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A robust numerical model to simulate propagation and runup of tsunami waves in the framework of non-linear shallow water theory is developed. The numerical code adopts a staggered leapfrog finite-difference scheme to solve the shallow water equations formulated for depth-averaged water fluxes in spherical coordinates. A temporal position of the shoreline is calculated using a free-surface moving boundary algorithm. For large scale problems, the developed algorithm is efficiently parallelized employing a domain decomposition technique. The developed numerical model is benchmarked in an exhaustive series of tests suggested by NOAA. We conducted analytical and laboratory benchmarking for the cases of solitary wave runup on simple beaches, runup of a solitary wave on a conically-shaped island, and the runup in the Monai Valley, Okushiri Island, Japan, during the 1993 Hokkaido-Nansei-Oki tsunami. In all conducted tests the calculated numerical solution is within an accuracy recommended by NOAA standards. We summarize results of numerical benchmarking of the model, its strengths and limits with regards to reproduction of fundamental features of coastal inundation, and also illustrate some possible improvements.

We simulated tsunami propagation for several scenario slip distributions for the 1938 MW 8.3 earthquake along the Alaska Peninsula and compared these to the observed records at Unalaska/Dutch Harbor and Sitka. The Sitka record is sensitive to the depth of slip but not the along‐strike location and is fit best by slip at shallow depth. The Unalaska record is sensitive mainly to the along‐strike location of slip and is fit best by slip that is concentrated in the eastern part of the presumed 1938 rupture zone. The tsunami data show that the actual 1938 earthquake rupture zone was likely ∼200 km in length or shorter and had no slip near the Shumagin Islands or in the 2020 Simeonof earthquake's rupture zone. The rupture models that best predict the 1938 tsunami lie within the region of high present day slip deficit inferred from GPS.

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