Wednesday Mar. 20, 2013
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Some music, "Like I Do", from Rupa and the April Fishes to get my newly acquired jumping beans dancing before class today.

Ultimately a grand total of 3 students found the short Optional Assignment that was hidden in Monday's online notes.  Don't worry if you didn't do the assignment, it was only worth 0.15 extra credit points.  A somewhat longer Optional Assignment, worth 0.5 points, was handed out in class today.  This latest assignment is due Mon., Mar. 25.


Roughly the first half of class today involved working through a couple of humidity problems.  As you work through the problems you will, hopefully, begin to better understand roles of the various humidity variables and when and why their values change. 

Example #1
I gave my notes from class to a student so I'm using notes from a previous class.
In this example you are given an air temperature of 90 F and a mixing ratio value of 6 g/kg.  You are supposed to determine the mixing ratio and the dew point temperature.


These notes from class would be hard enough to sort out even if you were in class.  So we'll work through this problem in a more detailed, step-by-step manner.


We're given an air temperature of 90 F and a mixing ratio (r) of 6 g/kg.  We're  supposed to find the relative humidity (RH) and the dew point temperature.  We start by entering this data in the table.

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 above.

(A) We imagined cooling the air from 90F to 70F, then to 55F, and finally to 45F.

(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 kind of a special point.  You have cooled the air until it has become saturated.  The dew point temperature in this problem is 45 F.

What would happen if we cooled the air further still, 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.

In many ways cooling moist air is liking squeezing a moist sponge (this figure 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 (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).

Example 2
We're given an air temperature of 90 F and a relative humidity of 50%; we'll try to figure out the mixing ratio and the dew point temperature.  Here's something like what we ended up with in class.


 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 might be able to figure out the mixing ratio in your head.  Air that is filled to 50% of its capacity could hold up to 30 g/kg.  Half of 30 is 15, that is the mixing ratio.  Or you can substitute into the relative humidity formula and solve for the mixing ratio.  The details of that calculation are shown above at B.


Finally you imagine cooling the air.  The saturation mixing ratio decreases, 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 to learn and understand a useful rule.


In the first example the difference between the air and dew point temperatures was large (45 F) and the RH was low (20%).

In the 2nd problem the difference between the air and dew point temperatures was smaller (20 F) and the RH was higher (50%). 

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 then would be 100%.

That was about all the time we had for relative humidity in class today.  We'll do a couple more example problems on Friday. 

Today is the Spring Equinox (it was actually at 4:02 am MST).  We can't let a big event like that go unnoticed.  The Fall Equinox will be on Sept. 22 this year.


The figure above shows the earth orbiting the sun. 

On or around Dec. 21st, the winter solstice, the north pole is tilted away from the sun.  Note that a small portion of the earth near the N. Pole (north of the Arctic Circle) spends 24 hours in darkness.  Days are less than 12 hours long in the northern hemisphere and the sun is low in the sky.  Both factors reduce the amount of sunlight energy reaching the ground.  That's why it's cold and wintry.

On June 21st, the summer solstice, the north pole is tilted toward the sun.  Now there are 24 hours of sunlight north of the Arctic Circle.  Days are more than 12 hours long in the northern hemisphere and the sun is high in the sky at noon.  A lot more sunlight energy reaches the ground; that's why it is summer.

The equinoxes are a time of transition.  On the equinoxes, the N. Pole still tilted just not toward or away from the sun.  The line separating day and night passes through the pole and the days and nights are each about 12 hours long everywhere on earth (except perhaps at the poles). 

The drawing below shows you what you would see at sunrise (about 6:30 am) on the Spring Equinox here in Tucson (the same would happen on the Fall Equinox).  The sun rises exactly in the east on the equinoxes.  The rest of the year it is a little to the north or south of east.


At noon you would need to look due south to see the sun.


