# coastal

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```					 Predictive Coastal Erosion Modeling
for Teshekpuk Lake Special Area

Tom Ravens (Univ. of Alaska, Anchorage)
with
Joel Schmutz, Ben Jones, Chris Arp (USGS, Anchorage)
Smith

Harrison
Bay
International Migratory Bird
WHY? and Subsistence Value
Thermo-erosional niche at Dalton Wellhead
Conceptual Model of Coastal Erosion
1. Thermo-erosional                        2. Niche growth
niche
active layer                                 active layer

bluff                                      bluff

Thermo-erosional
niche                                      Niche growth

3. Block collapse/                         4. Erosion of fallen
slump                                      block and sediment
dispersion
active layer                                 active layer

bluff                                       bluff
Mathematical models of thermo-erosional niche growth
(Kobayashi 1985)

heat used
to melt                      cooler       “warm”
water    q    water
ice

Rate of niche growth/erosion (m/yr) = dxm/dt = C H3/4(Ta-Tm)

where C is a constant (including latent heat of fusion),
H is wave height,
Ta is ambient water temperature, and
Tm is the melting temperature.
Model of rate of retreat of frozen
bluff (Kobayashi et al. 1999)

lc

Rate of retreat (m/year) = lc hc (Ta-Tm) /[Lc(Hc-Bc)]
where hc = convective heat transfer coef. = C2 H

Or, …. rate of retreat = C3 H (Ta-Tm)
Conventional coastal engineering approach
(Without accounting for permafrost melting)

  Cross-shore (offshore) sediment
transport will result if the beach profile is
not in equilibrium with the wave climate
and the sediment grain size

 Transport will be related to the wave
energy flux, F

F = E Cg = 1/8 ρ g H2 (gh)1/2 ~ H2.5
Our approach
• Assume an erosion rate (ER) expression:
ER = C Hn (Ta-Tm)

• Use measured erosion rates (from 1955-1979 and 2002-2007),
and data on H and Ta (from those two periods) to calibrate
model (i.e., determine “best fit” C and n)

• Use the model and projected H and Ta (for 2045) to estimate
future erosion rates
SWAN wave modeling
• Model accounts for wind generation,
refraction, breaking, and energy exchange
between frequencies
• Model was operated in quasi-steady mode,
using wind data from Barrow
• Extent of open water in four open water
months was determined from sea ice data
Example Beaufort
Sea Ice Data

Study site
Bathymetry for wave model
depth
Effective    [m]
Effective
ice edge         ice edge
October          October
1955-1979        2002-2007
latitude

study site
Barrow
longitude
SWAN-calculated wave height     wave
height
(12 m/s NE wind, Oct 2002-2007)    [m]

study site
Regional temperature increase in West Beaufort Sea 1970-2007

4

2
temp
0
[C]
-2

1960     1980      2000

From Steele et al. 2008
Nearshore/offshore
long-term
temperature differential

From Steele et al. 2008
Monthly average Prudhoe Bay
temperature (1991-1994)
6

5

4
temperaute (C)

3

2

1

0
July   Aug   Sept   Oct
-1
Assumed temperatures used in
erosion rate model
6
5
4
Water temperature (C)

3
2                            1955-1979
1                            2002-2007

0
Jul   Aug   Sep   Oct
-1
-2
-3
Increasing wind speed in 2002-2007

0.6

0.5
fraction of month

0.4

0.3
1955-79
2002-2007
0.2

0.1

0

2       7         12           17   22
wind speed (m/s)
Study site:   North of Lake Teshekpuk (70 53’ N, 153 52’ W)

Erosion rate: 5.3 ± 0.5 m/yr (1955-1979)
7.4 ± 0.6 m/yr (1979-2002)
13.0 ± 1.0 m/yr (2002-2007)
Model Calibration and Results
• Erosion rate = 11.3 H 2.6 (Ta-Tm)                                                                  [m/yr]
60

50              Erosion rate = 2.52 x 10-24 e0.0284 t
erosion rate (m/yr)

40

30

Model
20                                                                              calculation

10

Measured data
0
1960   1970   1980        1990         2000            2010   2020   2030   2040       2050
time (year)
Projection of cumulative erosion
1400

1200

1000
cummulative erosion (m)

800

600

400

200

0
2005   2010   2015   2020   2025      2030       2035   2040   2045   2050   2055
time (year)
Variation of erosion rate with month

0.5

0.45

0.4

0.35
erosion rate (m/mo.)

0.3

0.25                           1955-79
2002-7
0.2

0.15

0.1

0.05

0
Jul   Aug   Sep   Oct
Conclusions
• The erosion rate is likely to increase
significantly in the coming years
• The erosion rate on the Beaufort Sea coast by
Drew Point may increase to about 50 m/yr by
2045
• The erosion rate went as H2.6 but the
dependence on H might be reduced if water
level was explicitly accounted for by the model
Future work
• Extend erosion projections throughout study site (Smith Bay
to Harrison Bay).
• Develop a more mechanistic or physics-based accounting of
the erosion process.
– Account for niche growth, erosion of fallen block, dispersal
of sediments
– Include additional environmental variables (e.g., bluff
height, soil ice content, soil grain size, beach
elevation/slope, sea level rise)
– Storm-surge modeling
Future work (continued)
• Develop a better understanding of wave
generation and propagation in ice floes.
• More precise accounting of historic
temperature using original data
• More precise projection of future ice and
temperature conditions (if possible)
Evolution of a North Slope barrier island
(Narwhal Island, North Arctic Alaska) 1955-2007
Thomas M. Ravens and William Lee
University of Alaska, Anchorage
2007   1990   1955   Westward movement
~ 5 m/yr, 1955-1990
~ 24 m/yr, 1990-2007
Questions?

```
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