Thursday Oct. 19, 2006

The 1S1P Assignment #2a reports were collected today.  The Assignment #2b reports are due next Tuesday.  Remember you can only do a maximum of two reports as part of Assignment #2.

Two more Optional Assignments were handed out in class today.  They are both due next Thursday, Oct. 26.

The Reading Assignments page has been updated.
Here are the two remaining humidity example problems that we didn't have time for last Tuesday.

In the 3rd problem we are given RH=50% and r=10.5 g/kg.  We are supposed to determine the air temperature and the dew point temperature.

The air contains 10.5 g/kg of water vapor, this is 50% of what the air could potentially hold.  So the air's capacity, the saturation mixing ratio must be 21 g/kg (you can either work this out in your head or use the relative humidity formule).

Once you know the saturation mixing ratio you can look up the air temperature in a table.  Then you imagine cooling the air until the RH becomes 100%.  This occurs at 60 F.  The dew point is 60 F.
Now the 4th and last problem.  We're given an air temperature of 90 F and a dew point temperature of 50 F.  We need to determine the mixing ratio and the relative humidity.

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

Then we know that if we cool the 90 F air to 50 F the RH will become 100%.  Since we know the saturation mixing ratio value at 50 F is 7.5 g/kg we can say the mixing ratio is 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.
No we'll use air with the same characteristics as in the last problem and see how it is possible to dry out moist air.

We imagine cooling the moist air to its dew point.  The relative humidity reaches 100% at that point.  Then the air is cooled below the dew point, to 30 F.  The 30 F air can't hold the 7.5 g/kg of water vapor that was originally found in the air.  The excess moisture must condense (we will assume it falls out of the air as rain or snow).  When air reaches 30 F it contains less than half the moisture (3 g/kg) that it originally did (7.5 g/kg).  Next the 30 F air is warmed back to 90 F, the starting temperature.  The air now has a RH of only 10%.

Drying moist air is like wringing moisture from a wet sponge.

Cooling moist air below the dew point is kind of like squeezing out or wringing out a wet sponge.  You start to squeeze the sponge and nothing happens at first (that's like cooling the air, the mixing ratio stays constant as long as the air doesn't lose any water vapor).  Eventually water will start to drop from the sponge (with air this is what happens when you reach the dew point and continue to cool the air below the dew point).  Then you let go of the sponge and let it expand back to its orignal shape and size (the air warms back to its original temperature).  The sponge (and the air) will be drier than when you started.


These two figures show where this kind of thing can occur.  In the winter cold air is brought inside your house or apartment and warmed.  Imagine 30 F air with a RH of 100 % brought inside and warmed to 70 F.  The RH will decrease to 20%.

The air in an airplane comes from outside the plane.  The air outside the plane is very cold (-50 F perhaps) and contains very little water vapor (even if the -50 F air is saturated it will contain essentially no water vapor).  When brought inside and  warmed to a comfortable temperature the RH of the air in the plane will be very close 0%.  Actually I suspect the ventilation system in the plane will add moisture to the air so that it doesn't get that dry.

Here's an important cooling and drying out moist air example. 
We start with some moist but unsaturated air at Point 1 (the numbers were added after class).  As it is moving toward the right the air runs into a mountain and starts to rise.  This is one of the 4 ways of causing air to rise (the other three were convergence, convection, and fronts).  Unsaturated air cools 10 C for every kilometer of altitude gain.  This is known as the dry adiabatic lapse rate.  So in rising 1 km the air will cool to its dew point.

The air becomes saturated at Point 2, you would see a cloud appear.  Rising saturated air cools at a slower rate than unsaturated air.  We'll use a value of 6 C/km (an average value for the moist adiabatic lapse rate).  The air cools from 10 C to 4 C in next kilometer up to the top of the mountain.  Because the air is being cooled below its dew point at Point 3, some of the water vapor will condense and fall to the ground as rain. 

At Point 4 the air starts back down the right side of the mountain.  Sinking air warms.  As soon as the air starts to sink and warm, the relative humidity drops below 100% and the cloud evaporates.  The sinking air will warm at the 10 C/km rate. 

At Point 5 the air ends up warmer (24 C vs 20 C) and drier (Td = 4 C vs Td = 6 C) than when it started out.  The downwind side of the mountain is referred to as a "rain shadow" because rain is less likely there than on the upwind side of the mountain.

The air that arrives in Arizona from the west coast is often dry because it has travelled up and over the Sierra Nevada mountains in California and the Sierra Madre mountains further south in Mexico.
 


Here's an instrument that can be used to measure humidity, usually the relative humidity and the dew point temperature.  A sling psychrometer consists of two thermometers mounted side by side.  One is covered with a wet piece of cloth.  To make a humidity measurement you swing the psychrometer around for a minute or two and then read the temperatures from the two thermometers.  This is an expanded and enhanced version of what is found on p. 89 in the photocopied class notes.


On a warm dry day there will be a large difference (20 F in this example) between the dry and wet bulb thermometer readings.

