(Please give credit to this blog site if you use the numbers posted below!)
First, let me summarize the method. Professor Michael McIntyre of the University of Cambridge calculated the power in a tsunami using Bernoulli's theorem, and concluded that under certain conditions the power in a tsunami is about 1 megawatt per meter of shoreline, or 1 gigawatt per kilometer. The conditions are that the tsunami has a height of 1 meter in the open ocean, a velocity of 220 meters per second. I used these data directly and assumed a similar power, then estimated the length of shoreline attacked (one-half of the east coast of Honshu) and the duration of the tsunami (100-1000 seconds). The model applies to tsunamis on the open ocean.
There are still not a lot of data available, but the velocity of 220 meters a second for the speed of the tsunami is in the right ballpark to account for the time between the earthquake and the time that it took for the tsunami to reach the coast (30-60 minutes). The major uncertainty here is the height of the tsunami on the open ocean. I used the value of 1 meter that is typically used for tsunamis (because they are typically not even noticed on the open ocean). There were two ocean-bottom sensors in place that measured a height of 7 meters (Maeda, Takuto et al., Earth Planets Space, 63, 2011, in press) where the water was 1618 m and 1013 m deep respectively, and so I'll use a new value of 7 meters for the open-ocean height of the tsunami.
McIntyre's calculation of the power in the tsunami was based on an ocean depth of about 4.5 kilometers--deep open ocean. In order to make my calculation internally consistent, I need to use shallower depth of, say 1.5 kilometers.The power, as calculated by McIntyre, is proportional to the depth to the three-halves power.
The height of the tsunami comes into the calculation as h-squared; the depth of the ocean as a square root. Thus, the smaller ocean depth would reduce the power by a factor of 1.7 (sqrt 4.5/2) and the greater height of the tsunami would increase it by a factor of 49 (7 squared). The combined effects cause an increase of 28.8 in the power (let's round it up to 30).
Please see reader comments!