Modeling the Interaction of Landslides, Debris Flows, and the Channel Network
Stephen T. Lancaster1
and Gordon E. Grant2
1. Dept. of Geosciences, Oregon State University
(slancast@fsl.orst.edu)
2. Forestry Sciences Laboratory, Pacific
Northwest Research Station, U.S. Forest Service
Abstract:
Landscape-level models are increasingly being used
to evaluate effects of alternative management practices on key geomorphic
and biological processes. Where forest practices are of interest, as in
the Oregon Coast Range, landscape models need to be sensitive to the wide
range of potential influences and feedbacks between vegetation and geomorphic
processes such as landsliding, debris flows, and channel evolution. We
are developing such a model that incorporates vegetation influences on
landslide initiation, debris flow runout, and meso-scale (i.e., decadal
to century) channel morphologic change. The model data structure attempts
a balance between conflicting needs: to model large areas while retaining
as much information about the landscape as possible. Landslide modeling
requires detailed knowledge of the landscape, e.g., topography, vegetation,
and soil. Modeling the effects of debris flows on the channel network requires
knowledge of channel input from large debris flow source areas. Despite
advances in computing power, detailed process modeling of large areas at
fine discretization remains intractable. In our model, the landscape is
represented by a mesh with variable discretization. Contiguous, channel-adjacent
debris flow source areas are aggregated, and debris flows from these areas
are routed through the channel network and interact with the sediment and
wood stored in the channel. Preliminary simulations reveal the importance
of management history, cutting patterns, and drainage network architecture
on the pattern and timing of debris flows within the basin.
Most forests are managed. As a result, landslides and debris flows are
managed implicitly. Our objective is to model landsliding and debris flow
runout in some detail over large areas and a century in time as part of
the Coastal Landscape Analysis and Modeling Study (CLAMS). We want to capture
the interactions between the forest and the landslide/debris flow process.
What are the process implications of management decisions?
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``Area-Descriptiveness'' Space:
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Landscape modeling usually involves a trade-off between the
descriptiveness of the model and the area modeled.
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Process models usually describe a small area in detail over geologic time.
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GIS-based index models usually describe a large area in less detail at
a static moment in time.
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We attempt a compromise in area-descriptiveness space by lumping landslide
source areas and resolving the channel network at high resolution.
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Aggregation of landslide/debris flow source areas:
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Initial calculations on each small node (e.g., 10m x 10m) result in a fine-scale
map of landscape characteristics, e.g., soil depth, vegetation age, and
landslide susceptibility.
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Channel source basins and channel-adjacent areas form aggregates.
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In each aggregate, areas with similar landslide susceptibility are binned,
and average values of, e.g., soil depth, etc., are stored for each bin.
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Trial watershed: small tributary to Knowles Creek, Oregon Coast Range:
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The forest's influence on landslides and debris flows:
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Root strength enhances slope stability:
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Critical precipitation for shallow slope failure
(e.g., Dietrich, et al., 1995):
where Ksat is saturated soil hydraulic conductivity;
h is vertical soil thickness; b is flow width;
q is slope angle; rhos is soil material density;
rhow is water density;
Aeff is area contributing to flow and is dependent on storm duration;
phii is internal friction angle;
Cr is cohesive root strength;
Cs is soil cohesion; and g is gravitational acceleration.
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Root strength
(Sidle, 1991, 1992):
where the first term in brackets represents root
decay, and the second and third terms in brackets represent root growth;
t is time since stand death; kr is 0.5 yr-1;
nr is 0.73; ar is 0.95;
br is 19.05; cr is -0.05;
fr is 0.25 yr-1;
jr is 2.0 m-1;
CVmax is maximum vertical root strength, 4200 Pa;
and CLmax is maximum lateral root strength,
9800 Pa (values from Benda and Dunne, 1997).
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Soil production
(Heimsath, et al., 1997)
and diffusion:
where rhob is soil bulk density; betae
is 0.00028 m/yr.;
lambda is 0.30 m (A. Heimsath, pers. comm., 1998); KD
is 0.0032 m2/yr. (Benda and Dunne, 1997); and z is elevation.
In simulations, h set to 5 cm, then
6000 yrs. of evolution.
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Effect of stand age on landslide initiation:
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Landscape nodes' colors represent steady state rainfall intensity required
to initiate landslides in the trial watershed.
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Channel network (blue lines) is defined by a 1 ha. contributing area
threshold and corresponds reasonably with the observed network.
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Channel-adjacent and low-slope nodes are defined as ``valley'' nodes
(green lines).
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Landslide susceptibility is not significantly different for stands older
than 40 yrs.
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Wood component of debris flow increases resistance and standing trees resist
uprooting:
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For debris flow runout, use simplified downstream momentum conservation
equation (R. Iverson, pers. comm., 1999) and add terms for
woody debris resistance and uprooting force:
where h is slope-normal debris flow depth;
v is slope-parallel debris flow velocity; theta is slope angle;
g is gravitational acceleration;
pb is pore pressure at the bed (assumed hydrostatic);
rhom is debris flow mixture density;
s is the slope-parallel direction;
phib is bed friction angle;
hd is slope-normal depth of debris flow wood constituent;
Rd is wood-related deceleration,
guessed to be 3.0-5.0 m/s2;
Cr is the root strength; and L is the debris flow length.
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Debris flow velocity must conform to changes in flow direction:
where alpha is the angle between the new and old downstream
directions in the horizontal plane.
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Debris flow depth must conform to changes in flow width:
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Debris flow length is constant.
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Wood entrainment expends debris flow momentum:
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Debris flow must entrain fallen wood on the surface and standing trees
in its path to continue.
