While sailing off Mexico's Baja Peninsula recently, I saw a humpback whale breach and wondered whether that whale had ever been to Hawaii. But when I got home and looked up humpback migration patterns, I found myself tangled in a driftnet of statistics.

This isn't the fault of humpback whale researchers or the organizations publishing the reports. The facts are a maze because counting, tracking and observing these whales are such enormous tasks, biologists must do it in bits and pieces over periods of years.

The challenges these scientists face are staggering. First, humpback whales live in groups scattered throughout the Atlantic, Pacific, Indian and Southern oceans. As if that's not spread out enough, twice a year all these whales swim to different locations thousands of miles away.

Then there's the problem of counting animals that spend 90 percent of their lives underwater, diving to 700 feet for as long as 40 minutes. Add to that the political and philosophical differences of the countries within these whales' range and it's a wonder anyone has any numbers at all.

But whale researchers do have numbers. Some refer to the world population (estimated at 60,000, down from a pre-whaling estimate of 125,000) and some to the whales of a particular hemisphere. Other statistics pertain only to the humpbacks in one part of one group of one ocean, such as the whales that migrate to Hawaii.

Hawaii's humpback whales belong to a group called the North Pacific Stock, which includes all the humpbacks in the Pacific Ocean north of the equator. The most recent estimate of that population, derived from a 2004 through 2006 study involving 300 international researchers, is 18,000 to 20,000 whales.

Those numbers are more than 15 times the estimate in 1966, when international law banned whale hunting. At that time the North Pacific humpbacks had reached a low of about 1,200 individuals. Since a rough approximation of that stock before whaling began was 15,000, this group appears to be making a remarkable recovery.

Researchers divide the North Pacific Stock of humpbacks into three groups: Eastern, Central and Western. In summer all these whales feed in the cold waters of the North Pacific, but in winter they migrate to Mexico, Hawaii and Japan, respectively. Most North Pacific humpbacks migrate to the same place year after year, but a few occasionally switch breeding sites.

So although the odds were low that my Baja breacher had been to Hawaii, it's possible.

When it comes to food, though, these humpbacks don't roam. Regardless of where an individual spends the winter, it returns each summer to the same feeding grounds its mother first brought it to as a calf.

Of the North Pacific stock of humpbacks, about half winter in Hawaii. Researchers in airplanes counted 4,491 whales here in 2000, but this latest census means we now host 9,000 to 10,000 of these special visitors.

To see the North Pacific humpback whales' feeding and migration patterns, go to hawaiihumpbackwhale.noaa. gov/science/pdfs/splashinfosheet.pdf.

As I worked on this column, it became clear that gathering humpback whale data is about as hard as marine research gets.

The next chance I get, I'm going to thank a whale biologist.

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Susan Scott can be reached at http://www.susanscott.net.