Wednesday, Nov. 7, 2012

"Sometime Around Midnight" from The Airborne Toxic Event and "I Will Wait" from Mumford and Sons.

Now that the election is over I'll be able to get back to work (and not have to spend so much time looking at the latest swing state polls).  Here are some of the items I'd like to get done in the next few days.

I should have the Expt. #3 reports graded by Friday.  The Quiz #4 Study Guide Pt. 1 is already available online.  My hope is that you'll start to look through some of that material now.  There'll be at least one more 1S1P topic available by Friday. 

The weather forecasting people are predicting windy, cold,  and possibly wet weather for this coming weekend. 

Next Monday is a holiday (Veteran's Day).  The will hopefully give me time enough to grade the Scientific Paper reports and to produce updated grade summaries.

There's a common misconception involving the Coriolis force.  You might have heard that water spins in a different direction when it drains from a sink or a toilet bowl in the southern hemisphere than it does in the northern hemisphere.  You might also have heard that this is due to the Coriolis force or the Coriolis effect. 

The Coriolis force does cause winds to spin in opposite directions around large scale high and low pressure centers in the northern and southern hemisphere.  The PGF starts the air moving (in toward low, out and away from high pressure) then the Coriolis force bends the wind to the right (N. hemisphere) or to the left (S. hemisphere).

Here's what you end up with in the case of low pressure (you'll find these figures on p. 130 in the photocopied ClassNotes):

Air starts to move inward toward low pressure (the dots show this initial motion).  Then the Coriolis force causes it to turn to the right or left depending on which hemisphere you're in.  You should be able to say which of the pictures above is the northern hemisphere and which is the southern hemisphere picture.

The same kind of idea applies to high pressure except that the air starts moving outward  (the dots aren't included here).  The Coriolis force then turns it to the right or left.

There are situations where the PGF is much stronger than the CF and the CF can be ignored.  A tornado is an example.  The PGF is much much stronger than the CF and the CF can be ignored.  Winds can blow around Low pressure because the PGF points inward.

The wind can spin in either direction in either hemisphere.

Note that without the CF, winds can't spin around High pressure because there is nothing to provide the needed inward force.

OK, what about water draining from sinks, buckets, toilets etc.

There's just an inward pointing PGF, no CF.  Water can spin in either direction in either hemisphere.  What causes the inward pointing PGF?  The water at the end of the spinning water is a little deeper than in the middle.  Since pressure depends on weight, the pressure at the outer edge of the spinning water is higher than in the center.  This creates the inward pointing pressure gradient (pressure difference) force.

Water draining from a sink or toilet can spin in either direction.  It doesn't matter where you're located. 

But this something we should probably checkout for ourselves, so here is one of my favorite Optional Assignments of the semester.  You must submit the assignment by 5 pm on Friday.

The first thing we'll do today is look at and try to understand the development of a thermal circulation.

Differences in temperature like you might find between a coast and the ocean or between a city and the surrounding country side can create horizontal pressure differences. The horizontal pressure gradient can then produce a wind flow pattern known as a thermal circulation. 

When dealing with these usually small scale circulations, the pressure gradient force is often so much stronger than the Coriolis force that the Coriolis force can be ignored.

We will learn how thermal circulations develop and then apply to concept to the earth as a whole in order to understand large global scale pressure and wind patterns.  You really can't ignore the Coriolis force in a situation like that so the concept is not really applicable on that scale.  But much of what it predicts is actually found in the real world.  That's why we'll cover and study this topic. 

Thermal Circulations
You'll find this discussed on p. 131 in the photocopied Class Notes.

The figures below are more carefully drawn versions of what is in the ClassNotes.

The picture shows a sea coast.  There aren't any temperature differences yet in this picture (both the ocean and the land are shaded green), so the pressure at the ground and above the ground are the same over the land and over the ocean.

A beach will often become much warmer than the nearby ocean during the day (the sand gets hot enough that it is painful to walk across in bare feet). The ocean has higher specific heat, is much harder to warm, and won't change temperature much during the day.  The warm ground will warm the air above.  Pressure decreases more slowly as you move upward through warm low density air (this is something we covered early in the semester).  As you move from the ground to the level of the green line in the picture above pressure decreases 90 mb in the warm air and a little more, 100 mb, in the cooler denser air over the ocean.

Here's another way of arriving at the same result.

The layer of warm air on the left expands, ushing the 900 mb pressure level to a higher level than it would normally be found.  910 mb pressure from a little lower altitude moves in to take its place. 

The temperature differences at the ground have created an upper level pressure gradient (pressure difference), higher pressure (910 mb) on the left and lower pressure (900 mb) on the right.  The resulting pressure gradient force (PGF) causes air to start to blow from left to right.

The upper level winds (which remove air from the left side of the picture and add it to the right) will then affect the surface pressure pattern.

The sea level pressure is determined by the weight of the air overhead.  Air leaving the left side of the picture will lower the surface pressure (from 1000 mb to 990 mb).  Adding air aloft to the right side of the picture will increase the surface pressure (from 1000 mb to 1010 mb).  Surface winds will start to blow from right to left.

You can complete the circulation loop by adding rising air above the surface low pressure at left and sinking air above the surface high at right.  The surface winds which blow from the ocean onto land are called a sea breeze (the name tells you where the winds come from).  Since this air is likely to be moist, cloud formation is likely when the air rises over the warm ground.  Rising air expands and cools.  If you cool moist air to its dew point, clouds form.

