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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
263
DOI: 10.4408/IJEGE.2011-03.B-031
A NOVEL DEBRIS-FLOW FAN EVOLUTION MODEL BASED
ON DEBRIS FLOW MONITORING AND LIDAR TOPOGRAPHY
P. SCHÜRCH
(*,**)
, a.l. DENSMORE
(*)
, N.J. ROSSER
(*)
& B.W. M
C
ARDELL
(**)
(*)
Department of Geography and Institute of Hazard, Risk and Resilience, Durham University, DH13LE, United Kingdom.
Corresponding author: Schürch P. p-s@gmx.ch
(**)
Swiss Federal Institute of Forest, Snow and Landscape Research (WSL), 8903 Birmensdorf, Switzerland
titative understanding of both how debris-flow fans are
built up over time, and how their deposits and surface
morphology can be altered by post-depositional proc-
esses. Second, debris-flow fans form valuable low-gra-
dient surfaces that are commonly used for agriculture
or human habitation in mountainous areas, despite the
threat of flow inundation. Debris flow hazard assess-
ment usually involves modelling the effect of single
flows (of a specific volume) on the present day topog-
raphy. d
albey
et alii (2008) pointed out that traditional
debris flow hazard assessment often ignores the effects
of uncertainties in the input parameters (flow param-
eters and topography) on the output (hazard assess-
ment). To our knowledge no attempt has been made to
quantify the uncertainty in the hazard assessment due
to the evolution (i.e. incision, aggradation, avulsion) of
the channel system over a sequence of events.
Both the (unknown) interactions between process
and developing form on debris-flow fans, and the effects
of channel evolution over the course of multiple events
on hazard assessment, can be investigated through a
quantitative model of fan evolution over geological (10
3
to 10
6
y) time scales. Such a model must explicitly in-
corporate the complex interactions between debris flows
and the surface topography but must also be efficient
enough to allow multiple simulations over long time
scales. In this paper we review the conceptual basis for a
novel modelling approach that clarifies the long-term ef-
fect of debris-flow-specific patterns of erosion and depo-
sition on the evolution of debris-flow fan morphology.
ABSTRACT
In this paper we present the rationale for a new ap-
proach to the modelling of debris-flow fans. Understand-
ing debris-flow fan evolution is important for two rea-
sons: fans are potential archives of past environmental
conditions of mountain belts, and they are commonly
inhabited despite the threat of debris flow occurrence.
There are currently no models available that adequately
represent debris flows as agents of geomorphic landscape
change over the time scales (10
3
to 10
6
y) necessary to
construct fans, which severely limits our ability to under-
stand both short- and long-term fan behaviour. We de-
scribe in detail how results from debris flow monitoring,
LiDAR topography and geomorphic mapping of debris
flow fans, together with empirical relationships on debris
flow behaviour, can be used to inform a novel debris-
flow fan evolution model. The model we propose will
be useful for both the analysis of long-term fan evolution
and hazard analysis over short to medium time scales.
K
ey
words
: debris flow, fan evolution, modelling, erosion,
deposition
INTRODUCTION
Understanding debris-flow fan evolution is impor-
tant for two main reasons. First, debris-flow fans are
potentially valuable archives of past environmental
conditions of mountain belts and associated channel
systems (d
üHnfoRtH
et alii, 2007, d
ensmoRe
et alii,
2007). Reading this archive, however, requires a quan-
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P. SCHÜRCH, A.L. DENSMORE, N.J. ROSSER, & B. w. Mc ARDELL
264
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
the flow front and impacting on the bed (s
toCk
& d
i
-
etRiCH
, 2006; H
su
et alii, 2008). None of the first class
of models includes these effects explicitly.
The second class of models is designed to model
sediment transport by single debris flows in a physically
correct manner (e.g., i
veRson
, 1997; i
veRson
& d
enlin
-
GeR
, 2001; P
udasaini
, 2005; P
atRa
et alii, 2005). They
are based on grain-fluid mixture theory and yield depth-
averaged equations for momentum and mass conserva-
tion, generally assuming constant flow mass. A major
finding from simulations based on these models is that
the total flow resistance depends more on boundary ge-
ometry than on boundary shear stress (i
veRson
& d
en
-
linGeR
, 2001). This is important for understanding how
channel geometry affects flow behaviour. These models
are not suitable for simulating fan development over
long time scales because of their numerical complex-
ity and long run times. Individual model runs can take
from several minutes up to several hours depending on
the size and resolution of the model space. This problem
was discussed in detail by d
albey
et alii (2008) in the
context of hazard assessment, where due to uncertainty
in the input parameters hundreds of runs are necessary
to explore the range of possible outcomes.
