When will climate feedbacks fully function? Not for millennia

 Guest essay by Christopher Monckton of Brencheley

The splendidly-titled Alberto Zaragoza Comendador, commenting on my recent posting taking apart Mr. Mann’s latest fantasia in Scientific American, was startled by my statement that only half of equilibrium global warming would emerge after a couple of hundred years, because –

“Equilibrium climate sensitivity is a measure of the global warming to be expected in 1000-3000 years’ time in response to a doubling of CO2 concentration, regardless of how that doubling came about. It has nothing to do with fossil-fuel emissions scenarios.”

El Comendador wrote:

“Whoa. Whoa whoa whoa. The effects of a CO2 doubling aren’t felt until 1000 years later? So if we hit 560 ppm we’ll in theory get 2.5°C of warming. But only 1.25°C will happen in the first 200 years? Am I getting this right? Can anybody please confirm?”

In fact, he had to write again, because I did not reply at once, for the fascinating answer to his entirely proper question needs a head posting to address it properly. He wrote:

“I have to ask the question again: is the literature certain (or as certain as climate science can be) about the time it takes for warming to kick in? At one point in the article Monckton says only half of the warming happens in the first 200 years. The rest may happen over the following 1000-3000 years. Politicians have set this nonsense 2 Cº limit, whichm when compared to pre-industrial times, means we only have 1.1 Cº warming left of warming before mega-disaster happens. I always knew it was a matter of decades, but now it seems to be a matter of centuries. If true, this takes the absurdity of the whole dangerous-anthropogenic-global-warming bandwagon to another level. And I wonder how many in the public know this: 0.01%, maybe? Of course it’s extremely convenient for the usual suspects that it will take so much time for warming to kick in: they can always claim the thing hasn’t been disproved, therefore the money should keep flowing.”

El Comendador is quite right to press his excellent question, and I must begin by apologizing that I was not able to answer it sooner.

I must also issue an Equation Alert. We’re going to have to review – in the simplest fashion – the fundamental equation of climate sensitivity, and then go deep into the IPCC’s documents to work out what they have hidden by their now-traditional device of not making it explicit what their projections entail. So, hold on to your hats. Here goes.

Climate sensitivity: The global warming ΔT_t to be expected in response to a given proportionate increase in CO2 concentration over a specified term of years t is for present purposes sufficiently described by the simplified climate-sensitivity relation (1), where ΔT_t, denominated in Kelvin or Celsius degrees, is the product of three quantities: the reciprocal of the fraction q of total anthropogenic forcing that is driven by CO2; a time-dependent climate-sensitivity parameter λ_t, which is itself the product of the instantaneous or Planck sensitivity parameter λ₀ and a time-dependent temperature-feedback gain factor G_t; and the CO2 radiative forcing ΔF_t. Annex B provides a more detailed discussion of (1), and of the uncertainties to which it gives rise.

| Kelvin. (1)

Global warming ΔT_t: On business as usual, without mitigation, global warming of 2.8 K from 2000-2100 is the mid-range projection in IPCC (2007, table SPM.3). Since the Earth has warmed at a rate well below those projected in all five IPCC Assessment Reports and there has been no global warming since 1996 (RSS, 2014), 2.8 K 21^st-century warming will be taken as close to the upper bound.

CO2 concentration: On business as usual, unmitigated CO2 concentration over the 21^st century will attain the annual values (in μatm) in Table 1, derived from the mid-range estimates in IPCC (2007).

CO2 forcing: According to the IPCC, a radiative forcing is an external perturbation in a presumed pre-existing climatic radiative equilibrium, leading to a transient radiative imbalance that will eventually settle toward a new equilibrium at a different global temperature. Experiment and line-by-line radiative transfer analysis have demonstrated that the CO2 radiative forcing ΔF_t is reasonably approximated by the logarithmic relation (2),

| Watts per square meter, (2)

where (C_t/C₀) is a proportionate change in CO2 concentration over t years, with C₀ the unperturbed value. Myhre et al. (1998), followed by IPCC (2001), give the coefficient k as 5.35, so that, for example, the CO2 forcing that arises from doubled concentration is 5.35 ln 2, or 3.708 W m^–2.

Planck parameter λ₀: Immediately after a perturbation by an external radiative forcing such as anthropogenically-increased CO2 concentration, the climate sensitivity parameter by which the forcing is multiplied to yield the global temperature response will take its instantaneous or Planck value λ₀ = 0.31 K W^–1 m² (expressed reciprocally as 3.2 W m^–2 K^–1 in IPCC, 2007, p. 361 fn.).

The sensitivity parameter λ_n: To allow for the incremental operation of temperature feedbacks, considered by the IPCC to be strongly net-positive, λ_n is projected to increase over time. The IPCC implicitly takes λ_n as rising from the instantaneous value λ₀ = 0.31 K W^–1 m² via the centennial value λ₁₀₀ = 0.44 K W^–1 m² and the bicentennial value λ₂₀₀ = 0.50 K W^–1 m² (derived in Table 2) to the equilibrium value λ_∞ = 0.50 K W^–1 m². The equilibrium value is not attained for 1000-3000 years (Solomon et al., 2009).

Centennial parameter λ₁₀₀: This and longer-term values of λ_n allow for longer-term mitigation benefit-cost appraisals. The IPCC projects CO2 concentration of 713 μatm in 2100 against 368 μatm in 2000, and a mid-range estimate of 2.8 K warming by 2100, of which 0.6 K is pre-committed (IPCC, 2007, table SPM.3), leaving 2.2 K of new warming, of which 70% (derived in Table 2), or 1.54 K, is CO2-driven. Therefore, the IPCC’s implicit centennial climate sensitivity parameter λ₁₀₀ is 1.54 K divided by 5.35 ln(713/368) W m^–2, or 0.44 K W^–1 m², representing an increase of 0.13 K W^–1 m² over a century against the Planck value λ₀ = 0.31 K W^–1 m². This value is half of the equilibrium value λ_∞, derived below.

