- Understand and apply the idea of a balanced (long-term global average) heat budget to explain how the greenhouse effect works.
- Understand and apply the idea of an unbalanced heat budget to understand how humans are contributing to observed global warming.
Background Information. Some relevant facts:
- Atmospheric composition
- The atmosphere consists of (a) air (a mixture of gases); and (b) aerosols (solid particles of dust, smoke, ash, salt, pollen, microorganisms, cloud ice crystals, etc., and liquid cloud droplets).
- Air consists mostly of nitrogen gas (78% of dry air), oxygen gas (21% of dry air), and argon (1% of dry air), plus water vapor (up to 4% of air, but averaging more like 1% near the earth's surface and less than that higher up) and small amounts of other gases, notably carbon dioxide (0.039%), ozone (very small amounts, mostly in the stratosphere), methane, nitrous oxides, etc.
- Solar and terrestrial radiation
- Solar radiation consists of relatively short wavelengths of infrared radiation (40%), visible light (50%), and ultraviolet (UV) radiation (10%).
- The earth is much cooler than the sun and hence emits mostly longer wavelengths of radiation (longwave infrared [IR] radiation).
- Absorption and emission of radiation by the atmosphere
- Nitrogen, oxygen, and argon absorb and emit little or no radiation.
- Water vapor, carbon dioxide, ozone, methane, and nitrous oxides all absorb some wavelengths of longwave IR radiation. Because they absorb longwave IR, they also are capable of emitting longwave IR.
- Water vapor absorbs some shorter wavelengths of IR radiation, and ozone absorbs UV radiation, but gases in the atmosphere absorb no visible light.
- Clouds absorb all longwave IR radiation well (and hence are capable of emitting longwave IR well). They also reflect visible light well (they have a high albedo).
- The earth's long-term, global average heat budget
Why is the earth's surface so much warmer than the earth as a whole, based on the rate at which the earth emits radiative energy to space?
- The earth as a whole (atmosphere and surface combined) gains heat almost entirely from the sun (by absorbing solar radiation).
- The earth as a whole loses heat only by emitting radiative energy to space.
- In the long-term, global average, the earth as a whole gains heat from the sun about as fast as it loses heat by emitting radiative energy (that is, its heat budget is approximately balanced); however, small imbalances sustained over time are one cause of climate change.
- The earth as a whole reflects about 31% of the solar radiation striking it and absorbs the rest. The earth emits radiative energy at a rate that depends on its temperature (see a basic law of radiation, below). The average temperature that the earth as a whole must have to emit radiative energy as rapidly as it absorbs solar radiative energy, is around 0°F. That is about 60°F colder than the average temperature of the earth's surface.
Two relevant physical principles (besides two others embedded in the facts above):
- The law of conservation of energy: The rate at which the heat content of an object changes (and hence the rate at which its temperature changes) equals the sum of the rates at which the object gains heat by various mechanisms minus the sum of the rates at which the object loses heat by various mechanisms.
- A basic law of radiation: the warmer an object is, the more intensely it emits radiative energy.
In this exercise you will investigate the long-term, global average
heat budgets for the atmosphere and for the earth's surface. Like the budget for
the earth as a whole, each of these separate budgets, averaged over a sufficiently
long time (one year at a minimum), is very nearly balanced. Small imbalances, sustained over time (a number of years), lead to climate change.
We will refer to the accompanying diagram showing the earth's long-term, global-average rates of absorption and reflection of solar radiation, absorption and emission of terrestrial radiation, and transfer of heat between the earth's surface and the atmosphere by conduction and evaporation of water and condensation of water vapor in the atmosphere (to make clouds).
The left-hand part of the diagram shows what happens to solar radiation arriving at the top of the atmosphere, while the right-hand part shows what happens to terrestrial radiation emitted by the surface and by the atmosphere. The center of the diagram shows the average transfer of heat by conduction from the surface into the (on average cooler) atmosphere and transfer of heat from the surface into the atmosphere by evaporation of water from the surface followed subsequently by condensation of water vapor to form clouds.
The numbers represent energy intensity (also called energy flux). They tell us the rate at which energy passes through, into, or out of each unit of (horizontal) area of the surface or the atmosphere. (In the diagram, energy is represented in units of Joules, and rates of energy transfer are expressed in Joules per second, or Watts. Horizontal surface area is represented in square meters, or m2. Hence, the fluxes are expressed in Watts/m2.)
