Tue., Mar. 25 notes

Tuesday Mar. 25, 2008

Welcome back, I hope your Spring Break was enjoyable.

Quiz #2, the Expt. #1 revised reports, one or two optional assignments, and the 1S1P Topic 4 reports were returned in class today. A short "mid-term" grade summary was also handed out. Please check to be sure all of the grade information has been entered into the computer correctly. If you are concerned about your overall grade I would suggest you come by my office for a short visit. There is still enough work left this semester for you to raise your overall average significantly. But you need to start to take corrective action now, well before the next quiz.

The Expt. #2 report revisions are due on Thursday, Mar. 27.

The Expt. #3 reports are due next Tuesday, Apr. 1. You should collect your data, and return your materials this week so that you can pick up the supplementary information handout.

The Expt. #4 reports are due Tuesday, Apr. 8.

The following is an introduction to an important new topic: humidity (moisture in the air). The beginning of Chapter 4 can be a little overwhelming and confusing. This is one of those rare situations where I would suggest you not read the beginning of Chapter 4. Instead, study these online notes and the notes you take in class. We will work a number of humidity example problems later in class today and you should fairly quickly grasp the basic concepts.

We will be mainly interested in 4 variables, what they are and what can cause their values to change. The variables are : mixing ratio, saturation mixing ratio, relative humidity, and dew point. You will find most of what follows on pps 83-85 in the photocopied class notes.

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. Here are answers to the In class Optional Assignment that was collected at the end of class on Monday by the way.

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).

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. Saturation mixing ratio values for different air temperatures are listed and graphed on p. 86 in the photocopied class notes.

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 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 grams of water vapor have been added to each volume of air. The mixing ratio, r, is 3 g/kg in both cases.

The relative humidity is the variable most people are familiar with, it tells you how "full" the air is with water vapor.

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 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 or 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 is a measure 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 our students and classrooms analogy on the righthand side of p. 83. 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 temperature, at which point the RH becomes 100% and the air is filled to capacity, the air is saturated with water vapor.

And now for something completely different (see pps 81 & 82 in the photocopied Classnotes)

We have already learned that oceans moderate climate. A region next to an ocean or an island surrounded by ocean will have a smaller annual range of temperature than a location surrounded by land. Latitude also affects the annual range of temperature. The smallest seasonal variations are found at the equator because the days are always 12 hours long and the sun is always high in the sky at noon. These two factors and a couple of other factors are discussed in an online summary of the Controls of Temperature. Please have a look at that section. You will find a link to an Optional Assignment that you can download, print out, and complete. This Controls of Temperature Optional Assignment is due at the start of class on Monday Mar. 31.

We had a brief look at some climate data from Pohnpei Island in the Federated States of Micronesia. You'll find some information about Pohnpei and other nearby islands on pps 81 and 82 in the photocopied Class Notes.

Pohnpei island is located to the east of Guam. The current Survivor series was filmed in Palau. Kapingamarangi Atoll in the Federated States of Micronesia is located at 1 N latitude. Kapingamarangi Atoll is too small to have a weather station. There is a weather station and an airport on Pohnpei Island, however.

Pohnpei is a fairly large island and is a popular snorkeling and scuba diving destination. Pohnpei has a weather station that is operated by the US National Atmospheric and Oceanic Administration.

Because of its low latitude and the fact that it is surrounded by water you would expect a small annual range of temperature at Pohnpei. You can see in the table above just how small the annual range is: the average monthly temperatures in Pohnpei range from 80.8 F in February and March to 80.0 F in July. The annual range is less than 1 F. By comparison, the annual range in Tucson is about 34 F (52 F in December and January to 86 F in July). The temperature on Pohnpei has never dropped below 66 F.

The following precipitation data show that Pohnpei is also one of the rainiest locations on earth

The rainiest location on earth is in Hawaii with about 460 inches of rain per year.

Now back to humidity

In the time remaining in class we were able 4 humidity example problems. By doing these problems you should become more familiar with the humidity variables (mixing ratio, saturation mixing ratio, relative humidity, and dew point temperature). You'll also learn "how they behave" and what can cause each of these variables to change value.

Keep this compilation of saturation mixing ratio values (shown in a table and on a graph) handy, we will use it a lot as we work through the humidity problem examples. Remember that saturation mixing ratio is the maximum amount of water vapor that can be found in air. It is a property of the air and depends on the air's temperature.

