Journal of Geophysical Research – Earth Surface
Supporting Information for
Recent topographic evolution and erosion of the deglaciated Washington Cascades
inferred from a stochastic landscape evolution model]
Seulgi Moon, Eitan Shelef , George E. Hilley
Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305
Contents of this file
Text S1
Figures S1 to S7
Additional Supporting Information (Files uploaded separately)
Tables S1
Introduction
The supporting information contains one text file (Text S1) that describes details of the model
discretization and 7 supplementary figures (Figures S1 to S7). One supplementary table (Table
S1) is included as additional supporting information. The figures provide additional information
on studied region, model parameter calibration, and simulation model results.
Text S1.
The spatial resolution and time step of the landscape evolution model are determined
by the spatial resolution of input datasets, the spatial and temporal domain of our model, the
computational time to run simulations, and assumptions about geomorphic transport laws.
Because we are modeling landscapes with large spatial extents (~140 × 130 km2) over long
timescales (~1 Myr), we used a relatively coarse spatial resolution DEM (100-m resolution) and a
long time step (100 yr) in the simulations to reduce the computation time. The 100-mresolution of the DEM is between the resolutions of available topographic and precipitation
products; topography was downsampled from a 30-m-resolution DEM, and mean annual
precipitation (MAP) was resampled from an 800-m-resolution dataset [PRISM, 2006]. The grid
cell size of 100 m × 100 m is within the range of most frequent landslide size [Hovius et al., 1997;
Stark and Hovius, 2001].
The temporal resolution of the model is determined by the spatial resolution of the
DEM and two assumptions about landslide GTLs. In scenario SD, we assumed that failed
rockslide material is evacuated during the model time step. In scenario SS, we assumed that a
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1-m thickness of soil was available for removal at each time step; in this case, a 1-m thick
volume of soil is produced and transported during each model time step. The longer time step
(>100 yr) is preferred given the large amount of available bedrock landslide material and the
potential rate of soil production (~0.3 mm/yr). However, the maximum time step is limited in
the implementation of landslide GTLs.
For each topographic grid cell, we calculated the probability of failure within a time step
by multiplying the failure density P (landslides m–2 yr–1) by the topographic cell size and the
time interval. For example, for a topographic grid cell size of 100 m × 100 m and P = 1.0 × 10–6
m–2 yr–1, the failure probability will exceed 1 at time intervals of >100 yr. If the number of
topographic grid cells with failure probabilities exceeding 1 is large, and if landslide occurrences
are synchronous, then the spatial variations of the occurrences and the interactions between
occurrences and other postglacial surface processes cannot be resolved in our model
simulation. In this circumstance, a time step of <100 yr is required.
To determine a time step value that takes into account both the spatial resolution of
datasets and model assumptions, we performed an additional simulation with a time step of
1000 yr with parameters of scenario SD1. Both simulations show similar distributions of 5 kyraveraged denudation rates and response timescales (see Figures 6 and S7, respectively).
Denudation rates averaged over 1000-yr time intervals (gray points, Figures 6 and S7) show less
variation than those averaged over 100-yr time intervals. While our model uses a relatively
coarse spatial resolution and long time step, such approximations are necessary to resolve a
mountain-scale landscape response over a millennial-year timescale. For our study, we use a D8
routing scheme for simplicity, computational efficiency, and consistency between the flow
routing schemes used for drainage area calculation and the calculation of slope and failure
index in landslide GTL. This scheme is also preferred in situation where the hillslope extent and
channel width are smaller than or comparable to DEM resolution (Shelef and Hilley 2013), such
that dispersing flow through a multiple-flow-direction routing scheme such as Dinf is likely to
unrealistically shift flow out of channels and into neighboring hillslopes. In addition, the basinaveraged failure index using D8 and Dinf vary < 3% and show a strong correlation (R2=0.999), so
the impact of using different routing schemes on calibrating failure density will be minimal in
our case. However, in small-scale applications of our model, the spatial resolution of input
datasets, the time step of the simulation, and the flow routing scheme would require
refinement, according to the purposes of the study. For example, we discussed how single grid
cell failures can generate a wave of incision by landslides by increasing upstream slope angles.
Possibly, the occurrence of multiple failures on low-slope surfaces would accelerate those
propagations and produce increased denudation rates during initial time steps.
Boyd, T. G., and L. M. Vaugeois (2003), On the development of a statewide landslide inventory,
paper presented at Geological Society of America, Abstracts with Programs.
Hovius, N., C. P. Stark, and P. A. Allen (1997), Sediment flux from a mountain belt derived by
landslide mapping, Geology, 25(3), 231-234, doi:10.1130/00917613(1997)025<0231:sffamb>2.3.co;2.
PRISM (2006), United States Average Monthly or Annual Precipitation, 1971 - 2000, edited, The
PRISM Group at Oregon State University, Corvallis, Oregon, USA.
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Reiners, P. W., T. A. Ehlers, J. I. Garver, S. G. Mitchell, D. R. Montgomery, J. A. Vance, and S.
Nicolescu (2002), Late Miocene exhumation and uplift of the Washington Cascade Range,
Geology, 30(9), 767-770.
Reiners, P. W., T. A. Ehlers, S. G. Mitchell, and D. R. Montgomery (2003), Coupled spatial
variations in precipitation and long-term erosion rates across the Washington Cascades, Nature,
426(6967), 645-647.
Shelef, E., and G. E. Hilley (2013), Impact of flow routing on catchment area calculations, slope
estimates, and numerical simulations of landscape development, Journal of Geophysical
Research: Earth Surface, 118(4), 2105-2123, doi:10.1002/jgrf.20127.
Stark, C. P., and N. Hovius (2001), The characterization of landslide size distributions,
Geophysical Research Letters, 28(6), 1091-1094, doi:10.1029/2000GL008527.
Figure S1. Map of uplift and precipitation rates. a) The interpolated map of long-term
uplift rates using A-He ages [Reiners et al., 2002; Reiners et al., 2003]. b) The map of
mean annual precipitation from 1971 to 2000.
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Figure S2. a) Geometric construction of landslide thickness d for scenario SD. The
elevation before and after slope failure, Z and Zf, are calculated based on geometry of
topographic slope (S) and maximum stable failed slope (Sf) with horizontal distance x.
b) Probability distribution of slope from landslides from Boyd and Vaugeois, [2003].
Figure S3. Joint probability density functions of model parameters from scenario SS.
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Figure S4. The evolution of denudation rates from postglacial processes based on
scenario SS1.
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Figure S5. The temporal evolution of denudation rates from postglacial processes based
on scenario SD2.
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Figure S6. The spatial distributions of time-averaged denudation rates over 0-40 kyr, 4080 kyr, and 80-120 kyr for a-c) SD1 and d-f) SS1 in the extent of model domain. Warm
colors, drawn on a shaded relief map at the initial time (0, 40, and 80 kyr), represent
higher denudation rates.
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Figure S7. The evolution of denudation rates from postglacial processes based on SD1
with 1000 yr time step.
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