For some applications, the main interest lies in
predicting only the inundation area of a flow of given
volume over given terrain. This can be achieved at
lower computational costs using empirical or semi-
empirical relationships. For example, G
Riswold
&
i
veRson
(2007) and b
eRti
& s
imoni
(2007) found a
power-law relationship between total flow volume V
[m
3
] and inundated planimetric area B [m
2
]:
B = α V
2/3
where α is a site-specific coefficient determined by re-
gression. The smallest values of α = 6-7 were reported
by C
Rosta
et alii (2003) for 138 granular debris flows
with volumes of 2-10
5
m
3
(Central Italian Alps). A
value of α = 20 was reported by G
Riswold
& i
veRson
(2007) from a worldwide data set of 44 non-volcanic
debris flows ranging in volume from 10 to 10
7
m
3
. b
eR
-
ti
& s
imoni
(2007) suggested α = 33 based on a data set
of 24 granular debris flows with volumes of 500-5•10
5
m
3
in the Italian Alps. While limited, these empirical
relationships are appealing because of their simplicity.
EROSION AND DEPOSITION IN DEBRIS
FLOWS
Debris flows can continue to erode material after
REVIEW OF FAN AND DEBRIS FLOW
MODELS
In this section we review the concepts of existing
numeric fan evolution and debris flow models. A first
class of models has been developed to examine the
filling of accommodation over geological time scales
by sediment which is transported by fluvial processes.
Such alluvial fan or fan-delta models are commonly
based on general formulations of sediment transport
and flow resistance that average deposition in space
and time (P
aRkeR
et alii, 1998; d
e
C
Hant
, 1999). For
example, in the model of H
aRdy
& G
awtHoRPe
(1998)
sediment is transported at a constant rate by a ran-
dom walk algorithm from the source to the shore line.
These models have no actual representation of chan-
nels in the topography. A more recent model by s
un
et
alii. (2002) is based on a cellular approach capable of
representing channelized flow. Many of these models
have operated on a rectangular grid (e.g. C
oultHaRd
et
alii, 2000; s
un
et alii, 2002), but model behaviour can
be very sensitive to the grid orientation and spacing
(n
iCHolas
& Q
uine
, 2007). n
iCHolas
& Q
uine
(2007)
proposed a numeric fan evolution model with a radial
grid focussed at the fan apex to represent the fan sur-
face and a channel network represented by node po-
sitions. This model explicitly includes a process-form
feedback at the channel scale in order to regulate the
system response to erosion and deposition. However
these models cannot be used to model debris flows
because of a range of reasons: fluvial processes oper-
ate more continuously in time, changes to the surface
morphology take place gradually and the sediment flux
and maximum transportable grain size are typically
limited by the flow velocity or the available stream
power. In contrast, debris flows are events with a fi-
nite duration and a well-defined spatial extent. Debris
flows self-channelize by thalweg erosion and deposi-
tion of levees (b
laiR
& m
C
P
HeRson
, 1998) but may
be subject to abrupt avulsion, whereby relatively small
sediment volumes deposited in critical places along the
channel can force subsequent flows or flow surges in
new directions (b
laiR
& m
C
P
HeRson
,, 1998; w
HiPPle
,
1992). In a single debris flow all available grain sizes
are transported such that debris-flow deposits show
limited or no down-fan fining (b
laiR
& m
C
P
HeRson
,,
1998; k
im
& l
owe
, 2004). Observations imply that
erosion in debris flows may be largely a function of the
inertial stresses induced by coarse particles carried in
(1)
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A NOVEL DEBRIS-FLOW FAN EVOLUTION MODEL BASED ON DEBRIS FLOW MONITORING AND LIDAR TOPOGRAPHY
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
265
tions, there remains no simple rule for the onset of
deposition. f
annin
& w
ise
(2001) have shown that
channel confinement plays a major role in triggering
deposition. C
annon
(1989) showed for one particular
debris flow that channel geometry (triangular vs. rec-
tangular section), channel width and strength or rheol-
ogy of the flowing debris influence the rate of deposi-
