Friday, Mar. 16, 2018

Willie Nelson "I Never Cared for You" (5:01), "Still is Still Moving to Me" (3:07), "Stay a Little Longer" (3:25), "Nothing I Can Do About it Now" (2:49)

Quiz #2 has been graded and was returned in class today. 

I have mostly moved into my new office in Harshbarger 220.  From this point onward office hours will be held at that location.

An Optional In-class Assignment was handed out in class today and was collected at the end of the period.  If you weren't in class today and would like to complete the assignment and turn it in at the start of class next Monday you will receive at least partial credit.

We'll start the next block of material with a look at humidity variables.  These are ways of measuring and tracking the amount of moisture in the air. 

In the next 2 weeks or so we'll learn a little bit about how clouds form and will learn how to identify and name the 10 main cloud types.  Only 2 of these are able to produce significant amounts of precipitation.  It's not as easy to produce precipitation as you might think.  This is something else we'll be looking at and at the variety of types of precipitation that result. 

Today: introduction to humidity variables

 This topic and the terms that we will be learning are probably new and might be confusing.  So here's an introduction.  We will be mainly be interested in 4 variables:



Your task will be to learn the "jobs" of these variables, their units, and what can cause them to change value. 

Mixing ratio ( r )
The bottom half of the figure below can be found on p. 83 in the ClassNotes.


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).  A kilogram of air is about one cubic meter of air (about one cubic yard of air).  Mixing ratio 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 (with one exception - when 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 ( rS )

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 and depends on the air's temperature; warm air can potentially hold more water vapor than cold air.  It doesn't say anything about how much water vapor is actually in the air (that's the mixing ratio's job).    This variable has the same units: grams of water vapor per kilogram of dry air.  Saturation mixing ratio values for different air temperatures are listed and graphed on p. 86 in the ClassNotes. 


The sugar dissolved in tea analogy is still helpful.  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.  And not only that, the amount depends on temperature: 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 45 F air only has 6 open circles; this cooler air can only hold up to 6 grams of water vapor per kilogram of dry air.  The numbers 15 and 6 came from the table on p. 86.


Now we have gone and actually put some water vapor into the volumes of 70 F and 45 F air (the open circles are colored in).  The same amount, 3 grams of water vapor, has been added to each volume of air.  Three of the open circles have been colored in.  The mixing ratio, r, is 3 g/kg in both cases.   One of the figures is almost filled to capacity, with water vapor the other is not.  That's basically what the 3rd humidity variable, relative humidity, tells us

Relative humidity (RH)


The 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, how close the air is to being "saturated" with water vapor.  RH has units of %.

In the analogy (sketched on the right hand side of p. 83 in the photocopied notes) 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 actual number of students, as being analogous to the mixing ratio.  The classroom capacity is analogous to the saturation mixing ratio.  How full the room is is analogous to the relative humidity.

The figure below goes back to the volumes (1 kg each) of 70 F and 40 F air that could potentially hold 15 grams or 5 grams of water vapor.



Both the 70 F and the 45 F air each contain 3 grams of water vapor.  The 70 F air is only filled to 20% of capacity (3 of the 15 open circles is colored in) because this warm air's capacity, the saturation mixing ratio, is large.  The RH in the 45 F is 50% even though it has the same actual amount of water vapor because the 45 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 very different values of relative humidity.  You could just as easily have two volumes of air with the same relative humidity but different actual amounts of water vapor.

What is the RH good for if it doesn't tell you how much moisture is in the air?  When the RH reaches 100% dew, fog, and clouds form.  RH tells you whether clouds or fog are about to form or not.

Dew point temperature


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.  This is something we learned early in the semester.

The dew point is a temperature and has units of   oF or oC
Second the dew point tells you how much you must cool the air in order to raise the RH to 100% (at which point a cloud, or dew or frost, or fog would form).  This idea of cooling the air until the RH increases to 100% is important and is something we will use a lot.



Let's first imagine cooling the 70 F volume of air (Parcel A) down to 45 F.  Once there we see that Parcel A and Parcel B are identical.  They both have the same mixing ratios, the same saturation mixing ratios, and the same relative humidities.


If we cool the both the parcels of 45 F air to 30 F we 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 Parcel A, 70 F air that contained 3 grams of water vapor per kilogram of dry air.  It is also the dew point temperature for Parcel B, the 45 F air that also contained 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 student/classroom analogy.



The 4 students move into classrooms of smaller and smaller capacity.  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.


Humidity example problem #1
There are 4 humidity variables (mixing ratio, saturation mixing ratio, relative humidity, and dew point temperature).  Generally I'll give you values for two of them and you'll need to figure out values for the other two.
Here are the starting conditions for this first problem
Tair = 90 F
r = 6 g/kg
RH = ?
 Td = ?

We start by entering the data we were given


Anytime you know the air's temperature you can look up the saturation mixing ratio value on a chart (such as the one on p. 86 in the ClassNotes); the saturation mixing ratio is 30 g/kg for 90 F air.  90 F air could potentially hold 30 grams of water vapor per kilogram of dry air (it actually contains 6 grams per kilogram in this example). 

Once you know mixing ratio and saturation mixing ratio you can calculate the relative humidity (you divide the mixing ratio by the saturation mixing ratio, 6/30, and multiply the result by 100%).  You ought to be able to work out the ratio 6/30 in your head (6/30 = 1/5 = 0.2).  The RH is 20%. 

The numbers we just figured out are shown on the top line below.




(A) To figure out the dew point, we imagine cooling the air from 90F to 70F, then to 55F, and finally to 45F.  Note the effect this has on the mixing ratio, the saturation mixing ratio and the relative humidity.

(B) At each step we looked up the saturation mixing ratio and entered it on the chart.  Note that the saturation mixing ratio values decrease as the air is cooling.

(C) The mixing ratio (r) doesn't change as we cool the air.  The only thing that changes r is adding or removing water vapor and we aren't doing either.  This is probably the most difficult concept to grasp.

(D) Note how the relative humidity is increasing as we cool the air.  The air still contains the same amount of water vapor it is just that the air's capacity is decreasing.

Finally at 45 F the RH becomes 100%.  This is the dew point.  The dew point temperature is 45 F

What would happen if we cooled the air below the dew point temperature?


35 F air can't hold the 6 grams of water vapor that 45 F air can.  You can only "fit" 4 grams of water vapor into the 35 F air.  The remaining 2 grams would condense.  If this happened at ground level the ground would get wet with dew.  If it happens above the ground, the water vapor condenses onto small particles in the air and forms fog or a cloud.  Because water vapor is being taken out of the air (the water vapor is turning into water), the mixing ratio will decrease from 6 g/kg to 4 g/kg.  As you cool air below the dew point, the RH stays constant at 100% and the mixing ratio decreases.

This is the situation where cooling the air seems to be affecting the value of the mixing ratio.  But it's because we're cooling the air below the dew point and water vapor is condensing.  The air is actually losing water vapor and the mixing ratio (whose job it is to tell you how much water vapor is in the air) should decrease.

I couldn't find my sponge in the current chaos in my new office.  I'll keep looking and will try to bring it next week, because the following analogy is pretty good.

In many ways cooling moist air is liking squeezing a moist sponge



Squeezing the sponge and reducing its volume is like cooling moist air and reducing the saturation mixing ratio.  At first (Path 1 in the figure) when you squeeze the sponge nothing happens, no water drips out.  Eventually you get to a point where the sponge is saturated.  This is like reaching the dew point.  If you squeeze the sponge any further (Path 2) water will begin to drip out of the sponge (water vapor will condense from the air).