. The second approach, which is also known as the “equivalent fluid” approach, requires the compilation of an adequate number of case studies that are similar enough to the potential event in question. One criticism of this approach is that, with enough adjustable parameters, model flexibility can potentially be mistaken for model accuracy (Iverson, 2003). Calibration methods that can be applied in a probabilistic risk assessment framework are also still in their infancy (McDougall, McKinnon, & Hungr, 2012).

Debris-flow models can be initiated at the source of the potential triggering failure or at the fan apex using a hydrograph that simulates the debris-flow discharge (and associated sediment concentration or other spatially variable rheological parameters, if required in the model) as it passes that point. The former method requires the simulation of material entrainment along the path, such that the modeled debris flow reaches the fan with an appropriate total volume. Different approaches to simulating entrainment have been proposed, ranging from empirical methods that require the input of user-prescribed volume growth rates (e.g., McDougall & Hungr, 2005) to process-based methods that simulate entrainment as a function of basal shear stresses (e.g., Iverson, 2012). Models that are initiated at the fan apex do not necessarily require entrainment simulation capabilities, since entrainment usually occurs upstream of the fan apex, and can be more efficient if the elements at risk are all located on the fan or further downslope. As noted previously, rare debris-flow entrainment on fans is still poorly understood and will require further research.

As described further in the section Spatial Probability, a rigorous debris-flow risk assessment requires the simulation of multiple mobility scenarios for each hazard class to contour the spatial probability of impact within the runout zone. For example, high resistance parameters can be used to simulate events with relatively low mobility that deposit predominantly near the fan apex, while low resistance parameters can be used to simulate events with relatively high mobility that deposit predominantly near the distal fan margin. The latter would be associated with a relatively low runout exceedance probability. It is not always computationally practical to model a large number of mobility scenarios, so some approximations and interpretations are needed.

This practical limitation also applies to modeling multiple channel avulsion scenarios. Most advanced debris-flow models can simulate super-elevation and run-up around channel bends reasonably well, but avulsions may also occur if the channel becomes blocked by woody debris or coarse granular deposits. This behavior can be simulated by manually modifying the local sliding surface to force an avulsion in the model, and past observation of favorable avulsion points can guide their selection. However, even two or three avulsion scenarios can lead to very complicated risk event trees with nested conditional probabilities that can exceed budgetary limitations if the assignment is carried out commercially.

Debris-flow models are sensitive to the roughness of the topographic input, which must have a high enough resolution and accuracy to account for important topographic details, but not be so rough as to cause numerical instabilities through violation of the shallow flow assumptions. This is particularly important where micro-topography (for example, levees and paleochannels) can have an important effect on the outcome of the hazard delineation. The roughness of the surface can also inadvertently dominate the modeled flow resistance. A key to consistent model results is to strive for consistency in the resolution and roughness of the input topographic data between projects. It needs to be borne in mind that no model will ever be able to simulate exact flow behavior, as parts of debris flows are behaving randomly. The above considerations that are often based on expert judgment, however, allow a reasonable approximation of the process.

# Risk Analysis

In this section, we provide a framework for debris-flow risk analysis, describe the key steps, and discuss challenges and directions for future research.

Debris-flow risk assessment requires detailed knowledge of the hazard frequency (or probability), its magnitude, spatial and temporal probabilities of impact, and vulnerabilities of elements at risk. In most instances the estimation of those variables requires significant scientific effort; however the benefits of such systematic risk assessment mostly outweigh the costs associated with such studies. The primary benefits of quantitative risk assessments are that they allow a direct comparison of risks between different hazard locations, which permit a prioritization of sites with often rather disparate landslide hazards, and allows direct comparison between different risk reduction options.

Debris-flow risk analysis involves estimation of the likelihood that a debris flow will occur, impact “elements at risk” (e.g., persons, development, or other things of value), and cause particular types and severities of consequences. Each of these components is estimated separately and then combined analytically. The objective is to provide a systematic, repeatable analysis of key risks at an appropriate level of detail for the information available. The estimated risks can be compared to risk tolerance standards and then used for decision making and optimization of mitigation strategies.

Risk analysis requires development of “scenarios,” where hazard events could potentially result in specific losses. These are based on two components:

• Hazard intensity maps resulting from the hazard analysis.

• Identification of potential impacts (or chains of impacts) to elements at risk.

