Global Energy Balance

Energy Balance

An initial point of clarification is necessary for those students without background in the earth or physical sciences. When we use the term "radiation" in this course we are considering components of solar emissions ("sunshine") and thermal emissions from the earth. These definitions do not include nuclear or cosmic radiation. Likewise, the term "radiatively active" refers to emission or absorption of visible light or thermal (infrared) energy as from a wood-burning stove. So, except for the ultra violet component of solar radiation, the radiant energy we discuss in this course is benign to humans.

The earth receives energy from the sun, mostly in the form of visible radiation, as we showed in a previous unit. At the top of the atmosphere, a plane perpendicular to the line from the sun receives about 1360 W m^-2. The daily amounts of energy per unit area at different points on the earth are shown in Figure 1. Units used in this figure are cal cm^-2, where 1 cal cm^-2 min^-1 = 697.58 W m^-2. Note that the location receiving the maximum daily radiation is the South Pole in December! From the global perspective, some of this solar energy is reflected back to outer space as visible light and the rest is processed in various ways by the earth/atmosphere/ocean system and re-radiated back to space as infrared (IR) radiation. The detailed pathways for this energy transformation determine the climate conditions of our planet. The composition of the planet's atmosphere and the characteristics of the planet surface control the temperature distribution at the planet surface and hence the motions and processes of its atmosphere.

Once the visible solar energy is absorbed by the earth system - be it in clouds, the free atmosphere, or at the surface - it is transformed from electromagnetic energy to heat energy. This absorbed energy either raises the surface temperature or evaporates surface water to create atmospheric water vapor. If an object has a temperature higher than its surroundings, then it will lose energy to its surroundings by infrared radiation. Infrared radiation is not detectable by the human eye but can be detected by absorption by human skin. A heating element in an electric oven radiates with both infrared and visible radiation if it is glowing. If the current is turned off, it gradually loses its glow (its visible radiation) but continues to emit IR radiation, which can be felt by a hand close to the heating element.

The earth, compared with outer space, is very warm, and so it radiates energy away to outer space at a rate that is proportional to the fourth power of the temperature. Some of this energy radiated from the surface of the earth is directly lost to outer space, while some is absorbed by gases and clouds in the atmosphere. This absorption of infrared radiation by a planet's atmosphere is called the "greenhouse effect". Nitrogen, the dominant gas in the atmosphere, does not absorb infrared radiation, but oxygen, the second most abundant gas, does absorb in certain wavelength regions.

Water Vapor

Water vapor (as distinct from clouds, which are treated separately) is a strong absorber of infrared radiation. If you have been in both humid and dry climates and experienced the temperature change from day to night, you will have observed that in dry climates the temperature decreases rapidly near sunset, whereas in a humid climate, the drop in temperature is much less pronounced. The difference is due to radiation from the surface that is absorbed by water vapor in the humid atmosphere and re-radiated back to the surface. In the dry climate, this outgoing radiation penetrates the atmosphere and escapes from the earth to outer space. So, in fact, water vapor is the largest absorber of infrared radiation from the earth and is therefore the most important greenhouse gas in the earth's atmosphere.

Trace Gases

Other trace gases in the earth's atmosphere also absorb infrared energy. Carbon dioxide, nitrous oxide, methane, ozone, and the CFCs all are greenhouse gases. They absorb and re-radiate infrared radiation both upward and downward and contribute to maintaining a surface temperature that is higher than it would be in their absence. We have seen in our study of atmospheric chemistry that many of these trace gases are produced by humans through the use of combustion engines and other activities. By increasing the atmospheric concentrations of these gases, we are contributing to an enhanced warming of the earth's surface by the increased greenhouse effect. Current concentrations of greenhouse gases are posted by the Carbon Dioxide Information Analysis Center. We will come back to this topic as we seek to quantify the magnitude of this effect.

Quantifying the Global Energy Balance

We can summarize and quantify these concepts by defining the energy balance for the earth as is shown in Figure 2.

