Here's an analogy that may be worthwhile. We do not understand the physics of fluids very well. We are not even sure if their standard mathematical representation has general exact solutions. We don't understand the microscopic interactions of turbulence, and in many cases the system has a chaotic dependence on tiny fluctuations in the initial conditions.

However, we do know that in the case of most fluids, with flows of a low Mach number, gases are largely incompressible. There, Bernoulli's equation holds, 1/2 density v^2 + density * g * height + pressure = constant. It might not be perfectly accurate, but it will lift airplanes into the sky!

Bernoulli's equation doesn't work so well at boundary layers, such as those that form on the edges of wings. It doesn't work so well in regimes with a high Mach number, and therefore the air is compressed, such as on the edge of a propeller, or during supersonic flight. It doesn't operate so well under viscous flow. And it can't predict the turbulence which will alter the pressure and density, jostling passengers up and down in the air under rough winds.

Yet none of those things have affected the overall direction of the results. Planes have lift. We do not claim that airplane designers do not understand this. We just say that there are gaps in the understanding. It is not known in detail.

Similarly, greenhouse gas theory was only approximate. Throughout the study of climate science, people continue to add more and more to the simple physical theory, modifying the predictions in small ways. But throughout, some things have been constant. Climate change is driven by energy transfer. Energy comes from the sun, and is radiated back out by the earth. Greenhouse gases make that radiation by the earth less effective. This much isn't contested: the only question the magnitudes.

And yet, people say that 'I don't believe in the CO2 theory' or that 'humans are not contributing significantly to global warming.' This is like people saying that kinetic energy isn't proportional to the square of the velocity, and therefore ignore those insolent 'physicists'. Of course, it isn't proportional to the square of the velocity, exactly. But it isn't far off, and it's a good enough approximation unless we have reason to believe otherwise. How much reason do we have to say that the standard climate models are erroneously showing a significant temperature delta due to CO2? Does anyone anywhere have a reasonable physical or ecological model that could saturate its effect? That could reverse its direction? The most intriguing was variations in the sun's luminosity, but that doesn't account for nearly enough.

The point is that climate models are not testable. Bernoulli's equation is a "good" approximation because we know when it fails.

If we're going to rely on climate models to define policy, we should understand what they're good for. You say that 0.5 m v^2 is a good enough approximation until we say otherwise, but the same statement doesn't apply to climate models. The models are complicated, nonlinear, and the scientists running them have pressure to produce certain results.

Climate models are testable. It just takes a long time to test them, since they describe long term behavior. Fluid dynamics is nonlinear, and complicated, but certain effects, such as lift, or drag, are both simple and broadly applicable. So it is with radiative models of global heat balance. Heat powers the climate! Altering CO2 will alter the flux of infrared radiation which will alter the flux of heat. This basic mechanism is uncontested. I could be that the total heat flux doesn't change much because it's balanced by other effects. But we know of no other effects sufficiently strong to render the temperature change small. If we have a physically plausible model that fits measured datapoints, and we keep check its predictions against measurements, and we keep asking 'in which ways might this be different?' and looking for possible problems, or effects that we've missed, then this is science at work. If instead we say "it's complicated, and there are some areas in which there are gaps in understanding, therefore we should draw no conclusions and make no decisions," we achieve little.

This is tangential, but you seem like you are informed on the climate debate, unlike myself. Feel free to ignore this if you consider it a troll, or that I'm bringing up tired and often refuted points.

Anyways, I've been reading a climate change skeptic, James Hogan, and he makes a pretty interesting claim. James says that 90% of the earth's warming is caused by water vapor. Of the carbon dioxide that does contribute to warming, only about 2% (as I recall) of it is human contributed. I haven't checked his sources, but these numbers seem pretty hard to fudge. That means we contribute at most 0.2% to the earth's warming with our carbon dioxide.

James also made a number of other points, like the measurements used to prove global warming are taken around developing areas, and more objectively obtained warming and carbon cycles show very strong correlations with solar activity. But, the water vapor point stood out the most in my mind and seems to clearly demonstrate we're overreacting.

Is there some kind of fallacy that I'm missing? Am I significantly underestimating the potential for that 0.2% to push us over some kind of tipping point? Thanks for any input you can give.

[edited a couple times b/c I'm too tired to do basic math]

The IPCC models do account for both water vapor and solar irradiation. Water vapor is the dominant greenhouse gas. It is roughly correct to say that it accounts for 90% of the greenhouse effect (the lowering of infrared flux from the earth to space). However, it's not correct to say that 90% of the earth's warming is due to water vapor, if what one means by warming is change in average temperature over time. The amount of water vapor has apparently not changed very much.

Here's some figures tabulated from the standard models, from the fourth IPCC working group is found here:

http://ipcc-wg1.ucar.edu/wg1/docs/WG1AR4_SPM_PlenaryApproved...

And a nice graph can be found here:

http://en.wikipedia.org/wiki/Image:Radiative-forcings.svg

These figures are estimates of anthropogenic forcing, in other words, how the components of the heat flux of the world changed due to the ecological changes. There are quite a few things here which can be measured quite accurately: cloud albedo being one, stratospheric water vapor content being another.

These were estimates made in 2005. According to them, additional stratospheric water vapor accounts for less than a twentieth of a watt per square meter, and variation in solar activity less than a tenth. Anthroprogenic carbon dioxide accounts for around 1.7 watts per square meter, averaged over the year, over the earth.

Solar activity is a large component, but recent estimates point at it accounting for only '18 and 36% of warming from 1950 to 1999' http://climate.envsci.rutgers.edu/pdf/StottEtAl.pdf

As for the claims that measurements of global warming are taken around developing areas, I think that claim is most fraudulent. First of all, one can measure the surface heat quite accurately by satellite by looking at the ratio of radiation in different 'infrared windows'. This allows you to calculate, via the Stefan-Boltzmann radiation law, the temperature at a surface.

