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Wednesday May 28, 2008 at 9:39 am
The Heat Index


I know, it has been a long time since I posted.  I will try to post more often as the dog days of summer approach.  Before I get into an extremely complicated heat index equation, I want to answer a couple of frequently asked questions.

1. Will we have an animated radar on the website?  Yes.  We are working on getting that together.

2.  We had a bad thunderstorm and did not get the phone call from Ned.  This one is a bit more complicated.  Not all storms are severe.  Heavy rain, thunder, and lightning do not make a storm severe.  For a storm to reach severe status, it must have hail 3/4 inch in diameter and winds more than 58 mph.  Also, the new warning system is so specific, your address may fall just outside of the warning area.  If you still feel there's a problem, contact the people at weathercall or send us an e-mail.

Now onto the heat index.  Last weekend we hit 100 degrees with our heat index for the first time this year. The heat index is the apparent temperature due the the added moisture in the air.  That added moisture does not allow our bodies to cool itself. 

The equation and variables that go into the formula are complicated and a bit humorous as well.  Here are just a few of the variables...

  Dimensions of a human. Determines the skin's surface area. (5' 7" tall, 147 pounds)
Effective radiation area of skin. A ratio that depends upon skin surface area. (0.80)
Significant diameter of a human. Based on the body's volume and density. (15.3 cm)
Clothing cover. Long trousers and short-sleeved shirt is assumed. (84% coverage)
Core temperature. Internal body temperature. (98.6°F)
Core vapor pressure. Depends upon body's core temperature and salinity. (5.65 kPa)
Surface temperatures and vapor pressures of skin and clothing. Affects heat transfer from the
skin's surface either by radiation or convection. These values are determined by an iterative process.
Activity. Determines metabolic output. (180 W m-2 of skin area for the model person walking
outdoors at a speed of 3.1 mph)
Effective wind speed. Vector sum of the body's movement and an average wind speed. Angle
between vectors influences convection from skin surface (below). (5 kts)
Clothing resistance to heat transfer. The magnitude of this value is based on the assumption that
the clothing is 20% fiber and 80% air.
Clothing resistance to moisture transfer. Since clothing is mostly air, pure vapor diffusion is used
here.
Radiation from the surface of the skin. Actually, a radiative heat-transfer coefficient determined
from previous studies.
Convection from the surface of the skin. A convection coefficient also determined from previous
studies. Influenced by kinematic viscosity of air and angle of wind.
Sweating rate. Assumes that sweat is uniform and not dripping from the body.
As an aside, these assumptions are important for the forecaster to keep in mind. For example, a
common perception is that wind is not taken into account in the Heat Index. In actuality it is. It is assumed
to be 5 knots. This may seem trivial but a forecaster may be able to use this information creatively when
writing Public Information Statements regarding heat stress, heat stroke, etc.
Ventilation rate. The amount of heat lost via exhaling. (2-12%, depending upon humidity)
Skin resistance to heat transfer. A function of activity, skin temperature, among others.
Skin resistance to moisture transfer. A function of the vapor-pressure difference across the skin
(and, therefore, relative humidity). It decreases with increasing activity.
Surface resistance to heat transfer. As radiation and convection from the skin increases, this value
decreases.
Surface resistance to moisture transfer. Similar to heat transfer resistance but also depends upon
conditions in the boundary layer just above skin's surface.

YIKES.  Here is the mathematical formula...


HI = -42.379 + 2.04901523T + 10.14333127R - 0.22475541TR - 6.83783x10-3T2
- 5.481717x10-2R2 + 1.22874x10-3T2R + 8.5282x10-4TR2 - 1.99x10-6T2R2


where T = ambient dry bulb temperature (°F)
R = relative humidity (integer percentage).
Because this equation is obtained by multiple regression analysis, the heat index value (HI) has an error
of ±1.3°F. Even though temperature and relative humidity are the only two variables in the equation, all
the variables on the lists above are implied.

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Comments on The Heat Index
Danny Durey
In the formula, when you are multiplying by "10", does the dash indicate you are raising 10 to that power? Also, does a variable followed by a "2" imply that you are squaring that variable? For example, would 6.83783 X 10-3T2 be read as 6.83783 times ten to the (three times "T" squared) power?

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