According to the IPCC, global mean temperature rose 0.6 ± 0.2 °C from the late 19^th Century through 2000. From the same source ΔF from increased atmospheric carbon dioxide is calculated as +1.4 Wm^-2, while the increase from all greenhouse gases combined is supposed to be 2.4 Wm^-2. Ignoring the much-argued about solar influence over the period and using the "Hansen Factor" of 0.75 °C per Wm^-2, the world should have warmed ≈ 1.8 °C from enhanced greenhouse forcing alone -- 2.4 °C if we use the model's 1:1 ratio. Obviously a simplistic "greenhouse gas increase = n degrees warming" will not do since the real world has only delivered between one-sixth and one-third that value with the greatest confidence being one-quarter (0.6 ± 0.2 or 0.4 to 0.8 °C). Definitely marked as dubious.

Checking Hansen with Stefan's constant:

Looking at the problem another way -- maxing out Hansen's reduced ice age forcing of 6.6 ± 1.5 Wm^-2 we get 8.1 Wm^-2 for an observed ΔT of ≈ 5 °C. Presumably then 390.11 (from Stefan's constant, above) - 8.1 = 382 Wm^-2 and this, according to Hansen, should resolve to 288 - 5 = 283 K. However, (382/σ)^1/4 yields 286.49 K, giving us a cooling not of 5 K but 1.5 K -- less than one-third the expected value.

Working from temperature to derive the change in Wm^-2, σ283⁴ = 363.71 Wm^-2, which subtracted from 390.11 leaves us 26.4 Wm^-2 rather than at most 8.1 as per Hansen. Why the shortfall? Perhaps there being no negative listing for solar in Hansen's ice age forcings should have tipped us off.

Our calculations from Kiehl and Trenberth, along with those of both Idso and Pielke, indicate direct calculation using the Stefan-Boltzmann constant overstates climate sensitivity by a factor of 2 by omitting the Earth's natural negative feedback mechanisms. In turn, Hansen overstates S-B-derived figures by a factor of more than 3. The conclusion here is that the "Hansen Factor" is then at least 3 times too large and probably 6-8 times.

How well do we understand radiative forcings?

Going by the IPCC (alt: IPCC), not very well at all. Here's the LOSU index (LOSU = level of scientific understanding):

Figure 6.6 alt: Figure 6.6 with original caption: Global, annual mean radiative forcings (Wm^-2) due to a number of agents for the period from pre-industrial (1750) to present (late 1990s; about 2000) (numerical values are also listed in Table 6.11 alt: Table 6.11). For detailed explanations see Section 6.13 alt: Section 6.13.

(The "prettier" 06.01 is depicted at right) Apparently we have a high level of scientific understanding only of some greenhouse gases, moderate understanding of ozone, low of sulfate aerosols and a very low level of scientific understanding of combustion aerosols, mineral dust, indirect aerosol forcing, aviation-induced contrails and cirrus, land use (changing albedo) and, significantly, solar.

It would perhaps be fairest to say we have a "limited understanding" of how the atmosphere and climate forcing works. From our results above it appears there's large disagreement between empirical measures and models' expectations.

What do the modelers say?

From the Third Assessment Report (alt: Third Assessment Report) again:

"The climate sensitivity parameter (global mean surface temperature response ΔT_s to the radiative forcing ΔF) is defined as: ΔT_s / ΔF = λ. In the one-dimensional radiative-convective models, wherein the concept was first initiated, λ is a nearly invariant parameter, typically, about 0.5 K/Wm^-2. Although the value of the parameter “λ” can vary from one model to another, within each model it is found to be remarkably constant for a wide range of radiative perturbations. The invariance of has made the radiative forcing concept appealing as a convenient measure to estimate the global, annual mean surface temperature response, without taking the recourse to actually run and analyse, say, a three-dimensional atmosphere-ocean general circulation model (AOGCM) simulation."

"Overall, the three-dimensional AOGCM experiments performed thus far show that the radiative forcing continues to serve as a good estimator for the global mean surface temperature response but not to a quantitatively rigorous extent as in the case of the one-dimensional radiative-convective models. Several GCM studies suggest a similar global mean climate sensitivity for the spatially homogeneous and for many but not all of the spatially inhomogeneous forcings of relevance for climate change in the industrial era. Paleoclimate simulations also suggest the idea of similarities in climate sensitivity for a spatially homogeneous and an inhomogeneous forcing (arising due to the presence of continental ice sheets at mid- to high northern latitudes during the last glacial maximum). However, different values of climate sensitivity can result from the different GCMs which, in turn, are different from the λ values obtained with the radiative-convective models. ...

