“A) observational? Yes
B) Paleo ? No
C) Models ? No”
Models? Yes if you use lower aerosol forcing estimates and include things like the Iris effect. Models are also subject to confirmation bias due to the large number of parameters that need to be chosen and of course have numeric approximation issues.
Paleo? Yes! With respect to the Pleistocene, you just need to take Milankovitch cycles into account and also take into account that changes in radiative forcing in polar regions results in a larger change in global average temperature than changes in equatorial regions (due to the Stefan-Boltzman law) so many estimates overestimate climate sensitivity due to underestimating the relative strength between albedo feedbacks and GHG feedbacks.
I wrong a post a while back on this:
For climate sensitivity estimates that look at temperature changes prior to the Pleistocene, there are a number of issues with these estimates, including:
– Lack of a globally representative set of temperature reconstructions, large uncertainty in temperature reconstructions, and large uncertainty in atmospheric CO2 reconstructions result in estimates having so much uncertainty that not much confidence can be gained from these estimates. The estimates from Pleistocene + Holocene ice core data have far more confidence than the estimates of all the remaining Paleo data put together.
– Often these estimates do not properly take into account the effects of changes in the positions of the continents (which becomes significant at this timescale). Such changes can significantly affect the global distribution of albedo and the global pattern of heat transfer. Hansen et al. completely ignore the effect of changes in the position of continents, which means that they are overestimating climate sensitivity since the changes in the position of continents has led to a gradual cooling over the Cenozoic. The PALEOSENS 2012 paper does appear to try to address this issue by taking into account long term albedo changes though.
– When looking at temperature changes over large timescales such as the Cenozoic, it makes sense to take into account changes in solar irradiance. However, since solar irradiance and GHG forcing are negatively correlated in the Cenozoic, not taking into account the fact that solar irradiance is not distributed evenly across the surface of the planet can lead to an overestimation of the strength of changes in solar irradiance and therefore an overestimation in climate sensitivity estimates (I describe this effect in more detail further down).
– Most of these non-Pleistocene paleoclimate estimates are not taking into account changes in CH4 and N2O. Since CH4 and N2O are strongly correlated with temperature and were likely higher in the past when temperatures were higher, not taking CH4 and N2O into account results in an overestimation of climate sensitivity. Not only that, since radiative forcing is an approximately logarithmic function of CO2, but an approximately square root function of CH4 and N2O, as temperatures rise the relative importance of CH4 and N2O may rise relative to CO2.
In an attempt to quantify the magnitude of ignoring the effect of CH4 and N2O, look at Pleistocene ice core data. The 95% confidence interval for the change in global temperature from Holocene to LGM is 4.0 +/- 0.8 C (Annan and Hargreaves 2013). The difference in CH4 concentrations is approximately ~347 ppb and the difference in N2O concentrations is ~44 ppb. The early Eocene (55 mya) had global temperatures ~13C higher than current temperatures. If one were to treat N2O and CH4 concentrations as roughly linear functions of temperature, then this would suggest that there was ~1850 ppb of CH4 and ~413 ppb of N2O. If one uses the IPCC’s GHG radiative forcing formulas (http://www.esrl.noaa.gov/gmd/aggi/aggi.html) then this suggests that the CH4 and N2O levels would have caused ~0.95 W/m^2 more radiative forcing than pre-industrial levels. Alternatively, if the early Eocene had approximately 4 times current levels of CO2 then by http://www.pnas.org/content/108/24/9770.full.pdf, there would be ~3614 ppb of CH4 and 323 ppb of N2O, which gives a change in radiative forcing of ~1.22 W/m^2 relative to pre-industrial levels. In comparison, a quadrupling of CO2 causes a change in radiative forcing of ~7.42 W/m^2, so excluding changes in CH4 and N2O mean that climate sensitivity is being overestimated by ~16% (obviously there is a lot of uncertainty here, but the point remains).
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Paleoclimate estimates that use Pleistocene + Holocene ice core data are far more reliable and give better estimates than other Paleoclimate estimates. However, many of the studies that try to estimate climate sensitivity have flaws that cause an upward bias in estimates and an underestimation of uncertainty. These flaws include:
– Overestimation of temperature changes over the Pleistocene can cause overestimation of climate sensitivity and not taking into account uncertainty in temperatures changes over the Pleistocene can cause an underestimation of uncertainty of climate sensitivity. Some studies (such as those by Hansen et al.) use outdated estimates of temperature changes since the LGM (such as Shakun and Carlson 2010) to infer global temperature changes over the Pleistocene. My understanding is that the current best estimate for LGM-Holocene temperature difference is 4.0 +/- 0.8 C (Annan and Hargreaves 2013). This means that estimates that used higher LGM-Holocene temperature differences of ~5C are overestimating climate sensitivity by ~25%. The PALEOSENS 2012 paper you refer to though has a reasonable polar amplification factor + uncertainty, so avoids this issue.
– Milankovitch Cycles. This is my biggest gripe with Pleistocene estimates. What causes the ice ages? Milankovitch Cycles. What do most Pleistocene estimates ignore when estimating climate sensitivity? Milankovitch Cycles. It’s insanity!
The ‘argument’ that is consistently given to dismiss the effect of Milankovitch Cycles is something along the lines of “because changes in global annual solar irradiance are small due to Milankovitch Cycles, they can be neglected”.