If we assume that the earth receives 100 units of solar energy per unit time, then what happens to this energy? As shown in the accompanying sketch, about 25 units of this energy are reflected by the atmosphere, another 25 units are absorbed by particles and gaseous molecules in the atmosphere, and 5 units are reflected by the earth's surface. This leaves 45 units to be absorbed by the earth's surface.

Transfer of energy from the earth to the upper atmosphere in the amount of 29 units occurs by conduction, convection, and evaporation of surface water (absorption of latent heat) with subsequent condensation in clouds and fog (release of latent heat). Radiation from the surface accounts for 104 units of energy loss, with a concurrent gain of 88 units of radiation back to the surface from greenhouse gases, clouds and atmospheric particulates. The planet, as a whole, releases 70 units of infrared radiation to outer space, mostly as radiation from cloud tops and the upper atmosphere. The effective radiating temperature of the planet as seen from outer space is 255 K, or -18⁰C. Notice that the 70 units of outgoing longwave radiation, combined with 30 units of solar energy that is reflected, gives an outgoing energy total of 100 units, which balances the incoming amount.

Greenhouse Gases and Global Warming

The greenhouse gases are not limited to some narrow layer as suggested in the accompanying sketch but they are distributed quite uniformly throughout the troposphere. Ozone, which is produced by solar radiation in the stratosphere and by processes at the earth's surface, is less uniform and has a peak concentration in the stratosphere.

The surface warming produced by enhanced greenhouse gas concentrations leads to a vertical profile of atmospheric temperature that actually reduces the temperature at the base of the stratosphere. So when we use the term "global warming" we are referring to the earth's surface. We might even then say that a cooling of the lower stratosphere might be evidence of "global warming".

It is important to recognize that the energy the earth receives from the sun is fixed, and the energy the earth re-radiates to outer space is fixed. Global warming is a result of the redistribution of energy within the earth/atmosphere/ocean system and not a result of gaining more from the sun or losing less to outer space. In subsequent units we will quantify the contributions to warming from the anthropogenic increases in various greenhouse gases and other human factors influencing the energy balance.

Surface Reflectivity

The capability of a surface to reflect solar energy is measured by its albedo or reflectivity in the visible portion of the energy spectrum. The table of albedos gives values for different surfaces and materials (Figure 3).

We can relate values in this table with our experience by remembering that surfaces with high albedos are surfaces that appear bright when illuminated with visible light. So if we consider a photograph of the earth taken from the Space Shuttle, the brightest features are clouds and the large ice masses of Greenland and Antarctica. Deserts are brighter than vegetated surfaces, and the ocean is darker than land (except that at certain angles light is highly reflected off the surface of the ocean in what we call sun glint). NASA has produced a nice albedo map of the Earth.

A scan of the table will confirm these general observations, with clouds reflecting 70 to 90% of incident energy and clean snow reflecting 75 to 95% (you will note that "old snow reflects less). Sand has a relatively high reflectivity for a natural surface, and typical soil is somewhat less. Deciduous forests have a relatively low value of 10 to 20%.

Greenhouse Gas Absorption Spectrum

Figure 4 gives the amount of energy absorbed by greenhouse gases in various wavelength regions, from ultraviolet radiation on the left, to visible light in the middle, to infrared radiation on the right.

The CFCs are not plotted here but will be considered separately. For each gas is given a plot of the absorptance of the gas, ranging from 0 to 1, for each wavelength.

As an example, if we look at the plot for oxygen and ozone, we see that the absorption is very high in the ultraviolet region but essentially zero in the visible and infrared regions, except for isolated peaks. We interpret this to mean that this gas absorbs essentially all radiation in the ultraviolet but is transparent in the visible and mostly transparent in infrared portions of the spectrum. This gas then is responsible for shielding earth-based biological systems from lethal ultraviolet radiation, radiation with wavelengths less than 0.3 micrometers (or 300 nanometers), but allows visible light and infrared radiation to pass through without much absorption.