tion. Other researchers have proposed that deposition
starts at a particular bed slope angle, ranging from 3.5°
to 40° (H
unGR
, 2005). These data are derived from a
great variety of debris flows, comprising ranges in for
example volume, composition, channel geometry, and
show that slope alone is not a good predictor for the
onset of deposition. Work by i
veRson
(1997) suggests
that flow behaviour is best described by the granular
temperature. The granular temperature is not a con-
stant but rather a state variable that changes constantly
as the flow moves, deposits and erodes material. Ma-
terial with a high granular temperature is more likely
to keep moving. When the granular temperature de-
clines, the material will stop flowing eventually. All
these observations are important for understanding
the controls on debris flow deposition but they pro-
vide little guidance on how to predict the lag rate for
a specific flow. We are only aware of one relationship
that can be adapted to estimate the lag rate. G
Riswold
& i
veRson
(2007) suggested an empirical relationship
between total flow volume V [m
3
] of a debris flow and
the cross sectional area of the flow A [m
2
]:
A = ε V
2/3
where ε = 0.1 (regression based on 50 non-volcanic
debris flows, worldwide). For granular debris flows
in the Italian Alps (19 events) b
eRti
& s
imoni
(2007)
suggested ε = 0.03. This relationship can be inter-
preted as an upper limit on the rate of deposition, i.e.
according to Eq. 2 a debris flow cannot deposit more
than A m
3
of sediment per 1 m channel length. Where
only levees are deposited the lag rate will necessarily
be less because most of the flow cross section is made
up by the channel. Note, too, that Eq. 2 does not allow
for dependence on the channel geometry or gradient.
From field evidence it is known that debris flows
can stop suddenly in a channel, forming a snout of
coarse particles (e.g. w
HiPPle
& d
une
, 1992; m
CCoy
et alii, 2010). This can cause the next flow to avulse
into a new channel and lead to fundamental changes in
the locus of sedimentation (w
HiPPle
, 1992; b
Ryant
et
alii, 1995; f
ield
, 2001; d
ünfoRtH
et alii, 2008; R
eitz
et
initiation, but the same time material may be depos-
ited at the flow margins. The net rate of this two-way
exchange of material between the debris flow in mo-
tion and the channel bed is called the lag rate (C
annon
,
1989). The lag rate is defined as the volume per unit
downstream distance that is lost (dV/dx < 0) or gained
(dV/dx > 0) by the flow. While this is clearly a key pa-
rameter for understanding how debris flows interact
with their bed and banks and thus build topography,
the controls on debris flow lag rate are not well known.
Debris flow erosion is particularly poorly under-
stood (P
udasaini
, 2005; R
emaitRe
et alii, 2008) and
difficult to predict. It is clear, however, that the erosion
depth for transport limited conditions is highly variable
in different settings (H
unGR
et alii, 2005). Material can
be incorporated into the flow by lateral erosion of the
banks, bank collapse or entrainment of material from
the channel bed. Experiments in small flumes with erod-
ible beds of loose colluvium by e
GasHiRa
et alii (2001)
and P
aPa
et alii (2004) have shown that erosion rates
increase with increasing bed shear stress. b
eRGeR
et alii
(2010) monitored the timing of erosion in a natural de-
bris flow flowing on a bed of unconsolidated sediment,
and found that it took place during passage of the flow
front. s
toCk
& d
ietRiCH
(2006) proposed a bedrock in-
cision law for debris flows based on the inertial stress
imparted to the bed by grain-bed impacts. The model
predicts debris flows with long and coarse fronts and
high shear rates (surface velocity / flow depth) to be
most erosive. H
su
et alii (2008) found a dependence of
bedrock incision on grain diameter and to a smaller ex-
tent on shear rate of the flow, and suggested that most
of the wear occurs underneath the coarse granular front.
Despite these advances, a robust general model for de-
bris flow erosion - akin to the geomorphic transport laws
described by d
ietRiCH
et alii (2003) - is still lacking.
