Diego Arcas NOAA/PMEL University of Washington

Illustration of Deep Water Linearity

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.

Non-linear Behavior

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.

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

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

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

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

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