The difference between the dry and wet bulb thermometers will be smaller on a humid day (only 5 F here).

There won't be any difference in temperatures when the RH=100%.
When you cool air that is next to the ground to the dew point, water vapor condenses onto objects on the ground such as blades of grass, your automobile, your morning newspaper, maybe even your sleeping cat.


In the first example air  starts out with a temperature of 65 F early in the evening.  It cools to 35 F during the night.  When the air reaches 40 F, the dew point, the RH reaches 100%.  As the air temperature drops below the dew point and cools to 35 F water vapor will condense onto the ground or objects on the ground (such as an automobile).  This is dew.

The dew point is the same but the nighttime minimum temperature is below freezing in the second example.  Dew will form again on this night when the air temperature reaches 40 F.  Once the air temperature drops below 32 F though the dew will freeze and form frozen dew.

In the third example both the dew point and nighttime minimum temperatures are below freezing.  When the air temperature drops below the dew point, water vapor turns directly to ice (deposition) and forms frost.  The dew point in this case is sometimes called the frost point.

The air never becomes saturated in the fourth example because the nighttime minimum temperature never cools to the dew point.  You wouldn't see anything on this night.
When air above the ground reaches 100% relative humidity it is much easier for water vapor to condense onto small particles in the air called condensation nuclei.  It would be much harder for the water vapor to condense and form small drops of pure water.  You can learn why this is true by reading p. 92 in the photocopied class notes.

Water vapor will condense onto certain kinds of condensation nuclei even when the relative humidity is below 100% (again you will find some explanation of this on p. 92).  These are called hygroscopic nuclei.
A short video showed how water vapor would, over time, preferentially condense onto small grains of salt rather than small spheres of glass.

The start of the video at left showed the small grains of salt were placed on a platform in a petri dish containing water.  Some small spheres of glass were placed in the same dish.  After about 1 hour small drops of water had formed around each of the grains of salt (shown above at right).

In humid parts of the US, water will condense onto the grains of salt in a salt shaker causing them to stick together.  Grains of rice apparently will keep this from happening and allow the salt to flow freely out of the shaker when needed.

This figure shows how cloud condensation nuclei and increasing relative humidity can affect the appearance of the sky and the visibility.

The air in the left most figure is relatively dry.  Even though the condensation nuclei particles are too small to be seen with the human eye you can tell they are there because they scatter sunlight.  When you look at the sky you see the deep blue color caused by scattering of sunlight by air molecules together with white light scattered by the larger condensation nuclei.  This changes the color of the sky from a deep blue to a bluish white color.  The more particles there are the whiter the sky becomes.  This is called "dry haze."

The middle picture shows what happens when you drive from the dry southwestern part of the US into the humid southeastern US.  One of the first things you would notice is the hazier appearance of the air and a decrease in visibility.  Because the relative humidity is high, water vapor begins to condense onto some of the condensation nuclei particles (the hygroscopic nuclei) in the air and forms small water droplets.  The water droplets scatter more sunlight than just small particles alone.  The increase in the amount of scattered light is what gives the air its hazier appearance. This is called "wet haze."

Finally when the relative humidity increases to 100% fog forms.  Fog can cause a severe drop in the visibility.
We finished class with a demonstration - we attempted to make a cloud inside a bottle

We used a strong thick-walled 4 liter flask.  There was a little water in the bottom of the flask to moisten the air in the flask.  Next we pressurized the air in the flask.  At some point the pressure blows the cork out of the top of the flask.  The air in the flask expands outward and cools.  This cooling increases the relative humidity of the moist air in the flask to 100% (probably more than 100%) and water vapor condenses onto cloud condensation nuclei in the air.  A cloud became visible at this point.  The cloud droplets are too small to be seen with the human eye.  You can see the cloud because the water droplets scatter light.

The demonstration was repeated a second time (perhaps a third time) with one small change.  A burning match was dropped into the bottle.  The smoke from the match consisted of lots of very small particles that act as condensation nuclei.  The cloud that formed this time was somewhat "thicker" and easier to see.
The following figure wasn't shown in class (we had run out of time).  But I promised I would stick it onto the end of today's notes.


 Clouds are one of the best ways of cleaning the atmosphere (cloud droplets form on particles, the droplets clump together to form a raindrop, and the raindrop carries the particles to the ground).  A raindrop contains about 1 million cloud droplets so a single raindrop can remove a lot of particles from the air.  You may have noticed how clear the air seems the day after a rainstorm.  Gaseous pollutants can dissolve in the water droplets and be carried to the ground by rainfall also.

A cloud composed of a large number of small droplets is more reflective than a cloud composed of a smaller number of larger droplets.  This something that interests the people studying climate change.  Combustion of fossil fuels adds carbon dioxide to the atmosphere but also adds condensation nuclei.  The increasing greenhouse gas concentrations are expected to warm the earth.  More particles might make clouds more reflective though which could cool the earth.