The rates of deposition in a debris flow are closely
linked to the runout length (C
annon
, 1989; R
iCken
-
mann
, 2005, f
annin
& w
ise
, 2001). As a debris flow
enters channel reaches with lower gradients, deposi-
tion becomes progressively more important, and even-
tually comes to dominate over erosion, leading to a
net loss of flow volume (C
annon
, 1989; R
iCkenmann
,
2005; H
unGR
et alii, 2005; H
üRlimann
et alii, 2003;
f
annin
& w
ise
, 2001). The rate of deposition may in-
crease dramatically on the lower parts of a fan where
levee deposition is replaced by lobe formation (b
laiR
& m
CPHeRson
, 1998). Despite these general observa-
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P. SCHÜRCH, A.L. DENSMORE, N.J. ROSSER, & B. w. Mc ARDELL
266
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
terns and magnitudes of surface change due to single
debris flows (Figure 1). Preliminary analysis of the
data from individual flows shows that erosion and
deposition can occur in the same event. Deposition
in the form of levees along the flow margins (e.g., at
Z and Y in Figure 1) and as sheets on inset terraces
(W) occurs where flow depth is low. Along the centre
line of the channel (e.g., at X) flow depth is substan-
tially larger and incision is common. These observa-
tions have implications for the geomorphic impact of
debris flows. Firstly, the effect of a single flow on a
given channel depends not only on the flow magni-
tude (i.e. volume or peak discharge) but also on the
channel geometry, and the effect can be very differ-
ent across a given flow cross section. Secondly, flows
of different magnitude occupying the same channel
may behave differently because they “see” a differ-
ent cross-section geometry, i.e. a different maximum
flow depth and different inundation limits. We sus-
pect that this mechanism gives rise to a poorly under-
stood set of process-form feedbacks which influence
how debris-flow fan systems evolve over time.
alii, 2010). b
Ryant
et alii (1995) found an increase in
avulsion frequency with increased sedimentation rates
in a laboratory experiment of an alluvial fan. For un-
derstanding avulsion on debris-flow fans it is crucial to
think about the conditions required to stop debris flows
in a channel. m
CCoy
et alii (2010) suggested that the
amount and persistence of excess pore pressures in the
flow causes high mobility and long runout. Nevertheless
the process of debris flow deposition is not understood
well enough to make precise predictions of the location
of the depositional snout along a predicted flow path.
DIRECT OBSERVATIONS OF DEBRIS
FLOWS: IMPLICATIONS FOR MODEL-
LING FAN EVOLUTION
The Illgraben in Switzerland is well known for
frequent debris flows and is comprehensively moni-
tored (m
C
a
Rdell
et alii, 2007, b
adoux
et alii, 2008),
providing an ideal opportunity to constrain rela-
tionships for flow erosion, deposition, and channel
evolution on an active debris-flow fan. Since 2008
we have used a terrestrial laser scanner to map pat-
Fig. 1 - Channel geometry and elevation change due to a debris flow on 1 July 2008 of 60000 m
3
total volume and peak discharge
~100 m
3
/s, both measured at the toe of the fan at Illgraben, Switzerland. Black arrows indicate flow direction. Correspond-
ing locations in the photo and on the map are indicated by w, X, Y and Z. Elevations represent post-flow topography and
are given in meters above sea level, spacing of contours is 1 m. A: Portion of the monitored reach near the fan apex (look-
ing downstream). white dashed line indicates the maximum extent of inundation by the flow. Note levee deposits on flow
margins near Y and Z, sheet-like deposits near w on inset terrace and incision near X. B: Difference model obtained by
repeat terrestrial laser scanning of the study reach. Grey scale values indicate surface elevation change during the event
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A NOVEL DEBRIS-FLOW FAN EVOLUTION MODEL BASED ON DEBRIS FLOW MONITORING AND LIDAR TOPOGRAPHY
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
267
A NEW MODEL: CONCEPTUAL FRA-
MEWORK
The new debris-flow fan evolution model we pro-
pose in this paper overcomes some of the shortcom-
ings of existing fan evolution models by better repre-
senting the behaviour of debris flows. In the design of
the model we place particular emphasis on the afore-
mentioned process-form feedbacks which are most
relevant for landform generation. From observations
of erosion and deposition in debris flows we can for-
mulate a number of requirements for the new model:
(1) Flows should self-channelize when moving across
unconfined fan surfaces.