The beakers (beakers were also brought to class) are meant to show graphically the relative amounts of water vapor that air at different temperatures can contain.

Now the first of our example problems.

Here is the first sample problem that we worked in class. You might have a hard time unscrambling this if you're seeing it for the first time. The series of steps that we followed are retraced below:

We're given an air temperature of 90 F and a mixing ratio (r) of 7.5 g/kg. We're supposed to find the relative humidity (RH) and the dew point temperature.

We start by entering the data we were given in the table. Once you know the air's temperature you can look up the saturation mixing ratio value; it 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 contains7.5 grams per kilogram in this example).

Once you know mixing ratio and saturation mixing ratio you can calculate the relative humidity. The RH is 25%.

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

(A) We imagined cooling the air from 90F to 70F, then to 55F, and finally to 50F.

(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 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.

(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 50 F the RH becomes 100%. The dew point temperature in this problem is 50 F.

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

45 F air can't hold the 7.5 grams of water vapor that 50 F air can. You can only "fit" 6 grams of water vapor into the 45 F air. The remaining 1.5 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. Now because water vapor is being taken out of the air (and being turned into water), the mixing ratio will decrease from 7.5 to 6. That is why the mixing ratio is changing.

In many ways cooling moist air is liking squeezing a moist sponge (the figure below wasn't shown in class)

Squeezing the sponge and reducing its volume is like cooling moist air and reducing the saturation mixing ratio. At first when you sqeeze 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 (or cool air below the dew point) water will begin to drip out of the sponge (water vapor will condense from the air).

Here's the 2nd problem we worked

The work that we did in class is shown above. Given an air temperature of 90 F and a relative humidity of 50% you are supposed to figure out the mixing ratio (15 g/kg) and the dew point temperature (70 F). The problem is worked out in detail below:

First you fill in the air temperature and the RH data that you are given.

(A) since you know the air's temperature you can look up the saturation mixing ratio (30 g/kg).

(B) Then you can substitute into the relative humidity formula and solve for the mixing ratio (15 g/kg).

Finally you imagine cooling the air. Cooling causes the saturation mixing ratio to decrease, the mixing ratio stays constant, and the relative humidity increases. In this example the RH reached 100% when the air had cooled to 70 F. That is the dew point temperature.

We can use results from humidity problems #1 and #2 worked in class on Monday to learn a useful rule.

In the first example the difference between the air and dew point temperatures was large (40 F) and the RH was low. In the 2nd problem the difference between the air and dew point temperatures was smaller and the RH was higher. The easiest way to remember this rule is to remember the case where there is no difference between the air and dew point temperatures. The RH would be 100%.

Problem #3 is next.

This figure was redrawn after class. You are given a mixing ratio of 10.5 g/kg and a relative humidity of 50%. You need to figure out the air temperature and the dew point temperature.

(1) The air contains 10.5 g/kg of water vapor, this is 50%, half, of what the air could potentially hold. So the air's capacity, the saturation mixing ratio must be 21 g/kg (you can either do this in your head or use the RH equation following the steps shown).

(2) Once you know the saturation mixing ratio you can look up the air temperature in a table.

(3) Then you imagine cooling the air until the RH becomes 100%. This occurs at 60 F. The dew point is 60 F.

Problem #4 is probably the most difficult of the bunch.

The figure above shows what we did in class. We were given the air temperature and the dew point temperature. We're supposed to find the mixing ratio and the relative humidity.
Here's the step by step approach to answering the question.

We enter the two temperatures onto a chart and look up the saturation mixing ratio for each.

We ignore the fact that we don't know the mixing ratio. We do know that if we cool the 90 F air to 50 F the RH will become 100%. We can set the mixing ratio equal to the value of the saturation mixing ratio at 50 F, 7.5 g/kg.

Remember back to the three earlier examples. When we cooled air to the the dew point, the mixing ratio didn't change. So the mixing ratio must have been 7.5 all along. Once we know the mixing ratio in the 90 F air it is a simple matter to calculate the relative humidity, 25%.

Here's a copy of a handout distributed near the end of class. I thought it best not to discuss this in class, that would have been too much material for one day. As a matter of fact, if you have just read through all the information above on humidity, you might ought to take a break and come back to this material on another day. As a matter of fact I have moved the discussion of the handout below to the Thursday Mar. 27 online notes.