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Mark Shwartz, News Service (650) 723-9296; e-mail:

Beware of leap year when predicting climate change, warns researcher

A word of warning to scientists studying climate change: Don't forget to factor leap year into your calculations. Otherwise, you will end up either overestimating or underestimating the pace of global warming, says Stanford researcher Raphael Sagarin.

Writing in the Dec. 6 issue of the journal Nature, Sagarin focuses his attention on recent climate studies documenting the early arrival of spring an important indicator of global warming. He points out that by ignoring leap year climate experts inadvertently have allowed statistical bias to creep into their analyses, resulting in false estimates of spring's actual arrival.

"A number of international studies have shown that spring is coming significantly earlier each year. The question is how much earlier," notes Sagarin, a postdoctoral fellow in biological sciences at Stanford's Hopkins Marine Station in Pacific Grove, Calif.


Early spring

Sagarin, who began studying climate change as a Stanford undergraduate in the mid-1990s, has become immersed in the field of phenology, which uses historical records of annual bird migrations, ice melts and other natural events to establish trends in global warming.

In October, he co-authored a study in the journal Science documenting the early arrival of spring in Alaska based on the Nenana Ice Classic a popular betting contest that awards cash prizes for predicting the exact time of the annual ice breakup on the Tanana River. After examining Ice Classic archives dating back 84 years, Sagarin concluded that, on average, Alaska's springtime thaw is occurring 5.5 days sooner than it did in 1917.

"While I was researching the Science study, I realized that a lot of these phenological surveys of spring events were based on the calendar date rather than on their timing relative to the vernal equinox," Sagarin says.


Vernal equinox

The vernal equinox marks the true arrival of spring. It occurs on March 20 or 21 when the sun is directly above the equator and day and night are of equal length.

In leap years, an extra day is added to February, so the vernal equinox appears to come a day later. As a result, the date of the calendar equinox and the true equinox diverge as the years progress. Over the course of a century, the average calendar year consists of 365.25 days (accounting for leap years), while the more accurate tropical year (the average time between successive vernal equinoxes) is roughly 365.2422 days.

"This difference causes the equinox to arrive about 0.78 days earlier on the calendar year over 100 years," Sagarin writes in Nature. "This means that a given calendar date in spring will occur further from the vernal equinox towards the end of any century. As a result, trends towards earlier spring will tend to be overestimated."


Significant bias

The magnitude of the statistical bias in some studies turned out to be as great as 10 percent, according to Sagarin. For example, had he strictly relied on calendar year data in his Ice Classic study, the results would have shown that spring in Alaska is arriving 6.2 days sooner, rather than the actual 5.5-day trend based on the more accurate tropical year.

While some short-term studies exaggerated the advance of spring, others using records dating back two or three centuries underestimated its arrival.

"All of the phenological studies I reviewed are essentially correct the signs of spring are definitely coming earlier, but not quite as early as we originally thought," observes Sagarin.

Most climate experts are predicting a sharp increase in global temperatures in the next 50 to 100 years, so the need for accurate data is more important than ever, he concludes.

"The discrepancy between calendar year data and vernal equinox data will continue to grow in the twenty-first century, because the spring equinox will continue to arrive earlier on the calendar until the year 2100," notes Sagarin. "Now is the perfect time to correct these reports."


By Mark Shwartz

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