The following is an introduction to an important new topic: humidity (moisture in the air).  This topic and the terms that we will be learning and using can be confusing.  That's the reason for this introduction.  We will be mainly be interested in 4 variables: mixing ratio, saturation mixing ratio, relative humidity, and dew point temperature.  Our first job will be to figure out what they are and how they are used.  Then we see what can cause the value of each variable to change.



Mixing ratio tells you how much water vapor is actually in the air.  Mixing ratio has units of grams of water vapor per kilogram of dry air (the amount of water vapor in grams mixed with a kilogram of dry air).  It is basically the same idea as teaspoons of sugar mixed in a cup of tea. 



The value of the mixing ratio won't change unless you add water vapor to or remove water vapor from the air.  Warming the air won't change the mixing ratio.  Cooling the air won't change the mixing ratio (unless the air is cooled below its dew point temperature and water vapor starts to condense).  Since the mixing ratio's job is to tell you how much water vapor is in the air, you don't want it to change unless water vapor is actually added to or removed from the air.


Saturation mixing ratio is just an upper limit to how much water vapor can be found in air, the air's capacity for water vapor.  It's a property of air, it doesn't say anything about how much water vapor is actually in the air (that's the mixing ratio's job).  Warm air can potentially hold more water vapor than cold air.  This variable has the same units: grams of water vapor per kilogram of dry air.  You can look up saturation mixing ratio values for different air temperatures in a table. 


Just as is the case with water vapor in air,
there's a limit to how much sugar can be dissolved in a cup of hot water.  You can dissolve more sugar in hot water than in cold water.

 The dependence of saturation mixing ratio on air temperature is illustrated below:


The small specks represent all of the gases in air except for the water vapor.  Each of the open circles represents 1 gram of water vapor that the air could potentially hold.  There are 15 open circles drawn in the 1 kg of 70 F air; each 1 kg of 70 F air could hold up to 15 grams of water vapor.  The 40 F air only has 5 open circles; this cooler air can only hold up to 5 grams of water vapor per kilogram of dry air.

Now we have gone and actually put some water vapor into the volumes of 70 F and 40 F air (3 of the open circles are colored in).  The same amount, 3 grams of water vapor, has been added to each volume of air.  The mixing ratio, r, is 3 g/kg in both cases.


Relative humidity is the variable most people are familiar with, it tells you how "full" the air is with water vapor, how close it is to being filled to capacity with water vapor.

In an analogy 4 students wander into Classroom A which has 16 empty seats.  Classroom A is filled to 25% of its capacity.  You can think of 4, the number of students, as being analogous to the mixing ratio.  The classroom capacity is analogous to the saturation mixing ratio.  The percentage occupancy is analogous to the relative humidity.

Instead of students and a classroom you could think of the 70 F and 40 F air that could potentially hold 15 grams and 5 grams, respectively, of water vapor.

Here are the relative humidities of the 70 F and 40 F air that each contain 3 grams of water vapor.  The 70 F air has a low RH because this warm air's saturation mixing ratio is large.  The RH in the 40 F is higher even though it has the same actual amount of water vapor because the 40 F air can't hold as much water vapor and is closer to being saturated. 

Something important to note: RH doesn't really tell you how much water vapor is actually in the air.  The two volumes of air above contain the same amount of water vapor (3 grams per kilogram) but have different relative humidities.  You could just as easily have two volumes of air with the same relative humidities but different actual amounts of water vapor.



The dew point temperature has two jobs.  First it gives you an idea of the actual amount of water vapor in the air.  In this respect it is just like the mixing ratio.  If the dew point temperature is low the air doesn't contain much water vapor.  If it is high the air contains more water vapor. 

Second the dew point tells you how much you must cool the air in order to cause the RH to increase to 100% (at which point a cloud, or dew or frost, or fog would form).


If we cool the 70 F air or the 40 F air to 30 F we would find that the saturation mixing ratio would decrease to 3 grams/kilogram.  Since the air actually contains 3 g/kg, the RH of the 30 F air would become 100%.  The 30 F air would be saturated, it would be filled to capacity with water vapor.  30 F is the dew point temperature for 70 F air that contains 3 grams of water vapor per kilogram of dry air.  It is also the dew point temperature for 40 F air that contains 3 grams of water vapor per kilogram of dry air.Because both volumes of air had the same amount of water vapor, they both also have the same dew point temperature.



Now back to the analogy involving students and classrooms.  The 4 students move into classrooms with smaller and smaller capacities.  The decreasing capacity of the  classrooms is analogous to the decrease in saturation mixing ratio that occurs when you cool air.  Eventually the students move into a classroom that they just fill to capacity. This is analogous to cooling the air to the dew point.

If the 4 students were to move to an even smaller classroom, they wouldn't all fit inside.  The same is true of moist air.  If you cool moist air below the dew point, some of the water vapor will condense. 

We need to try to learn a litte bit more about saturation of air.  In particular why is there an upper limit to the amount of water vapor that can be found in air and why does that saturation amount depend on temperature?

The first thing we need to realize is that warm water will evaporate more rapidly than cool water.  You probably know that already.  If a cup of iced tea were set next to a cup of hot tea you probably be able to tell which was which by just looking at them.  You wouldn't need to touch or taste the tea or look for ice cubes in the iced tea.

You might notice that one of the cups of tea was steaming (the cup on the right above).  This would be the hot tea.  You're not actually seeing water vapor.  Rather water vapor is evaporating so quickly that it is saturating the air above.  The air isn't able to accomodate that much water vapor and some of it condenses and forms a cloud of steam.  That's what you are seeing.

Now we'll redraw the picture and cover both cups so that water vapor can begin to buildup in the air above the water in both cups.
 

Arrows represent the different rates of evaporation.  One arrow is shown evaporating from the cup of cold water.  The warmer water at right is evaporating 3 times more rapidly.  We've arbitrarily assigned rates of evaporation of 10 and 30 to the water in the two cups.

Water vapor will start to buildup in the air above each cup.  And, even though it has just evaporated, some of the water vapor will condense and rejoin the water at the bottom of each cup.  Let's just assume that 1% of the water vapor molecules will condense. 

The water vapor concentration in each glass will increase until it reaches a point where
water evaporation rate = water vapor condensation rate

for the cup of cold water
10 = 0.01 x water vapor concentration

The 0.01 is 1% expressed in decimal form.  Solving this equation gives you a water vapor concentration of 1000.  The air is saturated when you reach this point and the RH = 100%.


The saturation water vapor concentration in the air in the warm cup would be 3000.  And again the relative humidity would be 100%.

The fact that the rates of evaporation and condensation are equal when air is saturated (RH = 100%) is something we'll be using later when we study the formation of precipitation.  Here's a picture of how that would look inside a cloud.

The air inside the cloud is saturated.  The rate of evaporation from the cloud droplet (2 green arrows) is balanced by an equal rate of condensation (2 orange arrows).  The RH = 100%.  The cloud droplet won't grow any bigger or get any smaller.

Here's something to test your understanding of this material.


What information can you add to this picture?  Is the water in one of the glasses warmer than the other?  Is there more water vapor in the air in one of the glasses than the other?  Is the relative humidity in each glass more than 100%, less than 100% or is it equal to 100%.  The rates of evaporation and condensation aren't equal in either glass, so the pictures will change with time.  What will the glasses look once they have reached equilibrium?  Click here when you think you know the answers.
We'll end this lecture with a table that shows the dependence of saturation mixing ratio on air temperature.

Note that the value of the saturation mixing ratio doubles for every 20 F increase in temperature.  The same data are shown in graphical form below.