CHALLENGES IN OPERASTIONAL TSUNAMI FORECASTING
NEW AREAS OF RESEARCH
Diego Arcas, Chris Moore, Stuart AllenNOAA/PMELUniversity of Washington
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
Tsunami Generation
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~)(
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:
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:
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:
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
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.
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.
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
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
Illustration of Deep Water Linearity
Illustration of Deep Water Linearity
Linearity allows for the reconstruction of an arbitrary tsunami source using elementary building blocks
Unit source deformation
Forecasting Method
West Pacific East Pacific
Locations of the unit sources for pre-computed tsunami events.
Forecasting Method
Unit source propagation of a tsunami event in the Caribbean
Forecasting Method
Tsunami Warning: DART Systems
Forecasting Method: DART Positions
Forecasting Method: Inversion from DART
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
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
t1
t2
t4
t3
An uncombined connected solution is possible now.
DART 1
DART 2
EPICENTER
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
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
Forecasted Max Amplitude Distribution (Japan 2010)
Community Specific Forecast Models
Inundation Forecast Model Development
Tsunami inversion based on satellite altimetry: Japan 2010
Forecasting Challenges:Definition of Tsunami Initial Conditions
Forecasting Challenges:Definition of Tsunami Initial Conditions