It seems that the term "relative humidity" is ubiquitous when it comes to television broadcasters talking about the air's moisture content.  While I'm not sure how this started, nowadays people are used to hearing relative humidity, so when a meteorologist on TV mentions a relative humidity value, everyone knows what they are talking about.  Unfortunately, relative humidity values do not give you any indication of the air's moisture content unless you know the temperature.  Here's why...

There are many different ways to represent the amount of moisture in the atmosphere, but one of the most common methods meteorologists use to represent air moisture content is mixing ratio.  The mixing ratio can be found by taking the water out of a sample of air and dividing it's mass by the mass of the remaining air.  So for example, if you took a container of air and were able to separate the water out of it, and the water weighed 5 grams and the air weighed 1 kilogram, the mixing ratio would be 5 g/kg.  Typical mixing ratios are between 5-15 g/kg.  The key to learn here is that a mixing ratio is an exact measure of the amount of water per unit of air.

Now getting back to relative humidity.  A simplified definition of relative humidity is the amount of water vapor in the air, divided by the maximum amount of water vapor the air can "hold," multiplied by 100%.  In mathematical terms:


Relative Humidity = W / Ws * 100%

where W is equal to the current mixing ratio as we talked about above, Ws is the saturation mixing ratio, and 100% scales it to a 0-100 value.  So what is this Ws saturation mixing ratio term?  Well, it turns out that air can only hold so much water vapor.  Interestingly, the amount of water the air can hold is dependent only on the temperature of the air.  The saturation mixing ratio as a function of temperature looks something like this:


(Saturation Vapor Pressure, x is degrees C, y is mixing ratio in g/kg)

Notice the saturation mixing ratio is actually an exponential curve, so as the temperature of the air goes up, the amount of water vapor the air can hold increases very quickly.  This means that a hot desert can potentially be much more humid than the cold environment of Antarctica.  Indeed, this is often the case...and many people are surprised to learn that the driest places on Earth are not in the Sahara or other deserts, but instead are at the North and South Poles.  

Looking at the graph further, the line shows saturation mixing ratio, which is the maximum amount of water the air can hold, so it follows that any sample of air you take at a certain temperature will have an actual mixing ratio value below that curve.  So for instance, if your air temperature was 14C, you could have a mixing ratio of 8 g/kg, but not 20 g/kg because at that point you would have a mixing ratio greater than the saturation mixing ratio.  

It's pretty easy to calculate relative humidity from this graph.  Let's take our above example...we have air that is 14 degrees C, and a mixing ratio of 8 g/kg.  At 14C, the saturation mixing ratio is 10 g/kg.  

W = 8 g/kg
Ws = 10 g/kg
Relative Humidity = 8 / 10 * 100% = 80%

That's a fairly humid environment.  Let's consider that as a morning condition during the summer time though.  What if the temperature at mid-day increases to 20C, and the same 8 g/kg of water vapor is in the air?  Well, the saturation mixing ratio at 20C is about 15 g/kg...

W = 8 g/kg
Ws = 15 g/kg
Relative Humidity = 8 / 15 * 100% = 53%

Wait a second.  Our humid day just turned into a comfortable day, and we kept the same amount of water in the environment.  What gives?  Well, relative humidity is just what it says, relative.  It's relative to the saturation mixing ratio...but it doesn't account for a changing saturation mixing ratio.  This can be very confusing, which is why many meteorologists won't even work with relative humidity values.  

Often times you will see evidence of this in Seasonality's humidity graph.  During a typical day, as temperature goes up, you will notice the relative humidity go down.  Likewise, at the end of the day as the temperature drops, relative humidity will tend to go back up near it's original value.

So the next time you hear someone mention a relative humidity, ask them what the temperature was as well.  Or better yet, ask them about the dewpoint temperature.  I'll talk more about the meaning of the dewpoint temperature in a future posting.