Climate Change Science – Energy Imbalance of the Earth

Australia: The Land Where Time Began

Climate Change Science – Energy Imbalance of the Earth

The Earth would be in energy balance if the amount of energy arriving at the Earth equalled the amount of energy being radiated back to space. There is actually more energy arriving at the Earth system than there is being radiated away, the result of this imbalance is that the Earth system warms to compensate. The atmospheric carbon dioxide concentration had been stable for hundreds of years prior to the Industrial Revolution and the temperature of the Earth had undergone normal fluctuations resulting from an energy balance between energy being received and energy being emitted.

The ultimate source of virtually all energy reaching the Earth’s surface is the Sun. At the top of the atmosphere the energy measured for direct overhead Sunlight by satellite is 1,368 W/m²; As much of this energy is reflected off the top of the atmosphere, therefore the light being received at any typical location has an annual average of ~342 W/m². If albedo changes are neglected the average temperature of the surface of the Earth would be expected to be -19^oC if this were the total heat that was received at the surface. Instead, heat being emitted from the surface is recycled by the atmosphere which delivers an additional 324 W/m², the result being an average surface temperature of +15^oC. The process is the greenhouse effect which maintains the habitability of the Earth for living organisms.

The temperature of the visible surface of the Sun, the photosphere, which is about 6,000 K, determines the total solar energy. The Earth also emits an amount of energy that is determined by the temperature of the lower atmosphere, the troposphere, which is about 255 K (about -18^oC). The need of the Earth to balance the absorbed incoming solar energy, by emitting an equal amount of energy back to space to remain in equilibrium determines this.

The radiation from the troposphere also transmits energy down to the surface, the “back-radiation”, as well as radiating energy into space, and that back-radiation from the atmosphere penetrates the surface of the Earth heating the surface to about 288 K (about +15^oC). The energy balance of the Earth is achieved for a typical m² at the top of the atmosphere (TOA). It depends on the solar constant of about 1,368 W/m² divided by 4 (as the cross section of the Earth absorbing the solar energy is ¼ of the area of its emitting surface, as well as the albedo of the Earth, which is the fraction of the solar energy that is reflected by the land, ice and especially the clouds which combined constitute the Earth-atmosphere system. 1,368 W/m² divided by 4 = 342 W/m².

At the top of the atmosphere the incoming radiation is 342 W/m² and this would also be the amount of outgoing radiation if the Earth was in energy balance. Shortwave ultraviolet radiation comprises the majority of the incoming radiation, while the outgoing radiation is comprised of longwave infrared radiation. Of this outgoing radiation 342 W/m² are reflected back to Earth by atmospheric greenhouse gases where they are absorbed by the surface of the Earth and 325 W/m² are emitted to outer space.

The gases of the atmosphere of the Earth do not act as blackbodies, though the Sun and the Earth do act approximately as blackbodies. Radiation of some wavelengths is absorbed by certain atmospheric gases but they allow other wavelengths to continue on to outer space. All electromagnetic radiation impinging on blackbodies is absorbed by them and the rates of radiation they emit depend on their temperature.

A particular gas absorbs energy when the electromagnetic radiation frequency is similar to the vibrational frequency of the gas in question. The atmosphere is mostly transparent to light in the visible range of the spectrum but ultraviolet light, which comprises the incoming shortwave solar radiation, is absorbed to a significant degree by atmospheric ozone. Water vapour, carbon dioxide and other trace gases absorb radiation in the infrared range of the spectrum, which is the range of the longwave outgoing radiation. The terrestrial infrared radiation is of particular importance to the energy budget of the Earth’s atmosphere. The atmosphere is heated by such absorption, which stimulates it to emit more longwave radiation, some of which is released into space while the remainder is re-radiated back to the surface of the Earth. The net effect of this is that Earth stores more energy near its surface than it would if it had no atmosphere, therefore the temperature is higher by about 33 K (+15^oC).

The greenhouse effect is the popular name for this process, as was previously defined. The glass in a greenhouse is transparent to solar radiation, but opaque to terrestrial infrared radiation, therefore acting in a similar manner to some of the atmospheric gases, absorbing the outgoing energy. Much of this energy is then retransmitted back into the greenhouse which causes the temperature inside to rise. It has long been known that in an actual greenhouse the rise in temperature is higher than its surroundings mainly as a result of the sheltering effect rather than any warming by radiation. The name for the process has been retained partly because it would be too difficult to change it and it also considered to be a useful analogy.

Hence the infrared-absorbing atmospheric gases are known as greenhouse gases, including carbon dioxide, water vapour, nitrous oxide, methane and ozone. A common factor with all the greenhouse gases is that they all have molecules whose vibrational frequency is in the infrared part of the spectrum. There is an atmospheric window which allows the terrestrial infrared radiation to pass through, in spite of considerable absorption by these greenhouse gases. This is at the frequency of about 8-13 µm, and one of the effects of the increasing anthropogenic emissions of greenhouse gases is that this window is gradually closing. As this window continues to close the temperature of the Earth will rise even more rapidly than it is rising at the present.

Many energy transformations are involved in the energy cascade that is triggered by energy arriving at the top of the atmosphere. When the solar shortwave radiation enters the atmosphere some of it is absorbed by atmospheric gases, such as carbon dioxide and water vapour, some is scattered, some is absorbed by the Earth’s surface, and some is reflected back into space, either by clouds or the surface itself. The albedo, the reflectivity, determines the amount of shortwave radiation that is reflected. The albedo varies according to the surface, with ice and certain clouds having a high albedo, 0.6 (60 %) to 0.9 (90 %), and the oceans generally have a low albedo, 0.1 (10 %). The average for the entire Earth is about 0.3, i.e., 30 % of incoming solar radiation is reflected.

Most of the longwave radiation re-emitted from the Earth’s surface is re-absorbed by the greenhouse gases, only a small amount escapes directly through the atmospheric window. Longwave radiation re-emitted from the atmospheric greenhouse gases and clouds is either returned to the surface of the Earth or released into space. The increased amount of energy stored near the Earth’s surface is the net result of this greenhouse effect, the temperature increasing as a result. Associated with evaporation and transpiration there are additional heat fluxes which balance the energy fluxes into and out of all parts of the Earth-atmosphere system.

The energy flux that arrives at the top of the Earth’s atmosphere is only a very small fraction of the energy emitted by the Sun, as the Sun emits its radiation uniformly in all directions. The Earth’s small size compared to that of the Sun and its average distance of 93 million miles from the Sun, mean that it intercepts only a small amount of energy emitted from the Sun. The result of this is that the energy that arrives at the top of the atmosphere is lower than the amount leaving the Sun by many orders of magnitude.

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