of 4
1
Geophysical Research Letters
Supporting Information for
Sediment Entrainment and Slump Blocks Limit Permafrost Riverbank
Erosion
Madison M. Douglas
1
, Kieran B. J. Dunne
1
, and Michael P. Lamb
1
1
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA.
Contents of this file
Figure S1
Table S1
Figure S2
Figure S3
Introduction
The supporting information includes a figure of the raw data and representative hydrograph
and water temperature timeseries fo
r the Yukon River at Stevens Village, AK
and Pilot Station,
AK
(Figure S1)
. We also include a supplemental table summarizing the variable inputs to the
model and their values for our base case
(Table S1)
. Total
bank erosion rates vary
in response
to changing empirical parameters in the thaw
-limited erosion coefficient of heat transfer
(Figure S2) and permafrost temperature and mass fraction ice (Figure S3).
2
Figure S1.
(
a
)
Daily average discharge for Stevens Village (USGS gage 15453500) from 1976-
2022 (gray) with calculated median daily discharge (blue). (
b
) Daily average water
temperature for Pilot Station from 1976
-2022 (gray), intermittent water temperature
measurements at Stevens Village gage from 1970
-2005 (black), and average annual daily water
temperature time series from combined datasets (blue). (
c
) Paired water discharge and water
depth measurements at Stevens Village gage (gray). Power law fit to data:
H=-
0.97Q
w
0.41
(blue).
(
d
) Paired water discharge and water velocity measurements at Stevens Village gage (gray).
Power law fit to data:
U=
-1.42Q
w
0.4
9
(blue).
Variable
Description
Value
Units
Source
ρ
b
bulk density of mineral
sediment
861
kg/m
3
Lininger et al., 2019
f
ice
mass fraction of ice for
mineral sediment
0.2362
kg/kg
Lininger et al., 2019
T
i
initial bank temperature
-
1
°C
Global Terrestrial
Network
for Permafrost
S
channel slope
0.00016
m/m
Clement, 1999
σ
S
Shear strength
50000
Pa
Arenson & Springman, 2005
σ
C
compressive strength
1.12
10
7
±4.1
10
6
Pa
Bragg and Andersland, 1981
σ
T
tensile strength
2.40
10
6
±0.2
10
6
Pa
Bragg and Andersland,
1981
3
D
50
Median grain size
1
.00
10
-3
m
A
dimensionless constant
0.0078
Lunardini et al., 1986
α
dimensionless constant
0.3333
Lunardini et al., 1986
β
dimensionless constant
0.927
Lunardini et al., 1986
κ
w
thermal conductivity of
water
0.6
W/m/°C
ν
kinematic viscosity of water
1.00
10
-6
m
2
/s
T
f
Fusion temperature for
water ice
0
°C
Pr
Prandtl number
10
Costard et al., 2003
g
gravitation acceleration
9.81
m/s
2
ρ
s
density of sediment
2765
kg/m
3
ρ
w
density of water
1000
kg/m
3
M
coefficient for entrainment
equation
2.5
10
-5
kg/m
2
/s
Partheneides, 1965
n
exponent for entrainment
equation
1
Partheneides, 1965
Table S1.
Numerical model variables and their values for the base case, with uncertainties
shown as ±1SD.
All references ca
n be found in the main text.
Figure S2
.
Contour plots of mean annual erosion rate
E
avg
(m/yr)
for changing dimensionless
coefficient (
A
) and exponent (
β
) in equation (2) to compute
E
thaw
.
E
avg
is
smoothed with a 2
-D
gaussian filter with 1SD = 0.05 and the modeled example case displayed as a star (*)
.
4
Figure S3
.
Contour plots of mean annual erosion rate
E
avg
(m/yr)
for changing permafrost
temperature (
T
i
, °C) and mass fraction ice (
f
ice
, dimensionless).
E
avg
is
smoothed with a 2
-D
gaussian filter with
1SD = 0.05 and the modeled example case displayed as a star (*)
. For
model runs with
f
ice
< 0.20, sand with a typical 40% volumetric porosity is expected to have
under-saturated pore
space. Therefore, we set a maximum
f
sed
= 0.80 for all model runs with
f
ice
< 0.20. The base case has
f
ice
= 0.2362, so we expect that bank sediments on the Yukon River
near Stevens Village are near saturation and have
f
sed
= 0.7638.
0
0.2
0.4
0.6
0.8
1
f
ice
-15
-10
-5
0
T
i
(
°
C)
E
avg
(m/yr)
5
10
15
20
25
30
35
50
100
500
1000