(2) Debris flows should erode the fan surface when
certain criteria are met.
(3) Periodic avulsion and shifting of the depocenter
should be permitted when certain conditions are met.
(4) The emergent channel scaling should be compara-
ble to the scaling on natural fans.
(5) Flows should stop at a range of distances from the
fan head.
The model must be computationally efficient in
order to simulate the cumulative influence of a large
numbers of successive flows over geological time
scales. This can be achieved via a set of flow rules,
which must cover the routing of flows down the fan
surface, the rates and location of both erosion and
deposition, and criteria to stop flows on the fan.
MODEL STRUCTURE
The model reads the initial topography from a
DEM. Subsequently a flow routing algorithm identifies
the most likely flow path between the flow initiation or
entry point and the model boundaries. Then we extract
channel cross sections at defined intervals. At each cross
section we test whether the channel conveyance capac-
ity is exceeded or not and we estimate the flow depth in
each cross section. We then use this information to in-
form the flow behaviour (erosion, deposition, stop) and
calculate the lag rate. Next, we update both the DEM
and the flow characteristics dependant on the model
rules. With these updated values we move to the next
cross section. When the flow stops a new flow will be re-
leased onto the modified DEM. This approach requires a
series of approximations, which we will discuss below.
Starting at the topmost cross section we estimate
flow cross-sectional area as a function of total flow vol-
ume using Eq. 2. Then we test whether the channel at the
location of the active cross section can contain the flow
or not (Figure 2). If it does, we determine the degree of
in-channel erosion or deposition by applying the rules
outlined below. If the flow is not contained within the
channel, we estimate the required width to contain the
excess discharge. In this way we identify the inundated
area on both sides of the channel and assume deposition
in those areas. We apply the resultant amount of erosion
or deposition to the DEM area between the active and
the next cross section. After updating the volume of the
debris flow we test the stop criterion. As long as this is
not met we proceed to the next cross section.
INITIAL AND BOUNDARY CONDITIONS
We run the model on an irregular triangular mesh.
Debris flows are released into the model domain at the
fan apex with an initial volume and an initial sediment
concentration. For each flow we randomly choose these
values from a probability distribution function (PDF).
Fig. 2 - Application of erosion and deposition rule. Flow
direction indicated by arrow. Symbols: h, flow
depth;hm, maximum flow depth at channel convey-
ance capacity; d, thickness of deposits; p, entrain-
ment depth. A: Debris flow with peak discharge
smaller than channel conveyance capacity. B: Debris
flow with peak discharge exceeding channel capacity
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P. SCHÜRCH, A.L. DENSMORE, N.J. ROSSER, & B. w. Mc ARDELL
268
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
in the channel will spread over-bank until it reaches a
minimum flow depth of d and we assume that it will
stop flowing when it has reached this degree of spread-
ing. In a situation as shown in Figure 2A, where the
channel conveyance capacity is not exceeded, we can
apply the same concept and test whether the maximum
flow cross-sectional area (as determined by Eq. 2) leads
to a flow depth of more than the required minimum
flow depth defined by Eq. 3 in the given cross section.
EROSION RULE
For simplicity, we focus here upon entrainment
from the channel bed because bank collapse and later-
al erosion are not well represented at the fan scale. We
link the erosion rule to basal shear stress τ, defined as:
τ = ρ g h S
where ρ is density, g is gravitational acceleration, h is
flow depth and S is channel slope. This assumes that
the stresses imposed on the channel bed are larger for
greater flow depths, irrespective of the main driver of
erosion (e.g., bed shear stress or inertial stresses due to
grain impacts), and that erosion is most likely where
basal shear stress is largest (P
aPa
et alii, 2004). The
erosion rule is invoked when the flow depth exceeds
the threshold for deposition d (Eq. 3). We use data on
maximum flow depth versus erosion depth from mon-
itoring (Figure 1) to define probability distribution
functions (PDF) of erosion at a given level of basal
shear stress. The erosion depth is then determined by
random sampling from this PDF.