The diagram shows that the flux of solar radiative energy arriving on a horizontal surface (that is, the insolation) at the top of the earth's atmosphere, averaged over the whole globe for a long time (24 hours a day for many years), is 342 Watts/m2. The flux of solar radiation that is scattered and reflected back to space by clouds, aerosols, and air is 107 Watts/m2, which is (107/342) x 100% = 31% of the solar radiation arriving—hence, the long-term, global average albedo of the earth is about 31%. (Two thirds of this scattering and reflection is due to clouds, which reflect very well.)
The observations on which these numbers and the others on the diagram are based come from satellites (which have been making observations of solar and terrestrial radiation since the early 1970s) and from surface-based instruments.
- 67 Watts/m2 solar energy are absorbed each
year by the atmosphere. What wavelengths of solar radiation (UV, visible, or
short wavelengths of infrared) are being absorbed, and by what, exactly?
UV is absorbed mostly by ozone (mostly in the stratosphere); some short wavelengths of infrared radiation are absorbed by water vapor and by clouds. (Little visible light is absorbed in the atmosphere.)
- What is the intensity (flux) of solar radiation actually reaching the
earth's surface? How much is it, expressed as a percentage of the solar radiation arriving at the top of the atmosphere?
In the long-term global average (day and night for 365 days a year averaged over all latitudes), 342 W/m2 arrives at the top of the atmosphere. Of this amount, 67 W/m2is absorbed by certain gases in the air and by clouds [see Question #1 above], and 77 W/m2 is reflected and scattered back to space by clouds (mostly), aerosols (dust, smoke, ash, salt, etc.), and air molecules. The rest (342 - 67 -77 = 198 W/m2) reaches the surface.
- What is the average albedo of the earth's surface? [Note: To answer this, you must have a clear understanding of how albedo is defined.]
Albedo is defined generally as the amount of radiative energy reflected by a surface expressed as a percentage of the radiative energy that arrives at (strikes) a surface.
The amount reflected by the earth's surface is 30 W/m2, while the amount arriving on it (striking) it is 198 W/m2 [See Question #2 above]. Hence, the average albedo of the earth's surface is (30/198) × 100% = 15%. This is only about half of the albedo for the planet as a whole (31%). This is because clouds reflect visible light much better than ocean and land surfaces do, and clouds are responsible for most of the solar radiation reflected by the planet as a whole.
- What proportion of solar energy arriving at the top of the atmosphere is actually absorbed by the earth's surface?
Of what wavelength(s) does this energy consist, mostly?
The amount of solar radiation absorbed by the earth's surface averages 168 W/m2. This is (168/342) × 100% = 49% of the average solar radiation arriving at the top of the atmosphere. That is, about half of the solar radiation arriving at the top of the atmosphere is ultimately absorbed by the earth's surface, while the rest is reflected or scattered back to space (by the atmosphere and the earth's surface) or absorbed by the atmosphere.
- How does the amount of radiative energy
emitted by the earth's surface compare to the amount of solar energy arriving
at the top of the earth's atmosphere? How does it compare to the amount of solar
energy absorbed by the surface?
The earth's surface (on average) emits 390 W/m2, essentially all of it longwave infrared radiation. This is (390/342) × 100% = 114% of the amount of solar radiation arriving at the top of the atmosphere!. That is, the earth's surface emits more radiation (14% more) than arrives at the earth from the sun! Viewed another way, the earth's surface loses more heat each year than arrives at the earth from the sun, much less what the earth's surface actually absorbs (and hence converts into heat) from the sun.
- What proportion of the terrestrial (longwave IR)
radiation emitted by the earth's surface escapes directly to space? What happens to the rest of it?
Of the 390 W/m2 of (longwave infrared) radiative energy emitted by the surface, only 40 W/m2escapes directly to space, which is (40/390) × 100% ≈ 10% of what what the surface emits. The other 90% or so is absorbed by the atmosphere—in particular, greenhouse gases (water vapor, carbon dioxide, methane, nitrous oxides, ozone, chlorofluorocarbons, etc.) and clouds.
- In this figure, are the amounts of energy entering and leaving the top
of the atmosphere (in effect, the planetary energy budget) balanced?