Because it is not possible to assess every possible type of consequence that could occur during an event, key scenarios are developed to represent the spectrum of possible outcomes. These can range from high frequency, small events causing minor damage to low frequency, large events causing severe damage. Combined with their likelihood of occurrence, these scenarios form the basis for risk assessment and decision making. The scenarios must balance the competing requirements of being comprehensive yet practical to assess.

Click to view larger

Figure 6. Damages to development can result from avulsions occurring due to channel blockage or aggradation, or from bank erosion. The former can be quantified as part of debris-flow modeling. However, bank erosion is difficult to quantify and may need to be qualitatively assessed.

Artwork: Derrill Shuttleworth.

## Qualitative vs. Quantitative Approaches

Risk estimation may be qualitative or quantitative and should seek an appropriate level of detail for the information available. Qualitative risk estimation uses descriptive terms for the frequency of floods and expected consequences. It is particularly useful for comparing relative risks at different sites, and is ideal for prioritization of sites for mitigation efforts. Quantitative risk estimation uses numerical estimates of each risk parameter to calculate a probability of some level of damage or loss.

A quantitative approach is not inherently more accurate than qualitative methods, and it may be impractical for consequences that are difficult to quantify, such as traffic disruption, environmental or cultural losses as well as human psychological trauma. Quantitative approaches generally require a more detailed hazard assessment and more information about the vulnerability of elements at risk.

However, quantitative risk estimation is advantageous for safety risk estimates because it permits comparison with other risks that individuals face from other hazards (e.g., lightning, plane crash, vehicle collision), and comparison with loss-of-life risk tolerance standards. Quantitative risk estimation is also beneficial for assessing damage cost risks because it provides a basis for estimating annualized losses, which informs mitigation design optimization and can be used to justify costs associated with the risk reduction design. Moreover, it can allow more transparent estimation of uncertainties for each risk parameter (e.g., by the use of uncertainty bounds or ranges). For these reasons, we mainly focus on quantitative risk analysis in this chapter.

## Consultation Zone

The geographic area considered for a geohazard risk analysis is known as the consultation zone, which is defined as, “all proposed and existing development in a zone defined by the approving authority that contains the largest credible area affected by landslides, and where fatalities arising from one or more concurrent landslides would be viewed as a single catastrophic loss” (original use by the Hong Kong Geotechnical Engineering Office (GEO) 1998, defined as above by Porter et al., 2009; Porter & Morgenstern, 2013). Definition of this zone is particularly important to assess group safety risk, which is proportional to the number of persons exposed to a hazard. This zone would have been identified at the beginning of the hazard analysis.

## Risk Management Framework

Debris-flow risk assessment is part of a larger framework of geohazard risk management, which encompasses initial hazard identification through risk analysis and optimization of risk reduction and monitoring measures.

Table 1 provides an overview of a risk management framework, after Canadian Standards Association (CSA, 1997), AGS (2007), and ISO 31000, 2009. It has been adapted from CSA (1997), AGS (2007), and ISO 31000: 2009. Qualitative or quantitative risk analysis methods can be used within the framework.

Table 1. Risk Management Framework (adapted from AGS, 2007; CSA, 1997; and ISO 31000, 2009).

 Risk Communication and Consultation:By way of maps, reports, signage, warning systems, public meetings, and educational materials 1. Project Initiation a. Recognize the potential hazard b. Define the consultation zone (study area) and level of effort c. Define roles of the client, regulator, stakeholders, and QRP d. Determine “key” risks to be considered in the assessment 2. Hazard Assessment a. Identify and characterize the hazard b. Develop a hazard frequency-magnitude relationship c. Identify hazard scenarios to be considered in risk estimation d. Estimate hazard extent and intensity parameters for each scenario 3. Risk Assessment a. Characterize elements at risk and determine vulnerability criteria b. Estimate risk: the probability that hazard scenarios will occur, impact elements at risk, and cause particular consequences 4. Risk Evaluation a. Compare the estimated risk against tolerance criteria b. Prioritize risks for risk control and monitoring 5. Risk Control a. Identify options to reduce risks to levels considered tolerable. b. Select option(s) providing the greatest risk reduction at least cost c. Estimate residual risk for preferred option(s) 6. Action a. Implement chosen risk control options b. Define ongoing monitoring and maintenance requirements Land Management Planning and Regulation:Ongoing review of the risk management process for land use and development permitting

