The average change in the date of "first leaf" in the United States. Note that states farther to the north have seen greater change. Image from the interactive by Climate Central.
In Missouri, between 1981 and 2010 the average date at which trees first showed their leaves was two days earlier than the average between 1951 and 1980, according to this graphic by Climate Central.
You’ll also note the north-south trend, where change is greater as you go north. Most models predict that global warming/climate change due to increasing carbon dioxide will result in bigger changes as you get toward the poles.
Energy cannot be either created or destroyed, just changed from one form to another. That is one of the fundamental insights into the way the universe works. In physics it’s referred to as the Law of Conservation of Energy, and is the basic starting point for solving a lot of physical problems. One great example is calculating the average temperature of the Earth, based on the balance between the amount of energy it receives from the Sun, versus the amount of energy it radiates into space.
The Temperature of Radiation
Anything with a temperature that’s not at absolute zero is giving off energy. You right now are radiating heat. Since temperature is a way of measuring the amount of energy in an object (it’s part of its internal energy), when you give off heat energy it lowers your body temperature. The equation that links the amount of radiation to the temperature is called the Stefan-Boltzman Law:
where:
ER = energy radiated (W/m-2)
T = temperature (in Kelvin)
s = constant (5.67 x 10-8 W m-2 K-4)
Now if we know the surface area of the Earth (and assume the entire area is radiating energy), we can calculate how much energy is given off if we know the average global temperature (the radius of the Earth = 6371 km ). But the temperature is what we’re trying to find, so instead we’re going to have to figure out the amount of energy the Earth radiates. And for this, fortunately, we have the conservation of energy law.
Energy Balance for the Earth
Simply put, the amount of energy the Earth radiates has to be equal to the amount of energy gets from the Sun. If the Earth got more energy than it radiated the temperature would go up, if it got less the temperature would go down. Seen from space, the average temperature of the Earth from year to year stays about the same; global warming is actually a different issue.
So the energy radiated (ER) must be equal to the energy absorbed (EA) by the Earth.
Now we just have to figure out the amount of solar energy that’s absorbed.
Incoming Solar Radiation
The Sun delivers 1367 Watts of energy for every square meter it hits directly on the Earth (1367 W/m-2). Not all of it is absorbed though, but since the energy in solar radiation can’t just disappear, we can account for it simply:
Some if the light energy just bounces off back into space. On average, the Earth reflects about 30% of the light. The term for the fraction reflected is albedo.
What’s not reflected is absorbed.
So now, if we know how many square meters of sunlight hit the Earth, we can calculate the total energy absorbed by the Earth.
The solar energy absorbed (incoming minus reflected) equals the outgoing radiation.
With this information, some algebra, a little geometry (area of a circle and surface area of a sphere) and the ability to convert units (km to m and celcius to kelvin), a student in high-school physics should be able to calculate the Earth’s average temperature. Students who grow up in non-metric societies might want to convert their final answer into Fahrenheit so they and their peers can get a better feel for the numbers.
What they should find is that their result is much lower than that actual average surface temperature of the globe of 15 deg. Celcius. That’s because of how the atmosphere traps heat near the surface because of the greenhouse effect. However, if you look at the average global temperature at the top of the atmosphere, it should be very close to your result.
They also should be able to point out a lot of the flaws in the model above, but these all (hopefully) come from the assumptions we make to simplify the problem to make it tractable. Simplifications are what scientists do. This energy balance model is very basic, but it’s the place to start. In fact, these basic principles are at the core of energy balance models of the Earth’s climate system (Budyko, 1969 is an early example). The evolution of today’s more complex models come from the systematic refinement of each of our simplifications.
Advanced Work
If students do all the algebra for this project first, and then plug in the numbers they should end up with an equation relating temperature to a number of things. This is essentially a model of the temperature of the Earth and what scientists would do with a model like this is change the parameters a bit to see what would happen in different scenarios.
Feedback
Global climate change might result in less snow in the polar latitudes, which would decrease the albedo of the earth by a few percent. How would that change the average global temperature?