The sun reaches its highest point in the sky at noon.  On the equinoxes in Tucson that's almost 60 degrees.  The sun is lower in the sky (34.5 degrees above the horizon) on the winter solstice.  That together with the fact that the days are shorter means much less sunlight energy reaches the ground.  In the summer the days are longer and the sun gets much higher in the sky at noon (81.5 degrees above the horizon, nearly overhead).  Much more sunlight energy reaches the ground and it is much warmer.

The sun passes directly overhead at the equator at noon on the equinoxes.


The sun sets exactly in the west on the equinoxes at about 6:30 pm in Tucson.
This is the 2 pm class.  Most of you are more likely (perhaps) to see the sun set than see the sun rise.  The figure below shows you about what you would see if you looked west on Speedway (from Treat Ave.) at sunset.  In the winter the sun will set south of west, in the summer north of west (probably further south and north than shown here).  On the equinoxes the sun sets exactly in the west.  This is something you should check out for yourself this week before the sun moves noticeably to the north of due west.



Something else to note in this figure.  Note how the sun is changing color.  It changes from a bright yellow white to almost red by the time it sets..  This is due to scattering of sunlight by air.  The shorter wavelengths (violet, blue, green) are scattered more readily than the longer wavelengths.  At sunset the rays of sunlight take a much longer slanted path through the atmosphere and most of the shorter wavelengths are scattered and removed from the beam of sunlight.  All that's left in the beam of light that reaches your eyes are the longer wavelengths: yellow, orange, and red.

You might have noticed that the sketch seems to be pretty carefully drawn.  That's because several years ago I positioned myself in the median near the intersection of Treat and Speedway and pointed my camera west.  I took a multiple exposure photograph of the sun over a 2 or 3 hour period that ended at sunset.  Here's the photo I ended up with (it's a copy of a copy so that picture quality isn't all that great):



If you aren't careful, you can get yourself seriously injured, even killed, on or around the equinoxes.  Here's an article that appeared in the Arizona Daily Star at the time of the 2011 Fall equinox.
December 21, the summer solstice, is the shortest day of the year (about 10 hours of daylight in Tucson).  The days have slowly been getting longer since then. The rate of change is greatest at the time of the equinox.

This will continue up until June 21, the summer solstice, when there will be about 14 hours of daylight.  After that the days will start to shorten again as we make our way back to the winter solstice.
There was a very interesting coincidence a few semester's ago.  We were covering some of this same material in class on Friday Sep. 23.  There were a few parents in class because it was Parent's Weekend.  I showed these same pictures on that afternoon.  One of the parents came up to the front after class and mentioned having seeing the sun right at the end of 77th St. in New York City around this time of year.  That got me thinking that a picture of sunset at the end of one of the long streets with all the tall buildings might be spectacular.

When I started looking however I found that the major streets in Manhattan aren't oriented EW and NS.  You can see this on a Google map of Manhattan.  77th St. is oriented in more of a NW-SE direction.   So the sun doesn't shine straight down 77th St. at sunrise and sunset on the equinoxes.  I was pretty disappointed but then I stumbled on the this Manhattanhenge map which shows the direction of sunset (the left, west, side of the map) and sunrise (the right, east, side of the map) at various times of the year. 

  If you remember that as you move past the Spring Equinox toward summer sunrise move north of east and sunset is north of west.  On May 31 the sun has moved far enough north that it does set right at the west end of 77th St.  Sunset continues to move north up until the summer solstice on June 21.  Then the sunset starts to move back south.  You can again see the sunset at the west end of 77th St. on July 12 and 13.  Here's a gallery of Manhattanhenge images.  That would certainly make a worthwhile field trip in Atmo 170A1 if the semester went that long.  The "henge" part of the name comes from Stonehenge where the rising and setting sun aligns with stones on the solstices.

Manhattanhenge is a little confusing and hard to figure out.  But do look at the photographs with the idea that you can see something similar here in Tucson on the equinoxes (minus all the tall buildings).

You can also see the sunrise at the east end of 77th St.  But sunrise has to be in the southeast.  This takes place on Dec. 5 and Jan. 8, just before and just after the winter solstice.