Copyright 2009 by the American Geophysical Union.

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A tsunami hazard assessment for a model site can provide forecast guidance by determining in advance which subduction zone regions and tsunami magnitudes pose the greatest thread to the location. The validated forecast models, in combination with the forecast TSF database, provide powerful tools to address this long-term forecast.

Here, we apply our forecast modeling tools, including the previously described forecast models, to produce long-term forecast assessment for Hawaiian locations. 6197 tsunami scenarios in four different magnitudes, T_{Mw} 7.5, 8.2, 8.7 and 9.3, have been explored for this study. Modeled tsunami sources are detailed in **Table 4** and results are summarized in **Figure 12**. Figure 12 provides an overview of maximum amplitudes at offshore points from the TSFs (propagation results 1a–1d) and results of forecast model computations (forecast model results 2a–5d) for four Hawaiian locations, Nawiliwili, Honolulu, Kahului and Hilo. The forecast model results show the most dangerous tsunami source areas for a particular site and provide an overview of potential maximum amplitudes and arrival times.

**Table 4. Simulated tsunamis for the hazard assessment study.**

**Fig. 12. Bars in propagation results 1a–1d indicate η _{max} at four offshore locations at 4400–5000 m water depth for T_{Mw} 7.5 tsunamis, which are from the TSF database. Locations of the four offshore points are shown in Figure 2a. Here η_{max} at the coastal tide stations computed by the forecast models are plotted as bars at corresponding source locations in forecast model results 2a–5d for the T_{Mw} 7.5 (2a–2d), 8.2 (3a–3d), 8.7 (4a–4d), and 9.3 (5a–5d) magnitudes. Colors in forecast model results 2a–2d represent time of first tsunami arrival, t_{1}, which is the time of water level reaching 20% height of the first significant peak or trough. Colors in forecast model results 3a–3d, 4a–4d, and 5a–5d represent the difference in time between the arrival of the maximum elevation, t_{max}, and the first arrival, t_{1}.**

Bars in Figure 12 propagation results 1a–1d indicate the maximum amplitude, η_{max} at four offshore locations at 4400–5000 m water depth for the T_{Mw} 7.5 sources, which are from the TSF database. Locations of the four offshore points are shown in Figure 2a. The η_{max} computed by the high-resolution forecast models at the coastal tide stations are plotted as bars at corresponding source locations in Figure 12 for the T_{Mw} 7.5 (forecast model results 2a–2d), 8.2 (forecast model results 3a–3d), 8.7 (forecast model results 4a–4d) and 9.3 (forecast model results 5a–5d) magnitudes. Colors represent time of first tsunami arrival, *t _{1}*, which is the time of water level reaching 20% height of the first significant peak or trough. In Figure 12 forecast model results 3a–3d, 4a–4d, and 5a–5d colors represent the difference in time between the arrival of the maximum amplitude,

These results show an impressive local variability of tsunami amplitudes even for far-field tsunamis. The same source magnitude produces tsunami amplitudes that may be 5 times larger in Kahului than those in Honolulu. The location of the most "effective" source for a given location also differs from site to site. Even offshore tsunami amplitudes (Figure 12 propagation results 1a–1d) are not good indicators of the impact at a particular site—the intensities at tide stations (frames in lines 2 through 5) show quite different amplitude distribution. All these results illustrate the complexity of forecasting tsunami amplitudes at coastal locations. It is essential to use high resolution models in order to provide accuracy that is useful for coastal tsunami forecast.

To further investigate the transformations of tsunami amplitudes from offshore to the tide gauges, we have looked at the ratios of these amplitudes for each location. The ratio of the offshore and nearshore η_{max} for all computed scenarios are plotted for the four sites and the linear regression analyses were performed in **Figure 13**. To better illustrate the data trends, both the logarithmic and Cartesian coordinates were plotted with the same data sets. The logarithmic scales give a full picture of the wide range of values, while the Cartesian coordinates better illustrate the actual spread and trends of the data. In Figures 13e–13h, the red dots, which represent the T_{Mw} 7.5 tsunamis, are hardly seen due to the overlapping dots representing other magnitude scenarios. The solid black lines are the best fit to the data. The dashed black lines are the prediction bounds based on 95% confidence level. The results show: (1) The relationship between tide gauge maximum amplitude and offshore maximum amplitude appears to be complex and nonlinear in nature. (2) Larger amplitudes offshore do not necessarily produce larger amplitudes at tide gauges, and larger tsunami magnitudes may not produce larger waves either offshore, or at tide gauges. (3) The trends of offshore/tide gauge amplitudes are site specific. Different sites show different regression analysis curves. (4) The simple relationships obtained through regression analysis (Figures 13a–13d) are insufficient to provide warning guidance during an event. The 95% confidence interval is too wide to provide any certainty for the forecast accuracy.

**Fig. 13. Maximum computed water elevation at offshore deep water and coastal tide stations in (a–d) logarithmic and (e–h) Cartesian coordinates. Colors represent tsunami moment magnitudes. Solid
lines, the fits by regression analysis in logarithmic scale; dashed lines, the prediction bounds based on 95% confident level; R, square of the correlation; RMSE, root mean squared error; p _{0} and p_{1}, parameters.**

These results indicate that high-resolution tsunami models are essential for providing useful accuracy for coastal amplitude forecast. If the high-resolution tsunami nearshore dynamics is not included in the forecast procedures, the accuracy and the uncertainty of the amplitude forecast appear to be too high for practical guidance.

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