Tue., Sep. 18 notes

Tuesday Sept. 18, 2007

The optional assignments were returned in class today. The answers are available online. If you don't see a grade on your paper you received full credit (0.5 extra credit) points.

A copy of the Quiz #1 Study Guide was handed out. This week's quiz will cover material on both the Practice Quiz (~50%) and Quiz #1 (~50%) Study Guides.

The appearance of the Atmospheric Sciences webpage has changed significantly. Click on the Courses link near the top center of the page to find the web page for this class.

The Experiment #1 reports and the 1S1P Assignment #1 reports were collected in class today. It will take about a week to grade the experiment reports. It will take at least a week to grade all of the 1S1P reports.

Today we finish the section of understanding why warm air rises and cold air sinks. It has been a long 3-step process.

In the first step we learned about the 2 forms of the ideal gas law equation which show how the pressure produced by air inside a balloon depends on variables such as air temperature, air density, number of air molecules and the volume of the balloon.

In the second step we learned that when you warm a parcel of air in the atmosphere, the parcel volume will increase and the air density will decrease in order to keep the air pressure in the parcel constant. Cooling a parcel of air causes a decrease in volume and an increase in air density but pressure stays constant. This is Charles' Law and allows us to make the association warm air = low density air and cold air = high density air.

Now the final step, we must learn about the vertical forces that operate on a parcel of air in the atmosphere.

Air has mass and weight When an air parcel has the same temperature, pressure, and density as the air around it, the parcel will remain stationary. With gravity pulling downward on the air, there must be another force pointing upward of equal strength. The upward force is caused by pressure differences between the bottom (higher pressure pushing up) and top of the balloon (slightly lower pressure pushing down on the balloon).

If the balloon is filled with warm, low density air the gravity force will weaken (there is less air in the balloon so it weighs less). The upward pressure difference force (which depends on the surrounding air) will not change. The upward force will be stronger than the downward force and the balloon will rise.

Conversely if a balloon is filled with cold high density air, the balloon gets heavier. The upward pressure difference force doesn't change. The net force is now downward and the balloon will sink.

We modified the Charles Law demonstration (performed in class last Friday). We used a balloon filled with helium instead of air (see bottom of p. 54 in the photocopied Class Notes). Helium is less dense than air even when the helium has the same temperature as the surrounding air. A helium-filled balloon doesn't need to warmed up in order to rise.

We dunked the helium-filled balloon in some liquid nitrogen to cool it and to cause the density of the helium to increase. When removed from the liquid nitrogen the balloon can't rise, the gas inside is denser than the surrounding air (the purple and blue balloons in the figure above). As the balloon warms and expands its density decreases. The balloon at some point has the same density as the air around it (green above) and is neutrally bouyant. Eventually the balloon becomes less dense that the surrounding air (yellow) and floats up to the ceiling.

You might have a look at the material on Archimedes' Law on pps 53a and 53b in the photocopied Class Notes. That explains this same material in a slightly different, perhaps clearer, way.

Next learned a little bit about upper level charts. These maps show conditions at various altitudes above the ground. Conditions up there are important because they can strongly influence conditions at the ground. Many of the figures below differ somewhat from those used in class. The figures below have hopefully been drawn more carefully and clearly.

At this point there are three basic things to know about upper level charts. First the overall appearance is somewhat different from a surface weather map. On a surface map you generally find circular (more or less) centers of high and low pressure. You can also find closed high and low pressure centers at upper levels, but more generally you find a wavy pattern like sketched below.

The U-shaped portion of the pattern is called a trough. The n-shaped portion is called a ridge.

Troughs are produced by large volumes of cool or cold air. The western half of the country in the map above would probably be experiencing colder than average temperatures. Large volumes of warm or hot air produce ridges.

The winds on upper level charts blow parallel to the contour lines. On a surface map the winds cross the isobars slightly, spiralling into centers of low pressure and outward away from centers of high pressure. The winds generally blow from west to east.

Next we will look at some of the interactions between features on surface and upper level charts

On the surface map you see centers of HIGH and LOW pressure. The low pressure center, together with the cold and warm fronts, is a middle latitude storm.

