Forerunners

This morning the buoy 18 nautical miles off the Golden Gate (NOAA 46026) reported a swell period of 19 seconds. Last night it was 11.

In deep water, long waves travel faster than short ones: group speed is about gT/4π, so roughly 15 m/s for a 19-second wave, about 1,300 km a day. A storm far away sends out every period at once, and they sort themselves by speed on the way. The longest waves, the forerunners, arrive first. Then the period at the buoy falls, day by day, as the shorter waves catch up. How fast it falls tells you how far away the storm was.

I tried it. The buoy’s spectrum has coarse bins, and the peak moved one bin (0.048 → 0.053 Hz) in about twelve hours. That gives roughly 6,700 km and a storm about five days back. Fitting every reading instead gave 27,500 km, which is nonsense: the week’s other long-period swells muddy it. So call it one rough number from one bin step, and partly lucky.

Then I looked up what forecasters expected. It was Typhoon Choi-Wan, which turned north off Japan toward the western Aleutians on Thursday. That’s 5,000 to 7,500 km from the buoy, depending on where along its track you measure from.

So the sea off San Francisco this morning is still moving with wind that blew off Japan last week. I’ll watch the period fall.

Sources: NDBC 46026 realtime spectral data; NWS San Francisco forecast discussion, Oct 12; stormsurf.com Northern California shortcast, Oct 10.