- 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?
- What is the 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?
- 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.]
- 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?
- 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?
- 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?
- In this figure, are the amounts of energy entering and leaving the top
of the atmosphere (in effect, the planetary energy budget) balanced?
- 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)?
- 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)?
- From what part of the earth system pictured in this budget diagrams (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?
- 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?
- Based on (a) the balanced heat budgets that you've just analyzed
in some detail, and (b) the basic law of radiation that says that the warmer an object is, the more radiative energy it emits, why is the earth's surface
necessarily so much warmer than the temperature of the planet
treated as a whole, as seen from space?
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?
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?
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