FY 2007 Empirical orthogonal function in tsunami research Burwell, D., and R. Weiss In AGU Fall Meeting 2006, American Geophysical Union, San Francisco, 11-15 December 2006, T23A-0476 (2006) Atmospheric and oceanographic data are successfully analyzed with the help of empirical orthogonal functions (EOF). Mathematically, they were derived to the reduce the number of variables that explain most of the observed variance of a data set. This is achieved by linear combination of the original variables. They are also used to extract individual modes of variability from a data set. Furthermore, it is possible to examine the spectrum of the covariance matrix that accounts for the fraction of the total variance of a single mode. We report on a study focusing on near-shore evolution of tsunami waves. EOFs are applied to a modeled wave pattern in artificial and real coastal geometries, which represent bights, bays and harbors. Furthermore, tsunamis of different deep-water wave amplitude and frequency are considered. We can show that these different geometries respond differently to tsunami waves of different amplitudes, but still show characteristic behavior of the modes within each geometric category. EOFs have other uses in tsunami research and are not only capable of extracting modes for a physical interpretation of the wave pattern with time but can also be utilized in the identification of developing computational instabilities, the enhancement in the comparison of the model with data or with another model, and general insights into the behavior (of noise) in numerical computations, among others. The identification of developing numerical instabilities is possible because the instabilities start in one grid cell, oscillate, and spread out which result in a characteristic mode which is different from tsunami-related modes. The comparison with data can be improved by using EOFs to identify areas (patches) in coastal areas that behave similarly through time. The time series at the gauge point in the model could be located in a less than optimal place compared to the real gauge location, meaning that the water level fluctuations around the gauge point in the model might could belong to a different tsunami characteristic response patch when compared with the actual gauge position. In the same vein, the EOF can also show the sensitivity of the location of the gauge grid cell in the model for a data to model comparison. The different patches of an EOF also contribute to a more detailed comparison of tsunami evolution using different computer codes because of the sensitivity of the EOFs. The noise can be studied in higher ranks of modes and can be compared to the lower modes that contain the tsunami signal. EOFs applied to near-shore tsunami evolution represents another useful tool to analyze, check reliability and compare model results with real measurements. Methods such as the pure comparison of time series or spectral analysis tend to be one dimensional in space, and plots of the maximum wave elevation integrated over time have obvious drawbacks. The future will show if EOFs are able to satisfactorily enhance the analysis of tsunami. Feature Publications | Outstanding Scientific Publications Contact Sandra Bigley | Help