However, in a general sense and considering arbitrary forcing types, the variation in λ could be substantially higher (50% or more) and the climate response much more complex (Hansen et al., 1997a). It is noted that the climate sensitivity for some of the forcings that have potentially occurred in the industrial era have yet to be comprehensively investigated."

"Another important limitation of the concept is that there are parameters other than global mean surface temperature that need to be determined, and that are as important from a climate and societal impacts perspective; the forcing concept cannot provide estimates for such climate parameters as directly as for the global mean surface temperature response. There has been considerably less research on the relationship of the equilibrium response in such parameters as precipitation, ice extent, sea level, etc., to the imposed radiative forcing."

How do the models perform?

In modelers' own words, not very well:

There is nothing particularly egregious here, save perhaps this is identical to the deficiency statement of papers 2 years prior despite the massive funding expended on maintaining and running these video games. Models do not handle clouds and moisture at all well yet and NASA's Goddard Institute for Space Studies' pride and joy is no exception. Placing excessive trust in the models, however, is not a recommended procedure.

The infamous "smoking gun," from bombshell to bomb...

In Earth's Energy Imbalance: Confirmation and Implications Hansen, et al, state: Our climate model, driven mainly by increasing human-made greenhouse gases and aerosols, among other forcings, calculates that Earth is now absorbing 0.85 ± 0.15 watts per square meter more energy from the Sun than it is emitting to space. This imbalance is confirmed by precise measurements of increasing ocean heat content over the past 10 years.

The associated media release is entitled "Earth’s Energy Out of Balance: The Smoking Gun for Global Warming"

When that paper was written the model output was a fair wiggle-fit with Willis (2004) and Levitus (2004).

So, Hansen's model is dumping heat into the oceans at roughly 0.8 Wm^-2 and the bulk ocean heat rise mid-1993 - mid-2003 sort of matched that -- if only the world would remain constant and conform to the models we'd have this "global warming" thing sorted. Like all happy accidents, however, this good thing came to an end, too.

Lyman et al (2006), using updated data from the same source, show that the period 2003-2005 involves a sudden ocean cooling at a rate of -1.0 ± 0.3 Wm^-2 over the period, which means Hansen's model is calculating wrongly in both magnitude and sign. No one expected this loss of one-fifth of the heat stored in the ocean since 1955 and no model predicted it. Its cause is unclear but we appear to be witnessing Earth dumping heat to space via the atmosphere. NB: See correction to Lyman et al 2006

UPDATE: The Correction To The Lyman Et Al 2006 Paper Is Available - The correction to the Lyman et al paper “Recent cooling of the upper ocean” is available. It is “Correction to ‘Recent Cooling of the Upper Ocean’” by Josh K. Willis, John M. Lyman, Gregory C. Johnson and John Gilson. While this correction eliminates the cooling that they reported in the 2006 paper, the warming of the 1990s and very early 2000s has not continued. This absence of global ocean warming (which is consistent with the absence of a significant global average sea surface temperature anomaly trend for the last few years) is a challenge to the modelers and to the conclusions of the IPCC with respect to the ability to skillfully predict global warming. Indeed, it appears that with respect to the challenge on Climate Science of A Litmus Test For Global Warming - A Much Overdue Requirement, the models have failed so far. (Climate Science)

Now Hansen's model has three years of data (minimum) where it's incorrectly dumping heat into the oceans at a rate of >0.8 Wm^-2 when it should not, making it in error over more than 70% of the planet -- call it excess global forcing of at least 0.56 Wm^-2 for that period and thus out by a factor of 3.

Lyman et al. go so far as to state: Including the recent downturn, the average warming rate for the entire 13-year period is 0.33 ± 0.23 W/m² (of the Earth's total surface area). Think about that for a moment -- that's just 0.1 - 0.56 Wm^-2.

This means Hansen's pretty little fairy lights in the conceptual image above are far too prolific with ΔF ≈ 4 - 20 times larger than it should be over the modeled period since the early 1990s. The implications of this on forward projections are, of course, enormous -- essentially rendering them GIGO (Garbage In -- Garbage Out).

What if Hansen has misallocated some modern forcings?

We'll try some arbitrary manipulation on Hansen's ΔF table shortly to see what effect we get. Note that this is not a recommended procedure but a fudge on our part because forcings are relatively poorly understood and we are all on a voyage of discovery to see what we can see.