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For debris flow scour, use excess shear stress law for soil and deposits
(sediment and wood) and neglect bedrock erosion:
where Ke is erodibility, 0.1 m/s-Pa;
Cf is a friction factor, 0.02;
taucr is critical shear stress, 2000 Pa;
and the rate of scour is constrained to be positive (increasing debris flow depth)
or zero. Values are rough guesses.
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Depth increase (or decrease) results in velocity decrease (or increase).
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If no scour and debris flow decelerating, deposition moderates loss of
velocity.
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Tests of debris flow model under simple conditions:
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Simulation boundary conditions mimic those of the debris flow flume at
the H.J. Andrews Experimental Forest in Oregon.
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Simulations show the sensitivity of runout length to wood content of both
the initial flow and deposits in the flow's path.
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Greater initial wood content results in shorter runout.
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Greater deposit wood content also results in shorter runout such that
enough wood actually stops the flow before it reaches the bottom of the ramp.
``Channel'' width is constant. Porosity is 0.3. Sediment
deposits before wood. The model debris flow reaches velocities similar
to those measured in the flume under similar conditions.
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Effect of stand age on landslide initiation and debris flow runout and
deposition:
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Aggregate boundaries for the trial watershed are shown at right.
Small blue lines represent aggregate outlets to the channel/valley network.
Nominal aggregate size is 1 ha.
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System driven with 10 yr. stochastic storm series, exponentially
distributed storm intensities and durations and inter-storm durations
(Eagleson, 1978):
mean storm intensity 1.7 mm/hr; mean storm duration 20 hrs.
(Benda and Dunne, 1997);
mean interstorm duration 5 days (Duan, 1996).
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Over time, trees grow. Trees also fall, where the number of tree falls
at a node is exponentially distributed and depends on the ratio of storm
intensity to root strength. Tree fall re-distributes wood among neighboring
nodes, e.g., to channel nodes from valley nodes.
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Channel/valley networks shown in profile above for various initial forest
ages. Line color represents deposit composition, and line thickness represents
deposit thickness. Each line is associated with the node at its upstream
end and connects that node to its downstream neighbor.
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Maximum deposit thickness and total sediment and wood volume output (i.e.,
leaving the basin) are plotted vs. initial forest age at right.
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For youngest stand, thickest deposits are near the outlet. Older stands
result in thicker, woodier deposits further upstream along the channel
network.
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Sediment and wood output with the 20 yr.-old stand are dramatically lower
than with the 10 yr.-old stand. Likewise, sediment output with the 40 yr.-old
stand drops to zero (zero is plotted at 100 on the logarithmic axis). With
older stands (but younger than 200 yrs.), outputs are greater. Outputs
with the 200 yr.-old stand are lowest of all.
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Discussion:
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The model results are intuitively reasonable and indicate a strong
coupling between the forest and landslides/debris flows. The sensitivity of the
failure threshold to root strength is a large part of that coupling, but
the effect of the forest on debris flow runout is also important.
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Forest age affects the landslide frequency and, thus, the volume of debris
entering the channel network through greater root strength with age.
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Forest age also affects debris flow runout length and composition. More
wood in the system leads to shorter runout lengths and, thus, greater storage
and woodier composition of deposits higher up in the network.
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The cumulative effect of forest age on sediment and wood yield is
nonlinear. In particular, modestly older forests result in dramatically lower
sediment and wood yield at the basin outlet. Another intriguing result is that the
yields are not monotonically decreasing with increasing age.
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In the model's present form, increased root strength is likely responsible
for most of the decrease in yield. But, given our present uncertainty and
the complexity of the processes involved, the forest-runout coupling may
be more important than our results indicate. Future work will focus on
this coupling.
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Data are needed to assess the model results. We plan to carry out our own
field study and incorporate existing data where possible. In addition,
we must develop appropriate measures to compare data and model results.
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The model results have important implications regarding forest management
practices. If we wish to explicitly manage the forest with landslide and
debris flow hazards in mind, then addressing the root strength-slope failure
coupling is not sufficient. We must also address the forest-runout coupling.
Managing only the hillslopes could actually result in less frequent but
more hazardous events if the network is not ``clogged'' with woody debris.
References:
Benda, L., and T. Dunne, 1997. Stochastic forcing
of sediment supply to channel networks from landsliding and debris flow,
Water Resources Research, 33(12), 2849-2864.
Dietrich, W.E., R. Reiss, M.-L. Hsu, and
D.R. Montgomery, 1995. A process-based model for colluvial soil depth and
shallow landsliding using digital elevation data, Hydrological Processes,
9, 383-400.
Duan, J., 1996. A coupled hydrologic-geomorphic
model for evaluating effects of vegetation change on watersheds, Ph.D.
thesis, Dept. of Forest Engineering, Oregon State University.
Eagleson, P.S., 1978. Climate, soil, and vegetation
2. The distribution of annual precipitation derived from observed storm
sequences, Water Resources Research, 14(5), 713-721.
Heimsath, A.M., W.E. Dietrich, K. Nishiizumi,
and R.C. Finkel, 1997. The soil production function and landscape equilibrium,
Nature, 388, 358-361.
Iverson, R.M., 1997. The physics of debris
flows, Reviews of Geophysics, 35(3), 245-296.
Sidle, R.C., 1991. A conceptual model of
changes in root cohesion in response to vegetation management,
J. of Environment Quality, 20, 43-52.
Sidle, R.C., 1992. A theoretical model of
the effects of timber harvesting on slope stability,
Water Resources Research, 28(7), 1897-1910.
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Last Modified: June 25, 1999