Other gases have much different absorption properties. Methane (CH₄), for example, has a couple of very small wavelength regions in which it absorbs strongly and these occur at about 3.5 and 8 microns, which are in the infrared region. Nitrous oxide, N₂O, having peaks at about 5 and 8 microns, absorbs in fairly narrow wavelength ranges.

Carbon dioxide has a more complex absorption spectrum with isolated peaks at about 2.6 and 4 microns and a shoulder, or complete blockout, of infrared radiation beyond about 13 microns. From this we see that carbon dioxide is a very strong absorber of infrared radiation. The plot for water vapor shows an absorption spectrum more complex even than carbon dioxide, with numerous broad peaks in the infrared region between 0.8 and 10 microns.

The total spectrum of all atmospheric gases is given in the bottom plot. This shows a "window" between 0.3 and 0.8 microns (the visible window), which allows solar radiation (without the lethal UV component) to reach the earth's surface. "Earth radiation", the upwelling infrared radiation emitted by the earth's surface, has a maximum near 10 microns. The total atmosphere plot shows that a narrow window (except for an oxygen spike) exists in the range of wavelengths near 10 microns.

Surface Temperature Regulation

If a planet has no water vapor in its atmosphere, then its surface temperature is determined primarily by the abundance of carbon dioxide in its atmosphere. Planet Venus has an atmosphere consisting of 98% carbon dioxide and surface pressure 90 times that of Earth. Solar energy, which is mostly visible radiation, passes through the window in the visible range (carbon dioxide has no absorption between 0.4 and 0.7 microns) and strikes the surface where, according to the table of albedos, 24% is converted to heat. The large amount of carbon dioxide in the Venus atmosphere produces a very strong greenhouse effect that re-radiates infrared energy back to the surface giving a surface temperature of 477^oC. Planet Mars, on the other hand, has at atmosphere of 95% carbon dioxide but a surface pressure less than 1/100 of that of Earth. This rather low total mass of carbon dioxide can only create a very weak greenhouse effect on Mars, and its surface temperature is -53^oC. The temperature of a planet's surface is more related to the amount of carbon dioxide in its atmosphere than to its position relative to the sun.

The important concept from this discussion is that greenhouse gases in general, and carbon dioxide in particular, regulate the temperature at the planet surface. The fact that earth has far less carbon dioxide than Venus and considerably more than Mars gives earth a unique range of surface temperature that is favorable for plant, animal, and human life as we know it.

Effects of Adding Specific Amounts of Greenhouse Gases

We will now evaluate the effect of adding specific amounts of additional greenhouse gases to the earth's atmosphere. Figure 5 gives a quantitative description of the impact of each greenhouse gas in terms of the change in the heating rate per unit time per unit area (Watts per square meter per decade, Wm^-2decade^-1) at the earth's surface.

Recall that concentrations of greenhouse gases are about 370 ppmv for carbon dioxide, 1.7 ppmv for methane, and parts per trillion for nitrous oxide and for CFCs. Each formula given in the second column describes the surface heating rate in terms of gas concentration. Note the different functional forms for different gases. For carbon dioxide, the radiative forcing (atmospheric heating rate) is proportional to the natural logarithm of the concentration divided by some base concentration. For methane, nitrous oxide, and stratospheric water vapor, the leading term of the radiative forcing increases as the difference of square roots, and for gases that are less abundant, the forcing is directly proportional to the concentration.

The impact of adding one additional molecule of a greenhouse gas is much larger if the relative abundance of the gas is low. For example, the impact of adding one molecule of methane is 21 times as large as adding one molecule of carbon dioxide (see Figure 6).