Bicentennial parameter λ₂₀₀: Examination of the six SRES emissions scenarios for 1900-2100 (Table 2) demonstrates the IPCC’s implicit bicentennial sensitivity parameter λ₂₀₀ to be 0.50 K W^–1 m² on each scenario.

Equilibrium parameter λ_∞: Dividing the IPCC’s 3.26 K central estimate of climate sensitivity to a CO2 doubling (IPCC, 2007, p. 798, box 10.2) by the 3.71 W m^–2 radiative forcing in response to a CO2 doubling gives the implicit equilibrium sensitivity parameter λ_∞ = 0.88 K W^–1 m², attained after 1000-3000 years.

CO2 fraction: In Table 2, the fraction q = 0.7 of total anthropogenic forcing attributable to CO2 emissions is derived from each of the six SRES standard emissions scenarios.

Plotting the four values λ₀ = 0.31 K W^–1 m², λ₁₀₀ = 0.44 K W^–1 m², λ_∞ = 0.50 K W^–1 m², and λ_∞ = 0.88 K W^–1 m², produces curve A in Fig. 1. As the inset panel A shows, the temperature rises quite sharply in the first century or two.

Figure 1. Two equally plausible evolutions of the climate-sensitivity parameter λ_n. Version A is implicit in IPCC (2007). However, version B, an epidemic curve, is equally plausible.

Now, the various values of the climate-sensitivity parameter arise over time because temperature feedbacks do not take effect instantaneously, particularly in the IPCC’s very high-sensitivity regime. They unfold on timescales of centuries to millennia.

One example of a millennial-scale feedback is the melting of the land-based ice in Greenland, which the IPCC says will only happen if global temperatures remain 2 Cº higher than today for several millennia. And even this is probably an exaggeration. Most of you are too young to remember, but 8000 years ago the mean temperature at the summit of the Greenland plateau was 2.5 Cº higher than it is today (Fig. 2), but the ice there did not melt. So the most one might expect, even after several millennia, is some further loss of ice around the coastal fringes of Greenland.

In passing, there is a characteristically hysterical recent piece (in The Guardian, inevitably) by the accident-prone Australian professional bed-wetter Graham Redfearn, saying that from 2002-2011 some 260 billion tons of ice a year has melted from Greenland. Oo-er! Even if that were the case, sea level would have risen by just 0.7 mm a year, or little more than a quarter of an inch over the decade.

Figure 2. Reconstructed temperatures at the summit of the Greenland ice cap, 6000 BC to date.

For reasons such as this, it is no less plausible that feedbacks will come into play slowly to start with, as in inset panel B, than that they will act near-instantaneously in the first century or two, as in the IPCC’s implicit regime (Fig. 1, inset panel A).

The literature is pointing ever more clearly towards only the smallest net-positive feedbacks even at equilibrium. In that event, the global warming from a doubling of Co2 concentration will not much exceed 1 Cº, and that will come about within a century or two rather than several millennia. But even on the IPCC’s high-sensitivity central case, after 100-200 years the warming in response to a CO2 doubling would not have reached much more than 1.5 Cº, because the feedbacks under a high-sensitivity regime take longer to come into full effect.

Under the IPCC’s imagined regime, of course, the warming would continue to increase all the way to equilibrium, though at a slower rate than in the first couple of centuries.

To be fair, one should also bear in mind that CO2 concentration on business as usual will continue to rise even beyond the doubling from the pre-industrial 280 μatm to 560 μatm in around 2080. However, CO2 concentration would have to double again, from 560 to 1120 μatm, to have the same warming effect as that of the previous doubling.

Finally, it is worth reiterating that there is no, repeat no, consensus in the scientific literature in support of the IPCC’s assertion that recent warming is mostly manmade. Legates et al. (2013) established that only 0.3% of abstracts of 11,944 climate science papers published in the 21 years 1991-2011 explicitly stated that we are responsible for more than half of the 0.69 Cº global warming since we began to have a theoretically-detectable effect on global temperature in 1950.

Suppose that 0.33 Cº – just under half of the observed 0.69 Cº – was our contribution to global warming since 1950. Suppose also that CO2 concentration in that year was 305 ppmv and is now 398 ppmv.

Then the radiative forcing from CO2 that contributed to that warming was 5.35 ln(398/305) = 1.42 Watts per square meter. Assume that the IPCC’s central estimate of 713 ppmv CO2 by 2100 (Table 1) is accurate. Assume also that the CO2 forcing from now to 2100 will be 5.35 ln(713/398), or 3.12 W m^–2.

Assuming that the 0.7 ratio of CO2 forcing to that from other greenhouse gases (derived in Table 2) will remain broadly constant, and assuming that by 2100 temperature feedbacks will have exercised 0.44/0.31 of the warming effect seen to date, the manmade warming to be expected by 2100 on the basis of the 0.33 Cº warming since 1950 will be 3.12/1.42 x 0.33 x 0.44/0.31 = 1 Cº.

Broadly speaking, the IPCC expects this century’s warming to be equivalent to that from a doubling of CO2 concentration. In that event, 1 Cº is indeed all the warming we should expect from a CO2 doubling. And is that going to be a problem?

[No.]