What is the heat index? What you should know about metrics during a heatwave

Over the last few days, you may have seen or heard a lot of mentions about a measure of discomfort called the heat index, which is designed to measure how hot the air actually feels based on temperature and humidity.

You may also have noticed that the heat index is a higher number than the temperature – sometimes impressively, oppressively higher. For example, as I write these words, the temperature in Central Park is 98°, but the heat index is 105. Basically, it feels hotter when the humidity is higher because more moisture in the air means less sweat evaporating from the skin.

But what exactly is the heat index and how did “they” figure it out?

It turns out that the heat index is simply a more computationally intensive variant of the “It’s not the heat, it’s the humidity” maxim, where if T is the temperature and H is the relative humidity, the maxim looks like this:

“It’s not just the heat, it’s (T × 2.049) + (H × 10.143) – (T × H × 0.225) – (T² × 0.007) – (H² × 0.055) + (T² × H × 0.001) + (H² × T × 0.001) – (T² × H² × 0.000002) – 42.379.”

And how, you may ask, did they come up with this? We asked the author of the equation. His name is Lans Rothfusz, he is a retired National Weather Service meteorologist and recipient of the 2014 Operational Achievement Award from the National Weather Association.

Mr. Rothfusz, 66, said he developed the heat index equation in 1990 when he was “a punk intern” at the Weather Service’s Southern Region headquarters in Fort Worth.

Lans Rothfusz said he was a “punk intern” at the National Weather Service when he derived the equation for the heat index.Credit…via the National Oceanic and Atmospheric Administration

He said he was merely standing on the shoulders of a giant of heat measurement: an Australian textile engineer named Robert G. Steadman, who in 1979 published a paper entitled “The Assessment of Sultriness. Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science.”

Dr. Steadman died in 2022, but his daughter Jennifer Steadman said Thursday that he developed an apparent temperature scale because he was a competitive runner who had to figure out how to dress during training and found existing temperature models “totally inadequate.” He created a chart that took many variables into account. All Mr. Rothfusz did was use a mathematical technique called multiple regression analysis to develop an equation that roughly yields the Steadman diagram.

In his 1990 paper for the Weather Service, Mr. Rothfusz listed some of the Steadman humidity parameters that go into the equation, including convection from the skin surface (“influenced by the kinematic viscosity of the air”) and vapor pressure from skin and clothing.

He also pointed out that the Steadman calculation was based on a number of assumptions: It assumes that a person is 5 feet 7 inches tall and weighs 147 pounds. The clothing covering is assumed to be long pants and a short-sleeved shirt, which covers 84 percent of the skin. The activity level is assumed to be a walking speed of 5.1 miles per hour.

“It’s far more complicated to understand the heat index for individuals,” Mr. Rothfusz said Thursday, “because everyone is different — different weight, different height, that sort of thing.” In other words, the weather service’s heat index may not be your own.

The weather service also does not take variables such as sunshine into account in its heat index.

But another meteorological company does. Private forecasting giant AccuWeather has a product called RealFeel that takes sunshine, wind speed, precipitation and cloud cover into account, among other things. But exactly how these things are weighted is a trade secret, much like Colonel Sanders’ blend of 11 herbs and spices.

“The RealFeel Temperature is protected by two patents that ensure that no other index can encompass temperature and more than one other factor,” warns AccuWeather.

Mr. Rothfusz, whose work is public because it was prepared for the government, remains impressed by the scope of his calculation.

“I published this little paper that was just intended to be communicated within the National Weather Service,” he said, “and all of a sudden it just became a thing.”

We asked him if he felt a twinge of pride when he heard people talking about the heat index.

“I’m just glad the weather service is still communicating this information,” he said.