Re-visiting climate forcing/feedback concepts…

I haven’t been able to post much lately, so I just want to put in this post which outlines some of the basic radiative forcing and feedback physics which climatologists use to assess climate change. This is fairly standard material which should be understood by anyone with a deep interest in climate. This article is a bit lengthy so hopefully you have the patience to go through it (or put it on your favorites and come back). Also, a lot of discussion has come up recently over Richard Lindzen’s ERBE analysis in which he purports to show that global climate sensitivity is small, and that the net effect of climate feedbacks is to dampen the so-called Planck response. That basically provoked this post. I’m going to define all these terms below, so don’t worry if I’ve already lost you, and while I am going to do some math in this post, it should be accessible to most people who know a bit of algebra. Skipping over a few calculus steps won’t be detrimental and I’ve tried not to assume much climate background (although I do link to some side references for clarification on some matters). My focus is not on Lindzen’s analysis here, which I don’t feel to be robust at all, but rather building up simple mathematical models for understanding climate change. This will not be new to anyone who has followed the climate literature or discussions for some time, but hopefully it can be helpful to some, or at the very least, serve as a useful reference.

The primary focus of study within the atmospheric sciences for grasping how climate change works is in electromagnetic radiation, and how radiative fluxes interact with the surface and atmosphere interface. We can keep this simple and imagine that planets take in light only at short wavelengths of the EM spectrum from the sun (mostly in the visible region), and that planets emit light back to space only in the longer wavelengths, in the thermal infrared part of the spectrum. As seen below, we can distinguish easily between the solar radiation curves and terrestrial radiation curves, which hardly overlap at all across roughly the 4 micron threshold:


For all the terrestrial planets (Venus, Mars, Earth) we can say that the heating due to radioactive decay in the Earth’s interior is negligible, and they only gain and lose heat radiatively (since outer space is a vacuum).

The radiative balance at the top of the atmosphere acts as the fundamental boundary condition which constrains the global climate. In this model, we assume that the energy input by the sun at the top of Earth’s atmosphere ends up being balanced by the outgoing infrared radiation to space. This is true over sufficiently long timescales when the climate is not undergoing change. If it were not true, then the planet would either warm or cool depending on whether more energy was coming in than going out, or more was going out than coming in. The simplest model for radiative balance can then be written as:

A_{1}S_{0} (1-\alpha) = A_{2}\sigma T^{4}

The “A” terms describe the area of which the planet receives or emits radiation. For Earth, the outgoing energy leaves in all directions, so we can take the area to be 4 \pi r^{2} however, the incoming energy only comes in like a circle (essentially the shadow that would be cast by the planet) because the sunlight comes in from just one side and is not as intense over the whole half-sphere. Thus the A1 term is \pi r^{2}. In reality, the ratio of A2 to A1 is about 4.0034 (Loeb et al 2009) and not 4, since the Earth is not a perfect sphere, but the algebra is made much easier in assuming sphericity, and the radius of the Earth becomes irrelevant since those terms cancel out. S0 here is the solar constant, which is the radiative flux (in Watts per Square meter) that would be intercepted by a flat “wall” in space which stood perpendicular to the incoming solar rays. For a planet at the mean Earth-sun distance, the solar constant is about 1370 W/m2. S_{0} / 4 is thus the incoming solar radiation averaged over the spherical Earth, with a factor of S_{0} / \pi at the equator and declining like the cosine of the latitude angle as you move toward the poles. \alpha is the albedo of the planet, which is the fraction of incoming solar radiation that is reflected right back out to space (mostly clouds, but also by various land surfaces, brighter ones like ice or desert sand contributing strongly). The fraction of absorbed sunlight is therefore 1- \alpha. The albedo of the Earth is presently about 0.3 (i.e., 30% of the incoming solar energy is reflected back to space). \sigma T^{4} is the Stefan-Boltzmann law which relates the total power output (per unit area) of a body to a given temperature, and sigma is about 5.67 * 10-8 W/m2/K4. Basically it shows that hotter bodies radiate much more than cooler bodies, because of the strong fourth power dependence. Temperatures must be expressed in Kelvins. From all this, we can solve for an “effective temperature” of a hypothetical planet which essentially radiated like a perfect blackbody and had uniform temperature over the globe:

T_{eff} = (\frac{S_{0} (1-\alpha)}{4 \sigma})^{0.25}

Plugging in all the relevant parameters into the equation, the effective temperature becomes about 255 K, or about 0 degrees F. The reason why the planet is not actually this cold is because the atmosphere acts to inhibit the efficiency at which the outgoing infrared radiation escapes to space. This is the greenhouse effect, and is caused by molecules (water vapor, CO2, ozone, methane, mostly) which strongly interact with infrared radiation at Earth-like conditions. I’ve already done a couple of posts (see updated this post) on how the greenhouse effect works, and I’m assuming most readers are either educated in that or can get a somewhat decent understanding by reading the above links (wiki actually does a good job IMO). These will also help place the preceding discussion in better context.

We’ve already established that at equilibrium, the difference between the absorbed sunlight and outgoing energy at the top of the atmosphere is zero. Now suppose we perturb the climate system and force the global temperature to change by changing the amount of sunlight we get (or the planetary reflectivity), or as is the case in modern times, changing the outgoing infrared radiation with greenhouse gases. We quantify such a perturbation in terms of radiative forcing, or loosely the difference between the incoming radiation energy and the outgoing radiation energy (there’s some caveats in here about allowing the stratosphere to adjust to equilibrium, and some people define forcing at the tropopause or Top Of Atmosphere, and other alternate definitions have come up in the primary literature, but those details are not really important right now).

We can include a number of different forcings which may have competing effects (e.g., greenhouse gas increase would warm the planet, turning down the sun would cool, increasing sulfate-based aerosols would raise the albedo and cool the planet a bit). We can also introduce an efficacy factor \epsilon (described in Hansen et al 2005) which is the global temperature response per unit forcing for a given forcing agent relative to the response to a standard CO2 increase,

F_{total} = \sum \epsilon_{i} [FA]_{i}

Where FA is the climate forcing, and the summation includes all relevant radiative forcings over a certain time period. Efficacy arises because not all forcings produce the same relative impact, and some produce stronger or weaker changes in climate than CO2 (defined so \epsilon_{CO2} = 1) for the same forcing. The radiative forcing for CO2 (as described in Myhre et al 1998 and later papers) is

F_{CO2} = k * ln(C/C_{0})

Where the constant k (derived from line-by-line radiative transfer codes) is typically taken to be 5.35 W/m2, and C and C0 are the final and initial CO2 concentrations. Using this simple relation results in a forcing of nearly 4 W/m2 for each doubling of CO2. Note that the logarithmic relation suggests that the fractional change in CO2 is what is important, since every doubling produces the same effect. In that sense, adding 10 ppmv of CO2 to a background concentration of 20 ppmv would produce a much larger change than adding 10 ppm to a background concentration of 1000 ppmv. This relation holds well over relevant Earth-like conditions, however the forcing becomes stronger than logarithmic at very low or very high concentrations. Also note this is the forcing at the tropopause, not the surface. Here is a table of modern day forcings relative to 1750 values (IPCC 2007)


It makes sense to ask now what this actually means for us. In other words, how much temperature rise would you get for a given forcing? We use a matric called climate sensitivity to make sense of this. Climate sensitivity is the temperature response of the system per unit forcing. In other words, a high climate sensitivity means that it is very easy to change the global mean temperature, while a very low sensitivity would require an enormous forcing to get that same change. In the easiest case, we’ll consider what happens when you only increase some forcing (say double CO2) and allow the outgoing radiation to increase (according to the Stefan-Boltzmann law) to re-establish a new radiative equilibrium. Here, nothing else changes with the climate state (no cloud cover changes, no ice melts, etc) except for our forcing. This is the so-called Planck response. In a simple way, we can assume that the surface and emission temperature are linearly related, in which case the Planck-only feedback response can be computed as the inverse of the derivative of Stefan-Boltzmann with respect to temperature,

\lambda_{planck} = \left[\frac {\partial\left(\sigma T^{4}_{eff}\right)}{\partial T_{s}}\right]^{-1}

Which equals,

(4 \sigma T^{3}_{eff})^{-1} = 0.27 K(W m^{-2})^{-1}

The temperature response can then be linearly related to a forcing

\Delta T = \lambda F

Where \lambda is the Planck-feedback factor described above. It is important to note now that this is an equilibrium formula, meaning that we don’t see the full temperature response to show up right away if we instantly double CO2, since it takes time for the radiative imbalance to go to zero (it’s hard to heat up the oceans quickly!). We’ll see that when we actually allow other things like clouds,water vapor, albedo, etc to vary with the climate response (as opposed to the unrealistic stefan-boltzmann only feedback), then lambda becomes a function of all those things, and describes how the total forcing is connected to the temperature response. This formula implies that for a 4 Watt per square meter forcing (remember, about a doubling of CO2 equivalent), you get roughly a 1 K temperature rise (multiply these numbers by two to get changes in Fahrenheit).

To compute a radiative forcing for an increase in solar irradiance, we do

F_{solar} = S_{0} * (percent change/100)*(1/4)*(0.7)

where the 1/4 and 0.7 factor account for the geometry and albedo of the Earth, respectively. Depending on how radiative forcing is defined, this number can often be reduced further to account for ozone absorption of UV or other effects, but in general the forcing due to a realistic change in solar increase is very small. It follows that it would take about a 22 W/m2 change in solar irradiance to produce a 1 K change in global temperature. This is actually a very stable climate. This also demonstrates the intellectual bankruptcy of those who claim that the solar trend over the last half century (which has pretty much been a flat-line when you remove the 11-year oscillatory signal) is responsible for most of the observed late 20th century warming, and simultaneously argue for a low sensitivity.

Paleoclimate evidence suggests much larger climate changes have occurred than is possible under realistic forcing scenarios given this sort of sensitivity. The magnitude of glacial-interglacial cycles for instance is on the order of 4-6 K in the global mean, and when you go back in time far enough, much larger climate changes are possible. Even observed trends over the 20th century do not appear to be compatible with a very small sensitivity factor. A useful summary of Earth’s equilibrium sensitivity evidence can be found in Knutti and Hegerl 2008. The best available evidence over the last few decades of research (discussed in IPCC 2007 especially) hints at an equilibrium temperature sensitivity of 2 to 4.5 K (as opposed to 1 K) per doubling of CO2. It can thus be inferred (and supported by a larger body of evidence) that other things are acting to amplify the Planck-response to create a climate which is more sensitive to changes. This will be elaborated upon briefly.

The 2 to 4.5 K value range is the so-called Charney sensitivity. Remember this is the equilibrium response, not the immediate response, and so this is probably not a realistic realization for what to expect over the course of this century. The transient response for a doubling of CO2 (this is defined by assuming that CO2 increases by 1% per year and then recording the temperature increase at the time CO2 doubles) is about 1.3 to 2.6 K in the CMIP3 archive (USCCP 2008) which is less than the longer-term response, and also features less uncertainty. There is also a very long climate sensitivity response which is relevant on timescales of many hundreds to thousands of years and included “slow feedbacks” like ice sheet changes, and is on the order of around 5 K for a doubling of CO2.