If we take a slightly more sophisticated approach to net ΔF, (the adjacent graphic is titled "Climate forcing agents in the industrial era (1850–2000) (W/m²)"), the net change in forcing is shown as ≈ 1.6 Wm^-2, which should yield a warming of ≈ 1.2 °C using the "Hansen Factor", 150-300% of warming believed to have been measured over the period.

Three immediate distinct possibilities present here: positive forcings could be overstated, negative forcings understated or the "Hansen Factor" overestimates Earth's thermal response per Wm^-2, (or some combination thereof).

So, on the one hand we think we have done a moderate to fair job of measuring increase in forcings, with the notable exception of the sun where, depending on the research and paper consulted, there are differences in the order of ± 5 Wm^-2, sometimes much larger. Such differences obviously make these comparisons somewhat fraught and thus we have to take a great deal on trust. Recent papers, such as the one by Wigley et al suggest solar forcings are minimal.

The "Svensmark Effect":

With the "two handedness" of economists and researchers everywhere, there's the possibility both positive and negative forcings are underdone. Recently we had news of important work attempting to quantify some extraterrestrial influences on Earth's climate, which we featured in Cosmic Rays and Earth's Climate. This work is particularly interesting in that it indicates positive feedback mechanism for increased solar activity and negative reinforcement for reduced solar activity, thus explaining how relatively trivial changes in solar activity might equate to ΔF of several Wm^-2.

There is no doubt there has been a long-term decrease in Galactic Cosmic Ray (GCR) flux since the late 17^th Century, as evidenced by the ¹⁰Be and ¹⁴C cosmogenic isotope records (Stuiver and Reimer, 1993; Beer et al., 1994), and this mirrors the long-term increase in Total Solar Irradiance (TSI). In addition, direct observation shows this increase to be ongoing, see for example, NASA Study Finds Increasing Solar Trend That Can Change Climate, Solar Irradiance Reconstruction (Lean, 2000) see plot, Sun more active than for a millennium (New Scientist), Sunspots more frequent now than any time for 1000 years (New Scientist), The Sun is More Active Now than Over the Last 8000 Years (Max Planck Society) and so on.

Long-term cloud records are in short supply and thus the effect of cloud changes difficult to quantify.

Kaiser (1999) states: "Station and regional trends in annual and seasonal mean cloud amount clearly indicate decreasing total cloud amount over much of China from the early to mid-1950s through 1994. ... Most stations in central, eastern, and northeastern China show statistically significant decreases of 1-3% sky cover per decade. Annual and seasonal trends for selected regions of China show that the strongest and most consistent evidence for decreasing cloud amount is seen for the North and Northeast regions of China, where decreases ranging from 1-2% sky cover per decade (about 4.5-9% over the period of record) are observed."

Obviously a change of roughly 5-10% in cloudiness over just 4 decades is hugely significant although to what extent this is attributable to local evapo-transpiration and aerosol loading from changes to agriculture, pollutant emissions from rapid expansion of industry and power generation and exactly what influence changes in GCR flux had over China is as yet unclear.

Having now experimentally demonstrated the mechanism behind the GCR flux hypothesis Svensmark et al should expect more interest in this flexible forcing mechanism -- certainly the hypothesis had been under considerable assault from those who prefer to see enhanced greenhouse remain the prime suspect. For example Kuang et al (1998) showed high correlations with an El Niño-Southern Oscillation (ENSO) index difficult to distinguish from the GCR flux while Farrar (2000) showed that the pattern of change in cloudiness over that period, particularly in the Pacific Ocean, corresponds to what would be expected for the atmospheric circulation changes characteristic of El Niño.

On balance it appears solar forcing, in conjunction with both positive and negative feedback reinforcement according to current trend, might be significantly underestimated in the attribution of ΔF.

While the huge reduction in cloudiness in China does not necessarily mean that is the case for the entire globe, it most likely isn't, is does make the hypothesis of increased global cloudiness over the period significantly less plausible. After all, it would require large increase elsewhere just to offset China's apparent loss, a loss anticipated for other developing regions too, as well as the Asian Brown Haze suppressing Indian Ocean cloud formation and Indian Summer Monsoon Rainfall, Indonesian haze from land-clearing burns, Amazonia... .

In turn, this would suggest Hansen's -1 Wm^-2 ΔF from increased cloud albedo (reflection of incoming solar radiation by bright, low cloud) is somewhat dubious, likely even of the wrong sign.

Update: New data contradicts aerosol cooling hypothesis:

Atmospheric aerosols compete with carbon dioxide as an agent of warming.

... As much as half of the recent warming trend attributed to CO₂ and other greenhouse gases is thought to have been cancelled out by cooling from aerosols. But new observations show that in some regions black carbon is as culpable as CO₂ for the warming, and in some cases, has a greater effect.

