  In this paper we describe a general framework for incorporating tidal
uncertainty into probabilistic tsunami hazard assessment and propose the
Pattern Method and a simpler special case called the $\Delta t$ Method as
effective approaches. The general framework also covers the method developed by
Mofjeld et.al in 2007 that was used for the 2009 Seaside, Oregon probabilistic
study by Gonzalez et.al. We show the Pattern Method is superior to past
approaches because it takes advantage of our ability to run the tsunami
simulation at multiple tide stages and uses the time history of flow depth at
strategic gauge locations to infer the temporal pattern of waves that is unique
to each tsunami source. Combining these patterns with knowledge of the tide
cycle at a particular location improves the ability to estimate the probability
that a wave will arrive at a time when the tidal stage is sufficiently large
that a quantity of interest such as the maximum flow depth exceeds a specified
level.