Second of all, and perhaps more obviously, nearly all glaciers and icecaps are melting or receding, and these are not exactly developing areas! Melting ice-caps are measurements too!

Much appreciated.

Dani, I understand that all fields of science (except those snobs in string theory) must use models. But not all models can be reasonably tested.

I trust the Bernoulli model across a certain parameter range because it has been carefully tested in more than one controlled experiments. However, suppose the Bernoulli model was based solely on one experiment: a videotape of a large body, of mostly known shape, traveling through a fluid of unknown density and viscosity. Now some guys just built a glider. Do you want to pilot the glider off a cliff?

Note: I'm only applying the same level of skepticism to climate science that I do to astrophysics or economics. I take descriptions of the internal structure of the sun with a similar grain of salt; they are a good educated guess, but I'm not going to make claims like "95% certain."

Incidentally, I don't think anyone really trusts the models. If the models are as accurate as claimed, then we should be open to the idea of geoengineering. If we can accurately pinpoint the effect of CO2 among other forcings, we can predict the results of any reasonable forcing. Injecting sulfur dioxide into the stratsophere is a short term solution:

http://climate.envsci.rutgers.edu/pdf/GeoengineeringJGR9inPr...

If the models are accurate, all we need to do is run some simulations to figure out which geoengineering scheme is optimal. If the cost of geoengineering < cost of reducing CO2 emissions, then we should pursue that.

Of course, if one brings up such possibilities, environmentalists will deride them as "playing god", and point out that "who knows what will happen?" But that's silly; the models are either accurate or not.

By the way, I think you might be using the existence of nutty and incorrect skeptics as a straw man. There are wacko environmentalists out there too: notice the opposition to nuclear energy. But this doesn't make environmentalism crazy, just a few of it's proponents.

I don't think that it's entirely symmetrical. There are regions of confidence with any model. If you only have one shot, it's probably much safer to gradual remove, or at least reduce the magnitude of a forcing term from a nonlinear system than to add one that you think will counter it, even if you think you have a very, very good handle on what's going on, because it returns you to something you've seen before. This is especially important if that counteracting term has never been tested on the global system for even small magnitude changes.

It's like an amateur barber trying to balance a haircut. You can risk error in the model on one side to deflect the other, but it's probably wiser just to ask the clippers be put down. With each rebalancing the system gets further and further from the familiar.

As for geo-engineering, I'm not against it in principle as an alternative, but so far I have yet to hear of any schemes that might conceivably be cheap enough. Apparently Teller proposed some kind of balloon floating scheme, but, like his starwars proposal, it was entirely nutty; the math turned out that the assumptions were that balloons cost a tenth of a microdollar. And the sulfur dioxide model would be great if it were cheap enough to make, and there were a way to make sure it wouldn't come down and produce acid rain, which I'm afraid seems like quite a challenge.

I don't think I'm making a straw man argument. I mentioned the skeptic Tim Ball only in direct reply to a post quoting him.

But Dani, if the model is accurate enough to determine that warming is caused primarily by anthropogenic carbon, then it must also be accurate enough to correctly identify and estimate all other effects. After all, if we can't estimate them, how can we rule them out?

Perhaps the models are only valid in regions of phase space we have already visited, but in that case the model has little predictive power! We have a theory which fits some data from one experiment, and has no predictive power. Sounds like little more than a complex data fit to me.

Incidentally, sulfur has been tested for small magnitude changes; Pinatubo provides a natural experiment.

Anyway, I'm not trying to push any geoengineering scheme. I don't think we can accurately predict the effects of such things. But then again, I also don't think we can accurately predict what the earth's temperature would have been absent human intervention.

I'm just pointing out the fundamental point: if we understand climate well enough to determine the exact cause of a small change (which I don't believe we do), we also understand it well enough for geoengineering. But most people don't actually believe we can do geoengineering, even if they do believe AGW is proven.

As for Tim Ball, my bad. Didn't notice that.

I don't think it's true that the predictive accuracy of a model is always as accurate in one parameter as it is in another. I think that only holds if the model is believed almost for certain. In reality you have a distribution of models that you might believe. Suppose you impose some smoothness assumptions on the system: that the response isn't too wild anywhere that you're looking. Then you can make the successive approximations: first you assume that, in this domain, asymptotically, these are linear, separable PDE's. Then if you spend all your time jiggling one parameter, it gives you a bunch of information and constraints on the response for the one parameter. If you jiggle it still further, you might be able to ascertain some glimpse of the nonlinearity, and nonseparability of the system. So for example you might know a fair amount, might have constrained the space of possible models for CO2 - NO2 coupling, or CO2 - water vapor coupling, or CO2 - SO2 coupling. You might see some of the homogeneous CO2 nonlinearities. But you'll know way less about SO2 - acid rain coupling. That's much higher order.

Regardless, my point is that if we stay within the phase space that we know, it's a lot safer.

You need different levels of confidence depending on the choice you're considering. If the prediction is ecological disaster, 90% confidence is good enough to convince me not to try it. If the prediction is a 90% chance of it being okay, that has to be weighed against the much more confident prediction we have that if we gradually turn down the manmade forcing on the environment, things will stay pretty close to alright.

So it's less like your glider example than the reverse. Someone shows you a videotape of a large body, of mostly known shape, traveling through a fluid of unknown density and viscosity. We know that most things fall. We know that most gliders are unstable. Yet we are climbing this mountain and approaching this cliff ledge. And I think it's prudent to say, look. Ground is good. We had better be a lot more sure than this if we want to fly this thing. We shouldn't fly the climate recklessly.

[ps, I am going to sleep now.]