W/m2 of solar radiative energy arrive at the top of the atmosphere, while 107 W/m2 of solar radiative energy leaves (reflected back to space by the atmosphere and the surface without ever being absorbed and converted into heat) and 235 W/m2 of longwave infrared radiation leaves the earth (emitted to space by the atmosphere and the earth's surface). The amount of radiative energy leaving the earth is 107 W/m2 + 235 W/m2 = 342 W/m2, which equals the amount arriving, so the planetary energy budget is balanced (at least, to within less than 1 W/m2).
- Does the surface heat budget balance? If so, what is
it's primary source of energy (on the average)? What is it's primary
means of getting rid of heat (on the average)?
The surface absorbs 168
W/m2 of solar radiation and 324
W/m2 of longwave infrared (LWIR) radiation emitted downward by the atmosphere (more specifically, by greenhouse gases and clouds), for a total of 168 W/m2 + 324 W/m2 = 492
The surface loses 24
W/m2 of heat by conduction of heat into the atmosphere, and it loses 78
W/m2 by evaporation of water into the atmosphere. (Evaporation converts heat in the surface—mostly the ocean—into latent heat in the water vapor entering the atmosphere, so the surface loses heat this way.) The earth's surface also loses 390
W/m2 by emission of LWIR radiation, for a total of 24 W/m2 + 78 W/m2 + 390
W/m2 = 492 W/m2.
Hence, on the average the earth's surface gains as much heat as it loses (492 W/m2), and its heat budget is balanced (to within 1W/m2, anyway) .
- Does the atmosphere's heat budget balance? If so, what
is it's primary source of energy (on the average)? What is it's primary
means of getting rid of heat (on the average)?
On the average, the atmosphere absorbs 67 W/m2 of solar radiation, converting it into heat. It gains 24 W/m2 of heat by conduction of heat from the warmer (on the average) surface. It gains 78 W/m2 of heat due to condensation of water vapor to form the droplets of liquid water that make up clouds. (Condensation converts latent heat in the water vapor into heat in the air.) Finally, greenhouse gases and clouds absorb 350 W/m2 of LWIR radiation emitted by the earth's surface, converting it into heat. The total gain of heat by the atmosphere is 67 W/m2 + 24 W/m2 + 78 W/m2 + 350 W/m2 = 519 W/m2.
On the average, greenhouse gases emit 165 W/m2 of LWIR radiation to space, and clouds emit 30 W/m2 to space. Together, greenhouse gases and clouds also emit 324 W/m2 of LWIR radiation downward. Either way, emission of radiative energy converts heat in the atmosphere into radiative energy, and is therefore a mechanism for losing heat. The total loss of heat by the atmosphere is 165 W/m2 + 30 W/m2 + 324 W/m2 = 519 W/m2.
Hence, on the average the earth's atmosphere gains as much heat as it loses (519 W/m2), and its heat budget is balanced. The primary (easily the largest) source of heat is the absorption of LWIR radiation by GH gases and clouds (350 W/m2), where the LWIR radiation is emitted upward by the surface. The atmosphere's primary means of getting rid of energy—in fact, its only means of getting rid of heat, on the average—is clearly the emission of LWIR radiation (both upward to space and downward to the earth's surface), a combined total of 519 W/m2.
- From what part of the earth system pictured in this budget diagram (that is, the earth's surface, air, or clouds) does the most energy lost to
space come, and how (by what mechanism) is it lost?
largest mechanism by which the earth loses energy to space is by emission of LWIR radiation from greenhouse gases (165 W/m2), or more generally, by emission of LWIR from the atmosphere (greenhouse gases and clouds together: 165 W/m2 + 30 W/m2 = 195 W/m2). Relatively little energy that the earth loses to space comes directly from the surface (40 W/m2).
The solar radiation reflected back to space by the atmosphere and the earth's surface (107 W/m2) arrives and leaves as solar radiative energy. Because it is never converted into heat (absorbed) or converted from heat to radiative energy (emitted by the earth), it plays no direct role in the earth's heat budget—that is, scattering and reflection are mechanisms by which the earth neither gains nor loses heat. (They do reduce the amount of solar radiation that the earth absorbs, of course, so they do play an important indirect role in the planet's heat budget.)
- How does the radiative energy emitted by the earth's surface compare to the radiative energy that the earth as a whole emits to space?
The earth's surface emits 390 W/m2, while the earth as a whole emits only 235 W/m2directly to space. That is, the earth's surface loses a lot more heat by radiative emission alone than the planet as a whole does.