Here's a short cut that will allow you to quickly figure the directions of the winds in a thermal circulation without going through a long-winded development like we just done.  Just

remember that warm air rises 

Draw in a rising air arrow above the warm part of the picture, then complete the loop.

At night the ground cools more quickly than the ocean and becomes colder than the water (the water temperature didn't change at all in the picture below).  Rising air is found over the ocean water because it is warmer than the land.  The thermal circulation pattern reverses direction.  Surface winds blow from the land out over the ocean.  This is referred to as a land breeze.

Clouds now form out over the ocean.

Here are some additional examples of thermal circulations or large scale circulations that resemble thermal circulations. 

Cities are often warmer than the surrounding countryside, especially at night.  This is referred to as the urban heat island effect.  This difference in temperature can create a "country breeze."  This will sometimes carry pollutants from a factory or odors from a sewer treatment plant located outside the city back into town.

The Asian monsoon is a large scale circulation pattern and is much more complex than a simple thermal circulation.  However you can use the thermal circulation concept to get a general understanding of what to expect at different times of the year.  Before looking at that let's be clear about the meaning of the term monsoon.

Monsoon just refers to a seasonal change in the direction of the prevailing winds.  Most of the year in Arizona winds come from the west and are dry.  For 2 or 3 months in the summer winds come from the south and southeast.  This is when we get our summer thunderstorm season or summer monsoon.  The term monsoon is often used (incorrectly) to refer to the thundertstorms themseolves.

In the summer land masses in India and Asia become warmer than the oceans nearby.  Surface low pressure forms over the land, moist winds blow from the ocean onshore, and very large amounts of rain can follow.  A map view (top view) is shown at left, a crossectional view is shown at right (it resembles a large sea breeze).

The winds change directions in the winter when the land becomes colder than the ocean.

You can also use the thermal circulation to understand some of the basic features of the El Nino phenomenon (you find a discussion of the El Nino on pps 135-139 in the photocopied Classnotes). 

First here is what conditions look like in the tropical Pacific Ocean in non-El Nino years (top and side views again)

Cold ocean currents along the west coasts of N. America and S. American normally converge at the equator and begin to flow westward (see top view above).  As the water travels westward it warms.  Some of the warmest sea surface waters on earth are normally found in the western Tropical Pacific (this is also where hurricanes are most frequent).  A temperature gradient becomes established between the W. and E. ends of the tropical Pacific. The crossectional view above shows the normal temperature and circulation pattern found in the equatorial Pacific Ocean.   You would find surface high pressure in the east and low pressure in the west.  Note that the wind circulation pattern is the same as the simple thermal circulation we studied above.

During a La Nina event, waters in the Eastern Pacific are even colder than normal.  This generally produces drier than normal conditions during the winter in the desert SW.  This was the case last winter.  You can read more about La Nina here.

Every few years El Nino conditions occur and the cold currents don't make it to the Equator.  Warm water is carried from the western Pacific to the eastern Pacific.  The temperature and pressure basically reverses itself.

Now surface high pressure is found in the west and surface low pressure and rising air is found in the E. Pacific (the reversal in the surface pressure pattern is referred to as the southern oscillation).  Indonesia and Australia often experience drought conditions (and devastating wildfires) during El Nino years.  In the desert SW we expect slightly wetter than normal conditions (perhaps 20% wetter than normal).  Wetter conditions are also found in California and in the SE US.

Here's a map showing the effects of El Nino and La Nina conditions on winter weather in N. America (source).  This map wasn't shown in class.

Now we are next going to use the thermal circulation idea to learn something about global scale pressure and wind patterns on the earth.  Ordinarily you couldn't apply a small scale phenomena like a thermal circulation to the much larger global scale.  However if we make some simplifying assumptions, particularly if we assume that the earth doesn't rotate or only rotates slowly, we can ignore the Coriolis force and a thermal circulation would become established.

Some additional simplifications are also made and are listed below (p. 133 in the photocopied Classnotes).  The figures are more carefully drawn versions of what was done in class.

Because the earth isn't tilted, the incoming sunlight shines on the earth most directly at the equator.  The equator will become hotter than the poles.  By allowing the earth to rotate slowly we spread this warmth out in a belt that circles the globe at the equator rather than concentrating it in a spot on the side of the earth facing the sun.  Because the earth is of uniform composition there aren't any temperature differences created between oceans and continents.

You can see the wind circulation pattern that would develop.  You'd find rising air at the equator (the "warm air rises" shortcut rule again).  Upper level winds would blow from equator toward the N and S Poles.  Winds would converge and sink at the poles.  Surface winds would blow from the poles toward the equator.  The term one cell just refers to the single complete loop in each hemisphere.

Next we will remove the assumption concerning the rotation of the earth.  We won't be able to ignore the Coriolis force now.

Here's what a computer would predict you would now see on the earth.  The temperature pattern remains the same and things are pretty much the same at the equator in the three cell and one cell models: surface low pressure and rising air.  At upper levels the winds begin to blow from the equator toward the poles.  Once headed toward the poles the upper level winds are deflected by the Coriolis force.  There end up being three closed loops in the northern and in the southern hemispheres.  There are surface belts of low pressure at the equator (the equatorial low) and at 60 degrees latitude (the subpolar low). There are belts of high pressure (the subtropical high) at 30 latitude and high pressure centers at the two poles (the polar highs).

On Friday we will look at the 3-cell model surface features (pressure belts and winds) in a little more detail because some of what is predicted, even with the unrealistic assumptions, is actually found on the earth.