“For this case, we had to pretty much base our forecast on one dot, because of the timing,” said Vasily V. Titov, a researcher at the Pacific Marine Environmental Laboratory in Seattle who developed one of the three models used by the warning center. In 2004, there were six tsunami buoys. Now there are 39.

The data from the one buoy was enough for the computer model to figure out that the tsunami was smaller and less destructive. At 6:24 a.m. Saturday in Hawaii, about five hours before the arrival of the tsunami there, the tsunami center put out a bulletin with predictions that the wave might reach four feet at Hilo, where the bay tends to amplify the waves, and much lower elsewhere.

“In general, all of the numbers were bigger initially and went down,” Dr. McCreery said. The waves at Hilo were a bit less than three feet.

Dr. Titov said his model predicted the wave heights fairly accurately. This time, there were no deaths, and the tsunami pushed waters, at most, only a few feet above normal.

“It looks like we nailed it, at least for U.S. coastlines,” Dr. Titov said.

But officials said the decision to order an evacuation in Hawaii, the first since 1994, was the right one given the uncertainties of the models.

“We’re still in the incipient stages of using these models to constrain our forecasts,” Dr. McCreery said. “There are still lots of improvements we need to make before we can rely on them totally for our decision making.” For one thing, the models do not provide estimates of how far off they might be.

“We had to do what we did, because there was too much uncertainty to say it was safe to not evacuate,” Dr. McCreery said.