A molecule of nitrous oxide has the equivalent greenhouse effect of 206 carbon dioxide molecules, and the CFC molecules have an impact 12,000 to 18,000 times that of carbon dioxide. The absorption bands (wavelength regions) for carbon dioxide are nearly saturated, but those for other gases are not, so one additional molecule makes a larger impact. However, we should keep in mind that each person in the US on average puts about 20 metric tons (20,000 kg or 44,000 pounds) of carbon dioxide into the atmosphere from burning fossil fuels each year, compared to 100 kg of methane, 2 kg of nitrous oxide, and 2 kg of CFCs. Multiplying the CFC emission rate by 12,000 gives a CFC greenhouse impact comparable to that for carbon dioxide.

At the bottom of the last table are listed the possible replacements for the CFCs. Their impact, in some cases, is considerably reduced, but by no means do they eliminate radiative forcing.

Figure 7 gives a comparison of the radiative forcing of the CFCs and their possible substitutes.

This information can be used to evaluate the relative advantages of CFC substitutes for reducing global warming. Quantitative calculations such as these help policy makers appreciate and understand how science can assist in shaping new legislation. It also demonstrates to the private sector (e.g., power-generating industry and chemical manufacturers in this case) the relative impact of various greenhouse gases. The detrimental effects of CFCs are clearly evident, and these calculations, in addition to their calculated effect on ozone, led to the creation of the international agreement to eliminate CFCs (Montreal Protocol) and led DuPont Corporation to stop manufacturing CFCs before the international mandate to do so was implemented.

Greenhouse Gas Lifetimes in the Atmosphere

The insidious characteristic of most greenhouse gases is that they have long lifetimes in the atmosphere, as measured by their "half life" (the time for half of an initial amount released to be removed from the atmosphere by natural processes). Carbon dioxide has a half life of about 120 years, methane 10.5 years, nitrous oxide 132 years, and the CFCs 16 to more than 500 years, as shown in the accompanying table. So, for instance, of the 20,000 kg of carbon dioxide you put into the atmosphere in 2004, 10,000 kg will still be contributing to enhanced greenhouse warming in the year 2124, 5,000 kg will be remaining in 2244, 2,500 kg in 2361, ..., 1 kg in the year 3684. At least 1 kg of carbon dioxide you put into the atmosphere this past year will contribute to enhanced greenhouse warming for the next 1,680 years!

From these examples, you can see that there are two factors that combine to determine the "global warming potential" (GWP) of a greenhouse gas: (1) radiation absorbing capacity, and (2) lifetime in the atmosphere. We will come back to GWP in a later lecture.

Radiative Forcing

Calculations based on these considerations are used to produce Figure 8 that takes into account the effect of greenhouse gases that humans have put into the atmosphere since the Industrial Revolution.

Their radiative forcing effects are expressed in Wm^-2decade^-1 for five different periods, ending with the decade of the 1980s. Note that forcing due to carbon dioxide has increased but not directly in proportion to its increased concentration, as previously discussed. The impacts of others, such as the CFCs and HCFCs, have increased more dramatically even though their abundance is very low, because their impact per molecule is high and their lifetimes are large.

Note that the magnitude of the increase in radiative forcing for the most recent decade on the previous graph is about 0.55 Wm^-2 (Figure 9). The total cumulative radiative forcing since the Industrial Revolution due to anthropogenic greenhouse gases is about 2.77 Wm^-2.

Natural Variations of Radiative Forcing

We should ask how this 0.55 Wm^-2decade^-1 compares with natural fluctuations in radiative forcing (Figure 10). For instance, the luminosity of the sun fluctuates, which causes variations in the amount of energy the earth receives from the sun. It would be useful to compare measurements of this variation with present and projected future contributions due to enhanced greenhouse effects.

Other natural variations are due to orbital changes of the earth around the sun, changes in the radius of the sun, and effects of volcanoes. Large explosive volcanic eruptions produce copious amounts of SO₂ that combine with H₂O to form H₂SO₄ (sulfuric acid), which condenses rapidly in the stratosphere to form fine sulfate particles that remain suspended in the atmosphere for 1-2 years (Figure 14) before being removed by natural processes.

