The Earth’s Energy Budget

The energy budget for the Earth can be derived using a simple thermodynamic energy balance diagram.

If we consider the Earth to be in thermal equilibrium then DeltaE = O.

Being surrounded by a vacuum the Earth is well insulated and heat cannot be transferred by the usual means of conduction and convection. However, energy can be transferred to and from the Earth in the form of electromagnetic radiation.

To quantify the energy balance I will use the figures from Kiehl and Trenberth, ignoring the non-sensical upward – downward radiation exchange.

The illustration of Kiehl and Trenberth has been simplified as shown below:-

GH Warming
Careful consideration of Kiehl and Trenberth’s analysis reveals that 66 W/m2 of nett energy is radiated by the Earths surface. 40 W/m2 is radiated to space – this is energy radiated directly from the surface. 26 W/m2 is absorbed (or trapped) by the IR active gases in the atmosphere (these are called the Greenhouse Gases – other gases such as nitrogen and oxygen absorb very little IR energy).
It could be assumed that increasing the concentration of these Greenhouse Gases would mean less radiation from the Earth’s surface will escape to space. This is the basis of the hypothesis of Global Warming due to Greenhouse Gases.
The Atmosphere
However, the Earth’s surface also loses energy by way of convection (this includes air flow and evapo-traspiration mechanisms). In fact, according to Kiehl and Trenberth, 102 W/m2 of energy flows from the Earth’s surface to the atmosphere by way of this convective heat flow.
A close look at the above diagrams reveals that the atmosphere absorbs energy from various sources. There is the 40 W/m2 from Greenhouse gas absorption, 102 W/m2 due to convective flow fro the surface, and 67 W/m2 directly via absorption of incoming solar energy. This makes a total of 195 W/m2 absorbed by the atmosphere.
Ther is 235 W/m2 of energy absorbed by the Earth from incident solar radiation. (342 incident – 107 reflected. Of this 235,  168 is absorbed at the Earth’s surface and 67 is absorbed by the atmosphere (due to clouds etc –  this energy never reaches the Earth).
To balance the energy in we have 40 W/m2 directly radiated from the surface and 195 radiated by the atmosphere.
How is Energy Radiated by the Atmosphere?
The answer is – by Greenhouse Gases in the atmosphere!
Note: GHG are IR active, they can absorb IR radiation equally as well as they radiate IR radiation. Other gases will not radiate IR energy. If there were no GH Gases in the atmosphere the temperature of the Earth would have to increase significantly to allow sufficient cooling.
It is straightforward hypothesis that  greater concentration of GH Gases in the atmosphere will lead to increased cooling of the Earth.
The overall picture is that increasing GH gases will:-
  • warm the Earth by trapping some of the 66 W/m2 radiated from the surface
  • cool the Earth by radiating 195 W/m2 from the atmosphere

Kirchoff’s law states that emissivity = absorptivity. GH gases will emit 195 W/m2, but absorb part of the radiation from the surface (66 W/m2)- the nett result would be a cooling of the Earth if GH gas concentrations increased!

The energy flow of the atmosphere: energy in = 195 W/m2,  energy out = 195 W/m2.
If the concentration of GH gases increase then more heat energy would be radiated to space from the atmosphere
GH gases enable the atmosphere to radiate heat away from the Earth.
The energy which is conveyed by the atmosphere includes the convective energy from the surface of the Earth that would otherwise have been trapped in the atmosphere.
GH  gases help COOL the Earth

One Response to The Earth’s Energy Budget

  1. markus says:

    The balance the in earths surface temperature is dependent on the lapse rate, claimed to be withholding energy of the 122 Wm/2 IR radiation eventually emitted to space, longer, as it is radiated through these GHG’s to space.

    I disagree with that hypothesis, in as much as, the GHG’s would have obtained a saturation of absorption of 66 Wm/2 at the time they were emitted directly from the surface of the earth. Once atmospheric they cannot absorb any additional IR radiation, or back radiation, rendering them as same as O2 regards increasing T in the stratosphere.

    Increasing the percentage of human emitted Co2 to other atmospheric gases is not a material difference. The earth has many inter alia weather systems crowding the effects of our Co2 emissions. They are minor compared to Earth’s natural emmisions.These systems act as distributors of temperature around the earth.

    Of course, the earth never receives an equal amount of incoming IR radiation (solar cycles, sun spot activity, interplanetary alignments affecting earths gravity, etc), the lapse rate can also be affected (volcanoes, asteroid collision, biodiversity changes, etc. The the 66 Wm/2 absorption of GHG’s fluctuates,causing interglacials, glacial, warm periods, ice ages, little ice ages. A myriad of different climates though the ages.

    Chronology is the first port off call when seeking data to reconstruct past temperature, and is almost too big to understand. Today’s Earth has never had the exact same climate at any period before now, any matching of proxy records is likely to have massive error bars and be unusable as tools for modelling the current or future climate.

    These different climatic changes can occur over eons or short periods. Sometimes the geography of Earth itself throws up some nastiness. Imagine what happens when 2 enormous volcanoes erupts at close times and the tremendous increase in Earth albedo. these events could wipe out who ecosystems and species, like dinosaurs.

    My apologies, as this post not only seems like a layman’s gibberish, it is.

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