This is complete nonsense. For one, global annual solar irradiance is proportional to 1/sqrt(1 – e^2), where e is the eccentricity of the Earth’s orbit. So the above claim basically suggests that obliquity and precession do not matter as they don’t affect global annual solar irradiance. Perform a simple linear regression where global temperature over the Pleistocene is the dependant variable and eccentricity, obliquity and the precession index are the independent variables (add other explanatory factors if you want). You will find that obliquity is by far the most important Milankovitch Cycle, not eccentricity.
Obliquity has an effect on global temperatures beyond GHG or albedo feedbacks. This is due to the Stefan-Boltzman law. The earth’s surface does not have a uniform temperature; polar regions are colder than equatorial regions. Because of this, a change in the incoming radiation in a polar region will have a larger effect on global temperatures than a change in the incoming radiation in an equatorial region as the marginal change in emitted black body radiation due to a change in surface temperature is higher in the equator than in the poles. I’ll demonstrate the magnitude of this effect below:
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Not taking into account the unevenness of changes in the distribution of solar insolation can cause significant bias and underestimation of uncertainty in estimates of climate sensitivity. For example, Van Hateren 2012 assumes that a change in solar irradiance will have approximately 0.7/4 (1 – albedo of earth divided by the ratio of the surface area of a sphere to the area of a circle of comparable radius) times the effect of an equivalent change in W/m^2 in GHG forcing. This arguably overestimates the strength of the sun relative to GHG forcing because it doesn’t take into account the fact that extra sunlight in the tropics has less affect on global temperatures than an equivalent amount of extra sunlight in the poles due to the Stefan-Boltzman law.
To illustrate the magnitude of this effect, consider a grey model of earth where in equilibrium:
(1-α)*S(φ) + B = G*σ*T4(φ) + k*(d2T(φ)/dφ2 – tan(φ)*dT(φ)/dφ)
Where α is the Albedo of Earth, S(φ) is the annual solar insolation at latitude φ, B = 0.087 W/m^2 is the heat flux due to the Earth’s internal energy, G is a factor due to greenhouse gasses, σ is the Stefan-Boltzmann constant, k is the constant that determines the rate of heat transfer across the surface of the Earth and S(φ) is the temperature at latitude φ.
If I impose a restriction that the average temperature of this grey earth is 288 K and that the temperature at the equator is 300 K (which gives a temperature profile that is similar to that of Earth), then I get G = 0.1967 and k = -0.0452. If I use this model and vary solar irradiance by 1 W/m^2 then I get an equilibrium global average temperature change that is 5.44% the temperature change I get if I change greenhouse gas forcing by 1 W/m^2 (if you wish to see my matlab code that gives me this I am happy to share it).
Now if the assumption by Van Hateren were valid then the above value should be 0.7/4 = 17.5%, not 5.44%. So not taking the unevenness in the distribution of global insolation and temperature can cause one to overestimate the strength of the sun relative to GHG forcing by a factor of 3; which suggests that Van Hateren’s estimate is an underestimate of climate sensitivity. More realistically, one should take into account the unevenness of albedo distribution and the effect of cosmic rays; if I try to estimate a Van Hateren impulse response function from instrumental data and allow the effect of the sun to vary as a free parameter relative to the effect of GHG forcing, then I find that a change in solar irradiance has about 8% the effect of an equivalent change in W/m^2 in GHG forcing; so the assumption by Van Hateren overestimates the relative strength of Solar Irradiance to changes in GHG forcing by a factor of two.
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So clearly, changes in the distribution of incoming solar radiation causes global temperature changes beyond those caused by GHG or albedo feedbacks due to the Stefan-Boltzman law. In addition, the precession index is very relevant because the albedo distribution of the Northern Hemisphere is different from the albedo distribution of the Southern Hemisphere. So to have a decent climate sensitivity estimate using Pleistocene data, Milankovitch Cycles need to be taken into account.
Let’s say I take Dome C data of dO18, CO2, CH4 and N2O. I use Annan and Hargreaves 2013 to convert the dO18 into a proxy for global average temperatures and I convert the CO2 + CH4 + N2O data into GHG forcing. For albedo forcing, let’s assume for the sake of argument that the claim by Hansen et al. 2013 that the radiative forcing due to albedo changes from Holocene to LGM is 3.4 W/m^2 +/- 20%. I can then use a sea level reconstruction/dataset (say de Boer’s ANICE output) and an assumption of linearity to get a proxy for the albedo forcing.
For the effect of Milankovitch cycles, let’s use 3 variables: the change in solar irradiance (which is proportional to 1/sqrt(1 – e^2)), the sine of the obliquity, and the precession index (e*sin(precession). I can then perform a linear regression to estimate the model T = β0 + β1*(GHG + Albedo + 0.05*Solar) + β2*sin(obliquity) + β3*precession_index + model error. If I take into account all my sources of error (model error, temperature error and albedo error) and propagate error correctly my 95% confidence interval for ECS is (2.48 +/- 0.49) C.
And this is an overestimate of ECS since I am using a low value (0.05) of the strength of the sun relative to GHGs (my regressions using the instrumental data suggest this should be closer to 0.08) and I’m not taking into account the fact that the albedo changes are not uniform. As the albedo changes are higher in polar regions than equatorial regions the strength of albedo changes relative to GHG changes should be stronger than what is assumed in the model (due to the Stefan-Boltzman law).
In any case, I think I can conclude that a proper evaluation of the Pleistocene + Holocene ice-core data yields a 95% confidence interval of climate sensitivity that excludes ECS greater than 3 C. So an ECS greater than 3C is excluded at the 2.5% confidence level by Paleoclimate data!