Now we consider feedbacks to understand why the actual climate response differs so much from what you’d expect with just the radiative forcing and radiative adjustment. A feedback is essentially something which acts to amplify or dampen the initial forcing. The important distinction is that the forcing “pushes” the climate into a new state, and the feedback simply responds (it doesn’t occur on its own in a stable climate), either pushing the system further in the direction of the initial forcing (positive feedback) or dampening the response which brings the system closer to the initial climate state (negative feedback). The primary radiative feedbacks are water vapor feedback, the lapse rate feedback, cloud feedbacks, and surface albedo feedbacks. Useful summaries of this science can be found in Bony et al 2006 for example, although there’s a lot of good literature here. IPCC 2007 is generally the most comprehensive. I’ll briefly summarize the individual feedbacks below. We now see that lambda is not the Planck-feedback value, but instead is a function of all the possible feedbacks which can occur, and is thus different than the no-feedback scenario (unless all the possible feedbacks happened to cancel out perfectly)

\lambda = \lambda(Wv, LR, C, ALB)

Where these things can also be separated into longwave and shortwave radiation components. Note that the Earth is very inefficient at reflecting infrared radiation at all, so this is not an important term. Reflection of visible radiation is very important however as we’ve seen in describing albedo. Gases in the atmosphere are generally not very good at absorbing incoming sunlight, but rather make the atmosphere opaque to the outgoing infrared. If we change some external variable (e.g., solar constant, more CO2), which we’ll call \theta, and the response depends on a number of other variables, xj (which are then related to \theta), then

\frac{dT}{d \theta} = \frac {\partial T}{\partial \theta} + \sum  \frac {\partial T}{\partial x_{j}} \frac {dx_{j}}{d \theta}

where the summation ranges from j=1 to the number of important response variables, which could be large, with each component having different (or sometimes self-competing) effects that complicates the picture. Indeed, future projection for climate change to a given change in CO2 is much more uncertain in \lambda then it is in the forcing, since GHG forcing uncertainties are typically very small. Aerosol forcings are more uncertain (and restrict knowledge of the total 20th century forcing) but GHG changes should strongly outweigh aerosol changes over the 21st century. Accordingly, future prediction of temperature change depends very much on understanding the individual response variables to climate change and the total response. The following descriptions are far from sufficient, but just to get the feet wet

Water Vapor:

The saturation vapor pressure of water (loosely, “the amount of water the air can hold”) increases nearly exponentially with temperature. This follows from the Clausius-Clapeyron equation (Pierrehumbert et al 2007):

e_{s} (T) = e_{s} (T_{0}) * exp [-x* (\frac {1}{T} - \frac {1}{TR})]

Where TR and e_{s} (T_{0}) are a reference temperature and saturation pressure (614 Pa at 273 K) and x corresponds to the latent heat of the phase transition divided by the gas constant, and takes a value of 5419 K for condensation into liquid and 6148 K for condensation into ice. The dominant influence of the saturation vapor pressure is temperature, increasing sharply, with a 3 K temperature resulting in roughly 20% change in saturation pressure. However, the radiative influence of water vapor depends on the fractional change of water vapor (just like CO2) and not the absolute increase, and so the absorptivity goes as the logarithm of the vapor mass change. Note that this has nothing to do with relative humidity (the fraction of vapor held in air to its saturation amount), but rather specific humidity. Why relative humidity is often discussed in water vapor feedback context is to see how the actual water vapor change scales with the upper limit provided by Clausius-Clapeyron. In the global mean, RH tends to remain roughly constant, which coupled with a change in temperature will yield a positive feedback.

The effect of water vapor is to reduce the outgoing radiation vs. temperature curve, effectively making the climate much more sensitive to forcing. It is important to note that most of the water vapor feedback occurs in the higher altitudes where it is dry and temperatures are cold, and so can be most effective at reducing the outgoing radiation to space. It is also most important in the tropics. The lower level boundary layer water vapor has relatively little to do with water vapor feedback (although it does have implications for other hydrological responses to climate change). Furthermore, water vapor also absorbs visible radiation. This component is far less important than the infrared part, although it can be important in the polar regions where you have scattering from a high surface albedo.

Observations and models are in basic agreement that the upper troposphere becomes moister in a warming climate (e.g., Soden et al 2005), global relative humidity is approximately conserved, and thus enhancing the warming. A good summary of water vapor feedback science that is up-to-date is the Dessler and Sherwood 2009 perspective piece in Science. Water Vapor feedback is the most powerful positive feedback and enhances the warming forced by CO2 by a factor of roughly two.

Lapse Rate:

Because the greenhouse effect depends on the temperature decline with height, decoupling the atmosphere from its current vertical temperature structure will also change the surface temperature. As it is, the whole troposphere is pretty much created by convection, and when it warms or cools it does so as a unit in a way that keeps it near a moist adiabatic lapse rate. The lapse rate change tends to offset some of (but not all) the water vapor feedback. Counterbalancing the water vapor feedback results in warmer temperatures at the high altitudes, more water vapor meaning more condensation, and lifting to higher altitudes so that any given layer of the atmosphere is now radiating more efficiently to space. This can be seen in a simple diagram which shows a steepening of the moist adiabat curves as the climate warms. It follows that “moist regions” will tend to be amplified at altitude relative to the surface.


See here for a larger version of this diagram. The lapse rate feedback tends to thus be negative in regions of moist convection at the tropics, but positive in the high latitudes where surface warming is expected to be amplified. The net effect globally is a negative feedback. This issue also surrounds the whole “hotspot” argument that I’ve discussed before, and whether or not the low-latitude troposphere actually has been amplified relative to the surface. Note again that the hotspot is not a manifestation of higher CO2, just higher temperatures and the fact that we see a moist adiabatic structure during El Nino, the solar cycle, etc. In reality, if such a hotspot doesn’t exist, it just means a less negative lapse rate feedback.

Surface Albedo:

Because the reflectivity of the planet is so important (see Equation. 1) since it directly relates to the absorbed solar energy, changes in the surface that accompany climate change will act as feedback. This occurs when the ratio of a high albedo surface to a low albedo surface increases or decreases in time. The best example is with sea ice, since ice extent tends to increase (decrease) in a cooling (warming) planet, and since ice is much more reflective than surrounding ocean or land, you get a positive feedback. This is one large component of “polar amplification” which describes why high latitudes are more sensitive to climate change than lower latitudes. Warm (cold) climates are therefore characterized by weak (strong) pole-to-equator temperature gradients. Less ice in a global warming situation means more solar absorption which winds up resulting in higher surface air temperatures. The same idea applies to a once forested area which becomes a desert. Sea ice is included in the Charney sensitivity, but not long-term changes in the much larger ice sheets.

It is a very robust result seen in observations and universally across models that the Arctic will warm faster than the Northern Hemisphere as a whole. Over anthropogenic timescales, the Northern amplification is also much more pronounced than at the South Pole. A somewhat more complete picture is that as the climate warms, the summer melt season lengthens which results in reduced sea ice at summer’s end. The summertime absorption of solar radiation in open areas enhances the sensible heat content of the ocean, and thus ice formation in the autumn and winter is delayed. Note that the surface is not highly amplified in the summer where excess energy goes into evaporation or melt, but enhanced upward heat fluxes in the cooler months result in increased temperatures in the lower atmosphere.


Clouds are the largest source of uncertainty in quantifying the extent of climate feedbacks. I’m not actually going to talk about them here (maybe soon! I’d like to explore the various hypotheses and evidence in much better detail) but suffice to say that clouds have competing effects between reflecting sunlight (low clouds mostly) and influencing the outgoing infrared radiation (high clouds mostly). It is still not clear how these two effects will balance out, and thus the magnitude and even the sign of the feedback is not well constrained. It’s probably not very big in either direction, although much of the uncertainty range in the 2 to 4.5 K values for a doubling of CO2 is because we just don’t have clouds nailed down yet in a satisfactory manner. Cloud influence also depends on latitude, optical thickness, and a host of other issues.

Feedbacks behave in a power series like fashion, with small and diminishing gains as time progresses. This looks like g + g2 + g3… and so forth, so the temperature response can be related to the planck-only response and the gain factor as

\Delta T = \frac {\Delta T_{0}}{1 - \sum g}

Here, “the sum of g’s” must be less than unity to allow for the possibility of positive feedbacks while still not allowing a “runaway” effect that is unstable. Note also that the feedbacks operate dependently on each other, so a stronger water vapor feedback would mean warmer temperatures, still less ice, a still lower albedo, and so forth.

Below is a plot showing relative strengths of individual feedbacks for water vapor, water vapor+lapse rate, albedo, CRF (not discussed), and clouds, computed for 14 coupled ocean–atmosphere models.

Soden et al 2008


Bony, S., R. Colman, V.M. Kattsov, R.P. Allan, C.S. Bretherton, J.-L. Dufresne, A. Hall, S. Hallegatte, M.M. Holland, W. Ingram, D.A. Randall, D.J. Soden, G. Tselioudis, and M.J. Webb, 2006: How well do we understand and evaluate climate change feedback processes? J. Climate, 19, 3445-3482, doi:10.1175/JCLI3819.1

CCSP, 2008: Climate Models: An Assessment of Strengths and Limitations. A Report by the U.S. Climate Change Science Program and the Subcommittee on Global Change Research [Bader D.C., C. Covey, W.J. Gutowski Jr., I.M. Held, K.E. Kunkel, R.L. Miller, R.T. Tokmakian and M.H. Zhang (Authors)]. Department of Energy, Office of Biological and Environmental Research, Washington, D.C., USA

Dessler, A.E., and Sherwood, S.C. A matter of humidity, Science, 323, 1020-1021, DOI: 10.1126/science.1171264, 2009.

Forster, P., V. Ramaswamy, P. Artaxo, T. Berntsen, R. Betts, D.W. Fahey, J. Haywood, J. Lean, D.C. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz and R. Van Dorland, 2007: Changes in Atmospheric Constituents and in Radiative Forcing. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M.Tignor and H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

Hansen, J., Mki. Sato, R. Ruedy, L. Nazarenko, A. Lacis, G.A. Schmidt, G. Russell, I. Aleinov, M. Bauer, S. Bauer, N. Bell, B. Cairns, V. Canuto, M. Chandler, Y. Cheng, A. Del Genio, G. Faluvegi, E. Fleming, A. Friend, T. Hall, C. Jackman, M. Kelley, N.Y. Kiang, D. Koch, J. Lean, J. Lerner, K. Lo, S. Menon, R.L. Miller, P. Minnis, T. Novakov, V. Oinas, Ja. Perlwitz, Ju. Perlwitz, D. Rind, A. Romanou, D. Shindell, P. Stone, S. Sun, N. Tausnev, D. Thresher, B. Wielicki, T. Wong, M. Yao, and S. Zhang, 2005: Efficacy of climate forcings. J. Geophys. Res., 110, D18104, doi:10.1029/2005JD005776

Knutti, R. and G. C. Hegerl, 2008, The equilibrium sensitivity of the Earth’s temperature to radiation changes, Nature Geoscience, 1, 735-743, doi:10.1038/ngeo337

Loeb, N.G., B.A. Wielicki, D.R. Doelling, G.L. Smith, D.F. Keyes, S. Kato, N. Manalo-Smith, and T. Wong, 2009: Toward Optimal Closure of the Earth’s Top-of-Atmosphere Radiation Budget. J. Climate, 22, 748–766

Myhre, G., E. J. Highwood, K. P. Shine, and F. Stordal., 1998. New estimates of radiative forcing due to well-mixed greenhouse gases. Geophysical Research Letters, 25, 2715–2718

Pierrehumbert RT, Brogniez H, and Roca R 2007: On the relative humidity of the atmosphere. in The Global Circulation of the Atmosphere, T Schneider and A Sobel, eds. Princeton University Press

Soden, B. J., D. L. Jackson, V. Ramaswamy, M. D. Schwarzkopf, and X. Huang, 2005: The radiative signature of upper tropospheric moistening. Science, 310(5749), 841-844

Soden, B.J., I.M. Held, R. Colman, K.M. Shell, J.T. Kiehl, and C.A. Shields, 2008: Quantifying climate feedbacks using radiative kernels. Journal of Climate, 21, 3504-3520


88 responses to “Re-visiting climate forcing/feedback concepts…

  1. Wow, this is a really nice contribution to the web. I have not seen something written like this in such a clear, concise and comprehensive way. The only thing lacking is a description of how the constant ‘k’ is computed for the CO2 forcing. I presume it’s done using differential equations on a column of air, showing how IR radiation is transmitted, absorbed and emitted throughout the column?

    Since you seem to write well, can I humbly request, at some point, a discussion of unforced variability? It seems to me that ENSO/El Nino also can have cloud-related feedbacks that affect the radiation balance. But I have not seen anything written on this level that describes all the ways ENSO affects the surface temperature.

  2. Chris – nicely done.

    There seems a bit of a disconnect between the paragraphs where you discuss paleoclimate (and model) evidence for large sensitivities, and the section before (bare response) and after (feedbacks). Some missing words, or the paragraphs in the wrong order perhaps?

  3. Chris – I anticipate the rest of this is very good (I just jumped here straight from paragraph 2), but I recommend you correct this:

    “We can keep this simple and imagine that planets take in light only at the visible end of the EM spectrum from the sun, and that planets emit light back to space only in the thermal infrared part of the spectrum. We can treat these two components independently since emission in the infrared for the sun (at those wavelengths the atmosphere absorbs), and emission in the visible for Earth is negligible.”