In a study published recently in Nature, Veerabhadran Ramanathan, an atmospheric scientist at the Scripps Institution of Oceanography in La Jolla, California, and colleagues, report that aerosols locked up in brown clouds over Asia are significant contributors to regional warming. 'Atmospheric brown clouds', which appear as a dark haze on the horizon, are formed from a cocktail of warming and cooling aerosols in the atmosphere. Once thought to be a local phenomenon, brown clouds that originate in urban centres from Los Angeles to Beijing are now known to travel thousands of kilometres, transported by air currents and high winds. "Brown clouds from the United States cover the Atlantic, the European brown cloud goes over central Asia, and China's brown cloud crosses the Pacific over to us," says Ramanathan. "We are each a back yard to someone else, and we're polluting every other person's back yard."

Ramanathan and colleagues chose the Indian Ocean as the 'back yard' in which to study the warming effects of black carbon. In the winter and spring, heavily polluted air masses are transported over the Indian Ocean from central Asia, where the majority of black carbon is from cooking fires. Brown-cloud solar absorption usually takes place in the lower 3 km of the atmosphere and heats the atmosphere up to 5 km high. The scientists measured lower atmospheric heating in a 3-km-thick cloud layer over the Indian Ocean in March 2006 using 18 missions of three unmanned aerial vehicles (UAVs) launched from the island of Hanimaadhoo in the Maldives. Equipped with instruments to measure aerosol-particle concentrations and solar radiation, the UAVs were flown in a stacked manner, separated in height by only tens of metres and in time by less than ten seconds, making it possible to measure atmospheric heating rates directly. They found that the pollution cloud was responsible for 50% of the lower atmospheric heating, with the rest attributable to greenhouse gases.

Taking a longer-term perspective using climate-model simulations, Ramanathan's team estimated warming in the lower atmosphere from both aerosols and greenhouse gases at about 0.25 °C a decade, sufficient to account for the retreat of the Himalayan glaciers. Because the Himalayan glaciers lie at such high altitudes, they are directly affected by the atmospheric warming effect from brown clouds, yet can also be influenced by soot deposition. Black carbon from aerosols eventually condenses out of the atmosphere and settles on ice and snow, significantly increasing the amount of sunlight that is absorbed. Researchers have recently found that the influence of black carbon on temperature and the melting of snow is three times greater than that of CO₂ in Arctic regions.

This new information shows us that aerosol emissions have both heating and cooling effects and, on balance, that aerosols are unlikely to have been 'hiding' anticipated enhanced greenhouse warming as claimed.

The IPCC's 2007 Assessment Report 4 shows that models generally treat aerosols as strongly negative forcings (see adjacent graphic from AR4 Chapter 2, p136). Note that the uncertainty bars suggest potentially much greater cooling effect but zero potential for atmospheric warming.

Adding complexity to modeling requirements these aerosol clouds have now been shown to warm the atmosphere at least as much as increased carbon dioxide (telling us that models are excessively sensitive to CO₂ forcing) and that they should also cool the surface.

That's important:

• aerosols do not really behave as modeled
• aerosols do not appear to have been masking CO₂-driven warming
• aerosols appear to be responsible for roughly half the warming attributed to atmospheric CO₂
• this means that the warming potential of increased CO₂ is overstated once because aerosols are not 'hiding' warming previously hypothesised but never observed and a second time because aerosols are responsible for half the estimated warming attributed to CO₂
• this suggests that either estimated changes in forcing significantly understate Watts per meter squared or that climate sensitivity to said changes is dramatically overstated (or some combination thereof).

In turn the aerosol observations should strengthen the signature expected of enhanced greenhouse warming with the tropical troposphere warming significantly faster than the surface, along with cooling of the stratosphere.

AR4 Chapter 9 (p675) offers the following graphical representations, we've imported the greenhouse "bullseye" from the Second-Order Draft simply because it was conveniently to hand, only differences are cosmetic with the published version being color-enhanced:

Caption (from 2^nd-order draft): Zonal mean atmospheric temperature change during the 20th century (°C/Century) as simulated by the PCM model from (a) solar forcing, (b) volcanoes, (c) well-mixed greenhouse gases, (d) tropospheric and stratospheric ozone changes, (e) direct sulphate aerosol forcing, and (f) the sum of all forcings. Plot is from 1000 hPa to 10 hPa (shown on left scale) and from 0 km to 30 km (shown on right). Based on Santer et al. (2003a).