## Risk Estimation

### Risk Equation

Debris flow risk (PE) can be estimated quantitatively using the following equation:

$Display mathematics$
[2]

where:

$P(H)i$ is the annual hazard (debris flow) probability for event scenario i of n total scenarios

$P(S:H)i$ is the spatial probability that the debris flow will reach the element at risk

$P(T:S)i$ is the temporal probability that the individual will be present within the footprint of the hazard at the time of hazard occurrence.

describes the consequences, [3]

where:

$Vi$ is vulnerability, the probability elements at risk will suffer consequences given debris-flow impact, with a certain severity of destructive power

$Ei$ is a measure of the element at risk, quantifying the severity of potential consequences (e.g., number of persons, building value).

### Hazard Probability, P(H)

Hazard probability,

$P (H)i$, corresponds to the annual probability of occurrence of each hazard scenario as described in the section Hazard Scenarios.

### Spatial Probability

Spatial probability of debris flow impact addresses the question, “What is the chance that a debris flow will follow a particular trajectory that results in impact to an element at risk, given it is present in the hazard zone when the event occurs.”

Methods to estimate spatial probability of debris flow impact differ depending on the element at risk. For example, different methods may be required to estimate spatial impact probability for linear or single location structures, or for stationary or moving objects (e.g., buildings versus moving trains or vehicles).

In the simplest case, spatial probability can be based entirely on modeled debris flow extents. For example, probability of impact could be assumed as certain (

$P(S:H)i=1$) if the element is within the area impacted by modelled flows, with no impact (

$P (S:H)i=0$) assumed if the element is outside the extent of modelled flows.

Estimates of spatial probability become more complex if there are multiple possible debris-flow runout scenarios at a given magnitude class (see the section Current Modeling Approaches and Challenges). For example, this could be the case if there are several possible channel avulsion scenarios, or there is a range in possible flow characteristics that would affect flow mobility. It is not feasible in most practical assignments to address these through large numbers of model runs and probabilistic methods such as Monte Carlo simulation. Table 2 provides suggested approaches based on criteria and judgment to estimate debris flow spatial impact probability in such situations.

Table 2. Factors to Consider When Estimating Spatial Impact Probability

Spatial Probability Factor

Consideration

Probability of channel avulsion

Assign as conditional probability flows will avulse for a given volume class.

Runout exceedance probability

Use several model scenarios as the basis to interpret runout exceedance probability isolines. This approach addresses the question, “Given channel avulsion, what is the chance that a flow will extend at least as far as a given element at risk?”

Lateral impact probability

Assign conditional probability based on the typical width of a simulated flow path in relation to the possible corridor through which it might travel. This factor addresses the question, “Given channel avulsion, what is the chance that a flow will follow a particular trajectory that results in impact to an element at risk (as opposed to travelling past but missing the element)?”

### Temporal Probability

Temporal probability considers the proportion of time elements at risk are present within the hazard zone. For estimating risk to existing, permanent structures this is typically regarded as certain (

$P (T:S)i =1$).

For estimation of safety risk to persons within buildings, temporal probability is proportional to the time residents spend within the building. A lower average probability might be assigned to estimate group safety risk, with a higher probability used for individual risk estimates to represent the “individual most at risk” (e.g., a baby, elderly or sick person spending the greatest proportion of time at home). Other considerations include seasonality (e.g., summer cottages unoccupied during the winter), and whether evacuation is considered credible and/or the likelihood of its success.

To estimate risk to moving vehicles travelling through a debris-flow hazard zone, temporal probabilities can be estimated using a Poisson3 model, a discrete probability distribution that expresses the probability of a given number of events (vehicle passes) during a fixed interval of time and space. In this case, the model is applied to simulate random vehicle spacing and the probability of having 1, 2, … or n vehicles within the hazard zone at the time. In practical application the maximum number of vehicles that could be expected is limited by traffic frequency. For example, the probability of several vehicles within a hazard zone at a given time can be negligible for low traffic roads.