    It’s more accurate to set an approximate cut-off around the wavelength of 4 microns; there is a substantial amount of solar radiation in the infrared up to 4 microns, and very little terrestrial radiation shorter than 4 microns. Climatologically, it is useful to consider radiation divided into two large bands – shortwave (SW), shorter than about 4 microns, almost entirely from the sun, and longwave (LW), longer than about 4 microns, with relatively minor solar contributions.

  4. … Of course, I understand you are trying to describe a general idea and not get into too much detail, but my concern is that the visible = solar, infrared = terrestrial emission is too great an oversimplification, which may lead to much confusion later, for example, when a person finds out about water vapor absorption in infraread wavelengths shorter than 4 microns.

  5. Thanks for the comments and criticisms guys. I agree with the suggestions above, and have modified some aspects of my post accordingly. Hopefully it looks a little better. Part of the problem of doing these posts at 3 in the morning when you can’t get to bed is that you always understand what you’re talking about, but getting other people to is a challenge.

  6. Your intended audience sounds a lot like me, and I found it a really useful review. Thanks.

  7. Hi, Chris,

    Thanks for spending the effort in writing this post. These kinds of explanations are very helpful.

    To clarify:

    >although it does have implications for other hydrological responses to climate change)

    Does this refer generally to globally averaged increased evaporation and rainfall rates and subsequent regional changes in precipitation patterns?

    >where you have scattering from a high surface albedo.

    This refers to reflected short wave absorbed and re-emitted by near surface level water vapor?

    >It is important to note that most of the water vapor feedback occurs in the higher altitudes where it is dry and temperatures are cold, and so can be most effective at reducing the outgoing radiation to space.

    >The lapse rate change tends to offset some of (but not all) the water vapor feedback. Counterbalancing the water vapor feedback results in warmer temperatures at the high altitudes,

    I’ll admit to a potential lapse problem of my own, but I’m having trouble reconciling the two quotes above. How does counterbalancing the positive (warming) water vapor feedback result in warmer (more positive feedback?) temperatures.

    Thank you.

  8. Great tutorial. I just added this to my site. Thank you. 🙂

  9. You said “In a simple way, we can assume that the surface and emission temperature are linearly related, in which case the Planck-only feedback response can be computed as the inverse of the derivative of Stefan-Boltzmann with respect to temperature,”

    They are most certainly not linearly related.

    The Stefan Boltzmann equations are logarithmic.

    The Planck Response refers to emission temperature at the tropopause (top of the atmosphere whatever you want to place it since they are 4 different levels in the atmosphere at the right emission temperature).

    We are concerned mainly with the Surface Temperature which is 33K higher than emission temperature or an extra 150 watts/metre^2 higher than the emission radiation level.

    Add 4 watts/metre^2 to the surface temperature (at 390 watts/metre^2) and then recalculate the derivative. Now you are down to 0.18C per additional watt. Now things start to look a little different.

    Response– No. In this simple model radiative balance is set at the upper layers of the atmosphere, not the surface, and you simple don’t apply this logic to the surface. What was outlined here is not a bad approximation at all, and the fourth power energy flux from S-B is not the same thing as temperature. One can almost find the temperature of any tropospheric layer by knowing the temperature at one layer and extrapolating over some adiabat to a new layer (or using pressure as a vertical coordinate, can use Poisson’s equation) or something similar. Obviously full radiative transfer models are more complex, but something along the lines of a degree C per doubling of CO2 for the no-feedback response is relatively simple and very robust– chris

    • Chris,
      Thanks for this summary. Very useful.
      I have the same problem as Kyle John.
      And I think the problem we have here is the definition of Radiative Forcing (RF). How (and where) can we use these 4 W/m2?)
      If you apply to the surface, which have to emit 390 W/m2 and is 33C higher than the emission temperature, the derivative gives 0.18 C/Wm-2.
      If you apply to the tropopause, which have to emit 240 W/m2, the derivative gives 0.3 C/Wm-2.

      The definition of RF by the IPCC is not clear to me…
      Here it is:
      “The definition of RF from the TAR and earlier IPCC assessment reports is retained. Ramaswamy et al. (2001) define it as ‘the change in net (down minus up) irradiance (solar plus longwave; in W m–2) at the tropopause after allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values’.”

      How can you define RF at the tropopause keeping the surface temperature the same??
      Please help!

      Response– The primary constraint on the global climate is the Top-Of-Atmosphere energy balance, and this is basically where 4 W/m2 applies for a doubling of CO2. This is not the same for the surface perturbation, and the surface energy balance depends on much more than radiation (such as latent and sensible heat fluxes). So I’m not talking about the enhanced downward IR emission. The surface budget is another matter, but for a simple model like this, can be thought of as more or less being dragged along with the TOA perturbation and regulating the temperature gradient between the surface and atmosphere. It makes no sense to take the inverse derivative and use the surface temperature, since radiation balance is not set at the surface– chris

      • In fact I realise this is non sense to convert into temperature at the tropopause anyway. Who is radiating (I mean the main part)?. It is the Earth. Not the tropopause. The tropopause is fine when you talk about radiation balance. But it is an immaterial boundary.
        When you want to talk about consequences in temperature, you have to come back to the real black body concerned: the Earth.

  10. Chris,
    While I appreciate your effort at explaining some of the basic physics,
    I think that it is also important to state that this is (as you acknowledge yourself), a simple model. There are many things that are not taken into account: ocean convection currents, water vapour in the form of clouds, chemical processes within plants, chemical processes in the ocean, the earth’s orbital distance from the sun, etc.. Therefore one would be wise not to construe the results of your simple model as approximating what is really happening in the world or to believe that your simple model has any predictive capability.

    Response– I personally think one can learn very much from simple explanations, and much of what I have presented here happen to be relatively robust and important responses to climate change (e.g., enhanced lower tropospheric water vapor content, decrease in ice extent and increase in local solar absoprtion, etc). In many of these cases understanding everything about the chemical processes in plants is not going to change the basic picture. So these simple explanations do help to place modern and future warming in some context. Obviously, understanding the much smaller and subtle details, is going to require research, e.g., actual field observations, paleoclimatic inferences, and sophisticated modeling.– chris

  11. So it was Lindzen that provoked the post, but you chose not to go into his argumentation because you feel it’s not robust. So you write about something else, and we are not even given a reference to the provocation, which we must assume was the recent peer-reviewed article in GRL: – Wrong?

    Now please explain why it is not “robust”, based on something else than just feeling.

    Response– Some other qualified people (such as James Annan and Gavin Schmidt) have already commented on the modeling side of his paper (you should consult them for details) which involves an improper comparison, and others (including me) have commented before on why his results make no physical sense given the time-evolution of modern climate change and most importantly, the paleoclimate record (as I did touch upon in this post). I’ve blogged before about his earlier attempt to infer sensitivity, and his decision to ignore a body of literature that did not agree with him, and I still cannot find that he fully accounted for newer data adjustments (he uses Edition3 this time, but I don’t think he uses Rev1), and his results contrast significantly from Wong et al 2006 and the people putting out the data he used. Forster and Gregory (2006) also reach a different conclusion using Earth Radiation budget data. His results contrast with several decades worth of literature on the topic (as outlined in the Knutti and Hegerl reference), and inevitably there is that hint of sloppiness associated with Lindzen that I just can’t get out of my head. Also, I’m still not sure this is even the best approach to infer sensitivity, although it makes sense in theory, there are some practical limitations. So no, I don’t think his result is robust after just being published, and not having even been around enough time to be examined in detail by the literature. I suspect responses might follow in the literature but I haven’t heard of any new paradigm shifts recently, and I just can’t imagine that I will anytime soon– chris

    • “””…and inevitably there is that hint of sloppiness associated with Lindzen that I just can’t get out of my head.”””

      “””…Also, I’m still not sure this is even the best approach to infer sensitivity, although it makes sense in theory, there are some practical limitations.”””

      “””…So no, I don’t think his result is robust after just being published, and not having even been around enough time to be examined in detail by the literature. I suspect responses might follow in the literature but I haven’t heard of any new paradigm shifts recently, and I just can’t imagine that I will anytime soon– “””

      “hint”, “some practical limitations”, “can’t imagine”

      Not a very ‘robust’ critique.

  12. If someone came to me and proposed a perpetual energy machine, and had pages of seemingly valid calculations as to why it would work, I would still doubt it. I would doubt it strongly because at the top level, something is wrong. You simply can’t beat the system no matter how seductive the calculations.

    So this is what bothers me (based on my physics classes years ago): A perfect absorber of radiation, a black body, will on the average, only reach its black body temperature, it simply will go no higher. Now you take a planet, mix in some atmosphere, clouds, etc. and you can shift the warm spots and cold spots around. But your average temperature is still at, or below the black body temperature. SB assures us of that. CO2 or H2O absorbs infrared and other frequencies, but as part of that absorption, it gets warmer. And as it approaches and starts to surpass the black body temperature for that point in space, it too becomes part of the radiating ‘surface’ of the planet. Any mechanism that forces its temperature up also drives it into becoming part of the cooling process of the system. You can do layers of atmosphere and proposed mechanisms, but in the end, they are driven (as is the perpetual engine) by the overall limits of physics. There are no one-way heat valves, no Maxwell’s daemon to push the heat in one direction. In the end, it’s all got to come out.

    Has anyone ever physically demonstrated (i.e. a physical constuct, in a vacuum chamber, radiated by a controlled source) any mechanism that would even come close to Venusian temperatures? Not that I’m aware of. We seem to be carelessly assuming that somehow ‘runaway greenhouse effect’ can explain those high temperatures with no other input. (Put a highly efficient greenhouse in space and see how warm it gets)

    This whole thing does not ring true. Cellular models often have fatal flaws, from round off errors compounded millions of times, to assumptions and simplifications that are very close but not quite right. (Engineering models, much simpler systems much better understood, still suffer problems. No one would put a plane or any product into service based purely on a model). It may well be possible to create a model that shows a positive energy machine actually working, ..

    ….but my money is still against it in the real world.

  13. It is my understanding that the hypothetical planet would radiate from the surface and the atmosphere. So what is Teff? I don’t think you define it. Is it the effective temperature at an effective location somewhere between the surface and the top of the atmosphere? What does it mean? And how can you get the mean surface temperature from the effective temperature?

    Response– Sorry for being unclear. Teff is the temperature that the Earth would radiate to space at when considering only the incoming, absorbed solar radiation, and is thus 255 K for a solar constant of 1370 W m-2 and an albedo of 0.3. For a planet with no atmosphere, this “effective radiating level” is the surface. For a planet with an infrared absorbing atmosphere, Teff remains the same but now the layer of bulk emission to space occurs somewhere above the surface, at some pressure level prad. Adding greenhouse gases thus keeps the temperature of the effective radiating level constant, but causes it to shift to higher levels of the atmosphere (i.e., prad is reduced). In reality ,emission does come from all layers (including the surface and atmosphere), but increasing the infrared opacity effectively replaces warmer surface-based emission with radiation that emanates from colder layers aloft. We can then find a surface temperature by Ts = Trad*(ps/prad)^R/cp, Or if you prefer height z as a vertical coordinate then you can simple extrapolate down the appropriate moist or dry adiabat from the effective temperature to a warmer level below it. You can see then that adding greenhouse gases always causes surface warming insofar as the temperature drops with height in the atmosphere. Hope that helps– chris

  14. Hello from Russia!
    Can I quote a post in your blog with the link to you?

    Response: ok. — chris

  15. jay – the greenhouse effect is not a perpetual motion machine. If the atmosphere were transparent to LW and did not absorb any SW radiation, the surface would tend to reach the temperature at which it emits as much as it absorbs from the sun. Add in some SW absorption in the atmosphere, and the atmosphere would warm up to higher temperatures so that heat would flow downward to the surface, because the atmosphere could not cool radiatively to space with zero LW absorptivity. Add in some atmospheric LW absorptivity, however, and the atmosphere could start to radiatively cool to space, while also absorbing some LW emission from the surface and also radiating some LW emission to the surface, and so would not be as warm for the same SW absorbtion. Adding enough LW absorptivity to the atmosphere, and the atmosphere would cool more by LW emission than by SW heating if it remained at the temperature of the surface – it would then tend to cool below the surface temperature, so that heat from the surface would flow up to the atmosphere to balance the net SW+LW heating of the surface (SW heating + LW heating from the atmosphere – LW emission to atmosphere and space) and the net SW+LW cooling of the atmosphere (LW cooling to space + LW cooling to surface – SW heating). Note that greater LW opacity increases the necessary temperature gradient to sustain a given net upward LW flux. When the temperature gradient is convectively unstable, there is a net LW flux and a convective flux. The convective flux tends to keep the temperature gradient near neutral stability, so that the temperatures at various vertical levels within the troposphere tend to go up or down togethere in some way in response to radiative flux changes at the top of the troposphere (the tropopause).

