Happy Pi Day: How the infinite number is used in weather

Theories regarding the relationship of a circle’s circumference to its diameter are believed to have developed during the time of the ancient Babylonians and Egyptians, nearly 4,000 years ago. More accurate calculations involving pi were made public by Greek philosopher Archimedes around 200 B.C.

Forecasters rely on complex numerical weather prediction models to forecast weather patterns accurately.

There are often improvements, such as an upgrade to the High-Resolution Rapid Refresh (HRRR) model to HRRR version 4 or the development of an AI-generated weather forecast.

NOAA scientists said these advancements would not be possible without the mathematical constant of pi.

Pi is the ratio of a circle’s circumference to its diameter. Regardless of the circle's size, the ratio always equals an infinite number that most people round to 3.14. We won't attempt to write out the numerical sequence that goes beyond hundredths. 

According to Guinness World Records, a university student in India memorized pi to at least 70,000 decimal places. The group said recalling all the digits took Rajveer Meena nearly ten hours.


How pi is used in meteorology

Numerical weather prediction models rely on knowing that the Earth is a globe and not flat – one of the first instances of pi being of actual use to weather observers.

If pi failed to exist, scientists said that modeling would also be vastly different because the constant is used to understand everything from the size of water droplets to the scattering of sunlight by clouds.

Since pi is a constant, many National Weather Service meteorologists run their day without thinking about the figure, but it does provide an important foundation for modeling.

"These meteorologists look at all of the model guidance to help them understand the developing weather situation, and blend this with their education and extensive training to formulate a picture on what to expect," said David Turner, a senior scientist at NOAA’s Global Systems Laboratory. "Some models, like the HRRR, provide short-range predictions (i.e., out to 48 hours) but at a very high spatial grid (3 km or nearly 2 miles). Other models, like the GFS, provide medium-range predictions (i.e., out to 14 days) at a coarser spatial grid (13 km or about 8 miles)."



Celebrating Pi Day

Pi Day, observed on March 14th, celebrates the mathematical constant. 

The day also happens to be Albert Einstein’s birthday – one of the most influential scientists but an unlikely celebrator of the special day. Einstein lived most of his life in countries that use the date format that places the day before the month (dd/mm/yyyy), meaning March 14 would be known as 14/03 and not how it appears in the U.S. as mm/dd/yyyy or 03/14.

In addition to being an irrational number, pi can also lead you to savings, with numerous restaurants and businesses that offer deals on March 14. Many pizzerias, dessert shops and food chains have deals that sell items for $3.14 in commemoration of the day.