1. Diego Arcas NOAA/PMEL University of Washington

2. Illustration of Deep Water Linearity

3. Assumptions in the Non-linear Shallow Water Equations Continuity Equation: X-momentum equation: Y-momentum equation: Z-momentum equation: Unknowns: u,v,w and p Any term in the equations containing products of the unknowns or their derivatives will cause non-linear behavior.

4. Non-linear Behavior

5. 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.

6. Characteristic Form of the 1D Non-linear Shallow Water Equations Riemann Invariants: Eigenvalues:

7. Characteristic Form of the 1D Non-linear Shallow Water Equations Eigenvalues: Typical Deep Water Values:

8. 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.

9. 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

10. Illustration of Deep Water Linearity

12. Linearity allows for the reconstruction of an arbitrary tsunami source using elementary building blocks

13. Unit source deformation Forecasting Method

14. West PacificEast Pacific Locations of the unit sources for pre-computed tsunami events. Forecasting Method

15. Unit source propagation of a tsunami event in the Caribbean Forecasting Method

16. Tsunami Warning: DART Systems

17. Forecasting Method: DART Positions

18. Forecasting Method: Inversion from DART

19. Forecasted Max Amplitude Distribution (Japan 2010)

20. Community Specific Forecast Models

22. Inundation Forecast Model Development

23. Tsunami inversion based on satellite altimetry: Japan 2010 Forecasting Challenges: Definition of Tsunami Initial Conditions

24. Forecasting Challenges: Definition of Tsunami Initial Conditions