By Christopher Monckton of Brenchley
I propose to raise a question about the Earth’s energy budget that has perplexed me for some years. Since further evidence in relation to my long-standing question is to hand, it is worth asking for answers from the expert community at WUWT.
A.E. Housman, in his immortal parody of the elegiac bromides often perpetrated by the choruses in the stage-plays of classical Greece, gives this line as an example:
I only ask because I want to know.
This sentiment is not as fatuous as it seems at first blush. Another chorus might say:
I ask because I want to make a point.
I begin by saying:
You say I aim to score a point. Not so:
I only ask because I want to know.
Last time I raised the question, in another blog, more heat than light was generated because the proprietrix had erroneously assumed that T / 4F, a differential essential to my argument, was too simple to be a correct form of the first derivative ΔT / ΔF of the fundamental equation (1) of radiative transfer:
where F is radiative flux density in W m–2, ε is emissivity constant at unity, the Stefan-Boltzmann constant σ is 5.67 x 10–8 W m–2 K–4, and T is temperature in Kelvin. To avert similar misunderstandings (which I have found to be widespread), here is a demonstration that T / 4F, simple though it be, is indeed the first derivative ΔT / ΔF of Eq. (1):
Like any budget, the Earth’s energy budget is supposed to balance. If there is an imbalance, a change in mean temperature will restore equilibrium.
My question relates to one of many curious features of the following energy-budget diagrams for the Earth:
Energy budget diagrams from (top left to bottom right) Kiehl & Trenberth (1997), Trenberth et al. (2008), IPCC (2013), Stephens et al. (2012), and NASA (2015).
Now for the curiosity:
“Consensus”: surface radiation FS falls on the interval [390, 398] W m–2.
There is a “consensus” that the radiative flux density leaving the Earth’s surface is 390-398 W m–2. The “consensus” would not be so happy if it saw the implications.
When I first saw FS = 390 W m–2 in Kiehl & Trenberth (1997), I deduced it was derived from observed global mean surface temperature 288 K using Eq. (1), assuming surface emissivity εS = 1. Similarly, TS = 289.5 K gives 398 W m–2.
The surface flux density cannot be reliably measured. So did the “consensus” use Eq. (1) to reach the flux densities shown in the five diagrams? Yes. Kiehl & Trenberth (1997) wrote: “Emission from the surface is assumed to follow Planck’s function, assuming a surface emissivity of 1.” Planck’s function gives flux density at a particular wavelength. Eq. (1) integrates that function across all wavelengths.
Here (at last) is my question. Does not the use of Eq. (1) to determine the relationship between TS and FS at the surface necessarily imply that the Planck climate-sensitivity parameter λ0,S applicable to the surface (where the coefficient 7/6 ballparks allowance for the Hölder inequality) is given by
The implications for climate sensitivity are profound. For the official method of determining λ0 is to apply Eq. (1) to the characteristic-emission altitude (~300 mb), where incoming and outgoing radiative fluxes are by definition equal, so that Eq. (4) gives incoming and hence outgoing radiative flux FE:
where FE is the product of the ratio πr2/4πr2 of the surface area of the disk the Earth presents to the Sun to that of the rotating sphere; total solar irradiance S = 1366 W m–2; and (1 – α), where α = 0.3 is the Earth’s albedo. Then, from (1), mean effective temperature TE at the characteristic emission altitude is given by Eq. (5):
The characteristic emission altitude is ~5 km above ground level. Since mean surface temperature is 288 K and the mean tropospheric lapse rate is ~6.5 K km–1, Earth’s effective radiating temperature TE = 288 – 5(6.5) = 255 K, in agreement with Eq. (5). The Planck parameter λ0,E at that altitude is then given by (6):
Equilibrium climate sensitivity to a CO2 doubling is given by (7):
where the numerator of the fraction is the CO2 radiative forcing, and f = 1.5 is the IPCC’s current best estimate of the temperature-feedback sum to equilibrium.
Where λ0,E = 0.313, equilibrium climate sensitivity is 2.2 K, down from the 3.3 K in IPCC (2007) because IPCC (2013) cut the feedback sum f from 2 to 1.5 W m–2 K–1 (though it did not reveal that climate sensitivity must then fall by a third).
However, if Eq. (1) is applied at the surface, the value λ0,S of the Planck sensitivity parameter is 0.215 (Eq. 3), and equilibrium climate sensitivity falls to only 1.2 K.
If f is no greater than zero, as a growing body of papers finds (see e.g. Lindzen & Choi, 2009, 2011; Spencer & Braswell, 2010, 2011), climate sensitivity falls again to just 0.8 K.
If f is net-negative, sensitivity falls still further. Monckton of Brenchley, 2015 (click “Most Read Articles” at www.scibull.com) suggest that the thermostasis of the climate over the past 810,000 years and the incompatibility of high net-positive feedback with the Bode system-gain relation indicate a net-negative feedback sum on the interval –0.64 [–1.60, +0.32] W m–2 K–1. In that event, applying Eq. (1) at the surface gives climate sensitivity on the interval 0.7 [0.6, 0.9] K.