  16. “Add in some atmospheric LW absorptivity, however, and the atmosphere could start to radiatively cool to space, while also absorbing some LW emission from the surface and also radiating some LW emission to the surface, and so would not be as warm for the same SW absorbtion. ”

    The upper part of the atmosphere in particular would cool off; there would be some lower portion would not cool off to much below the surface temperature, which itself would become warmer.

  17. What you say here is useful and, though my grasp of the maths is insecure, it’s rare to find such an accessible description, Chris, so thank you.

    The magnitudes of the radiative forcings in the IPCC table are minor, resulting in only a small change to OLR. Later, in quantifying the warming effect of the sun, you say “this is actually a very stable climate,” implying that small changes to the forcings will have little effect on temperature. But, though clouds are “the largest source of uncertainty in quantifying the extent of climate feedbacks”, you ignore them. So does the IPCC. Am I the only one to wonder what rank they actually take in the IPCC table? Because they do have an effect, even if we don’t know what it is.

    Response– The context of my quote about forcings having a small effect on temperature applies only to a situation in which the climate is governed by net neutral or negative feedbacks. The radiative forcings are actually quite large, in fact. Clouds do not appear in the radiative forcing graphic in my post simply because they are moreso regarded as feedbacks, much like why water vapor, albedo, etc are not regarded as forcings.

    I did ignore clouds only with the caveat that it is a very large topic to cover, and probably deserving of another post in the future, but the IPCC 2007 report certainly does not ignore them, and there’s a lot of refereed literature out there (some of which is referenced in this post) where you can pick up some more information– chris

    In ordinary experience, clouds cause large variation in solar heating of earth and ocean. The perceived difference is similar to sheltering, or not sheltering, under a tree. Clearly, by their absence or presence, they make an immediate difference of several degrees and can maintain that influence over hours, days, weeks or months, perhaps years — we need more data. In contrast, the magnitudes of aerosol, GHG and other forcings in the table are undetectable by the senses. They are obviously less significant than clouds.

    Response– This is odd. I understand your daily intuition for what cloud cover changes do, but a planet with no greenhouse gases would be frozen over, so I don’t know if I agree that “they are obviously less significant.” Aerosols also have a very detectable and uncontroversial effect on aspects of the hydrologic cycle and on radiative balance, which makes them an important variable in understanding modern climate change.– chris

    Is our concern over the radiative properties of GHGs justified, when cloud effects are much more significant? Isn’t it rather like over-emphasising the insignificant volcanic aerosol effects on temperature and then fretting needlessly about the next eruption? Clouds clearly overpower the effects of GHGs but, without investigating, we will never quantify it.

    Response– Clouds are being studied extensively. But the fact is that understanding how cloud effects on radiative balance will change as a function of GHG change is not trivial, and just tossing more research at it does not guarantee that the answer will all of a sudden become obvious. Clouds have many (and often competing) effects, observational data is limited, and various models produce different results as to the magnitude or sign of feedback. And again, the cloud changes being considered are a response to an underlying climate state, which itself is dictated by something else (like GHG’s). There are plenty of independent lines of evidence that do not rely on direct numbers for cloud changes (e.g. using the paleoclimatic record) which also help constrain sensitivity, and this is probably the best evidence that sensitivity is not very low. — chris

    In any case, to transport significant amounts of heat, the ocean must warm, but the atmosphere, no matter how it warms, does not heat the ocean for, as you know, hot air rises and downward radiative heating is insignificant. There is very strong correlation of near-surface temperature with the Thermohaline Circulation (THC), indicating that the oceans warm the atmosphere, not the contrary.

    Response– No, greenhouse gas increase will heat the ocean. I’m not even sure what to say to this remark.– chris

    You point out that we cannot quantify cloud effects or even say whether they provide a net positive or negative feedback to temperature.

    Since there is so much we don’t know about clouds, would you recommend we put research funds into discovering more? What about water vapour and the other forcing factors mentioned?

    I would say that, without knowledge of what clouds are doing, funding research into the effects of warming, and especially preventing warming, is akin to putting the cart before the horse. The science is far from settled, as I read it, for the climate system.

    Response– There is always going to be uncertainty in something. Welcome to the world of science. If it weren’t clouds, then you’d find something else to delay action. Uncertainty is not unbounded however, and there is virtually no doubt that adding GHG’s will causes warmer temperatures which can be troublesome on an ecological and socio-economic level.– chris

    It appears to me slapdash to become preoccupied with what is by any measure a minor component of atmospheric circulation while, just below, the great ocean shifts vast quantities of heat energy around the globe that dwarf the energy in the air, and as soon as they appear those ghostly, insubstantial white clouds reflect even the irresistible, blazing sun with a casual invincibility. They are to the light as shields to the sword.

    I know you don’t concern yourself here with policy matters, but I wonder: Would you advise we get better knowledge of that system before committing human society to expensive and disruptive “corrective” action on the basis of what the IPCC and you yourself acknowledge is a low level of scientific understanding?

    Response– I believe current understanding is sufficient to promote action on climate change, and a “no action” viewpoint does not follow rationally from the remaining uncertainties that still lurk around. The past record has plenty of examples of “surprises” (e.g., abrupt climate changes during the last glaciation), and plenty of support for a system which is sensitive enough to change for us to care about– chris

    Richard Treadgold,
    Climate Conversation Group.

  18. Richard Treagold –

    – “In ordinary experience, clouds cause large variation in solar heating of earth and ocean.”

    Locally. Regionally. Daily. Seasonally.

    Yes of course they do. But have you noticed any persistent shifts in cloud types, amounts, qualities, and their distributions in space and time, or does one year’s annual cycle and all the hourly, daily, and weekly, etc, fluctuations seem largely familiar from one year to the next, one decade to the next? If not, then how could there be any cloud forcing or feedback helping a climate change. Of course, there probably are cloud variations, fluctuations associated with such things as ENSO and volcanic eruptions, and solar changes, and anthropogenic greenhouse and aerosol forcings. But then, what causes them, and how much is their effect, and is there any persistent trend? What can sustain a significant long-term persistent shift in clouds, in humidity, in temperature, in snow and ice, besides some external forcing, such as a change in CO2? Can you find any sufficient long term oceanic heat redistributions – large enough?

    Heat takes time to build up or be released from the climate system due to it’s heat capacity (dominated by the ocean, but with contributions from the specific heat of the land surface and air and the latent heat of melting or freezing ice, and evaporation of water, as total amounts of ice and atmospheric water vapor may change). (Short lived fluctuations can have local effects particularly at the edges of clouds or humidity variations and especially on and immediately above land surfaces, especially dry land surfaces at high elevations and/or under clear dry skies, but such local and regional fluctuations of heat are ultimately dispersed by atmospheric motions if not dissipated locally/regionally by radiative heating/cooling.)

    – “but the atmosphere, no matter how it warms, does not heat the ocean for”

    That, and the notion that the atmosphere cannot heat the surface.

    What these ideas represent is an incomplete understanding. There is downward flow of solar energy that declines going downward as it is absorbed. This flux convergence would by itself cause heat to build up. There is emission of radiation to space, which originates over a distribution from the surface through the atmosphere, and would by itself cause cooling. These distributions are displaced from each other due to the physical characteristics of the system, including the greenhouse effect. The warming and cooling act to drive heat fluxes within the system so as to approach a state of balance where, globally and in the time average, each vertical layer’s solar heating is balanced by LW radiative and convective cooling, where the radiative cooling is the sum of radiative cooling to space and the radiative cooling to other layers minus radiative warming from those layers, and the convective cooling is the convective cooling to other layers minus convective warming from other layers. Note that convection cannot by itself remove heat from the climate system (and within the air, is mainly limited to the troposphere); essentially all solar heating must be balanced (on average) by LW radiative cooling to space if the climate is in a (time-averaged) equilibrium. When considering regional or local conditions over short time periods, the solar heating – net LW cooling – net vertical convective cooling is balanced by net cooling by horizontal heat transports plus a rate of heat storage.

    The distribution of temperature and optical properties, and salinity in the oceans, etc., shapes these heat fluxes. On a net basis, the ocean cools (by radiation and convection) to the atmosphere. If the atmosphere warms, that changes the fluxes, and the oceans generally will not cool as much to the atmosphere, so unless the solar heating is also reduced by the same amount, the oceans will warm in response. And so on over the land surface. And so on for layers of air, etc.

    Outside on a cold winter day, your exposed skin will be warmer than the air and lose heat to the air, but it will remain warmer than the air because of the heat supplied by your metabolism and transported from deeper inside your body. Now, if you walk into a warm room, the temperature of your skin will rise. Not because it is necessarily cooler than the warm room (although that is possible), but because it is losing heat less rapidly to the environment, while still being heated from within.

    If you stayed outside but put a coat on, the coat would slow the heat loss from your skin by impeding convection (including removal of latent heat (perspiration)), slowing conduction, and blocking direct radiant transfer from your skin. With the same heat flow to the skin from below, it will heat up to higher temperature. Heat could still flow outward from your skin, through your coat, and to the environment, but to sustain the same heat flow as there was before you put on your coat, the temperature difference has to have increased, so your skin will have a higher equilibrium temperature.

    Of course, the higher skin temperature may reduce the flow of heat to the skin from below, but you get the idea.

    Replace metabolism with solar heating and replace the coat with the greenhouse effect. The greenhouse effect does not impede convection, molecular diffusion, or conduction, but the last two are only effect in transporting heat from the surface to the air immediately above it and from the water immediately below it, and within the land surface material. Convection is mainly limited below the tropopause because radiative conditions keep the air above that level stable to convection (there is some large-scale overturning above the tropopause (driven by a relatively small amount of kinetic energy that comes from the troposphere) but the global average vertical heat transport associated with this is quite small so far as I know). So a change in the greenhouse effect acts on LW radiative fluxes, and the resulting heating or cooling, however distributed within the troposphere and surface, tend to be spread out vertically (and horizontally, but especially vertically) by convection (because vertical variations in temperature changes would change the convective fluxes) so that the temperature at the surface and at other vertical positions within the troposphere tend to rise and fall by similar amounts in response to the tropopause-level radiative forcings and feedbacks.

  19. “If not, then how could there be any cloud forcing or feedback helping a climate change.”

    The “If not” refers to the first part of the preceding sentence; “If so” would refer to the last part.

  20. Climate Change or global Warming has been the topic lately. So let me share my little story how climate change affected me. About three weeks ago, we were hit by two very strong storms. We never had that in decades. They left our country with still so many flooded areas, a lot were homeless and lost so many loved ones. Until now, we are still sweeping the streets from mud and tons of ruined appliances drowned from the flood. The effects of those twin storm were devastating. It’s not wet season for us here, but we we were informed that we are still expecting four more storms on this last quarter of the year. And just this morning, local news says, weeks from now, we are expecting a strong earthquake to hit the metro city including the nearby provinces. This is the same Metro city hit by the twin storms. And the news says its all because of global warming/climate change. I’m blithely about the issue before, but when the twin storm hit us plus all the bad news, I thought, I must do something too. To solve the global warming problem, it must be stormed at the national and international levels.But the total success is built upon the action of every individual, regardless of nationality, to conserve energy and live in a greener, cleaner community.

  21. My understanding is that CO2 concentration has increased by 40% since the Industrial Revolution and that average temperatures have increased about 0.8 Deg K (or C). This is a minuscule 0.3% change, even with all the forcings and feedbacks in effect. Given that, as you say fundamental CO2 effect acts logarithmically, even a doubling of CO2 concentration would only increase average temperatures by a further 1.6% K, a level of change which hardly anyone would characterise as ‘Dangerous.’

    I regard this as a reasonable base line scenario. The burden of proof is now on Global Warming Mitigation Advocates to prove their case- preferably with a higher level of argument than name- calling.

    Response– This is kind of tedious. Your 0.3% number is utterly meaningless. It is like saying a meter of sea level rise is small compared to ocean which is miles deep. This quantity is not useful to people on low-lying areas. The small numbers in consideration can be dangerous because we’re talking about the derivative, not absolute numbers. *Only* a 4 or 5 C decrease in global temperatures can give you another ice age, for context.

