Thursday, Mar. 22, 2018

Music from the Brittany region (I think) in France where I used to live and work: Digresk "Larrakia" (4:18), Plantec "Androide" (4:13),
Dour/Le Pottier "Avel Gorn" (4:49), Startijenn "Strak ha pak" (4:23), Remy Geffroy "La Fuite du Chat Noir" (3:14)


Here's a quick review of the 4 humidity variables covered in class on Tuesday.  Also included are the answers to the In-class Optional Assignment

We don't usually work out the problem below in class but I'll include it in the notes nonetheless.
Humidity example problem #3
Tair = ?
r = 10.5 g/kg
RH = 50% Td = ?


You're given the the mixing ratio = 10.5 g/kg and a relative humidity of 50%.    You need to figure out the air temperature and the dew point temperature.  Give it a try before you have a look at the step by step solution below:


(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 above). 

(2) Once you know the saturation mixing ratio you can look up the air temperature in a table (80 F air has a saturation mixing ratio of 21 g/kg)

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

Humidity example problem #4

One of the "jobs" of the dew point, to give you an idea of the actual amount of water vapor in the air, is the same as the mixing ratio.  The next problem will demonstrate that if you know the dew point temperature you can quickly figure out the mixing ratio and vice versa.
Tair = 90 F
r = ?
RH = ?
 Td = 50 F






We enter the two temperatures given on 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%.  So on the 50 F row, we can set the mixing ratio equal to the value of the saturation mixing ratio at 50 F, 7.5 g/kg.  The two have to be equal in order for the RH to be 100%.


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%.
Drying moist air
The figure below is on p. 87 in the photocopied ClassNotes.  It explains how you can dry moist air. 






At Point 1 we start with some 90 F air with a relative humidity of 25%, fairly dry air.   These are the same numbers that we had in Example Problem #4.  We imagine cooling this air to the dew point temperature, 50 F.  While doing that the mixing ratio, r, would stay constant.  Relative humidity would increase and eventually reach 100%.  A cloud would form (Pt. 2 in the figure above). 

Then we continue to cool the air below the dew point, to 30 F.  Air that is cooled below the dew point finds itself with more water vapor than it can contain.  The excess moisture must condense (we will assume it falls out of the air as rain or snow).  Mixing ratio will decrease, the relative humidity will remain 100%.  When air reaches 30 F it contains 3 g/kg, 40% of the moisture that it originally did (7.5 g/kg). 

The air is being warmed back up to 90 F along Path 4.  As it warms the mixing ratio remains constant.  Cooling moist air raises the RH.  Warming moist air, as is being done here, lowers the RH.  Once back at the starting temperature, Point 5, the air now has a RH of only 10%.

Drying moist air in this way is basically like wringing moisture from a wet sponge.



You start to squeeze the sponge and it gets smaller.  That's like cooling the air and reducing the saturation mixing ratio, the air's capacity for water vapor.  At first squeezing the sponge doesn't cause anything to happen (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 original shape and size (the air warms back to its original temperature).  The sponge (and the air) will be drier than when you started.


Dry air indoors in the winter
The air indoors in the winter is often quite dry (low values of the mixing ratio and relative humidity).


In the winter, cold air is brought inside your house or apartment and warmed.  Imagine foggy 30 F air (with a RH of 100% this is a best case scenario, the cold air outdoors usually has a relative humidity less than 100% and is drier). Bringing the air inside and warming it will cause the RH to drop from 100% to 20%..  This can cause chapped skin, can irritate nasal passages, and causes cat's fur to become charged with static electricity. 




The air in an airplane comes from outside the plane.  The air outside the plane can be very cold (-60 F perhaps) and contains very little water vapor (even if the -60 F air is saturated it would contain essentially no water vapor).  When brought inside and warmed to a comfortable temperature, the RH of the air in the plane would be essentially 0%.  The RH doesn't get this low because the airplane adds moisture to the air to make to make the cabin environment tolerable.  Still the RH of the air inside the plane is pretty low and passengers often complain of dehydration on long airplane flights.  This may increase the risk of catching a cold (ref)

The rain-shadow effect

Next a much more important example of drying moist air (see p. 88 in the photocopied ClassNotes).


We start with some moist but unsaturated air (the RH is about 50%) at Point 1 (the air and dew point temperatures would need to be equal in order for the air to be saturated).  As it is moving toward the right the air runs into a mountain and starts to rise (this is the 4th way of causing rising air motions).  Rising air expands and cools.   Unsaturated air cools 10 C for every kilometer of altitude gain (this is known as the dry adiabatic lapse rate but isn't something you need to remember).  So after rising 1 km the air will cool to 10 C which is the dew point.

