We now have most of the tools we will need to begin to study energy balance on the earth.  It will be a balance  between incoming sunlight energy and outgoing energy emitted by the earth.  We will look at the simplest case first, the earth without an atmosphere (or at least an atmosphere without greenhouse gases).


You might first wonder how, with the sun emitting so much more energy than the earth, it is possible for the earth (with a temperature of around 300 K) to be in energy balance with the sun (6000 K).  At the top right of the figure you can see that the earth is located about 90 million miles from the sun and therefore only absorbs a very small fraction of the total energy emitted by the sun.  The earth really only needs to emit a very small fraction of what the sun emits to be in balance.

To understand how energy balance occurs we start, in Step #1, by imagining that the earth starts out with a temperature of absolute zero (0 K) and is not emitting any EM radiation at all.  It is absorbing sunlight however so it will begin to warm.  This is like opening a bank account, the initial balance will be zero.  But then you start making deposits and the balance starts to grow.

Once the earth starts to warm it will also begin to emit EM radiation, though not as much as it is getting from the sun (the slightly warmer earth in the middle picture is now colored blue).  Once you find money in your bank account you start to spend it.  Because the earth is still gaining more energy than it is losing the earth will warm some more.

Eventually it will warm enough that the earth (now shaded green) will emit the same amount of energy (though not at the same wavelength) as it absorbs from the sun.  This is radiative equilibrium, energy balance.  The temperature at which this occurs is about 0 F.  That is called the temperature of radiative equilibrium.  You might remember this is the figure for global annual average surface temperature on the earth without the greenhouse effect.

Before we start to look at radiant energy balance on the earth with an atmosphere we need to learn about filters.  The atmosphere will filter sunlight as it passes through the atmosphere toward the ground.  The atmosphere will also filter IR radiation emitted by the earth as it trys to travel into space.

We will first look at the effects simple blue, green, and red glass filters have on visible light.  This is just to become familiar with filter absorption graphs.




If you try to shine white light (a mixture of all the colors) through a blue filter, only the blue light passes through.  The filter absorption curve shows 100% absorption at all but a narrow range of wavelengths that correspond to blue light.  Similarly the green and red filters only let through green and red light.

The following figure is a simplified, easier to remember, representation of the filtering effect of the atmosphere on UV, VIS, and IR light.
You can use your own eyes to tell you what the filtering effect of the atmosphere is on visible light.  Air is clear, it is transparent.  The atmosphere transmits visible light.

In our simplified representation oxygen and ozone make the atmosphere pretty nearly completely opaque to UV light .  We assume that the atmosphere absorbs all incoming UV light, none of it makes it to the ground.  This is, of course, not entirely accurate.

Greenhouse gases make the atmosphere a selective absorber of IR light - the air absorbs certain IR wavelengths and transmits others.  It is the atmosphere's ability to absorb (and also emit) certain wavelengths of infrared light that produces the greenhouse effect and warms the surface of the earth.

Note "The atmospheric window" centered at 10 micrometers.  Light emitted by the earth at this wavelength (and remember 10 um is the wavelength of peak emission for the earth) will pass through the atmosphere.  Another transparent region, another window, is found in the visible part of the spectrum.

A more realistic picture of the atmospheric absorption curve is shown below.  The simplified version above will work fine for us.


Now back to radiative equilibrium.  Here's the outer space view on the earth without an atmosphere.  The important thing to note is that the earth is absorbing and emitting the same amount of energy (4 arrows absorbed balanced by 4 arrows emitted).



We will be moving from an outer space vantage point of radiative equilibrium (figure above) to the earth's surface (figure below).

Don't let the fact that there are
4 arrows are being absorbed and emitted in the top figure and
2 arrows absorbed and emitted in the bottom figure
bother you.  The important thing is that there are equal amounts being absorbed and emitted in both cases.

The next step is to add the atmosphere.
The figure below is a simplified version of radiative equilibrium on the earth with an atmosphere.  This will be easier to understand. 




We'll examine the various parts of this figure individually.
1.   The figure shows two rays of incoming sunlight that pass through the atmosphere, reach the ground, and are absorbed.  100% of the incoming sunlight is transmitted by the atmosphere.  This wouldn't be too bad of an assumption if sunlight were just visible light.  But sunlight is about half IR light and some of that is going to be absorbed.
The ground is emitting 3 rays of IR radiation.

2.   One of these (pink arrow above) is emitted by the ground at a wavelength that is NOT absorbed by greenhouse gases in the atmosphere.  This radiation passes through the atmosphere and goes out into space.

3.  The other 2 units of IR radiation emitted by the ground are absorbed by greenhouse gases is the atmosphere.


4.   The atmosphere is absorbing 2 units of radiation.   In order to be in radiative equilibrium,the atmosphere must also emit 2 units of radiation.  1 unit of IR radiation is sent upward into space, 1 unit is sent downward to the ground where it is absorbed.

Before we go any further we will check to be sure that every part of this picture is in energy balance.

The ground is absorbing 3 units of energy (2 green arrows of sunlight and one bluish arrow coming from the atmosphere) and emitting 3 units of energy (one pink and two red arrows)

The atmosphere is absorbing 2 units of energy and emitting 2 units of energy

2 units of energy arrive at the earth from outer space, 2 units of energy leave the earth and head back out into space.


The greenhouse effect is found in the absorption and emission of IR radiation by the atmosphere.  Here's how you might put it into words:



The greenhouse effect warms the surface of the earth.  The next two figures explain why this is so.


Energy balance without an atmosphere (left) and with an atmosphere that contains greenhouse gases (right) the greenhouse effect.  At left the ground is emitting 2 units of energy, at right the ground is emitting 3 units.  Remember that the amount of energy emitted by something depends on temperature.  The ground in the right picture must be warmer to be able to emit 3 arrows of energy rather than 2 arrows.


Here's another explanation.  At left the ground is getting 2 units of energy (from the sun).  At right it is getting three, two from the sun and one from the atmosphere.  Doesn't it seem reasonable that ground that absorbs 3 units of energy will be warmer than ground that is only absorbing 2?