    CO2 radiative forcing is a logarithm, but your number (100th of a degree Celsius!) comes out of nowhere, and is completely wrong. As I said, it is more like 1 C with a doubling of CO2 (without feedbacks) and more around 3 C with feedbacks.– chris

  22. Chris,
    Excellent resource. It is bookmarked just in case I ever come across a denialist who actually wants to learn something. Any takers?

    [crickets chirping]

  23. Has anyone ever physically demonstrated (i.e. a physical constuct, in a vacuum chamber, radiated by a controlled source) any mechanism that would even come close to Venusian temperatures?

    The temperature of the Venusian atmosphere at the 1000mb level — roughly Earth’s at sea level — is (IIRC) right about 100 deg F. That is not very far off Earth’s, particularly considering how much closer to the sun Venus is.


    Thanks for the nice summary. I noticed the treatment of the Earth to the sun’s radiation as a disk equivalent, taking the angle of incidence into account.

    However, I didn’t note that when talking about albedo. At Arctic latitudes (i.e., low angles of incidence) in the summer, water is actually a pretty good reflector — just less than newly fallen snow.

  24. Dr Phillip Bratby

    Ray Ladbury: What’s a denialist? It’s not in my dictionary. Does it have anything to do with the holocaust?

  25. Pingback: Some comments on AGW « the Air Vent

  26. Well, “Dr.” Phillip Bratby, a denialist is someone like you, who believes there is a vast conspiracy by scientists to extract extra money from your pocket (we’ve seen your comments on Bishop Hill’s site, WUTW, and Climate Audit). In that sense there is some overlap between climate change deniers and holocaust deniers: both believe in a conspiracy, both totally neglect scientific research, or actively attack scientific research as biased, and then both refer to their ‘own’ scientists as absolute authorities, and both claim their voice is being suppressed (because of the supposed conspiracy…). Nice circle, eh?!

  27. “denialist” – or if you prefer an analogue that is less of a flashpoint:

    Apollo Moon landing deniers

    Flat earthers

    Evolution (as in biological, genetic diversity + selective pressures, speciation, etc.) deniers (actually may have some serious repercussions in society, though)

    Beware of loading too much baggage into one word when taking into different contexts. Consider usages of “crusade”, “jihad” (kind of the same thing (at least in some ways, any way), so don’t assume that another culture’s casual reference to jihad is automatically sinister – “sinister” as in “bad”, not as in “left-handed”). “mein kompf” – that’s just my struggle – if you were in Germany you might concievably here mein and kompf used with no intent to refer to you know what (I would assume). “taliban” = students. Capital letters can make all the difference, of course.

  28. Paul Mason – it is true that after adding in other anthropogenic forcings, the net anthropogenic forcing has been estimated to be near the forcing from the CO2 increase (there is some uncertainty with aerosol-forcing). So while aerosol cooling has masked some of the warming, to a first approximation one could expect the warming up to this point to be near that which would be caused by the CO2 alone.

    However, there is also a lag in the climate response to forcing, mainly from the heat capacity of the ocean.

    Feedbacks that respond to temperature can’t act immediately with the forcing but grow as the temperature changes, so the time scale for climate equilibration actually tends to be in proportion to climate sensitivity; the initial rate of response is equal to the (change in) forcing divided by the heat capacity.

    There is a lack of strong evidence to support a low climate sensitivity (less than 2 deg C per doubling of CO2 or equivalent forcing). Paleoclimatic evidence, both from glacial-interglacial variations and from earlier times when the climate was warmer, are at least in broad agreement with modelling results for climate sensitivity (the more ancient climate and forcing records give more room for uncertainty, though).

    But it is established that radiative forcing has an effect on climate, and it is established that there are feedbacks. So the burden of proof is more on any claims that the climate sensitivity is significantly different than what is reasonably expected, as well as any claims that reduce the range of uncertainty from where it is now.

  29. “Hey Skipper ”

    Venus, and Mars and other planets, are opportunities to test physical models and theories. But in so doing one must make sure the physics are not held specific for Earth.

    For example, the convective lapse rate is a function of the thermodynamic and physical properties of air and any substances which undergo phase transitions within the atmosphere (like water on Earth). Gravity also affects the relationship between vertical pressure variation and mass density, the later in combination with composition being of great importance to optical properties.

    Consider the stratosphere, as defined by the layer of air above the convecting troposphere that is stable to vertical convection. On Earth, the stratosphere is generally characterized by increasing temperature with height, or in the lower stratosphere away from the tropics, little temperature variation with height (there may be some decrease of temperature with height at high latitudes in winter). In contrast, my impression has been that in the lower part of Venus’s stratosphere, there is still significant temperature decrease with height.

    (In some contexts, the entirety of the atmosphere above the troposphere may be labelled ‘stratosphere’, although in other contexts, the uppermost layer which begins at it’s base with significant increasing temperature with height may be called the ‘thermosphere’. Earth has distinct stratosphere, mesosphere, and thermosphere layers because of the solar heating of the ozone layer.)

  30. Dr Phillip Bratby

    Well Marco “anonymous”. My name is down in the black book is it? You keep a record of all sceptical scientists do you? Nice. Who are the “we” who have seen my comments? BTW, you’ve missed a few other sites where I comment. Also, why do you put the Dr as “Dr”? For your information, I don’t believe in a conspiracy, I don’t neglect scientific research, but there is no doubt that some scientists do not use the proper scientific methodology and wittingly or unwittingly introduce bias, I don’t believe in “absolute authorites” in science and finally I don’t claim my voice is being suppressed.

    Thank you for the definition of a denialist. Which dictionary can I find it in?

    • No need to keep a record, google does just fine. I write “Dr.”, because there’s no other reason than attempting to gain ‘authority’ by quoting one’s academic title when reacting on a blog where they don’t know you.

      That you do not believe in a conspiracy is contradicted by your remarks. Just a few examples:
      1. “Hansen and Gore are linked by their desire to deceive the world with their contorted view of the truth and their manipulation of the data for political purposes”

      2. “The whole jamboree was a political scam, pre-designed to scare the world about a problem for which there is no scientific evidence.”

      3. [Briffa] “Having hidden his data for over 10 years”

      4. [Hockeystick] “a fraud perpetrated and encouraged by a small clique of like-minded (or negligent, in the case of peer reviewers; take your pick) supporters”

      5. “The concept of anthropogenic global warming is politically–driven by the Intergovernmental Panel on Climate Change (IPCC)”

      6. [peer-review] “although one could argue that it succeeds in its purpose because it allows non-scientific alarmism to masquerade as science”

      7. [new scientist] ” It doesn’t examine the evidence and just repeats the political mantra “I believe in man-made global warming”.”

      8. “The climate change scam”

  31. “both totally neglect scientific research… and then both refer to their ‘own’ scientists as absolute authorities”

    Contradiction alert.

  32. “Plugging in all the relevant parameters into the equation, the effective temperature becomes about 255 K, or about 0 degrees F. The reason why the planet is not actually this cold is because the atmosphere acts to inhibit the efficiency at which the outgoing infrared radiation escapes to space. This is the greenhouse effect, and is caused by molecules (water vapor, CO2, ozone, methane, mostly) which strongly interact with infrared radiation at Earth-like conditions.”

    From your part 1:
    “The mean temperature of the Earth’s surface is actually 288 K, which says that the greenhouse gases are responsible for a 33 K enhancement.”

    This is incorrect. You need to take into account the ideal gas law first. Even if the atmosphere contained no greenhouse gasses, the surface temperature would be higher than SB black body calculations suggest. The true “greenhouse gas” forcing is therefore much less than 33K and is actually closer to 3K.

    Response– Not really. — chris

  33. Patrick:

    Venus, and Mars and other planets, are opportunities to test physical models and theories. But in so doing one must make sure the physics are not held specific for Earth.

    No doubt. My point, though apparently not well made, was that many people consider Venusian surface temperatures and CO2 concentration as a point in favor of runaway GHG warming.

    It isn’t. Temperatures at the same pressure altitudes on Earth and Venus are fairly close, particularly when counting from zero Kelvin, and especially when taking distance into account.

  34. Response– Not really. — chris

    Not really what? Surely you are not suggesting that the ideal gas law is wrong – you cite the (dry) lapse rate, yet seemingly fail to take it into account when determining what the surface temperature should be. Can you show the calculations on what surface temp should be without any greenhouse gasses but still with an atmosphere – that would show where I’ve gone wrong.

    Response- You say out of nowhere that the ideal gas law suggests that the greenhouse effect keeps surface temperatures around 3 K above the effective value, and that the commonly cited 33 K value is incorrect. This is nonsense, and it came out of nowhere.- chris

  35. Good point Neil. If Teff is the temp at the elevation in the atmosphere at which greenhouse gases are emitting IR to space at some pressure, then the temperature at the surface has to take into account the ideal gas law as the pressure increases towards the surface.

    Where does the ideal gas law come into your calculation of the surface temperature Chris?

  36. Chris, I didn’t think this was going to be controversial, so I will attempt to explain and perhaps you will be good enough to point out my errors.

    As a first order approximation only.

    If we assume that earth is in radiational balance (and Hansen suggests a radiaitive imbalance of less than 1%, so for our approximation, that’s good enough), then there is some point in the atmosphere where the temperature is at the theoretical BB temp. (that’s your Teff, right?) If we measure this empirically we get a height of around 5km. Using your dry lapse rate approximation of 6.5C/km (which is related only to pressure changes ie, ideal gas law based) we multiply and get 32.5C which is pretty close to the 33C figure that we measure empirically.

    Now this does not, of course, take into account the so-called greenhouse gasses, but then again neither does it take into account convection, latent heat etc etc. Just the pressure changes, nothing else.

    Response– Greenhouse gases are the whole reason we don’t use the surface as being the primary place of emission to space, but rather some other height in the atmosphere. They are the reason for the 33 K difference. So it makes no sense to say it doesn’t take into account greenhouse gases. Convection plays a large role as well, and in this case serves to establish the adiabatic lapse rate (which you use the moist value, not dry). Indeed, I am not sure what is controversial here.– chris

    • Chris: Surely the starting point in any discussion of the lapse rate is the equation of state (or ideal gas law). After that, the temperature distribution is affected by convection and the greenhouse effect. How much of the lapse rate is due to each of these effects?

  37. Response– Greenhouse gases are the whole reason we don’t use the surface as being the primary place of emission to space, but rather some other height in the atmosphere. They are the reason for the 33 K difference. So it makes no sense to say it doesn’t take into account greenhouse gases. Convection plays a large role as well, and in this case serves to establish the adiabatic lapse rate (which you use the moist value, not dry). Indeed, I am not sure what is controversial here.– chris

    Well, upon checking I certainly agree that I have quoted your moist adiabatic lapse rate, although I do note that this is closer to what really happens in the atmosphere. Frankly, I don’t see how you can ignore the lapse rate and suggest that the surface being 33C warmer than BB is all due to greenhouse gasses, but carry on…

  38. Thanks for the OP. I found it useful and informative. Once the comments started to alternate between technical and ad hominem, I skipped most.

    My Geology:Global Warming bookmarks are divided into
    News, and

    I placed this page in “Data”.

    I found my way here from a “Deniers” blog, where I hang with mostly kindred spirits. With my background in geology and paleoclimatology, I interpret the current data sets as consistent with a low sensitivity for CO2, due to negative feedbacks.

    I believe that focusing on CO2 as a “pollutant” distorts our response to more pressing concerns such as population control, energy sufficiency and independance and regional environmental degradation. IMO, focusing our global resources to provide education and basic health services for the world’s population will give us more bang for the buck than CO2 controls.

  39. I was wondering if there would be any reason for the lapse rate to vary. Is it always going to follow the current situation.

    We know the moist lapse rate varies considerably depending on humidity and thermals. The formula for the wet adiabatic contains both specific humidity and temperature terms (both of which should vary according to theory).

    Response– There’s good reason to suspect that the lapse rate in a changing climate provides a feedback which is positive at the poles, negative closer to the tropics, and net negative over the globe, and also depends on the water vapor feedback. How “negative” that feedback is may be difficult to constrain by observations (this relates to the whole “tropical hotspot” argument which skeptics like so much) although it is widely agreed that it offsets some of the water vapor positive feedback.– chris

  40. Hey Skipper –


    on the Runaway greenhouse effect

    A runaway positive feedback occurs when climate sensitivity is infinite or negative (along an unstable equilibrium).