The air becomes saturated at Point 2 (the air temperature and the dew point are both 10 C).  Would you be able to tell if you were outdoors looking at the mountain?  Yes, you would see a cloud appear. 

Now that the RH = 100%, the saturated air cools at a slower rate than unsaturated air (condensation of water vapor releases latent heat energy inside the rising volume of air, this warming partly offsets the cooling caused by expansion).  We'll use a value of 6 C/km (an average value).  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.  Moisture is being removed from the air and the value of the mixing ratio (and the dew point temperature) decreases.

At Point 4 the air starts back down the right side of the mountain.  Sinking air is compressed and warms.  As soon as the air starts to sink and warm, the relative humidity drops below 100% and the cloud disappears.  The sinking unsaturated 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 = 10 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.  Rain is less likely because the air is sinking and because the air on the downwind side is drier than it was on the upslope side.





We can see the effects of a rain shadow illustrated well in the state of Oregon.  The figure above at left shows the topography (here's the source of that map).  Winds generally blow from west to east across the state. 

Coming off the Pacific Ocean the winds first encounter a coastal range of mountains.  On the precipitation map above at right (source) you see a lot of greens and blue on the western sides of the coastal range.  These colors indicate yearly rainfall totals that range from about 50 to more than 180 inches of rain per year.  Temperate rainforests are found in some of these coastal locations.  The line separating the green and yellow on the left side of the precipitation map is the summit, the ridgeline, of the coastal mountain range.

That's the Willamette River valley, I think, in between the coastal range and the Cascades.  This valley is somewhat drier than the coast because air moving off the Pacific has lost some of its moisture moving over the coastal range. 

What moisture does remain in the air is removed as the winds move up and over the taller Cascades.  The boundary between yellow/green and the red is the ridgeline of the Cascade Mountains.  Yearly rainfall is generally less than 20 inches per year on the eastern side, the rain shadow side, of the Cascades.    That's not too much more than Tucson which averages about 12 inches of rain a year.

Death valley is found on the downwind side of the Sierra Nevada mountains (source of left image).  The Chihuahuan desert and the Sonoran desert are found downwind of the Sierra Madre mountains in Mexico (source of the right image).  Mexico might be a little harder to figure out because moist air can move into the interior of the country from the east and west at different times of the year.  It does appear that the eastern slopes of the two mountain ranges are the wettest so much of that precipitation must come from moist air moving in from the east (rising air motions on the eastern mountain slopes).

Most of the year,  the air that arrives in Arizona comes from the west, from the Pacific Ocean (this changes in the summer).  It usually isn't very moist by the time it reaches Arizona because it has traveled up and over the Sierra Nevada mountains in California and the Sierra Madre mountains further south in Mexico.  The air loses much of its moisture on the western slopes of those mountains.   Beginning in early July in southern Arizona we start to get air coming from the south or southeast.  This air can be much moister and leads to development of our summer thunderstorms.

Just as some of the world's driest regions are found on the downwind side (the rain shadow side) of mountain ranges, some of the wettest locations on earth are on the upwind sides of mountains.  There seems to be some debate whether Mt. Wai'ale'ale in Hawaii or Cherrapunji India gets the most rain per year.  Both get between 450 and 500 inches of rain per year.


Processes that cause air to rise
You might not have noticed that while covering the rain shadow effect we came across another process that causes rising air motions.  Rising air expands and cools.  Now you should know that if you cool moist air to its dew point, the relative humidity increases to 100% and clouds form.   Here's a pictorial summary of the four processes that cause rising air motions.


The newest process is called orographic or topographic lifting.

One way of measuring humidity - a sling (swing) psychrometer

A short discussion of how you might try to measure humidity (short because it's a topic that tends to put people to sleep).  One of the ways is to use a sling (swing is more descriptive) psychrometer.



A sling psychrometer consists of two thermometers mounted side by side.  One is an ordinary thermometer, the other 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.  The dry thermometer measures the air temperature. 

Would the wet thermometer be warmer or colder or the same as the dry thermometer?   You can check it out for yourself - go get one of your hands wet.  Does it feel the same as the dry hand?  You might blow on both hands to increase the evaporation from the wet hand.  I think you'll find the wet hand feels colder.  That's what happens with the wet bulb thermometer.


What could you say about the relative humidity in these two situations (you can assume the air temperature is the same in both pictures).  You would feel coldest on a dry day (the left picture indicates dry air).  The evaporative coolers that people like me use in Tucson in the summer work much better (more cooling) early in the summer when the air is dry.  Once the thunderstorm season begins in July and the air is more humid it is hard to cool your house below 80 F (but by then you're used to it and it doesn't matter too much).