Note how the counterclockwise winds spinning around the LOW move warm air northward (behind the warm front on the eastern side of the LOW) and cold air southward (behind the cold front on the western side of the LOW). Clockwise winds spinning around the HIGH also move warm and cold air. The winds are shown with thin brown arrows on the surface map.

Note the ridge and trough features on the upper level chart. We learned that warm air is found below an upper level ridge. Now you can begin to see the source of this warm air. Warm air is found west of the HIGH and to the east of the LOW. This is where the two ridges on the upper level chart are also found. You expect to find cold air below an upper level trough. This cold air is being moved into the middle of the US by the northerly winds that are found between the HIGH and the LOW.

Note the yellow X marked on the upper level chart directly above the surface LOW. This is a good location for a surface LOW to develop and strengthen (the surface low pressure will get even lower) We will find that this is frequently a location where there is upper level divergence. Similary the pink X is where you often find upper level convergence. This could cause surface high pressure to get even higher.

Now we need to look in a little more detail at how upper level winds can affect the development or intensification of a surface storm.

The surface winds are spinning counterclockwise and spiralling in toward the center of the surface low in the figure above (see p. 42 in the photocopied Class Notes). This adds air to the cylinder of atmosphere. Adding air to the cylinder means the cylinder will weigh more and you would expect the surface pressure (which is determined by the weight of the air overhead) to increase.

We'll just make up some numbers, this might make this clearer.

You'll find this figure on p. 42a in the Class Notes. At the top we will assume the surface low has 960 mb pressure. Imagine that each of the surface wind arrows winds brings in enough air to increase the pressure at the center of the LOW by 10 mb. You would expect the pressure at the center of the LOW to increase from 960 mb to 1000 mb.

This is just like a bank account. You have $960 in the bank and make four $10 dollar deposits. You would expect your bank account balance to increase from $960 to $1000.

But what if the surface pressure decreased from 960 mb to 950 mb as shown in the following figure?

The next figure shows us what could be happening (back to p. 42 in the Class Notes).

There may be some upper level divergence (more arrows leaving the cylinder than going in ). Upper level divergence removes air from the cylinder and would decrease the weight of the cylinder.

We need to determine which of the two (converging winds at the surface vs divergence at upper levels) is dominant. That will determine what happens to the surface pressure.

Again some actual numbers might help (see p. 42b in the Class Notes)

The 40 millibars worth of surface convergence is shown at Point 1. Up at Point 2 there are 50 mb of air entering the cylinder but 100 mb leaving. That is a net loss of 50 mb. At Point 3 we see the overall result, a net loss of 10 mb. The surface pressure should decrease from 960 mb to 950 mb. That change is reflected in the next picture (found at the bottom of p. 42b in the Class Notes).

The surface pressure is 950 mb. This means there is more of a pressure difference between the low pressure in the center of the storm and the pressure surrounding the storm. The surface storm has intensified and the surface winds will blow faster and carry more air into the cylinder (the surface wind arrows each now carry 12.5 mb of air instead of 10 mb). The converging surface winds add 50 mb of air to the cylinder (Point 1), the upper level divergence removes 50 mb of air from the cylinder (Point 2). Convergence and divergence are in balance (Point 3). The storm won't intensify any further.

Click here for some additional examples. By working through some additional examples you might increase your understanding of this material and build up your confidence (of course there's always a chance that more examples will just make this topic more confusing - the choice is yours)

We're almost done, one last figure (it's the figure on p. 41 in the photocopied Class Notes again with some new information added (redrawn here for improved clarity)

Now that you have some idea of what upper level divergence looks like you are in a position to understand another one of the relationships between the surface and upper level winds.

One of the things we have learned about surface LOW pressure is that the converging surface winds create rising air motions. The figure above gives you an idea of what can happen to this rising air (it has to go somewhere). Note the upper level divergence in the figure: two arrows of air coming into the point "DIV" and three arrows of air leaving (more air going out than coming in is what makes this divergence). The rising air can, in effect, supply the extra arrow's worth of air.

Three arrows of air come into the point marked "CONV" on the upper level chart and two leave (more air coming in than going out). What happens to the extra arrow? It sinks, it is the source of the sinking air found above surface high pressure.

We spent the last few minutes of class watching another short segment of video featuring Auguste and Jacques Piccard. In this video they descended to a depth of 10,000 feet in the ocean in a bathyscaph.