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Numerical schemes of the first and second order of approximation introduce numerical distortion when the wave propagation over a long distance is investigated. To alleviate this problem, the fourth-order leapfrog scheme is constructed. The standard leapfrog method is based on the truncated Taylor series expansion which depicts an error proportional to the second-order terms. In the proposed method the numerical solution is corrected for these terms. The space and time corrections work well in diminishing numerical dispersion and dissipation.

Storm surges in the Beaufort Sea present a severe problem for navigation as well as for offshore oil drilling activities. Influence of ice cover on storm surges in the Beaufort Sea is examined making use of a numerical model as well as a set of observations. The automated shallow-water model of Henry has been modified to incorporate ice cover and is adapted to the Beaufort Sea. The leading edge of the permanent ice is calculated from the loci of identifiable points. Generalized similarity theory is employed to compute wind stresses. Simulations are made using model-predicted ice concentrations and observed ice concentrations. Ice motion is relatively small in units of model grid distance (approximately 18 km) during surges. Spherical effects are important and should be included in future adaptations of the model. Comparison of the computed surges with observed surges for eight different events showed reasonable agreement.

Possible tsunamis in the Pacific Ocean, especially in its northeastern part, are discussed in relation to a predicted major earthquake in the Shumagin Seismic Gap (located in the eastern part of the Aleutian Island Chain) and to a major eruption of the St. Augustine volcano in Cook Inlet, Alaska. The deep-water propagation of the tsunami generated in the Shumagin Gap is simulated through the use of a spherical polar coordinate grid of the approximate size of 14km. The tsunami generated by the St. Augustine volcano is studied through the fine mesh grid confined to the Cook Inlet only. The numerical models were calibrated against historical tsunami data. The properties of the tsunami signal are described by the maximum amplitude which occurs in the tsunami record. This allows us to single out the direction along which a maximum tsunami is to be expected.