### Vulnerability

Vulnerability is defined as the degree of loss of a given element at risk that results from debris-flow impact with a certain level of destructive power. Methods to estimate vulnerability differ depending on the type of element at risk. For example, estimating vulnerability for elements at risk potentially exposed to direct impact (e.g., buildings, vehicles, rail cars) will be different than for buried infrastructure vulnerable to channel scour (e.g., pipelines or buried utilities). We focus in this section on estimation of vulnerability of buildings and persons within buildings to debris-flow impact.

Estimating building vulnerability based on modeled debris-flow scenarios requires a relation between modeled debris-flow velocities and depths, and severity of building damage. Determining this relation is challenged by factors that are poorly known. These factors include the variable nature of flow behavior and individual boulder impacts, presence of large woody debris, a lack of data on building structures and their resistance to flow impact, that damage can occur by both hydrostatic pressure and flood inundation, and that damage can occur due to factors that are absent or poorly represented in runout models, such as channel bed scour and bank erosion. Moreover, in contrast to flood hazards where relations between inundation and damage are well studied, less data are available to empirically estimate debris-flow vulnerability based on recorded damages in past events.

These limitations notwithstanding, Jakob et al. (2011) documented 66 case studies where characteristics related to flow intensity, such as flow depth and velocity, were recorded or could be estimated and related to recorded building damage.

Debris-flow intensity was represented by Jakob et al. (2011) as follows:

$Display mathematics$
[4]

where: d is flow depth (m) and v is flow velocity (m/s).

Values of IDFwere plotted on a log scale against recorded building damage to estimate probabilities of a certain proportion of building damage. Table 3 shows ranges in IDF identified as typical for a certain damage range. The criteria shown in Table 3 may require adjustment depending on site conditions and apply where debris-flow impact is the primary factor for damage. They are less applicable for low velocity areas (e.g., v< 1 m/s), where IDF will approach zero for any flow depth (e.g., in areas of backwater flooding). Flood vulnerability criteria such as depth-damage curves may be more appropriate to estimate building vulnerability in such areas.

Table 3. Damage Categories for Buildings

IDF Range

Damage description

Typical damage proportiona

Description

<1

Some sedimentation

0.2

Moderate likelihood of building structure damage, but high likelihood of major sediment and/or water damage. Building repairs required but primarily to non-structural elements.

1–10

Some damage

0.33

High likelihood of moderate to major building structure damage and severe sediment and water damage. Building repairs required, possibly including some structural elements.

10–100

Major damage

0.66

High likelihood of major to severe building structure damage and sediment and water damage. Major building repairs required including to structural elements.

>100

Destruction

>0.99

Very high likelihood of severe building structure damage or collapse. Complete building replacement required.

Note: a Damage proportion in terms of building replacement value. Actual damage level applied to a given study may change depending on details of the hazard scenarios.

Within buildings, human vulnerability can be estimated as an indirect outcome of building damage or collapse, where estimated probabilities of fatality are linked to estimated levels of building damage. These estimates require judgment and calibration based on known events and can be influenced by factors unique to a given study, such as the presence of occupied basements and mixed-use residential-commercial buildings, and by assumptions about warning time (e.g., whether persons can be credibly expected to escape impact). Using estimate ranges can be helpful to consider uncertainties.

## Safety Risk Estimation

Safety risk analysis involves estimation of the risk that debris flows will occur, impact person(s), and cause loss of life. It is typically quantified in terms of risk to individuals and risk to groups, for comparison to safety risk tolerance criteria. Individual risk evaluates the chance that a specific individual (the person judged to be most at risk) will be affected by the hazard. For example, an analysis of individual risk evaluates the chance that a specific person living in a dwelling would be affected by the hazard. Individual risk is independent of the number of people exposed to the hazard, as it focuses on a single individual.

Group risk, also known as societal risk, evaluates the chance that any people present in the area will be affected by the hazard. A low frequency, high magnitude event might result in a very small, tolerable risk to an individual, but the same event may be considered intolerable if a large number of people are affected. Group risk analyses are completed in addition to individual risk analyses because society is less tolerant of events that affect multiple people. In a given home, the probability of any individual being affected (group risk) will be at least as high as the probability of a specific individual being affected (individual risk).

Individual risk is reported as the annual Probability of Death of an Individual (PDI). Individual risk levels are independent of the number of persons exposed to risk.

Group risk is represented graphically on an F-N curve (see the section Risk Evaluation, Figure 7). The Y-axis shows the annual cumulative frequency, $fi$, of each hazard scenario, and the X-axis shows the estimated number of fatalities, $Ni$, where:

$Display mathematics$
[5]

and $Ni$ is represented by equation [3].

