diego arcas, chris moore, stuart allen noaa/pmel university of washington
TRANSCRIPT
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CHALLENGES IN OPERASTIONAL TSUNAMI FORECASTING
NEW AREAS OF RESEARCH
Diego Arcas, Chris Moore, Stuart AllenNOAA/PMELUniversity of Washington
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NOAA National Oceanic and Atmospheric Administration
Ocean and Atmospheric Research
National Weather Service
Pacific Tsunami Warning Center
Alaska/West Coast Tsunami Warning Center.
NOAA Center for Tsunami Research
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Tsunami Generation
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Physical Characteristics of a Tsunami in Deep Water
• Maximum Amplitude, z: between a few cms and1.5 meters.
• Typical Wavelength: L = 300 km (period ~ 600 s-3000 s)
• Propagation speed: Speed depends on the ocean depth, H.
In practice: H=5 Km, v=220 m/s (~=800 Km/h)
gHk
vkHgkTanh kH 0~)(
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x
p
z
uw
y
uv
x
uu
t
u
1
y
p
z
vw
y
vv
x
vu
t
v
1
gz
p
z
ww
y
wv
x
wu
t
w
1
Assumptions in the Non-linear Shallow Water Equations
gz
p ztyxggdztzyxp
z
),,(),,,(
0
z
w
y
v
x
uContinuity Equation:
X-momentum equation:
Y-momentum equation:
Z-momentum equation:
Hydrostatic Approximation:
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x
p
xg
1
Assumptions in the Non-linear Shallow Water Equations
y
p
yg
1
xg
z
uw
y
uv
x
uu
t
u
yg
z
vw
y
vv
x
vu
t
v
ztyxggdztzyxpz
),,(),,,(
Hydrostatic Approximation:
X-momentum equation:
Y-momentum equation:
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0
z
w
y
v
x
u
Assumptions in the Non-linear Shallow Water Equations
0
ddd
dzz
wdz
y
vdz
x
u0
ddd
dzz
wdz
y
vdz
x
uWe assume constant velocity profiles for u and v along z
0),,(),,(
dzyxwzyxwdy
vd
x
u
Now we use the surface kinematic boundary condition
yv
xu
tzyxw
),,(
And the bottom boundary condition
y
dv
x
dudzyxw
),,(We have rewritten w in terms of u,v and h= h+d
Continuity equation:
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0
z
w
y
v
x
u
Assumptions in the Non-linear Shallow Water Equations
Replacing the values of w on the bottom and at the water surface in the depth integrated continuity equation and grouping terms together we get:
0
y
vh
x
uh
t
h
plus the two momentum equations:
x
dg
x
hg
z
uw
y
uv
x
uu
t
u
y
dg
y
hg
z
vw
y
vv
x
vu
t
v
0
x
uh
t
h
x
dg
x
hg
x
uu
t
u
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Assumptions in the Non-linear Shallow Water Equations
-Long wavelength compared to the bottom depth.
-Uniform vertical profile of the horizontal velocity components.
-Hydrostatic pressure conditions.
-Negligible fluid viscosity.
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Assumptions in the Non-linear Shallow Water Equations
Confirmation of the estimated values of wavelength, amplitude and period of tsunami waves
Non-linear Shallow Water Wave Equations seem to provide a good description of the phenomenon.
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Assumptions in the Non-linear Shallow Water Equations
Arcas & Wei, 2011, “Evaluation of velocity-related approximation in the non-linear shallow water equations for the Kuril Islands, 2006 tsunami event at Honolulu, Hawaii”, GRL, 38,L12608
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Characteristic Form of the 1D Non-linear Shallow Water Equations
0
x
uh
t
h
Riemann Invariants:
ghup 2
x
dg
x
hg
x
uu
t
u
xxt gdpp 1
xxt gdqq 2
ghuq 2
Eigenvalues:
ghu 1
ghu 2
Typical Deep Water Values:
sec/2.0 mu
sec/220mgd gd 21
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Illustration of Deep Water Linearity
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Illustration of Deep Water Linearity
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Linearity allows for the reconstruction of an arbitrary tsunami source using elementary building blocks
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Unit source deformation
Forecasting Method
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West Pacific East Pacific
Locations of the unit sources for pre-computed tsunami events.
Forecasting Method
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Unit source propagation of a tsunami event in the Caribbean
Forecasting Method
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Tsunami Warning: DART Systems
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Forecasting Method: DART Positions
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Forecasting Method: Inversion from DART
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t1
t2
teq t1 t2
t1t2teq
teq t1 t2
Soft exclusion sourcesHard exclusion sourcesValid sources
Source Selection for DART data Inversion
DART
EPICENTER
DART data
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t1
t2
t4
t3
Rupture length is constrained but a connected solution is not possible at this point. Seismic solution is used.
DART 1
DART 2
EPICENTER
t1 t2teq
t3 t4teq
t1 t2teq
t1 t2teq
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t1
t2
t4
t3
An uncombined connected solution is possible now.
DART 1
DART 2
EPICENTER
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1 hr
3 hr
0.5 hr 2 hr0 hr
0 hr
1 hr 3 hr
2 hr
.5 hr
A partially combined connected solution is possible at this point.
DART 1
DART 2
EPICENTER
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1 hr
3.5 hr
0.5 hr 2.5 hr0 hr
0 hr
1 hr 3.5 hr
2.5 hr
.5 hr
DART 1
DART 2
A fully combined and connected solution is
possible now. EPICENTER
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Forecasted Max Amplitude Distribution (Japan 2010)
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Community Specific Forecast Models
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Inundation Forecast Model Development
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Tsunami inversion based on satellite altimetry: Japan 2010
Forecasting Challenges:Definition of Tsunami Initial Conditions
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Forecasting Challenges:Definition of Tsunami Initial Conditions