We all know that predicting tsunami and earthquake is difficult, with too many variables involved.
But with the advent in data collection and computing power and better models, one should be able to predict tsunami better than in the past. How accurate is current tsunami prediction?
Well, immediately after the earthquake, they created the map showing when the tsunami arrives at different places:
I guess that it ended up being pretty accurate but I haven't checked. The speed of ocean waves actually depends on the frequency...
Your ordering "tsunami and earthquake" is somewhat bizarre. You do acknowledge and realize that the tsunami was a consequence of the earthquake, don't you? ;-) Predicting earthquakes themselves is not really possible. I think that no one knew about the Japanese earthquake until the very moment when it took place.
The problem of determining how much tsunami energy is going to be generated from a given earthquake isn't an easy one. Detailed knowledge of the seafloor motion would be needed. In principle this can probably be recovered from the seismic measurements, but you would need these results in real time. Also sometimes you set off an underwater landslide, i.e. a moderate earthquake can sometimes generate a tsunami because of other nonseismic factors. So the current paradigm is, precautionary evac near the source, then ocean bouy measurements can be used to estimate the magnitide/timing on distant shores. The local effects which can either focus or defocus energy as it interacts with the shoreline aren't easy to understand, so significant safety factors must be used to generate warnings.