Variability of orbital parameters of the earth's revolution about the sun is reduced by internal feedback mechanisms, but its effect is estimated to be about 0.035 Wm^-2decade^-1, which is much less than the 0.55 Wm^-2decade^-1 due to anthropogenic greenhouse gases. Variability of total output of the sun over short periods (e.g., a few years) is about 1.4 Wm^-2decade^-1 (see Figure 11), but this variability tends to be cyclical over longer periods. Averaged over the last 100 years, variability of total output of the sun has been about 0.1 Wm^-2decade^-1, again far less than 0.55 Wm^-2decade^-1. The rate of heat loss due to heat flow from the center of the earth is 0.06 W m^-2.

Changes in radius of the sun and changes in sunspot activity also lead to natural variability of about 0.1 Wm^-2decade^-1. A major volcano releases large amounts of sulfate and other particles that may persist in the stratosphere for 1 to 3 years and lead to global cooling due to reflection of incoming solar radiation. This can change radiative forcing by 0.2 to 0.4 Wm^-2decade^-1 for the period of time that the dust lingers in the stratosphere. Because such major eruptions occur only once per decade or so, their average effect is far less than 0.55 Wm^-2decade^-1.

Increase in Radiative Forcing due to Humans

What about the effect of changes in landuse? A previous table showed different albedos (reflectivities) for different types of surfaces. Humans have deforested Europe and the US and are now deforesting tropical areas and changing them to agricultural land. Humans also have built cities, eliminated natural prairies, and installed irrigation systems enabling crops to be grown in near-desert regions. These anthropogenic changes have increased the albedo of the planet by approximately 0.006 over the last 1,000 years, giving a change in radiative forcing of about 0.01 Wm^-2decade^-1.

From these comparisons, it should be apparent that human emission of greenhouse gases have increased the radiative forcing of the planet far in excess of natural variations.

It has been discovered recently that sulfur dioxide released by burning of coal further complicates the calculations of human impact on planetary surface temperatures. Sulfur dioxide (SO₂) emitted when coal is burned is transformed into sulfate particles in the atmosphere which reflect solar radiation directly back to outer space. When the sulfate particles dissolve in cloud droplets, they tend to "brighten" the cloud and further increase the solar radiation reflected back to outer space from the top of the cloud. Therefore sulfate particles make both direct and indirect contributions to cooling the lower atmosphere. As we learned in the discussion of the sulfur cycle, sulfates have a relatively short lifetime in the atmosphere (1-3 weeks). This means that the cooling effect of sulfate particles is not global but rather occurs near and downwind of major industrial areas. The magnitude of this effect on a regional climate is thought to be about -0.3 to -0.9 Wm^-2 for direct forcing and as much as -0.8 Wm^-2 for indirect forcing. The impact of this negative forcing is a cooling effect of 0.8 to 1.6⁰C in the global mean temperature. An important difference between CO₂ warming and aerosol cooling is that the longer lifetime of CO₂ means continuing emissions even at a non-increasing rate, lead to increased radiative forcing. For aerosols, with limited lifetimes, constant emission rates simply replace the aerosol particles being washed out of the atmosphere. So the aerosol radiative forcing for emissions is constant.

Recent estimates of the effects of sulfate aerosol particles are shown in the next two global maps (Figure 12) that give warming due to carbon dioxide with and without considering the sulfate cooling.

This issue will be further discussed in units on climate modeling.

One goal of the US Clear Air Act and its amendments (and comparable actions in Europe) over the last 25 years is the reduction of sulfur emissions from combustion of coal. These efforts have achieved some success, as is shown by Figure 13 , which shows that the ratio of sulfur to carbon dioxide in emissions has decreased. The dilemma presented by this situation is that our continuing efforts to reduce sulfur emissions will unmask increasing amounts of global warming due to rising CO₂.

1-12: Global Energy Balance