STOP RULE
We make two simple assumptions about the con-
ditions that define when debris flows stop. A flow ob-
viously needs to stop when all or almost all material
is deposited. Further, we assume that debris flows
can only entrain material to a certain maximum vol-
ume fraction of sediment (e.g. 0.8) before internal
friction prevents further motion. Critical to this is a
consideration of channel bed saturation. The channel
bed may be dry or saturated before the event accord-
ing to a probability specified by the user. If the bed
is saturated (e.g. vol. fraction of 10%), then erosion
not only adds sediment to the flow but also water,
and hence the flow mobility is expected to increase.
In the case of a dry channel bed, the maximum volu-
metric sediment concentration is reached faster and
the flows are therefore less mobile. The sediment-
For debris flow magnitude we use published data
(H
elsen
et alii, 2002; H
unGR
et alii, 2008; J
akob
&
f
Riele
, 2010), and data from 10 years of debris flow
monitoring at Illgraben, Switzerland; synthetic distri-
butions such as log-normal or double Pareto may be
defined. The initial sediment concentration is based
upon observations at Illgraben that span a range of
volume fractions of 0.15-0.75 (data from 35 events).
DEPOSITION RULE
Debris flow deposits can be grouped into two
types: levees and lobes (b
laiR
& m
CPHeRson
, 1998;
k
im
& l
owe
, 2004). Levees are deposited while the
major part of the debris flow is still in motion and are,
given sufficient accommodation, left behind on one or
both sides of the flow path. They are often triangular
or box-shaped in cross profile (b
laiR
& m
CPHeRson
,
1998; k
im
& l
owe
, 2004), where the height is similar
to the size of the largest particles in the flow (m
C
C
oy
et alii, 2010) and rarely higher than ~2-3 m (b
laiR
&
m
CPHeRson
, 1998; k
im
& l
owe
, 2004). The geometry
of depositional lobes is more difficult to generalize, al-
though their thickness may be similar to the height of
levees (b
laiR
& m
CPHeRson
, 1998). The spatial extent
of lobes depends on a variety of factors such as accom-
modation, available flow volume to be deposited (b
laiR
& m
CPHeRson
, 1998) and possibly surface slope.
With these observations in mind, Eq. 1 can be re-
written in terms of average deposit thickness d (b
eRti
& s
imoni
, 2007)
d = 1/α V
1/3
which is supported by the observation that debris flow
lobe deposits have a roughly constant thickness for
any given event (i
veRson
et alii, 1998; l
eGRos
, 2002).
With 1/α = 0.06 (b
eRti
& s
imoni
, 2007) Eq. 3 predicts
a deposit thickness of 0.6 m for a flow of V = 1000 m
3
,
or 2.7 m for V = 10
5
m
3
. These estimates are roughly
compatible with our own observations for flows and
associated deposits at Illgraben, Switzerland.
We use the fact that deposition in a cross section
occurs where flow depth is low compared to the deeper
parts of the channel (Figure 1), and that Eq. 3 can in-
form a minimum flow depth below which deposition
occurs, to define our deposition rule. Figure 2B illus-
trates this: a flow with a peak discharge exceeding the
channel conveyance capacity will have very different
flow depths along the centreline of the channel and in
the overbank area. The excess discharge not contained
(3)
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A NOVEL DEBRIS-FLOW FAN EVOLUTION MODEL BASED ON DEBRIS FLOW MONITORING AND LIDAR TOPOGRAPHY
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
269
PRELIMINARY RESULTS
In Figure 3 we show preliminary results of a pilot
version of the proposed model. In the pilot version we
model the evolution of a single channel cross section
at a distance R of 250 m from the fan toe over a se-
quence of 500 debris flows (Figure 3C). Debris flow
volumes are sampled from a lognormal distribution
with a mean of 27’000 m
3
and a standard deviation of
13’000 m
3
. The probability of avulsion is set to 0.08,
with ε = 0.1 and α = 20 (Eq. 2 and 3). Changes in chan-
nel thalweg elevation (E) due to erosion or deposition
affect the channel slope: S = E / R. Thalweg elevation
and channel slope fluctuate as a function of erosion
and deposition (Figure 3A). Periods of gradual inci-
sion (time steps 150-200) occur as well as phases of
aggradation corresponding to avulsion events (e.g.
time step 302). Figure 3B shows the relative lag rate
per event; this is the erosion or deposition volume di-
vided by initial volume V. The negative spikes with
values of -100% represent avulsion events.