The discovery of such a belt of rapidly warming atmosphere spanning one third of the globe at an altitude of about 20,000' to 50,000' would lend great support to the enhanced greenhouse hypothesis but has not been found despite diligent searching. There might have been a small step warming in the tropical mid-troposphere a few years ago but HadCRU shows far greater surface warming for the period and GISTEMP suggests even more.

Shaking the mix:

This is where we commence arbitrarily hacking at Hansen's table to see if shaking it up a bit results in figures near anything previously derived. Shifting clouds from the negative to the positive side of the equation would make Hansen's net ΔF ≈ 3.6 Wm^-2, which should yield a warming of ≈ 2.7 °C using the "Hansen Factor," roughly three to seven times the IPCC-estimated value. However, dividing the median estimate of contemporary change (ΔT) of 0.6 °C by our revised Hansen estimate of 3.6 Wm^-2 ΔF, we derive ≈ 0.17 °C per Wm^-2, coming back into line with our total greenhouse divisions performed above. Implied by this newly discovered "consensus" of numbers then is that we have not a good understanding of ΔF and/or global temperature during a major glaciation since the derived 0.75 °C per Wm^-2 appears to be out by a large margin -- "corrected" simply by treating clouds differently.

Where does this leave us?

While there are no certainties in climate science we now have a few clues regarding possible invalid assumptions.

If Kiehl and Trenberth did a fair job of untangling and attributing downwelling radiation then we should expect ΔT ≈ 0.1 °C per Wm^-2 ΔF. This is virtually identical to the figure derived from Pielke and that of Idso derived from 8 natural experiments. It is also similar to the figure derived from revising Hansen for probable change in global cloudiness, as is our Stefan-Boltzmann-derived greenhouse value.

Arrayed against these we have the numbers 0.3 °C (which is seemingly close but certainly overestimates current warming), 0.4 - 0.7 K and 0.75 ± 0.25 °C per Wm^-2, from the NAS, Huang and Hansen respectively, all apparently derived from paleo-reconstruction analyses.

From these derived numbers and modern measures the implication is that climate sensitivity to ΔF <5 Wm^-2 is low, perhaps between one-tenth and one-fifth °C per Wm^-2 ΔF while attempts to reconstruct ancient climes and forcings from proxy measures suggest much greater sensitivity.

At the extreme end of the scale we have climate models using 1:1 °C per Wm^-2 ratios, at least 5 and probably 10 times greater than recent observations would suggest. Models might be state of the art but that does not make them useful for predicting future climate states or global mean temperature.

Our best guess at conversion values?

As near as we can figure, ΔF 1 Wm^-2 = ΔT 0.2 ± 0.1 °C, although this probably overstates sensitivity by omitting Earth's natural negative feedback mechanisms. Observed change occurs with a net sensitivity of 0.1 °C per Wm^-2, while theoretical calculation suggests 0.2 °C per Wm^-2. Hypothetical rates derived from paleo-climate estimates range upwards from 0.3 °C per Wm^-2 but cannot be reconciled against observed contemporary changes and are considered highly unreliable.

Conclusion:

Real-world measures suggest moderate to strong negative feedback, currently unnamed and un-quantified, mitigates the Earth's thermal response to additional radiative forcing from both human activity and natural variation.

Justification for amplification factors >2.5 for unmitigated positive feedback mechanisms is not evident in empirical measures. It is not clear whether any amplification factor should be applied or even what sign any such factor should be. Nor is there evidence to support such large λ values in GCMs.

Division of real-world measures continue to exhibit the same surface thermal response derived by Idso for contemporary local, regional and global climate, for ancient climate under a younger, weaker sun and for Earth's celestial neighbors, Mars and Venus.

In the absence of support for amplification factors and in view of their erroneously large λ values it is apparent that the wiggle fitting so far achieved with climate model output is accidental or that these models contain equally large opposing errors in other portions of their calculations such that a comedy of errors produce seemingly plausible results in the short-term. In either case no confidence is inspired.

On balance of available evidence then the current model-estimated range of warming from a doubling of atmospheric carbon dioxide should probably be reduced from 1.4 - 5.8 °C to about 0.4 °C to suit observations or ≈ 0.8 °C to accommodate theoretical warming -- and that's including ΔF of 3.7 Wm^-2 from a doubling of pre-Industrial Revolution atmospheric carbon dioxide levels, a figure we suspect is also inflated.

The bottom line is that climate models are programmed to overstate potential warming response to enhanced greenhouse forcing by a huge margin. The median estimate 3.0 °C warming cited by the IPCC for a doubling of atmospheric carbon dioxide is physically implausible.

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