Climate change: a non-controversial post on climate sensitivity

Let’s put together a consensus report:  things about the Earth’s sensitivity to various forcings that AGW-skeptics, AGW-deniers, and AGW-affirmers will all sign off on.  We remember, of course, that just because something isn’t controversial doesn’t mean it’s true.

The Earth’s average temperature has substantial yearly variations, and no theoretical model is going to be able to capture those–because of extreme sensitivity to initial conditions, if nothing else.  However, the equilibrium mean temperature for a given average solar irradiation, CO2 and water vapor concentration, albedo, etc can be determined theoretically, irrespective of initial condition issues, because it’s just energy conservation.  The net energy absorbed by the Earth from the sun has to be equal to the net energy radiated away by the Earth.  Therefore, the fact that we can’t predict the weather more than a few days in advance doesn’t mean that we can’t predict the climate decades in advance (up to unmodelable changes in forcings, either regarding solar, volcanic, or human input).

Climatologists describe the Earth’s thermal sensitivity in ways that may be not be intuitive to some, so it’s worth reviewing them.  They start out from some reference state, usually the Earth at pre-Industrial times.  This reference state is presumed to be in equilibrium.  Now suppose the system is perturbed.  The perturbation is described by a change in the radiative forcing of the Earth, measured in energy per time per area (W m^-2).  In equilibrium, the net forcing is zero (radiation in = radiation out).  Let’s call the forcing “F“, so F=0 in the original equilibrium.  F can become nonzero if the solar input increases or if the radiation out of the atmosphere is reduced.  The latter is what the greenhouse effect does.  Radiation is absorbed in the atmosphere and reradiated up and down.  If the temperature profile doesn’t change, the net radiation leaving the earth will decrease.  The net forcing is now F=dF=/=0.

For carbon dioxide greenhouse forcing, there is a simple formula (actually an analytic fit to 1D radiative equilibrium models):

F = 5.5 ln(C/C_0)

where C is the CO2 concentration, and C_0 is its preindustrial level.  So, doubling the CO2 concentration (which humanity will probably do by mid-century) means a forcing of 3.7W m^-2.  AGW-skeptics sometimes talk as if that natural logarithm is a big secret, but really it’s discussed on quite a few AGN-affirming websites e.g. (here and here).  If the effect of C on T_s were linear, we’d be talking about a much larger temperature change than 3 degrees.

For the terrestrial system to come back into equilibrium, the surface temperature T_s must increase.  Heating produces a forcing, F_T, to counteract the greenhouse forcing.  This forcing is proportional to dT_s, the change in temperature.  We can write this as F_T = Φ_T dT_s, introducing a new constant,  Φ_T, the  (temperature) climate feedback parameter.  Assuming no other forcings (which will turn out to be a bad assumption), equilibrium will be reestablished when F_T=F and dT_s=F/Φ_T.  So, to find the change in surface temperature, we just need to know Φ_T.  The climate feedback parameter for temperature change with everything else held constant (water vapor, clouds, ice cover, etc) is one of the less controversial calculations–skeptics like Happer cite it.  One gets Φ_T = 3.7-4.4 W m^-2 K^-1.  Then the equilibrium temperature change for a doubling of CO2 is about one degree K.

As you all know, the IPCC favored value for the actual expected climate change for CO2 doubling is 2.1-4.4 K.  The first thing to notice is that even the simple, uncontroversial calculation gives something of this order of magnitude.  Changes of order a degree are what should be expected.  However, the actual number is a factor of three different, the reason being that everything else does not stay constant when added CO2 heats the atmosphere.  There are feedbacks.  Three are particularly important:  1) water vapor changes (H2O being an important greenhouse gas in its own right), 2) ice/snow cover changes (melting reduces the Earth’s albedo, so it absorbs more solar radiation–a positive feedback), 3) cloud cover (increased clouds increases albedo, meaning more of the sun’s radiation is reflected–a negative feedback, while clouds can also increase greenhouse trapping of infrared waves–a positive feedback, so the net effect of clouds is complicated).  So we can define a total climate feedback parameter Φ, which sums over all the forcings (forcings being additive for small changes):

F = Φ dT_s

Φ = Φ_T + Φ_H2O + Φ_ice + Φ_clouds

In the standard picture, Φ_H2O, Φ_ice, and Φ_clouds all work out to be positive feedbacks, meaning that they are all negative, so that the total Φ<Φ_T.  Note that, for our purposes, low Φ is bad, because it means more heating to offset a given forcing, while high Φ is good.  The current best guess for Φ is around 0.9-1.6 W m^-2 K^-1.  This is based on an ensemble of computer models, meaning there are almost certainly systematic uncertainties that are not captured, and the real uncertainty is larger than this range.  We can put limits on Φ by looking at past climate variability if we know both the external forcing and temperature change.  For example, if Φ=∞, the temperature would never change, and we know that’s not right.  If Φ<=0, the atmosphere would be thermally unstable to a greenhouse runaway, something that may actually have happened on Venus in the distant past.  Observations of temperature change within recorded times from the solar cycle and from volcanic eruptions give Φ around a range of 1-4 W m^-2 K^-1, meaning a CO2 doubling dT_s of around 1-4 degrees.  Of course, these numbers assume that researchers have at least correctly estimated their uncertainty in the forcings that were active during these times/events.

