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Scope of This Post: The role of water and carbon di-oxide (CO₂) - the two main actors - in global warming has generated much controversy and confusion.
The subject of global warming (or climate change) is controversial because
(a) the science is complex,
(b) most serious damage won't be felt for a few decades,
(c) outcomes depend on what actions are taken now and in the near future;
(d) The situation is further compounded by deliberate attempts by vested interests actively spreading misinformation.
This post is prepared at two levels;
The first part is suitable as an outreach feature where I explain that while water vapour is responsible for the greatest amount of warming, changes in the atmospheric concentration of CO₂, through feedback loops, determine the amount of water in the atmosphere and thus control the extent of the greenhouse effect - CO₂ is the control knob.
In part 2, we shall compare the role of water and CO₂ in global warming in more detail. The science of how radiation energy interacts with water and CO₂ is well understood; however, predictions of global climate change still suffer from an incomplete understanding of the ways in which earth's feedback loops respond to changes brought about by changing concentrations of the greenhouse gases (GHGs). Our understanding of such feedbacks has greatly improved over the past few decades. Most outcomes point to the predictions erring on the side of caution - many observations point to a more severe climate change than predicted.
Part 1: CO₂ is the Control Knob: The earth receives radiation energy from the Sun over a range of wavelengths. In turn, the earth radiates infra-red radiation from its surface. (See Appendix for discussion of black-body radiation). The earth's atmosphere acts like a blanket in preventing some of the radiation emitted by the earth from escaping to outer space. Our planet is 33⁰C warmer than it would be without the atmosphere - so-called greenhouse effect (without the atmosphere, earth's mean temperature will be -18⁰C). (For background reading please see: Making Sense of our Climate Change: 3. The Science of Global Warming)
Water vapour is the most abundant (~ 1%) heat-trapping gas in the atmosphere and detailed scientific analysis confirms that it keeps the earth warmer by about 20⁰C (responsible for about 60% of the greenhouse effect). CO₂ (~0.04%) and other greenhouse gases (GHGs) contribute about 25%. There is some remaining uncertainty in the role of clouds, but they are deemed to trap about 15% of the earth's radiation from escaping into space.
There are three points to note:
(1) Water vapour is a condensable gas - its amount in the atmosphere is fixed by the earth's temperature - any excess water vapour returns to earth via rain or snow within a short time period of a few days. Other GHGs stay in the atmosphere for much longer (CO₂ stays for several hundred years) and, unlike water, their amounts and hence the warming effects accumulate independent of conditions on earth.
(2) Most water in the atmosphere is found in the first 3 km. 99% of atmospheric water is found in the troposphere - below about 12 km altitude (see slide A7 in the appendix). CO₂ and other GHGs mix much more uniformly throughout the atmosphere. Water plays a minor role in the absorption of outgoing radiation above the troposphere - for altitudes from about 12 to 100 km.
(3) Water vapour does not absorb outgoing radiation in the wavelength range from 8 to 15 microns while CO₂ and O₃ have strong absorption bands in this range. To a good extent, water vapour and other GHGs complement each other in trapping outgoing radiation in different parts of the spectrum.
Before we started burning fossil fuels in large quantities, atmospheric water vapour provided (and continues to provide) a steady contribution to warming by trapping ~60% of the radiation emitted by the earth. The increase in atmospheric greenhouse gases - CO₂, CH₄ & N₂O - over the past 200 years has changed the dynamics of the absorption of outgoing infra-red (IR) radiation. To a large extent, this increase has been responsible for mediating additional global warming that we are witnessing today. CO₂ is more abundant and longer lasting than other GHGs and is the most important influence in the observed additional warming over historic levels during the past several decades.
However, many news articles, without mentioning the significant role of water vapour, claim that carbon di-oxide (CO₂) is the most important GHG and convey the impression that CO₂ alone is responsible for global warming. This is obviously not correct. The unfortunate misrepresentation has engendered increased scepticism about climate change. In turn, this has made it more difficult for the public and politicians to accept the highly damaging long-term predictions based on sound scientific analysis and take effective timely actions. It is important that the science of global warming is shared more accurately with the wider public whose lives will be seriously impacted in not too distant future .
The science of how radiation interacts with atmospheric constituents is well understood. Also, since 1969 satellites and ground based instruments have been providing good quality observational data. It is possible to calculate, with good confidence, how the earth energy budget looks like (slide A4), and how it might be affected by changes in the concentration of particular atmospheric constituents. Some uncertainty remains about the contribution of clouds - cloud cover is highly changeable and depending on their type, clouds can cause warming (by trapping earth's outgoing radiation) or cooling (by reflecting Sun's incoming radiation back to space). On the global level, it is estimated that the two effects roughly cancel each other with the clouds causing a small amount of net cooling.
The Three Actors: Earth's temperature is dertermined by three actors - The Sun, the Earth and the atmosphere.
The Sun is the primary source of all energy and the top of Earth's atmosphere (TOA) receives energy from the Sun at a rate of 1362 Wm⁻² (Watt per meter squared) in the wavelength range from 0.15 to 4 µm with a maximum around 0.5 µm (1 µm = 10⁻⁶ m = 1000 nm). Over the past 50 years, total solar irradiance, measured at TOA, has been constant to within 1 Wm⁻².
On a clear day, 40% of the solar radiation received at the earth's surface is visible radiation (0.4 to 0.7 µm) while 51% is infra-red (IR) in the spectral range 0.7 to 4 µm. Most of the ultraviolet (< 0.4 µm) radiation is absorbed by ozone in the stratosphere. We shall call the Sun's radiation (wavelength < 4 µm) the short-wave radiation (SWR).