    However, such conditions can occur over limited ranges. For example, if the Earth were cooled to a point where snow and sea ice reached close enough to the equator, then any little further cooling would cause the ‘ice line’ to shift equatorward by an amount sufficient to cause cooling equal or greater to the initial cooling. The effect ‘runs away’ until the ice reaches the equator. But it stops there, though it gets quite cold. There is hysteresis in this case, since now the Earth must be warmed up by some amount (such as by gradual slow buildup of CO2 from geologic emissions) just to get the equator to thaw, but once that starts, the runaway effect goes in reverse. In this case, depending on other conditions, the ice line may reach the poles and dissappear, and the Earth will get quite warm. Negative chemical weathering feedback may (depending on forcings) bring CO2 out of the air enough to initiate ice growth at the poles. But the ice line will tend to approach (given forcings) a stable equilibrium so long as it is not too close to the equator. (There may be another range with unstable equilibrium when the ice line is close to the poles.) This is a simple model and other complexities may change things. See ‘Snowball Earth’.

    The runaway global warming thought to have happened on Venus is not a significant risk from anthropogenic climate change. It would have happened because of Venus’s proximity to the sun; the temperature was high enough that enough water vapor reached the stratosphere and upper layers from below, that the rate of hydrogen escape (after photodissociation of H2O) to space was large enough to remove the oceans (and then some if water was resupplied from the mantle – but Venusian plate tectonics are apparently different (they might not even be, though I haven’t read up on that very much) ); once the oceans are removed, all the CO2 that had been in the oceans that wasn’t able to get into carbonate minerals was released to the atmosphere, and … this part I’m not sure about, but carbonate minerals might not be stable in those higher temperatures, plus the different geological processes on Venus might not have supplied silicate minerals to feed the chemical weathering process in the first place ???

    This is expected to eventually happen on Earth, but not for some hundreds of millions of years yet (or more?) – this is from the gradual brightenning of the sun over geologic time.

  41. manonthemoon –
    “How much of the lapse rate is due to each of these effects?”

    The answer is yes and no.

    In the situation where we artificially inhibit convection, radiative processes, shaped by greenhouse gases and the distribution of solar heating, would cause the lapse rate (which will vary with height) to reach radiative equilibrium. For the greenhouse effect and solar heating as they are, radiative equilibrium would make the lowermost part of the atmosphere unstable to convection. Hence, radiative fluxes drive convection. The convection occurs over a layer that attains a thickness at which convective and radiative fluxes are in equilibrium. Within that layer, the lapse rate tends towards a moist adiabatic lapse rate, regardless of the numerical values of radiative and convective fluxes, just so long as the upward convective flux is larger than zero.

    PS this is why radiative forcing at the tropopause level is so important. A change in net outgoing radiation at the tropopause corresponds to some amount of heating (or cooling) occuring below the tropopause. However it is distributed vertically, any heating will tend to increase convection above and reduce it below, and any cooling will do the opposite, so the radiative heating plus the convective response tend to result in an even distribution, so that the surface and levels of the atmosphere up to the tropopause height tend to shift temperature by similar amounts, except for some adjustment due to changes in the moist adiabatic lapse rate

    The moist adiabic lapse rate gets smaller at higher temperatures because of the roughly exponential relationship of saturation water vapor pressure to temperature. At low temperatures, the moist adiabatic lapse rate becomes similar to the dry adiabatic lapse rate.


    Of course, below cloud base level, convection is dry. Also, the physical boundary of the surface reduces the size scale of convective motions and makes convection less effective in achieving an adiabatic lapse rate next to the surface, so the surface can be a bit warmer than the atmosphere just above it when there is solar heating of the land surface or when cold air blows over warm water, etc. Sometimes at night, and generally at high latitudes, especially in winter, the lowest part of the troposphere has an inversion, with temperature increasing with height – this occurs because the surface radiates energy, some of which (in clear skies) escapes to space, and some more escapes to higher levels of the atmosphere; the strong diurnal cycle of solar heating tends to bring the surface up to a temperature sufficient to support convection, sometimes through the whole troposphere, during some portion of the daytime, and during the night, it cools. But this process is affected by wind-forced mixing. Thermally-driven motions can also force mixing when the kinetic energy reaches into convectively stable layers; the energy of thermals could conceivably cause air to be entrained into a boundary layer from above even when the boundary layer air is on a different adiabat. Tropospheric air in polar regions recieves heat from horizontal transport from lower latitudes, so polar regions tend to be more stable to convection (this, plus the positive albedo feedback at the surface, contribute to a tendency to increase the lapse rate at high latitudes (especially in winter, I think) in response to global warming). It must be kept in mind that the convection that reaches over the whole tropospheric thickness that tends to maintain the tropospheric lapse rate occurs somewhat episodically and in particular configurations, in particular in the ITCZ and also in large scale overturning in the Hadley cell, monsoonal circulations, and extratropical cyclones and anticyclones. The dry descending regions may become more stable to convection (?) (descent would be on a dry adiabat, but there is continual radiative cooling at the same time; there will tend to be horizontal heat transport into regions above the descent.), although strong surface solar heating may occur that could destabilize the lowermost layer. Increasing the greenhouse effect tends to reduce the diurnal range of temperature (which is generally seen over land, not so much the ocean due to mixing of surface heat downward over a large heat capacity).

    Neil Fisher-
    “Frankly, I don’t see how you can ignore the lapse rate and suggest that the surface being 33C warmer than BB is all due to greenhouse gasses, but carry on…”

    The lapse rate isn’t ignored; it’s taken as a given.

    Without any greenhouse effect, the atmosphere would not radiate any energy to space. Hence, all the radiation to space necessary to balance solar heating would come from the surface – if all solar heating occurs at the surface, the atmospheric temperture has no bearing, although conduction would tend to have it become isothermal with the surface (or the surface daily high temperature, if we include a diurnal range – the air over significant height will be more sensitive to the daily high than the daily average because cooling can convectively decouple the surface and lowest air from air higher up); if some solar heating occured in the air, then in equilibrium, this heat would have to flow downward to the surface.

    If you start adding some LW opacity (greenhouse gases, clouds, etc.), then the atmosphere would start radiating to space, to the surface, and less radiation from the surface would reach space. The surface would warm, the atmosphere would cool. If there was some solar heating of the atmosphere, the initial top of atmosphere radiative forcing would be negative, because of the increase in outward LW radiation from the atmosphere, but the surface radiative forcing with an equilibrated atmosphere would be positive (for comparison, with the present climatic state, the LW forcing at the tropopause is generally (might be different for stratospheric ozone changes) greater than at the top of the atmosphere for additional greenhouse forcing, but the top-of the atmosphere forcing is still positive) – the atmosphere would be cooler than it was before, but it wasn’t radiating any energy before – now it is radiating downward to the surface, so the surface would warm up (there would be some warming of the atmosphere in response to warming of the surface, and vice versa, until complete equilibrium is reached, at which point the atmosphere is still cooler than before the initial addition of greenhouse gases). Continuing to add greenhouse gases, at some point the surface temperature become convectively unstable with the atmosphere immediately above, due to atmospheric cooling and surface warming (over the globe, this will start at different places and times – noon or afternoon over low-latitude land would be the start). This produces a troposphere. From that point on, surface and tropospheric temperatures tend to warm together in response to the tropopause level forcing, with some adjustments for changes in the moist adiabatic lapse rate and some regional, diurnal, seasonal, and other temporal variations from the basic pattern, while the air above the tropopause continues to cool off, and the tropopause height rises.

  42. Hey Skipper – about CO2 release as oceans dissapear:

    “all the CO2 that had been in the oceans that wasn’t able to get into carbonate minerals was released to the atmosphere, and”…

    Another point – maybe more important (?), is that with water sufficiently removed, there isn’t a chemical weathering sink to balance geologic emissions of CO2 (and the higher temperature is less favorable to carbonate mineral formation, as I understand it – the chemical weathering feedback on a wet planet is a negative feedback because – ***I presume***- of the effect of climate (and CO2 concentration, I’d think) on the rate of the process (the kinetics), and not the thermodynamic equilibrium.)

  43. Let’s use this framework for the Last Glacial Maximum.

    The Teff is about 3K to 3.5K less now due to the increased Albedo of the ice or let’s say 252K (-3.0K from current).

    CO2 is 180 ppm or -1.9K less than current at 3.0K per doubling.

    What is the surface temperature now? Is the Greenhouse Effect now 31.1K (33K – 1.9K)?

    The tropopause should be roughly 500 metres lower now. How does the lapse rate impact the surface temperature in this scenario?

  44. A hypothetic question:
    Suppose CO2 is doubled, then stops there and stays constant. What happens to temps? Do they reach some new level of balance, say, at +3C and stop there too, or is some positive perpetual feedback started that never stops, and keeps raising temps even if GHG concentrations don’t change ?

    Response– The +3 C rise is an equilibrium amount of warming, so (roughly speaking) temperatures will tend to stay there. It will get a bit warmer in the very long term after you include slower feedbacks relating to ice sheet changes and other things, but I’m not sure why you think there is a runaway feedback– chris

    • OK. I had the impresion, maybe mistaken, that peple said there are tipping points, which, when you pass them, there is a runaway feedback loop.
      It didn’t make sense to me, I am glad you think the same.

      Response– Usually the word “tipping point” in the scientific literature refers to some threshold that you cross in a changing climate which is not easily reversible or is distinctly different from the previous climate state. It has nothing to do with runaway warming. Such examples include the loss of sea ice in the Arctic summer, the loss of the Amazon, a shutdown of the thermohaline Circulation, etc. These depend on the amount of warming you get as well as the timescale involved. For a very good review of various possible “tipping points” and conditions in which they may occur, I suggest the Lenton et al (2008) paper that was published in PNAS.

      On “runaway warming,” such conditions are possible when the atmospheric opacity is strongly dependent on temperature, and some condensable greenhouse gas (e.g., water vapor on Earth) continues to build up in the atmosphere (due to the strong saturation vapor increase with respect to temperature) but does not condense out. Such conditions occurred on Venus, and can (and will) occur on Earth in the distant future, although this is not an immediate threat for anthropogenic climate change– chris

  45. Re Bill Illis –

    It must be kept in mind that in general, the temperature of the tropopause level might concievably warm or cool for a surface warming, depending both on what happens to the lapse rate, if anything much, and what happens to the height of the tropopause, … although I’m not sure about all the possibilities.

    It makes sense that the tropopause level rises with increasing greenhouse effect in general, because the pattern of a warming surface and troposphere and cooling upper atmosphere should tend to allow thermally-direct (hot rising, cold sinking) convection to penetrate upward a bit farther, and the tropopause level can even be colder as a result.

    I’d guess the same type of relationship could happen with surface albedo radiative forcing/feedback, since an increase in surface albedo (or clouds, for that matter) would reduce solar heating of the surface + troposphere but not the stratosphere.

  46. PS some might wonder what happens with kinetic energy. When compositional variations are insignificant for effects on density (to a first approximation, this fits the Earth’s atmosphere – under hot humid conditions, the air is a bit more buoyant than otherwise, and liquid/solid water content in clouds will increase the macroscopic average density a little bit, but compositional variations are much more important to oceanic buoyancy variations) kinetic energy is produced by thermally-direct circulation, wherein hot air rises and cold air sinks – specifically, if both follow the dry adiabatic lapse rate, then as equal masses pass by the same pressure level, changing pressure at the same rate in opposite directions, it can be shown that the rising warmer air loses more enthalpy than the colder air gains, and this net loss of ‘sensible heat’ is converted to kinetic energy by the combination of the motion and the forces that are caused by the horizontal variations in density. (The dry adiabatic lapse rate is only approximately constant in the troposphere at 10 K/km). When radiative or latent heating/cooling occur, mathematically they can be considered to act at the endpoints of infinitesimal endpoints, adding or removing ‘available potential energy’ (APE) to the system in between time steps when APE is converted to kinetic energy (KE) or vice versa (as in thermally-indirect circulation: hot sinking, cold rising) – this is calculus.