MODEL OUTPUT AND DISCUSSION
With this model we can investigate a set of ques-
tions related to the deposition and erosion dynamics of
debris-flow fans. A first application concerns debris-
flow magnitude-frequency distributions. These distribu-
tions for particular fans are usually poorly constrained
due to incomplete historical records (J
akob
& f
Riele
,
2010). With our model we can test whether different
concentration criterion is designed to reproduce the
stochastic nature of avulsion events and to force the
model to abandon established channels and establish
new depositional lobes and channels.
MODEL VALIDATION
As this model will be useful for both landscape
evolution analysis and short-term hazard analysis we
need to validate it for both types of applications. The
short-term performance of the model is validated us-
ing a series of well documented debris flows at the Ill-
graben. This requires high-resolution topographic data
(e.g. airborne LiDAR) of the fan surface, event data
on flow magnitude and discharge, and the geometry
of associated deposits. The long-term performance of
the model is compared against two well-documented
debris flow fans. The first test case is the Illgraben fan
in Switzerland where we have a good understanding of
the historical magnitude-frequency distribution of de-
bris flows and of their properties. In addition we have
established a depositional chronology for this fan from
the analysis of airborne LiDAR and field mapping. The
second test case is the Shepherd Creek fan in Owens
Valley, California, for which similar data on topogra-
phy and fan chronology are available. d
üHnfoRtH
et
alii (2007) have applied cosmogenic dating to con-
strain ages of depositional lobes on the Shepherd Creek
fan which can be used to constrain sedimentation rates
and avulsion frequencies produced by the model.
Fig. 3 - Preliminary model results showing the evolution of a single channel cross section over a sequence of 500 debris flows.
A: Evolution of thalweg elevation and channel slope. B: Relative lag rate dV/dx, normalized by initial flow volume
V. Note: positive values mean entrainment and negative values mean deposition. C: Event volumes sampled from a
lognormal probability distribution with a mean of 27’000 m
3
and a standard deviation of 13’000 m
3
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P. SCHÜRCH, A.L. DENSMORE, N.J. ROSSER, & B. w. Mc ARDELL
270
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
input magnitude-frequency distributions of debris flow
volumes have a significant effect on fan morphology or
evolution. In particular we can look at variables such
as channel scaling, the distribution of runout distance
preserved in the deposits, or the frequency of avulsion
events. If these vary for different model input volume
distributions, they could be used to infer the input mag-
nitude-frequency distribution of debris flow volumes
from geomorphic mapping of fan surfaces.
Secondly, we can investigate the causes of fan
head incision. The mechanisms of fan head inci-
sion on alluvial and debris flow fans are widely
discussed (H
aRvey
, 1984; H
aRvey
, 2005; d
avies
&
k
oRuP
, 2007; d
üHnfoRtH
et alii, 2008). A range of
external and internal forcing mechanisms has been
proposed (see full discussion in d
üHnfoRtH
et alii,
2008). With our model we can investigate whether a
process-form feedback is sufficient to create incised
channels and judge how stable such a configura-
tion might be. In other words, we ask whether the
random selection of events (picked from a PDF of
flow volumes) is sufficient for the development of
an incised state. Our preliminary results (Figure 3)
suggest that this is the case.
Thirdly, we can use the model to investigate
channel avulsion and the switching between different
depositional lobes. Channel avulsion is a major con-
cern on many fans where lives or infrastructure are at
risk. With this model we can test an existing channel
configuration obtained from real fan topography with
a finite number of randomly chosen possible flows.
This experiment highlights: 1) where in the channel
network avulsion is most likely to occur, and 2) what
conditions are most likely to lead to avulsion.
ACKNOWLEDGEMENTS
Funding for this research has come from NERC
grant NE/G009104/1 and the Department of Geog-
raphy at Durham University. Peter Schürch was em-
ployed on a Durham University doctoral fellowship.
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