Alternatively, there could be more snow due to increased evaporation from the oceans, which would mean an increase in albedo …
This would be a good chance to talk about systems and feedback since these two scenarios would result in different types of feedback, one positive and one negative (I’m not saying which is which).
Technology / Programming
Setting up an Excel spreadsheet with all the numbers in it would give practice with Excel, make it easier for the student to see the result of small changes, and even to graph changes. They could try varying albedo or the solar constant by 1% through 5% to see if changes are linear or not (though they should be able to tell this from the equation).
A small program could be written to simulate time. This is a steady-state model, but you could assume a certain percent change per year and see how that unfolds. This would probably be easier as an Excel spreadsheet, but the programming would be useful practice.
Of course this could also be the jumping off point for a lot of research into climate change, but that would be a much bigger project.
References
Yochanan Kushnir has a page/lecture that treats this type of zero-dimesional, energy balance model in a little more detail.
Paths of hurricanes in 2010. The North Atlantic hurricane season was the 3rd most active on record. Visualization from NOAA's excellent Historical Hurricane Tracks interactive map. Forest fires in the Amazon. Image from NASA.
Jeff Masters has an impressively detailed post laying out the argument that 2010, with its record setting snowstorms, droughts, heatwaves, flooding, hurricanes, etc, had the most extreme weather since 1816, the year without a summer.
Looking back through the 1800s, which was a very cool period, I can’t find any years that had more exceptional global extremes in weather than 2010, until I reach 1816. That was the year of the devastating “Year Without a Summer”–caused by the massive climate-altering 1815 eruption of Indonesia’s Mt. Tambora, the largest volcanic eruption since at least 536 A.D. It is quite possible that 2010 was the most extreme weather year globally since 1816.
The cold front of this mid latitude cyclone spawned several fatal tornados on April 28, 2011. The cold front is the blue line with triangles pointing toward the east. Image via NOAA HPC.
The cold fronts of mid-latitude cyclones bring thunderstorms, rain and spawn tornadoes like the ones we’ve seen over the last few days. In the spring and fall, these cyclones just sweep across the southern U.S. again and again. The line of their passage sort-of marks the northward migration of the sub-polar low in picture of the global atmospheric circulation system.
The circulation cells of the global atmospheric circulation system migrate north and south with the seasons. Image links to larger version (1 Mb).
Each individual front, with its storms, is a feature of the weather. Climate, on the other hand, is the result of the average position over time: the series of fronts which make the southern U.S. wet in the spring and fall.
The sub-polar low is not the only feature that brings lots of seasonal rain. The ITCZ does also, and the rains that the ITCZ’s movement north and south of the equator bring, are what we call the monsoons. The yellow star on the animation, just to the north of the equator, sees monsoonal rains in the summer. Since the ITCZ follows the sun with the seasons, the monsoons always come in the summer; even in the southern hemisphere.
As climate changes, biomes move, and the range of the brown recluse spider migrates north and east (blue area) from its current location (red dashed line). Image adapted from Saupe et al. (2011).
Just in time for us to learn about global change, this interesting study on the expanding range of brown recluse spiders came out. Once restricted to the southern U.S. and the midwest, future climate change will allow them to expand north to Minnesota and east into Pennsylvania.
The researchers, Saupe et al. (2011), used ecological niche modeling. This method takes known information about where the spiders live, such as climate (e.g. summer temperatures) or topography (e.g. mountains versus plains), to figure out the current extent of their ecological niche. Then they use climate models to figure out where those same conditions will apply in the future. Thus the spiders march north.
We’re studying biomes and I don’t know a better way to consider how they’re distributed around the world than by talking about the global atmospheric circulation system. After all, the primary determinants of a biome are the precipitation and temperature of an area.
Diagram showing global atmospheric circulation patterns.
It’s a fairly complicated diagram, but it’s fairly easy to reproduce if you remember a few fairly simple rules: hot air rises; the equator is hotter than the poles; and the Earth rotates out from under the atmosphere.