    (APE is the difference between the gravitational potential energy and the gravitational potential energy that would exist if circulation eliminated all horizontal temperature variations (along isobaric surfaces – there is still potential energy if isobaric surfaces are isothermal (this situation is called barotropic) but not at constant geopotential height; I’m not sure if such remaining potential energy in a barotropic atmosphere is considered part of APE or not) and the atmosphere is stable or neutral to dry adiabatic convection, without mixing, friction, or radiational or latent heating or cooling. APE is larger when horizontal temperature variations (along isobaric surfaces) are larger and when the lapse rate is higher (less stable))

    Of course, almost no kinetic energy can actually escape to space (it’s possible to imagine a tiny tiny tiny amount could be converted to radio waves via motions in part of the ionosphere??). Most is converted by mixing/friction back to heat, but it will generally be at greater entropy than the heat that produced the the kinetic energy. Very little frictional heating is ever converted back to kinetic energy. My understanding is that majority of this takes place at the surface (including frictional heating within the water) or in the troposphere. Some portion of kinetic energy does cross the tropopause level and actually drives thermally-indirect large-scale overturning in the stratosphere and mesosphere, being converted to heat in the process. My understanding is that the amount of energy involved is small enough to be ignored for at least some purposes in heat energy budgets of the climate system (though I have never seen the numerical value) – kinetic energy production is itself relatively small compared to heat fluxes.

  47. (PS here’s one back-of-the-envelope calculation of total kinetic energy production in the troposphere:


    convective cooling of the surface and heating of the atmosphere (essentially, the troposphere) is roughly 100 W/m2.

    determine kinetic energy production based on carnot heat engine efficiency:

    average surface temperature is ~ 288 K

    Because the convective heating of the troposphere is distributed over it’s thickness, I’ll try taking the heat sink temperature to be roughly 255 K (not to say that the heat sink of the troposphere would act like the a heat sink at the Earth’s effective blackbody emitting temperature (some heat radiated to space comes from the surface and from the stratosphere), but it’s a good place to start).

    efficiency ~= 1 – 255/288 ~= 1 – 0.8854 ~= 0.115

    So kinetic energy production might be ~ 11.5 W/m2, give or take.

    But the heat source temperature should probably be a bit warmer than the global average surface temperature. What if I use 295 K ? Then I’d get about 13.6 W/m2. This is just to give a sense of what it might be, though, because I’m not sure which combination of numbers would be most representative.)

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  49. Michael Chisnall

    “Plugging in all the relevant parameters into the equation, the effective temperature becomes about 255 K, or about 0 degrees F.”

    When I try to calculate the Teff for the Moon or Mercury using this method I get the wrong answer. The conclusion I reach from this is that this method for calculating Teff isn’t valid and is ignoring some of the physics in which case the calim that GHG’s add 33 degrees is also in doubt. Is there any independent method for determing that the atmosphere adds 33 degrees or is it all based on this mistake (if thats what it is)?

    P.S. As to Venus – it doesn’t have plate tectonics. The surface is geologically young so the assumption, last I heard, is that every so often all the pent up geothermal energy causes a global overturning of the entire planet surface. As to why it doesn’t have plate tectonics – its too dry. I also seem to recall that there is some doubt as to whether or not Venus ever had oceans to begin with.

    Response– Probably not very useful for a planet or moon with very large diurnal temperature gradients. T_eff is pretty much a “uniform temperature” over the globe, since we assume sigmaT^4 is the outgoing flux over the globe, and the non-linearity shows up strong in examples like this– chris

  50. Michael Chisnall

    But why should the size of the diurnal temperature gradient matter? Without an atmosphere – the very situation we’re considering – the Earth’s temperature would also presumably vary a lot more.

    The Moon is in radiative equilibrium. If the formula for T_eff doesn’t work for the moon what are the grounds for thinking that it does work for the Earth? Are there, for example, detailed computer models that do a better job of modeling the physics which correctly predict the lunar temperature and which also give a 33 degree for the Earth without atmosphere?

    Response– There’s two articles you might want to read here, one is this (section on ‘Example of the Moon’)and Arthur Smith’s article. — chris

  51. Michael Chisnall

    I’m not sure I follow the calculation at the top of page 15 (or 16) of the Halpern et al paper. They/you divide the absorbed flux of 1205 W/m^2 by \sigma to get a figure close to the observed average for the whole hemisphere of the moon. Shouldn’t the division be by 2\sigma in that case?

  52. Michael Chisnall – Chris linked to my article, which does the calculation you mention for the Moon, Mars, Mercury, and Venus, as well as Earth (see Table I) – although I couldn’t find temperature measurements for Mercury as that planet had only been visited once briefly by a space probe at the time I wrote. There may be more data now – I wonder if you have pointers on that.

    Anyway, you tell us “When I try to calculate the Teff for the Moon or Mercury using this method I get the wrong answer.” but you haven’t said what numbers you get. Post your calculation and we can look through for what the problem might be.

    A common issue is that you need to divide incoming solar flux by a factor of 4 (not 2) to take account of the curvature of the planetary surface – the surface area of a sphere is 4 pi r^2, while the area associated with the solar flux is that in a plane normal to its motion, i.e. a circle of area pi r^2, hence the factor of 4.

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  54. Chris, I think you are to be commended for posting this where we can all read it and comment on it, and for generally being respectful and polite to those who argue with you. Many of the published articles are unavailable to those of us who have no university affiliation.

  55. I am naive about all this, and so thank you for posting the relevant physics behind the CO2 forcing. But it leads me to the following “back of the napkin” question.

    1) Anthropogenic increases in C02 are mostly attributed to the use of fossil fuels. Specifically the combustion of fossil fuels that creates the increased C02. Successful combustion of fossil fuels requires O2 – usually taken from the atmosphere. Thus, for X amounts of CO2 created and emitted by combustion, there is some Y of O2 removed from the atmosphere. For simplicity here I will assume X=Y.

    2) In the LR portion of electromagnetic spectrum, O2 has an absorption band at roughly 10um. CO2 has two absorption bands at roughly 3um and at 14um.

    Thus, the forcing equation due to the anthropogenic portion of the CO2 increase can be constructed as follows:

    F_{CO2 + O2} = k * ln(C/C_{0}) + k *ln(O/O_{0})

    Since the O_{0} initial is greater then O final, it is a negative forcing, and in fact using a 1 to 1
    ratio, makes F_{CO2 + O2} equal zero.

    Again, very simplistic, but it does lead to a reduction in the forcing value F of C02 for the
    anthropogenic caused increase in C02.

    Response– O2 is not a greenhouse gas.– chris

  56. Why not? Is not the definition of GHG’s those which absorb and emit in the infrared spectrum – of which O2 clearly does?

    Regardless, O2 absorbs and emits at roughly ~10um and therefore must have some contribution for temperatures related to LR.

    Does the equation

    F_{total} = \sum \epsilon_{i} [FA]_{i}

    not cover O2 then?

    and the k constant in

    F_{CO2 + O2} = k * ln(C/C_{0}) + k *ln(O/O_{0})

    not apply?

    Response– O2 is a diatomic gas, and therefore is infrared inactive, and thus has essentially zero contribution to the greenhouse effect. This is the first stuff you learn about in undergrad chemistry or Envi. Sci textbooks about greenhouse gases. Check David Archer’s chapter on GHG’s for a good start. So no, your relation does not apply. Even if O2 was a greenhouse gas though, there’s no reason its forcing would look like CO2.– chris

  57. I am misunderstanding this graph (which I have seen replicated in multiple places):

    Which seems to show that O2/O3 are attributed the absorption of LR around 10um.

  58. Chris,
    Regardless of undergraduate Climate text books and being a diatomic molecule, O2 has several strong absorption bands in the LR region. To see why please see:

    In addition, the HITRAN DB shows the O2 absorption spectra roughly between 5.5um and 7.25um and then very strongly after 30um.

  59. Also, my earlier statements about the ~10um band is all due to O3.

  60. kevoka – O2 is not the same as O3. O3 is a greenhouse gas.

    Of course, there might be some absorption by diatomic molecules in the LW spectrum, perhaps due to molecular collisions or …

    But something which is very weak can often be usefully approximated as zero.

    If a gas has a few strong absorption lines (not sure if this is the case you’re considering or not), it might not do much overall. I don’t know how many individual lines make up the CO2 band centered at 15 um, but it’s a lot.

  61. Patrick 027 –

    1) In the HITRAN DB O2 the 7th ranked molecule for absorption in the infrared range of the atmospheric gases. The peak of O2 at between 5.5 and 7.25 is comparative to the peaks of N2O, CH4 and CO in their respective bands. The two main peaks of CO2 (~16um and 4.25um) are 4 orders of magnitude higher than O2. Now treating this a zero would be fine, except for the fact that the k constant in forcing equation used for C02 above is fundamentally based on the the number of CO2 molecules present. The same would apply to the O2 forcing equation.

    I would suspect that O2 at 20% of the atmospheric composition versus C02 at .0388%, or CH4 at .00018%, or N2O at .0000319% would render it a significant factor.

    You are correct about the number lines that make up CO2 at 16um and 4.25um being numerous ( I do not have an exact count given my access to this data at the moment). However, the overall absorption energy is also dependent on the number of molecules, for each line – whereby O2 makes up it.

    2) The issue I have, is that if indeed 1 is correct, then you can no longer use man released CO2 as strictly additive to the the energy balance equation. You must subtract out the atmospheric O2 consumed by it. Again, almost all anthropogenic sources of C02 released into the atmosphere consume atmospheric O2. I used a 1 to 1 ratio above, but I think that is low, my bet is it is closer to 1.5 O2 to 1 CO2.

    • See also Patrick’s reply. Note that oxygen has a very low IR transition probability. In other words, the extinction coefficient of O2 for IR radiation is really, really, really low.
      If you have any knowledge about IR spectroscopy: this is due to the absence of an oscillating dipole in oxygen.

  62. kevoka – from your source:

    I get the impression that the ordering of importance takes into account abundances.

    In addition, while so far as I know it is true that more O2 must be taken up than 1 to add 1 CO2 to the atmosphere because a signficant fraction of additional CO2 amount ends up in the ocean even in the short term, even assuming 2 O2 per CO2, an increase of CO2 from 280 ppm to 380 ppm – a 100 ppm increase, is about a 36 % increase. A 200 ppm decrease in O2 is about a 0.1 % decrease.

    A doubling of CO2 has a tropopause-level (equilibrated stratosphere) radiative forcing of around 3.7 W/m2. Do you have a radiative forcing value for a 0.56 % decrease in O2?

  63. Patrick027 –

    It is not clear to me what the HITRAN DB basis for ranking is. It could be abundance, or it could be just in number of linestrengths. I initially thought it was abundance. However, looking at the data I have been able to view I am thinking it is now on linestrength. I have registered to get access, but that is a couple of weeks away.

    This is the HITRAN data I have been able to view:

    but it does not give individual lines, just plots.

    I do not have a O2 forcing value, and so far I not found it having been done anywhere. I am not sure anybody has ever calculated the k constant (used above) for O2, in order to derive the forcing. If they have, I have not found it.
    That is not to say it has not been calculated – just that I am too naive to find it.

    I understand the ratios ( a little counter intuitive to me for a replacement rather than additive process) – I am wondering how it all comes out in the wash, but can’t find if anybody has done the laundry.

    I understand the extinction coefficient. However, O2 looks to absorb IR at certain wavelengths as strongly as N20 and CH4 do at their respective peaks, and stronger than other GHG’s. So, given its abundance versus the other GHG’s how does that play out? Keep in mind it is also absorptive above the 30um spectrum. This is in the lower ranges of the earths black body emissions.

    • Kevoka,
      Oxygen simply does not absorb IR in the mid-IR region, which is the most relevant region. I regularly measure IR spectra (well, my students do), and I have yet to see any absorption bands in plain air that are different than those of CO2 or water vapor.

      Are you sure you are not looking at ozone IR absorption? I’ve already seen at least one website mixing up oxygen and ozone.

      • Marco,
        Initially, I was confusing O2 and O3, with my first post using the ~10 um bands. However, further looking has lead me to the data from the HITRAN database that O2 does absorb in the roughly 5.5um to 7.25 bands.

        Currently, my only view of the HITRAN data comes from this website,

        which used the RFM tool to access the HITRAN database at (hosted by Harvard). I do not know if these values are calculated or observed.

        It makes a clear distinction of O2 versus O3. However, I do not have independent verification that HITRAN is not commingling O2 and O3.

  64. Marco – let me rephrase that ” I understand the extinction coefficient” to this

    I understand what you mean by its being really really low for O2.

  65. Thanks for that website (the HITRAN plot)

    It appears to show the optical thickness for the whole atmopshere along a vertical path (zenith is directly overhead).

    I do see that O2 does have some significant opacity in the atmosphere over some wavelengths.