The Earth warms by receiving SWR but radiates energy in the IR between 2 and 70 µm wavelength range with a maximum around 10 µm. On its way to outer space, energy radiated from the earth passes through the atmosphere and interacts with its constituents. We shall call the radiation emitted by the earth (wavelength > 4 µm) the long-wave radiation (LWR).
The Atmosphere is a collection of stratified gases and extends to an altitude of roughly 100 km above the earth's surface (see slide A7). It plays a complex role in interacting with SWR and LWR - gaseous layers reflect, absorb, re-radiate the radiation passing through the atmosphere. Interactions in the atmosphere comletely change the nature and amount of longwave radiation going to outer space - this is discussed next.
Earth's Energy (Radiation) Budget: The following slides show what happens to the incoming radiation from the Sun and outgoing radiation from the Earth and the role of the atmosphere. Only a small fraction of the earth's radiation (mainly in the atmospheric window from 8 to 14 micron) goes directly to space - almost 90% is first absorbed by the atmosphere which then emits it in all directions (see slide 2 and A4)
Slide 1:
Slides 1 and 2 explain how earth's energy (radiation) budget (EEB or ERB) is determined. In slide 2, the width of arrows indicate (for guidance only) the amount of energy transferred (for quantitative description see slide A4 in the appendix).
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Slide 14 shows what happens to the longwave flux at the top of the atmosphere in the two scenarios. By doubling water vapour, we introduce much greater absorption of LW radiation in the atmosphere and less radiation flux reaches TOA - effectively greenhouse effect is enhanced by about 17 Wm⁻² for a short period but is rapidly corrected as water levels reset to normal (slide 13). When all water is removed, the most important absorber is no longer present and much more of the LW flux reaches TOA - the greenhouse effect is weakened by almost 50 Wm⁻², but again resetting to normal values very quickly.
APPENDIX
Blackbody Radiation: All bodies radiate energy in the form of electromagnetic waves - the energy radiated per second (power) dependes on the surface area and temperature of the body (Stefan-Boltzmann Law) and the range of wavelengths emitted is given by the Planck distribution curve. Note that the temperature is the absolute temperature of the body in unit of Kelvin and is related to degree centigrade as: T (Kelvin) = T (⁰C) + 273. The situation is demonstrated in Slide A1 below:
The total energy radiated per second from a given area changes rapidly with the temperature (T) of the body - as fourth power of T. Doubling the temperture increases the energy emitted by a factor of 16. Sun's surface is about 20 times hotter than the earth; and the Sun radiates 20⁴ or 160,000 times more energy per unit area. Also the Sun is much bigger than the earth.
The wavelength at which peak energy is radiated depends on the temperature of the emitting body. There is a simple relation called the Wien's displacement law that tells us where the maximum intensity of the Planck curve is:
Wavelength (max intensity) in microns = 2898/Temperature in Kelvin
Remember: 1 micron = 10⁻⁶m = 0.001 mm; and T (Kelvin) = T(⁰C)+273
We can summarise the discussion by plotting the spectral distribution of radiation from the Sun and the Earth. In Slide A2, the Sun's radiation intensity has been scaled down to compare its shape with the earth's emitted radiation. The main take away is that the Sun radiates in regions around the visible wavelengths while the earth's radiation is totally in IR extending from 4 to 70 micron wavelengths.
Slide A2:
From the well understood properties of gases and how they interact with radiation, it is possible to calculate earth's energy budget (EEB) with good confidence. To keep the task manageable, the atmosphere is treated as consisting of a small number of layers:
Slide A3: Earth Energy Budget (results from models):
The properties of the atmospheric layers are chosen to reproduce the measured energy fluxes at top of the atmosphere (TOA) and current climate parameters. Slide A4 shows the result for EEB assuming a 3 layer atmosphere. These comprehensive calculations (KT97) were performed in 1997 and have since been revised with minor changes in the results. I show the original results - for recent updates (TFK09, Trenberth Diagrams, Lacis). KT97 and Lacis describe the details of how properties of the layers are chosen and all other relevant information.
Slide A4:
In the diagram above, the incoming energy is equal to the outgoing energy both at the top of the atmosphere (342 Wm⁻²) and at the earth's surface (492 Wm⁻²) - this represents a state of equilibrium and the temperature of the earth and its atmosphere will stay constant. Notice that the total energy flux of 492 Wm⁻² arriving at the earth's surface is much greater than 342 Wm⁻² arriving at TOA because atmospheric gases absorb and re-emit substantial amount of LWR emitted by the earth back towards it.
Vapour Pressure of Water: The equilibrium between water vapour and liquid water in any system depends on the temperature of the system. The equilibrium (also called saturated) water vapour pressure (VP) increases as temperature goes up. The Clausius-Clapeyron equation describes how the VP changes with temperature.
Slide A6: 
It is straightforward to understand the variations shown in slide 7. The earth warms by receiving solar radiation; the increase in surface temperature causes water to evaporate - water vapour has much greater internal energy than liquid water (latent heat of vaporization) and evaporation represents net energy transfer from earth to the atmosphere (slide A4). Gases at the earth surface also heat up and rise (convection) and carry energy to the atmosphere. As water and gases rise, they expand and cool until their temperature is equal to that of gases at higher altitudes (of the order of -65⁰C) - this layer is called the tropopause that is about 10 to 12 km above the earth's surface. Beyond tropopause temperature rises again and cooler gases of the troposphere cannot rise higher and can only move sideways. There is very little mixing of gases between the troposphere and stratosphere.