Hot air rises
Light from the Sun hits the equator directly but hits the poles at a glancing angle, so the equator is warmer than the poles. Warm air at the equator rises while cold air at the poles sinks.
The equator receives more direct radiation from the Sun. A ray of light from the Sun hits the ground at an angle near the poles so it’s spread out more. More radiation at the equator means the ground (or ocean) is warmer, so it warms up the air, which rises.
The warm air can’t rise forever, gravity puts a stop to that. If we did not have gravity the atmosphere would float off into space (and the universe would be a fundamentally different place). Instead, when the air reaches the upper atmosphere at the equator it diverges, heading either north or south toward the poles.
From all around the hemisphere the air converges on the poles. The air is cooling as it moves away from the equator, and when it gets to the pole it sinks to ground level and then makes the journey back to the equator. It’s a cycle, aka a circulation cell.
Hot air rising near the equator and sinking near the poles creates a cycle, a circulation cell, in each hemisphere. In this picture, the winds at ground level (dashed blue lines) would always be blowing from the poles toward the equator. This is what the world might be like without the coriolis effect.
Standing on the ground, the wind would always be blowing towards the equator from the poles. If you were in the northern hemisphere, in say Memphis, you would always be getting northerly winds.
The ITCZ and the Polar High
At the equator the rising air also takes with it water vapor that was evaporated from the oceans or from the land (evaporation and transpiration, which are together called evapotranspiration). The warm air cools as it moves up in the atmosphere and the water vapor forms clouds.
You get a lot of clouds and rainfall anywhere there is a lot of rising air.
Because air is coming together, converging, from north and south at the equator, and the equator is in the middle of the tropics, the zone where you get all this rising air is called the Inter-Tropical Convergence Zone or ITCZ for short (that’s an acronym by the way). The ITCZ is pretty easy to identify from space.
The line of clouds near the equator shows where air is converging at ground level and rising to create clouds. It's called the ITCZ. (Image via NOAA, which also hosts real-time images of the Tropical Atlantic that show the ITCZ very well).
All the rain from the ITCZ, and the warmth of the equator means that when you go looking for tropical rain forests, like the Amazon and the Congo, you’ll find them near the equator.
Locations of rainforests (more or less). Notice that in addition to the Congo and Amazon, Indonesia is pretty well forested too. All because of the ITCZ.
Now at the pole, the air is sinking downward from the upper atmosphere. Sinking air tends to be very dry, and places with sinking air also tend to be dry (it’s not a coincidence). So although the poles are covered with ice, they actually tend to get very little snowfall. What little snow they get tends to accumulate over tens, hundreds and thousands of years but the poles are deserts, arctic deserts, but deserts all the same.
The region of sinking air near the poles is called the polar high because of the high pressure generated by all that descending air.
We’ll complicate the picture of atmospheric circulation now, but the ITCZ and the polar high don’t change.
The Earth Rotates
The complication is the coriolis effect. You see, as the Earth rotates it kind-of drags the atmosphere with it. After all, the atmosphere isn’t nailed down. It’s got it’s own motion and intertia, and doesn’t necessarily want to rotate with the Earth.
Deflection of the wind, represented by a ball, because of the movement of the Earth beneath it. The ball here moves in a straight line but it appears to curve because the Earth is rotating out from under it. Click the image for a bigger, better version.
So a wind blowing from the North pole to the equator gets deflected to it’s right; the northerly wind becomes an easterly.
I could write an entire post about coriolis (and I will) but for now it shall suffice to say that the low-level wind from the pole gets deflected so much that it never reaches the equator. The high-level wind from the equator never reaches the pole, either. Instead of the one, single, circulation cell in each hemisphere, three develop, and you end up with the picture at the top of this post.
In this diagram, the convention is that it shows the circulation cells along the side of the globe, in profile, while the arrows within the circle of the globe show the wind directions on surface.