There are good reasons to believe that the last half-century’s global warming has been due to greenhouse forcing of some kind.  There is the fact that the stratosphere has cooled while the troposphere has warmed, something that would be expected from an increase in the infrared opacity of the atmosphere but not, for example, from an increase in solar radiation.  There is the fact that average nighttime temperatures have raised more than average daytime temperatures.  Again, this is expected from stronger radiation trapping in the atmosphere.   Finally, satellites cannot yet accurately measure the radiation imbalance that’s heating the troposphere (some AGW-affirming websites seem a bit misleading on this point), but they have registered the effect of increased greenhouse gas concentrations on the IR spectrum of the atmosphere, and these spectra can be used to validate 1D radiation transfer models that contain the expected greenhouse forcing.

So, is the skeptic’s case sunk?  Not necessarily; it depends on what his alternate explanation or prediction is.  Some alternative explanations of global warming (increased direct solar heating, volcanic CO2) are definitely excluded by observations.  Among the more respectable objections to the AGW position:

  1. Freeman Dyson thinks the feedback from stimulated plant growth and resulting carbon sequestration has been underestimated.  He points out that human policy may actually have a significant effect on this feedback and suggests an appropriate change in focus.
  2. William Happer thinks that the net effect of feedbacks will turn out to be small, or even slightly negative.  That is, he thinks Φ is about equal to, or slightly greater than, Φ_T.  He cites the many unknowns of cloud physics as the main source of uncertainty.  The climate establishment admits there’s a lot of uncertainty here, but thinks Happer is being recklessly optimistic.
  3. Some have speculated that other forces, e.g. a dearth of cosmic rays, have caused a reduction in cloud cover, and that this has contributed somewhat to recent warming.  Mostly they argue that we don’t understand cloud formation well enough to say anything.  IPCC thinks we understand it well enough to say it’s not the main driving force of GW.  Also, if you just change the albedo, you don’t recover all the greenhouse markers, but clouds do lots of things and other feedbacks can come into play, so I don’t know that we can rule this out.  I’ll have to look into it more.

Since this is a consensus report, I won’t agree or disagree with any of these claims here.

Coming up next, I’d like to go deeper into a few issues:

  • ocean heat storage–it’s role in delaying equilibrium
  • the early 20th century warming, to which anthropogenic emissions only made a modest contribution
  • more on alternate (non-AGW) theories
  • whether traditionalist conservatives have a dog in this fight

4 Responses

  1. My understanding of chaos theory is that systems that incorporate multiple (3 or more) non-linear actors -that interact- are incapable of producing “stability” or any sort of “equilibrium”. Indeed, the pre-industrial climate of our planet was never really stable or predictable.
    And it never will be.

  2. For how long has there been good data for the relative temperatures of the upper and lower atmospheres? I think I get why this is an important approach to this subject but my gut tells me there needs to be a lot more context available – long time frame context – to really evaluate its meaning.
    What is known about changes over deep time regarding heat transfer thru the earths crust – to and from the mother of all heat sinks – the earths interior? When I hear the word “assume” … never mind.
    Clouds have been used as metaphors for whimsy and unpredictability for eons. Maybe our poetic fore-bearers had functioning instincts.
    The whole climate-gate thing really got to me. I read a lot of the hacked emails. Imho, those guys were not so much guilty of corruption as they were guilty of making too many assumptions.
    I make my living in a field where making too many assumptions = death.

  3. Hi Rum,

    That’s a good point. I can’t imagine that we have good stratosphere temperature records going back more than half a century. That would be enough to capture the post 70′s warming, but not much else.

    The solid earth must be absorbing heat, but the effects are hard to measure. Climate models take the lithosphere as fixed, from what I’ve read, based on timescale arguments. They expect the main heat sink on century timescales to be the oceans.

    You are also certainly right that climatologists make lots of assumptions, often with questionable justification. That’s how science usually works, and it’s not unhealthy as long as one keeps track of one’s assumptions and tests them as opportunities arise. Unfortunately, in this case, there’s been all this pressure to come out with THE TRUTH, and congressmen don’t want to see error bars.

  4. Hi Rum,

    Even chaotic systems conserve energy. That being said, I was a bit too categorical in my statement. If there are multiple states with the same energy in different areas of state space, it may be possible that the Earth would random-walk from one to another, and whether this will happen couldn’t be predicted. We don’t know whether this is the case or not. There are certainly lots of complex nonlinear systems, such as turbulent flows, where one is able to make statistical predictions. And we do see the Earth responding in intelligible ways to observed forcings, e.g. major volcanic eruptions. I prefer to be optimistic about our ability to model climate until it’s proven unfeasible.

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