PowerPoint Presentation

Challenges in operastional Tsunami forecasting

New areas of research

Diego Arcas, Chris Moore, Stuart Allen

NOAA/PMEL

University of Washington

NOAA

National Oceanic and Atmospheric Administration

Ocean andAtmosphericResearch

NationalWeatherService

PacificTsunamiWarningCenter

Alaska/WestCoast TsunamiWarningCenter.

NOAA Centerfor TsunamiResearch

Tsunami Generation

Cartoon showing tectonic stress on a subducting plate.

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Physical Characteristics of a Tsunami in Deep Water

• Maximum Amplitude, z: between a few cms and1.5 meters.

• Typical Wavelength: = 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)

Assumptions in the Non-linear Shallow Water Equations

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Continuity Equation:

X-momentum equation:

Y-momentum equation:

Z-momentum equation:

Hydrostatic Approximation:

Assumptions in the Non-linear Shallow Water Equations

Hydrostatic Approximation:

X-momentum equation:

Y-momentum equation:

Assumptions in the Non-linear Shallow Water Equations

We assume constant velocityprofiles for u and v along z

Now we use the surface kinematic boundary condition

And the bottom boundary condition

We have rewritten w interms of u,v and h= +d

Continuity equation:

Assumptions in the Non-linear Shallow Water Equations

Replacing the values of w on the bottom and at the watersurface in the depth integrated continuity equation andgrouping terms together we get:

plus the two momentum equations:

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

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Confirmation of the estimated values ofwavelength, amplitude and period of tsunamiwaves

Non-linear Shallow Water Wave Equationsseem to provide a good description of thephenomenon.

Assumptions in the Non-linear Shallow Water Equations

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Arcas & Wei, 2011, “Evaluation of velocity-relatedapproximation in the non-linear shallow water equations forthe Kuril Islands, 2006 tsunami event at Honolulu, Hawaii”,GRL, 38,L12608

Characteristic Form of the 1D Non-linear Shallow Water Equations

Riemann Invariants:

Eigenvalues:

Typical Deep Water Values:

Illustration of Deep Water Linearity

Illustration of Deep Water Linearity

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Linearity allows for the reconstruction of an arbitrarytsunami source using elementary building blocks

Unit source deformation

Forecasting Method

West Pacific

East Pacific

Locations of the unit sources for pre-computed tsunami events.

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Forecasting Method

Unit source propagation of a tsunami event in the Caribbean

Forecasting Method

Tsunami Warning: DART Systems

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Forecasting Method: DART Positions

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Forecasting Method: Inversion from DART

t1

t2

teq

t1

t2

t1

t2

teq

teq

t1

t2

Soft exclusion sources

Hard exclusion sources

Valid sources

Source Selection for DARTdata Inversion

DART

EPICENTER

DART data

t1

t2

t4

t3

Rupture length is constrained but aconnected solution is not possible at thispoint. Seismic solution is used.

DART 1

DART 2

EPICENTER

t1

t2

teq

t3

t4

teq

t1

t2

teq

t1

t2

teq

t1

t2

t4

t3

An uncombined connectedsolution is possible now.

DART 1

DART 2

EPICENTER

1 hr

3 hr

0.5 hr

2 hr

0 hr

0hr

1 hr

3 hr

2 hr

.5 hr

A partially combined connectedsolution is possible at this point.

DART 1

DART 2

EPICENTER

1 hr

3.5 hr

0.5 hr

2.5 hr

0 hr

0hr

1 hr

3.5 hr

2.5 hr

.5 hr

DART 1

DART 2

A fully combined and connected solution ispossible now.

EPICENTER

Forecasted Max Amplitude Distribution (Japan 2010)

Community Specific Forecast Models

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Inundation ForecastModel Development

Tsunami inversion based on satellite altimetry: Japan 2010

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Forecasting Challenges:

Definition of Tsunami Initial Conditions

Forecasting Challenges:

Definition of Tsunami Initial Conditions