diego arcas, chris moore, stuart allen noaa/pmel university of washington

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