For example, a point on the F-N curve can be read as the estimated frequency of at least a certain number of fatalities. Zones on the graph define generally accepted risk tolerance thresholds. Comparison of results to these thresholds helps guide risk reduction decision making.

## Direct Damage and Loss Estimation

Table 4 lists examples of elements at risk and types of direct damages that can be systematically, if not necessarily quantitatively, assessed. Consequences indirectly resulting from debris-flow impact (e.g., loss of business activity in affected areas, or intangibles) may form part of qualitative discussion but are rarely quantified in debris-flow studies due to the uncertainty involved in such estimates. Where insufficient data exists to quantify direct consequences, potential for loss can be assessed by identifying the location, type, and value of infrastructure in affected areas.

Table 4. Types of Consequences

Element at risk

Possible consequences assessed

Buildings

• Quantitative estimation of damage to building structure or contents expressed as a proportion of appraised building value and direct damage cost.

• Quantitative estimation of vulnerability of persons located within buildings to loss of life.

“Critical” Facilities

• Identification of facilities considered critical for function during an emergency, where debris impact in a given scenario would likely result in some duration of loss of function (e.g., school, fire station, police station, hospital, or any facility a community considers critical for emergency response).

• Categorical estimation of consequence level: Low, Moderate, and High consequence categories described in terms of road traffic frequency, damage type, and duration to restore function.

• Quantitative estimation of cost of loss of use, based on estimated cost of outage per unit time (if known).

Bridges and Culverts

• Categorical estimation of consequence level, as Low, Moderate, and High consequence categories, described in terms of road traffic frequency, damage type, and duration to restore function.

# Risk Evaluation

## Safety Risk

Risk evaluation involves comparison of estimated risks to risk tolerance criteria. The use of quantitative risk tolerance criteria began in other disciplines, such as industrial and nuclear engineering, and has been adapted to landslide risk management. However, their use in debris-flow assessments is not yet widespread, and few jurisdictions around the world have adopted legally binding risk tolerance criteria. Those that have include Hong Kong and the District of North Vancouver (DNV), Canada (DNV, 2009; GEO, 1998). Jurisdictions without risk tolerance criteria often evaluate risk based on comparison to criteria existing in other jurisdictions.

The DNV criteria for individual landslide risk tolerance are as follows (DNV, 2009):

• Maximum 1/10,000 (10−4) risk of fatality per year for existing developments.

• Maximum 1/100,000 (10−5) risk of fatality per year for new developments.

Group risk tolerance criteria reflect society’s general intolerance of incidents that cause multiple fatalities. Group risk tolerance thresholds based on criteria adopted in Hong Kong (GEO, 1998) are shown on Figure 7. Three zones can be defined as follows:

• Unacceptable—where risks are generally considered unacceptable by society and require mitigation.

• As low as reasonably practicable (ALARP)—where risks are generally considered tolerable by society only if risk reduction is not feasible, or if the costs of risk reduction measures are grossly disproportionate to the improvement gained (this is referred to as the ALARP principle).

• Acceptable—where risks are considered broadly acceptable by society and do not require mitigation.

In addition to the above thresholds, an “intense scrutiny zone” may be added where the potential for fatalities exceeds 1,000, reflecting societal aversion to large numbers of fatalities.

Click to view larger

Figure 7. Group risk tolerance criteria as defined by GEO (1998).

## Economic Risk

Absolute risk tolerance criteria do not exist for economic risk evaluation. Rather, the evaluation consists of comparing the costs of hazard occurrence to the costs of risk reduction to optimize and justify costs associated with risk reduction.

Economic risk can be estimated as costs for individual event scenarios or as an annualized figure considering all scenarios. Annualized costs can be calculated by determining a relationship between damage costs and event return periods. The area under a damage cost—return period curve represents the annualized direct damage cost for the period under consideration.

Notwithstanding work by researchers or academic groups, economic risk analysis for applied studies is commonly limited to determining direct damage costs (as opposed to indirect costs of lost economic activity, for example). Moreover, it is not feasible to foresee and estimate damages to every possible type of infrastructure that could be affected by flows. As such, economic risk analyses often capture only a portion of the risk associated with debris flows.