Note also that the winds in the region just north of the equator (where the label says “Tropical Air”, come from the northeast. These are the northeast trade winds that were vital to the transatlantic trade in the days of sailing ships. Know about them help a lot in the Triangular Trade game.
The Sub-Tropical High and the Sub-Polar Low
With three circulation cells you add the sub-tropical high, and the sub-polar low to the ITCZ and polar high as major features that affect the biomes.
Remember, rising air equals lots of rain, while descending air is dry.
So the sub-tropical high, with its descending air, makes for deserts. Since it’s in the sub-tropics these are hot deserts, the type you typically think about with sand-dunes, camels and dingos.
Sub-tropical deserts from around the world. They're located in the zones 30 degrees north and south of the equator at the sub-tropical high. Base map by Vzb83 via Wikimedia Commons.
The USGS also has a great map that names the major deserts.
Biomes
So if we now look at the map of biomes and climates from around the world we can see the pattern: tropical rainforests near the equator, deserts at 30 degrees north and south, temperate rainforests between 40 and 50 degrees latitude, and arctic deserts at the poles.
Map of biomes from around the world. The different biomes are closely related to the general atmospheric circulation model. (Image adapted from Sten Porse via Wikipedia)
Like addicts racing to get their overdue fix, my students raced to the computers this afternoon after having had to survive all day without power and without the internet. I’ll confess that I felt the same urge, but was able to restrain it. Until now.
We usually don’t have internet access during our immersions, but then it’s expected and students are not inside needing to refer to the study guides to figure out their assignments. At the beginning of the year I gave everyone paper copies of the study guides, but now there are just a core few who request them.
Fortunately, we had a couple of smart-phones so one student would look up the reading assignment and post the page numbers on the whiteboard. Fortunately, the reading assignments were out of the book.
We weren’t quite surviving without technology, but it was close, and students were getting innovative.
We’ve had storms every few days for the last couple of weeks, which is typical for Memphis at this time of year. Over the last few days a frontal system has just been pushing back and forth over us. When it pushes south we get a cold front with thunderstorms and rain, but clear skies afterward. When the front pushes north it gets warm and humid, and the sky goes overcast for most of the day.
Weather map for Wednesday, April 20th. The blue and red line passing through the southeastern U.S. show the mixed warm and cold fronts that have been oscillating past Memphis for days. Image from the National Weather Service.
This line of fronts marks the general location of the sub-polar low, which is moving north with the spring. But more on that tomorrow.
These maps show the difference between last winter's average temperatures and the long term average (from 1951-1980). Notice that the scale goes up to 11. Image from Hansen and Sato, 2011.
For much of the U.S., last winter was pretty cold. If you look at the maps above, you can see that the eastern United States was up to 4 °C colder than normal in December. However, if you look a little further north into Canada, you’ll see a broad, pink region, where the temperatures were up to 11 °C warmer than normal.
The rate at which the world has been warming has been accelerating. It’s been interesting watching the predictions of the relatively crude computer models of the 1980’s coming true.
The red line show that the actual warming has been awfully close to the middle scenario predicted by climate modelers. The figure was slightly adapted from Hansen and Sato (2011).
Although, it’s really the broadest, more general predictions that tend to be more reliable. One of those predictions, that’s been consistent for a long time and with a lot of different models, is that the poles would warm significantly faster than the rest of the planet.
What’s also been interesting, if somewhat depressing, is seeing the political consensus lag behind the scientific consensus. Twenty years ago there was a real debate in the scientific community about if global temperatures were rising. Now scientists argue mainly about what to do: reduce greenhouse gas pollution, adapt to the inevitable, or some mix of the two. Yet two weeks ago the House Science Committee heard testimony from a professor of marketing, advocating for an end to all government funding of climate research. Perhaps the belief is that if we don’t look it won’t happen.
At the same time, Kate (on climatesafety.org) observes that NASA’s James Hansen has had to add a new color (pink on the graphs at the top of the page) to his climate anomaly maps because of the unexpectedly large warming over last winter.
