Diego Arcas, Chris Moore, Stuart Allen NOAA/PMEL University 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:  = 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 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 velocity profiles for u and v along z Now we use the surface kinematic boundary condition And the bottom boundary condition We have rewritten w in terms 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 water surface in the depth integrated continuity equation and grouping 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 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 Riemann Invariants:Eigenvalues: Typical Deep Water Values:

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 PacificEast 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

t1t1 t2t2 t eq t1t1 t2t2 t1t1 t2t2 t1t1 t2t2 Soft exclusion sources Hard exclusion sources Valid sources Source Selection for DART data Inversion DART EPICENTER DART data

t1t1 t2t2 t4t4 t3t3 Rupture length is constrained but a connected solution is not possible at this point. Seismic solution is used. DART 1 DART 2 EPICENTER t1t1 t2t2 t eq t3t3 t4t4 t1t1 t2t2 t1t1 t2t2

t1t1 t2t2 t4t4 t3t3 An uncombined connected solution is possible now. DART 1 DART 2 EPICENTER

1 hr 3 hr 0.5 hr2 hr0 hr 1 hr3 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 hr2.5 hr0 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