- Based on (a) the balanced heat budgets that you've just analyzed
in some detail; (b) the basic law of radiation that says that the warmer an object is, the more radiative energy it emits; and (c) the fact that the earth's surface heat budget is very nearly balanced, why is the earth's surface
necessarily so much warmer than the temperature of the planet
treated as a whole (as seen from space)?
First, note that there is no direct way to measure the earth's temperature from space, but satellites can record the intensity of longwave infrared radiation emitted by the earth, and we can relate that to the planet's temperature. Hence,
"the temperature of the planet treated as a whole (as seen from space)" really means "the temperature based on the intensity of radiative energy emitted by the planet as measured from space".
The fact that the energy budget for the planet as a whole is virtually balanced means that it must emit as much LWIR radiative energy as it absorbs solar radiation from the sun. The atmosphere absorbs 67 W/m2 of solar radiation and the surface absorbs 168 W/m2 of solar radiation, for a total of 235 W/m2. Since the planet emits a total of 235 W/m2 of LWIR to space, balancing its budget, we must conclude that the planet must be at just the right temperature to emit 235 W/m2.
That temperature turns out to be just below 0°F. (This might seem very cold (it is!), but remember that since 90% of what the earth emits to space comes from the atmosphere, the figure of 0°F is a rough indication of the average temperature of the atmosphere, parts of which we know from radiosonde balloon soundings can be very cold.)
Now, the energy budget of the surface is also balanced, and the surface also loses most (80%, or 390 W/m2 out of a total of 519 W/m2) of its heat by emitting radiative energy. Hence, the surface must also be at about the right temperature to emit
most of the heat that it gains via absorption of solar radiation and LWIR radiation (emitted downward by the atmosphere), a total of 519 W/m2. (The remaining 20% of what the surface loses to balance its heat budget it loses by conduction of heat to the atmosphere and by evaporation.) The temperature that the earth's surface must have to emit enough radiative energy to balance its heat budget is, on the average, about 60°F. Hence, the average temperature of the surface is about 60°F warmer than the average temperature of the planet as a whole as viewed from space. Or, restating: the surface is much warmer than the planet as a whole because the surface gains a lot more heat than the planet as a whole and, since both have a balanced heat budget, the surface must therefore get rid of more heat than the planet as a whole does. It does it by being much warmer and hence emitting more radiative energy.
The bottom line is that the planet as a whole absorbs less radiative energy (235W/m2) than the surface does (519 W/m2), because the surface has an additional large source of energy that the planet as a whole doesn't have—absorption of LWIR radiation emitted downward by greenhouse gases and clouds in the atmosphere. Both budgets are balanced, though, so both the planet as a whole and the earth's surface must lose as much energy as they gain, which they do mostly by emitting radiative energy. To balance its budget the surface must lose more energy by radiative emission than the planet as a whole does, and a basic law of radiation tells us that the surface has to be warmer to emit more—in fact, about 60°F warmer.
This is what atmospheric scientists call the "greenhouse effect" (though it is only partly how greenhouses actually work to keep warm inside, so it isn't a particularly good analogy).
- Suppose that all gases that absorb terrestrial radiation (notably
water vapor and carbon dioxide, but other, less important ones, too) were removed
from the atmosphere. (Note that removing water vapor would also mean that no
clouds could be present, either, which would reduce the earth's albedo. For the sake of simplicity, suppose that the albedo doesn't change—the answer will be qualitatively the same.) What implications would this have for the surface temperature, if the heat budget were balanced?
[We haven't addressed this question yet.]
- Suppose that more carbon dioxide were added to today's atmosphere.
(Humans are doing this by burning coal, oil, and natural gas and by cutting down forests.)
What effect would this have on the absorption of longwave IR radiation by the atmosphere and the longwave IR emitted by the surface that escapes directly to space? How would the atmosphere's temperature respond? What would happen to the amount of radiation it emits? What would happen to the temperature of the surface as a result?
[We haven't addressed this question yet.]
Physical relationships for your reference:
| Conservation of energy relation: |
Rate at which
an object's heat content
(and hence temperature)
|| Sum of rates
at which the object gains heat
by various mechanisms
|| Sum of rates
at which an object loses heat
by various mechanisms
| One of the Basic Laws of Radiation:
| Objects emit radiative energy faster
(and hence lose heat by this means faster) when they are warmer than when they are colder