    I note that whereever O2 contributes a significant optical thickness, H2O contributes 100 to 1000 to 10,000 times as much (roughly). (The small corner at long wavelengths where O2 comes to dominate is insignificant for climatically-relevant energy fluxes, which are concentrated elsewhere in the spectrum). So removing all O2 (replacing it with the same number of molecules of a hypothetical more transparent gas with same molecular mass, etc, to preserve other physical atmospheric properties) would reduce the optical path length by around 0.01 to 1 % at those wavelengths.

    Of course, unlike O2 (and N2, Ar, and CO2, and CH4, and maybe a few others), H2O concentration as a fraction of total air drops rapidly with height. So O2 could be less overwhelmed by H2O near the tropopause and going into the stratosphere. Relative to the whole atmosphere, H2O concentration in the stratosphere is somewhere around 270 (?) to 5300 times smaller (?)… (though this comparison leaves out whether the vertical variation in line strengths and line broadenning have different overall effects on H2O vs O2).

    “Global Physical Climatology” Hartmann – from the masses and molecular masses of water vapor and total atmosphere, average water vapor concentration is around 3.3 g/kg (water vapor/air mixing ratio) or by volume: 0.53 % = 5300 ppm.
    “Notes and Correspondence
    Stratospheric water vapour measurements over Australia 1973-1976
    P. Hyson
    “Stratospheric and mesospheric latitudinal water vapor distributions obtained by an airborne millimeter-wave spectrometer”
    Peter R.
    “Radiometric Inference of Stratospheric Water Vapor
    P. M. Kuhn and S. K. Cox”
    “Stratospheric Water Vapour Increase due to Human Activities
    (did I just see a ghost?)
    “Water-vapor Measurements in the Lower Stratosphere

    • Patrick
      If I am reading your calculation correctly about the .1% to 1% pathlength, you are leaving H2O in the mix. I agree that H2O is much stronger. However, everybody seems to have agreed to ignore H2O in the calculations.

      To make the argument that water vapor absorption is greater than the absorption of O2 at overlapping frequencies, then ignore water vapor in other forcing calculations is suspect. This puts us in a position that if we are going to ignore H2O, then O2 becomes a factor in the mathematics.

      How large is the question.

  66. Marco, your experimental results show that water vapor overrides O2 in the mid IR absorption spectra (and Patrick goes into some detail about this above). The HITRAN data does reflect this – water vapor does dwarf O2 absorption in the indicated bands.

    However, all the discussions about GHG and forcings (see Chris’s post above) ignore water vapor – evidently due to the complexities (acknowledged in the IPCC AR4 report). Therefore, I am leaving it out of my discussions as well. That leaves me with an O2 versus CO2 absorption energy balance question. I do believe it is a topical question as water vapor is not uniformly distributed in the atmosphere (especially at the poles) but O2 and C02 are.

    I will agree with everybody so far that the forcing value of O2 negating the forcing value C02 looks to be small. But, to date, I have not found it having been answered. This is curious to me since the forcing values for molecules like CFC-11, HCFC-22, etc, have been calculated (IPCC AR4 WG1 chapter 2 pg 141 – Yet, (again via the RFM-HITRAN) data) these are of less consequence than O2.

    I could be all wet (yes – pun intended), but I think it still should be answered. Especially in light of the ignorance (no pun intended – read to be ignoring) of water vapor in the forcing calculations.

    Just to throw more uncertainty into all of this – almost all combustion of carbon fuels generates as much water vapor as C02.

  67. kevorka –

    “However, everybody seems to have agreed to ignore H2O in the calculations.”

    No, not at all.

  68. “Especially in light of the ignorance (no pun intended – read to be ignoring) of water vapor in the forcing calculations. ”

    No, see the ‘original’ (1997) Kiehl and Trenberth

    Click to access RadiationBudget.pdf

    You can estimate from fig 1 how the LW radiation is distributed over the spectrum – the following describes (imprecisely – I can come back later with actual calculations) LW flux emitted from the surface (approximated as a blackbody).

    graphically-estimated blackbody flux per wavelength interval, W/m2:

    ** 50 – inf. um: ~ 14 ((see below) assuming most of this is between 50 and 200 um, that’s about 0.1 per um)

    40 – 50 um: ~ 10 (~ 1 per um)
    30 – 40 um: ~ 23 (~ 2.3 per um)
    24 – 30 um: ~ 30 (~ 5 per um)
    20 – 24 um: ~ 35 (~ 8.7 per um)
    18 – 20 um: ~ 23 (~ 12.5 per um)

    18 – 50 um: ~ 121 (dominated by H2O)

    17 – 18 um: ~ 14
    16 – 17 um: ~ 16
    15 – 16 um: ~ 17.3
    14 – 15 um: ~ 19.5
    13 – 14 um: ~ 21.5
    12 – 13 um: ~ 23

    12 – 18 um: ~ 111 (the band dominated by CO2)
    13 – 17 um: ~ 74 (the band REALLY dominated by CO2)

    11 – 12 um: ~ 24.5
    10 – 11 um: ~ 25.3
    9 – 10 um: ~ 25.5
    8 – 9 um: ~ 24

    8 -12 um: ~ 99 (the atmospheric window (interupted by ozone) – high clouds make a big difference here)

    7 – 8 um: ~ 20
    6 – 7 um: ~ 14
    5 – 6 um: ~ 8
    4 – 5 um: ~ 3

    4 – 8 um: ~ 45 (dominated by H2O)

    4 – 50 um: 45 + 99 + 111 + 121 = 376
    If 4 – infinity um is 390, then 50 um to infinity is ~ 14.

    NOTE that these values are not the amounts that can be blocked from reaching space by a greenhouse effect based on absorption and emission; the minimum brightness temperature seen seems to be around 220 K, give or take, and if you follow the blackbody curve from the water vapor absorption around 20 to 50 um, to the CO2 plateau from 14 to 16 um, to the H2O peaks from ~ 5 to 8 um (visually filling in the gaps), you can see that the greenhouse forcing is ~ 1/3 of the surface flux from around 30 to 50 um, around 1/2 the surface flux around the CO2 plateau, and ~ 3/4 of the surface flux around 6 to 7 um, and almost 100 % of the surface flux near 4 um. This is because, while the whole spectrum blackbody flux is proportional to the fourth power of temperature, for different parts of the spectrum, the flux is more sensitive to temperature at shorter wavelengths, and becomes nearly linearly proportional to temperature at the longer wavelengths.

    Going back to
    (first, it would be really cool if the horizontal axis were scaled by the blackbody spectrum at 288 K or 255 K, or perhaps the difference between them, or the difference between 288 and 220 K, etc.)

    So the optical thickness of O2 seems to be near or greater than 10^-2 between about 7.1 and 5.7 um, give or take, and over 10^-1 between about 6.84 and 5.97 um, approaching perhaps 0.5 around 6.4 to 6.5 um.

    IF there is a fractional change FC in concentration, this will result in a fractional change FC in optical thickness OT.
    The fraction transmitted over a path is exp(-OT), and the difference made in transmission by FC is then exp(-OT*(1+FC)) – exp(-OT).

    For a given FC, the greatest change in transmission occurs when the range in the initial and final OT encompasses 1.

    A decrease of 0.5 % of an absorber with OT = 1 results in a transmission increase of 0.0018; for OT = 0.5, the change is 0.0015.

    This is an imprecise approach, but:

    For an upper bound (I think) on radiative forcing change, one could take a wavelength interval * blackbody flux (for warmest level of any significant opacity, generally the surface) per unit wavelength, and multiply this by the change in transmission.

    Replacing the blackbody flux by the difference between blackbody fluxes of the warmer and colder levels would be more accurate.

    Then it should be noted that transmission over all directions will be less than the vertical transmission, so the maximum effect of a small change in OT will occur around a vertical OT somewhat less than 1. On the other hand, as transmission decreases, the radiation is not immediately replaced by the smaller blackbody flux, but by fluxes that are an effective average over the layer.

    But starting with the upper bound.

    (0.0015, 0.00045) * 14 W/m2 = (0.02, 0.006) W/m2 – this is a rough approximation of the increase in outgoing LW radiation between about 5.9 and 6.9 um for a 0.5 % decrease in O2 in the absence of any other absorbers (the lower values are for an OT = 0.1).

    A smaller value will be obtained for the O2 band which first goes above OT ~ 0.1 near 70 um, but is still generally smaller than 0.1 (there are fluctuations) until out around 100 um.

    Note that where this happens (a 0.5 % decrease in O2 OT which may be 0.1 to 1, thus a change in OT of 0.005 to 0.05) and water vapor OT is up around 100 to 10,000, the initial OT has to be the total of all OTs at the wavelength considered, and that essentially is water vapor’s OT. exp(-99.95)-exp(-100) = 2.67 * 10^-44, which, multiplied by 14 W/m2, gives a ‘forcing potential’ of 3.7 * 10^-43, or written out longer, 0.000000000 000000000 000000000 000000000 00000037 W/m2 – that’s for O2’s OT = 1 and H2O’s OT of 100 – the ‘potential forcing’ can get smaller.

    Now, H2O concentration drops with height greatly, but then, the stratosphere is only about 15 % of the atmosphere on average (20 or 25 % or so at midlatitudes, varies). And the temperature variation that one can work with is smaller, and what is of concern to surface and tropospheric climate is the tropopause level forcing, not Top-of-atmosphere forcing. Nonetheless, dropping O2 OTs by a factor of ~ 5 to account for the smaller stratospheric mass (leaving out changes in line strengths and broadenning, which would on a band-average basis result in further OT reductions), we could get maybe 0.004 W/m2 in each of the two O2 bands, for a total of 0.008 W/m2, if we are really, really generous.


    looking at the overall trends in CO2 OT where it crosses the OT=1 mark and in other parts of the band from 11.76 to 18.18 (but not taking trends that cross the 15 um peak),

    I get magnitudes, in um per log(OT), of around 0.38 to 0.62 – the last value applying where log(OT) is generally lower than -1.8 (between about 12.5 and 11.76 um); a more restricted range is from 0.4 to 0.5.

    Since the peak in CO2 is saturated (log(OT) is large; in this case, over 2), it is easier to consider the effect of adding CO2 as a widenning of the interval that exceeds any given opacity of significance. A widenning of 0.38, 0.4, 0.5, or 0.6 um per increasing CO2 level by factor of 10 implies a widening of around 0.11, 0.12, 0.15, or 0.18 um, respectively, for a CO2 doubling. Multiplying this by the average W/m2 per um flux for the CO2 band and then multiplying by 2 to account for the widenning on each side of the band, I get radiative forcings, in W/m2, of


    respectively. If I look at the W/m2 per um values at the locations where CO2 OT = 1 (near 17 and 13 um – ~ 15 and ~ 22 W/m2), I get about 4.6.

    But I should try taking the difference between blackbody curves. This is a real off-the-cuff guesstimate, but I’ll try 9 and 13 W/m2 for the two sides of the band, and then I get 2.7 W/m2 forcing per CO2 doubling.

    Why is this so low? I was expecting to get something more than 3.7 W/m2, because there is a little overlap with H2O (not as much as you’d think looking at the OT graphs, since H2O is concentrated into warmer layers) and there is some cloud overlap.

    Well, I said this was an imprecise approach. At least I got within the ballpark. Assuming I managed the same for O2, you can see that the O2 forcing change is insignificant in comparison to the CO2 change for a doubling of CO2 (with oxydation of twice the amount of C, half that amount accumulating in the atmosphere to result in a doubling.)

  69. “Well, I said this was an imprecise approach.”

    Well, guess what. Shortly after I finished that comment, I realized that I was comparing my rough estimate of 2.7 W/m2 (no overlap accounting) to the 3.7 W/m2 approximate forcing (with overlaps accounted) – problem is that this is a comparison of TOA (top of atmosphere) forcing to tropopause level forcing with equilibrated stratosphere.

    More on that coming soon…

  70. Chris, will you please take a shot at explaining the too-short-time-periods flaw of Roy Spencer’s in-press article and May 7, 2010 web site post? I think it’s the same flawed approach that Tamino took apart in 2008, but Tamino’s explanation is too technical for some audiences. It would be great if you provided a shorter, higher-level explanation and concluded by pointing to Tamino’s post for readers wanting more detail. (Or maybe I’m wrong that Tamino’s 2008 post is relevant to Spencer’s latest; I’ve asked Tamino.)

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