# Conclusions and Outlook for Further Research

Debris flows are frequently noted as one of the most destructive and lethal landslide processes worldwide (Petley, 2012). A number of factors unite in suggesting that the future will witness an increasing number of debris-flow related disasters, particularly in the developing world, where systematic mapping and risk reduction measures are still in their infancy while population growth is highest. The world’s population increases by 1.1% every year, and even though the growth rate is projected to decline to 0.5% per year by 2050, the expected increase in the world’s population in 2016 is approximately 75 million. Some of this population growth will invariably occur in mountainous terrain, where new dwellings, villages, and towns are constructed with their respective infrastructure, and thus will be potentially susceptible to debris flows. Similarly, larger piedmont cities are likely to see development at their mountainous fringes. Furthermore, deforestation and other detrimental human-caused landscape alteration may increase debris-flow activity locally. In addition, it is now well established that hydro-climatic extremes are increasing in frequency and magnitude in many parts of the world (IPCC, 2014). In most regions of the world, this should result in an increase of debris-flow activity.. These tendencies are only offset in those nations where systematic debris-flow mitigation is instituted and where sufficient funds are available to maintain and replace old structures and construct new ones. Since this is, globally, the exception rather than the rule, rising human and economic losses due to debris flows are anticipated. This highlights the necessity to understand, quantify, and manage debris-flow risks, to which we hope that this article contributes.

Methods employed in debris-flow risk analyses have advanced considerably over the past 30 years, with numerous research groups contributing to related fields. Dating methods to quantify debris-flow frequency, such as dendrochronology, have witnessed an explosion of research. Methods to decipher debris-flow magnitudes through empirical methods and better modeling approaches have also improved, some of which allow for debris entrainment along the flow path. Methods to determine frequency-magnitude relationships still have limitations in terms of satisfactory statistical treatment and quantification of all uncertainty sources, even though those are increasingly being discussed in the scientific literature (Jakob, 2012).

Despite these notable advances, gaps still exist, and there is plenty of room for methodological refinements s. Specific research venues revolve around the creation of realistic debris-flow models that can incorporate bank erosion and bed scour, avulsions, and multi-rheological/multi-phase flow behavior in three dimensions. In terms of the risk analysis, gaps exist in estimating vulnerabilities of buildings and people residing in buildings, in vehicles as well as pedestrians. It is still rare to see systematic evaluation of all-encompassing hazard scenarios and their translation into model runs leading to composite hazard maps that feed into the risk analysis and risk maps. To some degree this is associated with the significant costs of performing such studies, but it is also due to the lack of familiarity of the associated methods by many practitioners. Further development of professional practice guidelines and standards in the mountainous nations of the world would help improve the consistency of risk assessments supporting development permitting and land use planning. Improvements in computational speed for debris-flow modeling may, in the future, allow larger numbers of scenarios to be practically considered in an analysis.

For pipelines and other buried linear infrastructure, debris-flow risk associated with channel scour needs to be assessed; few methods are available to estimate scour potential on fans that are historically regarded as purely depositional landforms.

For large landslides (rock slides, rock avalanches, and rapid earthflows), little is known about their potential or detailed mechanics to evolve into debris flows in time and space.

For risk assessment methodology itself, it is notable that the two nations with the longest history of debris flow research and mitigation (Japan and Austria) do not yet use an explicitly risk-based approach to managing debris-flow hazards. The advantages of such an approach over a hazard-based one, in which a standard return period is chosen and mitigation is designed for the corresponding magnitude, are manifold: First, quantitative risk assessment allows risk-based prioritization and optimization of mitigation works, and affords a way to demonstrate the effectiveness of such mitigation in reducing risk. Second, larger events than those chosen as the design event are possible and may pose high residual risks that will be unrecognized if not assessed. Finally, risk assessments completed periodically can better accommodate changes to elements at risk or the frequency or magnitude of the hazard itself, and thus better support land use and risk reduction decision making.

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## Notes:

(1.) This general paradigm stands for all geophysical phenomena (floods, earthquakes, tornados, hurricanes, etc.).

(2.) A debris flood can be defined as: “a very rapid surging flow of water heavily charged with debris in a steep channel” (Hungr et al., 2014).

(3.) A Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events (here vehicle passes) during a fixed interval of time and space. It is widely used in traffic engineering, for example, to predict vehicle arrival times.