Heat index

The National Weather Service (NWS) issued a heat advisory for the mid-Hudson Valley today.  Temperatures in the mid-90's plus high humidity levels will give a heat index over 100 F.

The official NWS criteria for issuing a heat advisory is:

Issued within 12 hours of the onset of the following conditions: heat index of at least 105°F but less than 115°F for less than 3 hours per day, or nighttime lows above 80°F for 2 consecutive days.

A heat index is a measure of how hot it really feels given the air temperature and relative humidity.  We all know it feels hotter when it's humid out.  There's a physical reason for that and it has to do with water.

Water (H2O) can exist in three states at the normal range of Earth surface temperatures and pressures - solid ice, liquid water, and gaseous vapor.  When water changes state from ice to liquid to vapor, you have to add heat energy.  When water goes from gas to liquid to solid, heat energy is released.

When you get hot, your body responds by signaling sweat glands in your skin to perspire.  The liquid sweat on your skin will evaporate into the air and that change of phase from liquid to vapor requires heat energy - the heat of your skin.  In this way, the evaporating sweat essentially uses up heat energy off your skin and cools you down.

Now let's look at the air.  You can think of air as "holding" a certain amount  of water vapor (I know, I know, this isn't true at all but explaining it more correctly usually loses people and takes a lot more time - if you want to real story, click here).  The warmer the air, the more water vapor it can "hold."

Here's a graph illustrating this by showing the maximum amount of water vapor the air can "hold" (called saturation) at different temperatures...

The horizontal (x) axis is temperature in degrees Celsius (0 C = 32 F).  The vertical (y) axis is absolute humidty, that's how much water vapor is actually in the air.  The units are grams per cubic meter (g/m3).  Imagine an absolute humidity of 10 g/m3 - this means that a cube of air 1 meter on each side will only have 10 grams of water molecules floating around in it.

Looking at the graph, we see that at 0 C (32 F), the air can hold a maximum of 5 g/m3 of water vapor.  At 20 C (68 F), it jumps up to 20 g/m3, and at 40 C (104 F), it's up to 50 g/m3.  That's why we say that hotter air "holds" more water vapor (again, technically not really correct, but we don't want to get into vapor pressures and such).

From this, we can understand the concept of relative humidity (RH).  It's a percentage measure of how saturated the air is at that temperature.  For example, 0% RH means there's absolutely no water vapor in the air (never happens) and 100% RH means the air is saturated for that temperature (frequently happens - whenever it's raining out, the RH is typically 100%).  We said in the previous paragraph that at 20 C, the air can "hold" 20 g/m3 of water vapor.  Suppose it's 20 C, and we measure the amount of water vapor in the air as 10 g/m3.  What's the RH?

     RH = [(amount of water vapor in the air) / (what the air can "hold" at that temp)] x 100%
     RH = [(10 g/m3) / (20 g/m3)] x 100% = 0.5 x 100% = 50%

The relative humidity is 50% because the air is half saturated (it has 10 g/m3 of water vapor and can "hold" 20 g/m3 at that temperature).

The higher the relative humidity, the longer it will take sweat to evaporate off your skin.  When the air is dry, it evaporates quickly.  If you've ever been to an arid climate, you'll have experienced this.  Just last month, I was in Moab, Utah hiking in Arches and Canyonlands.

Air temperature was over 100 F.  I drank several liters of water but my skin was dry and, while the sun was strong, I felt relatively comfortable.  Today, if I did a hike here in NY, I'd be drenched and dripping with sweat.  The difference?  In Utah, the very low RH allows sweat to evaporate almost instantaneously while here in NY the higher RH means it evaporates more slowly or not at all.  The evaporating sweat cools you so 100 F in Utah is often more comfortable than 90 F in NY.

That's where the heat index comes in.  Here's a chart from the NWS.

Right now, at my house, the air temperature is around 90 F and the RH is 60%.  This gives a heat index of 100 F.  Meaning if you are outside, it feels like 100 degrees (and it's not even the hottest part of the day yet).  If the air temperature goes up a few degrees, the heat idex can significantly increase.  It's not just the temperature that makes you feel it, however, it's also the fact that you'll be sopping wet with perspiration.

If you want something a bit more exact, the NWS has a heat index calculator online where you enter the temperature and RH (easily obtained for your hometown from the NWS website) and get the heat index.  How is the heat index calculated?  It was worked out in the 1970s by a researcher named Robert Steadman who made a bunch of assumptions on things like body mass, height, type of clothing, amount of physical activity, sunlight exposure, wind speed, among other factors.  It's an approximation - if the wind is blowing, or you're taller than average, or you're jogging in the full sun, how hot you feel can be significantly different from the heat index.

The formula is actually quite complex (HI is the heat index, T is the degree F temperature, and R is the relative humidity)...

HI = [(-42.379)] + [(2.04901523) * T] + [(10.14333127) * R] - [(0.22475541) * T * R] -
        [(6.83783x10^-3) * T^2]  - [(5.481717x10^-2) * R^2] + [(1.22874x10^-3) * T^2 * R] +
        [(8.5282x10^-4) * T * R^2] - [(1.99x10^-6) * T^2 * R^2]

As some of you will recognize, this is an approximation formula, as you add more terms you get more decimal point accuracy.

However you calculate it, it's damn hot today in the Hudson Valley and I'm glad to have air conditioning!