You feel colder because energy is needed in order for water to evaporate.  The energy in the cases above come from your body.  When your body starts to lose energy you feel cold.

Here are a bunch of details that you can read through if you're so inclined.  My goal is that you understand the basic principle behind a sling psychrometer.  If you'd rather not worry about the details skip to the summary a few pictures further on. 

You need to be aware of a few things to understand the details that follow:
(1a) evaporation is a cooling process
(1b) warm water evaporates more rapidly than cold water

(2a) condensation is a warming process, whenever there is any moisture in the air there will be some condensation
(2b) the rate of condensation depends on how much water vapor is in the air

(3) these two phenomena, evaporation and condensation, operate independently of each other

Here's the situation on a day with low relative humidity.

The figure shows what will happen as you start to swing the wet bulb thermometer.  Water will begin to evaporate from the wet piece of cloth.  The amount or rate of evaporation will depend on the water temperature  Warm water evaporates at a higher rate than cool water (think of a steaming cup of hot tea and a glass of ice tea).

The evaporation is shown as blue arrows because this will cool the thermometer.   The water on the wet thermometer starts out at 80 F and evaporates fairly rapidly.

The figure at upper left also shows one arrow of condensation.  The amount or rate of condensation depends on how much water vapor is in the air surrounding the thermometer.  In this case (low relative humidity) there isn't much water vapor.  The condensation arrow is orange because the condensation will release latent heat and warm the thermometer.

Because there is more evaporation (4 arrows) than condensation (1 arrow) the wet bulb thermometer will drop.  As the thermometer cools the rate of evaporation will decrease.  The thermometer will continue to cool until the evaporation has decreased enough that it balances the condensation.


The rates of evaporation and condensation are equal.  The temperature will now remain constant.

The figure below shows the situation on a day with higher relative humidity.  There's enough moisture in the air to provide 3 arrows of condensation. 


The rate of evaporation stays the same, the rate of condensation is higher.  The rate of evaporation is still higher than condensation but not by much. 




There'll only be a little cooling before the evaporation is reduced enough to be in balance with condensation.

Here's the summary



A large difference between the dry and wet temperatures means the relative humidity is low.  A small difference means the RH is higher.  No difference  means the relative humidity is 100%. 

We saw the same kind of relationship between RH and the difference between air and dew point temperature.


The drinking bird
Evaporative cooling and the dependence of saturation mixing ratio on temperature are both involved in the "drinking bird".


I'm very proud of the bird I found online.  It is about twice as big as what you normally find.  The bird is filled with a volatile liquid of some kind (ether?).  Initially the bird's head and tail are the same temperature.  The liquid inside the bird evaporates and saturates the air inside with vapor.

Next you get the bird's head wet.  Instead of water I cheat a little bit and use isopropyl alcohol (rubbing alcohol) because it evaporates more rapidly than water.  The evaporation of alcohol, just as with water, cools the bird's head.

As we saw last week, the saturation mixing ratio (saturation vapor concentration) of water depends on temperature.  Warm air can contain more water vapor than colder air.  The same applies to the ether vapor in this case.  The head is still saturated with vapor but there is less vapor in the cool head than there is in warm saturated air in the bird's tail.

The differences in amounts of vapor produce pressure differences.  The higher pressure at the bottom pushes liquid up the stem of the bird.  The bird becomes top heavy and starts to tip.

At some point the bottom end of the stem comes out of the pool of liquid at the base.  Liquid drains from the neck and the bird straightens up.

 
You can arrange the bird so that when it tips its beak dips into a small cup of water (or alcohol).  This keeps the head moist and cool and the dipping motion could go on indefinitely.  Here's a video.

We took away the bird's supply of alcohol, the bird warmed up and stopped tipping.

Wind chill and heat index




Cold temperatures and wind make it feel colder than it really is.   The wind chill temperature tells you how much colder it will feel ( a thermometer would measure the same temperature on both the calm and the windy day).  If your body isn't able to keep up with the heat loss, you can get hypothermia and die.

There's something like that involving heat and humidity.  High temperature and high humidity makes it feel hotter than it really is.  Your body tries to stay cool by perspiring.  You would feel hot on a dry 105 F day.  You'll feel even hotter on a 105 F day with high relative humidity because your sweat won't evaporate as quickly.  The heat index measures how much hotter you'd feel. The combination of heat and high humidity is a serious, potentially deadly, weather hazard because it can cause heatstroke (hyperthermia).  A thermometer (a dry thermometer) would measure the same 105 F temperature on both a dry and a humid day.