Two conclusions are possible. Either one ought not to use Eq. (1) at the surface, reserving it for the characteristic emission altitude, in which event the value for surface flux density FS may well be incorrect and no one has any idea of what the Earth’s energy budget is, and still less of an idea whether there is any surface “radiative imbalance” at all, or the flux density at the Earth’s surface is correctly determined from observed global mean surface temperature by Eq. (1), as all five sources cited above determined it, in which event sensitivity is harmlessly low even under the IPCC’s current assumption of strongly net-positive temperature feedbacks.
Table 1 summarizes the effect on equilibrium climate sensitivity of assuming that Eq. (1) defines the relationship between global mean surface temperature TS and mean outgoing surface radiative flux density FS.
|Climate sensitivities to a CO2 doubling|
|AR5 (2013) upper bound||300 mb||0.310 K W–1 m2||+2.40 W m–2 K–1||2.3 K||4.5 K|
|AR4 (2007) central estimate||300 mb||0.310 K W–1 m2||+2.05 W m–2 K–1||1.6 K||3.3 K|
|AR5 implicit central estimate||300 mb||0.310 K W–1 m2||+1.50 W m–2 K–1||1.1 K||2.2 K|
|AR5 lower bound||300 mb||0.310 K W–1 m2||+0.75 W m–2 K–1||0.8 K||1.5 K|
|M of B (2015) upper bound||300 mb||0.310 K W–1 m2||+0.32 W m–2 K–1||0.7 K||1.3 K|
|AR5 central estimate||1013 mb||0.215 K W–1 m2||+1.50 W m–2 K–1||0.6 K||1.2 K|
|M of B central estimate||300 mb||0.310 K W–1 m2||–0.64 W m–2 K–1||0.5 K||1.0 K|
|M of B upper bound||1013 mb||0.215 K W–1 m2||+0.32 W m–2 K–1||0.5 K||0.9 K|
|M of B lower bound||300 mb||0.310 K W–1 m2||–1.60 W m–2 K–1||0.4 K||0.8 K|
|M of B central estimate||1013 mb||0.215 K W–1 m2||–0.64 W m–2 K–1||0.4 K||0.7 K|
|Lindzen & Choi (2011)||300 mb||0.310 K W–1 m2||–1.80 W m–2 K–1||0.4 K||0.7 K|
|Spencer & Braswell (2011)||300 mb||0.310 K W–1 m2||–1.80 W m–2 K–1||0.4 K||0.7 K|
|M of B lower bound||1013 mb||0.215 K W–1 m2||–1.60 W m–2 K–1||0.3 K||0.6 K|
Table 1. 100-year (ΔTS,100) and equilibrium (ΔTS,∞) climate sensitivities to a doubling of CO2 concentration, applying Eq. (1) at the characteristic-emission altitude (300 mb) and, boldfaced, at the surface (1013 mb).
It is worth noting that, even before taking any account of the “consensus’” use of Eq. (1) to govern the relationship between TS and FS, the reduction in the feedback sum f between IPCC’s 2007 and 2013 assessment reports mandates a corresponding reduction in its central estimate of climate sensitivity from 3.3 to 2.2 K, of which only half, or about 1 K, would be expected to occur within a century of a CO2 doubling. The remainder would make itself slowly and harmlessly manifest over the next 1000-3000 years (Solomon et al., 2009).
Given that the Great Pause has endured for 18 years 6 months, the probability that there is no global warming in the pipeline as a result of our past sins of emission is increasing (Monckton of Brenchley et al., 2013). All warming that was likely to occur from emissions to date has already made itself manifest. Therefore, perhaps we start with a clean slate. Professor Murry Salby has estimated that, after the exhaustion of all affordably recoverable fossil fuels at the end of the present century, an increase of no more than 50% on today’s CO2 concentration – from 0.4 to 0.6 mmol mol–1 – will have been achieved.
In that event, replace Table 1 with Table 2:
|Climate sensitivities to a 50% CO2 concentration growth|
|AR5 (2013) upper bound||300 mb||0.310 K W–1 m2||+2.40 W m–2 K–1||1.3 K||2.6 K|
|AR4 (2007) central estimate||300 mb||0.310 K W–1 m2||+2.05 W m–2 K–1||0.9 K||1.8 K|
|AR5 implicit central estimate||300 mb||0.310 K W–1 m2||+1.50 W m–2 K–1||0.6 K||1.3 K|
|AR5 lower bound||300 mb||0.310 K W–1 m2||+0.75 W m–2 K–1||0.4 K||0.9 K|
|M of B (2015) upper bound||300 mb||0.310 K W–1 m2||+0.32 W m–2 K–1||0.4 K||0.7 K|
|AR5 central estimate||1013 mb||0.215 K W–1 m2||+1.50 W m–2 K–1||0.3 K||0.7 K|
|M of B central estimate||300 mb||0.310 K W–1 m2||–0.64 W m–2 K–1||0.3 K||0.6 K|
|M of B upper bound||1013 mb||0.215 K W–1 m2||+0.32 W m–2 K–1||0.3 K||0.5 K|
|M of B lower bound||300 mb||0.310 K W–1 m2||–1.60 W m–2 K–1||0.2 K||0.4 K|
|M of B central estimate||1013 mb||0.215 K W–1 m2||–0.64 W m–2 K–1||0.2 K||0.4 K|
|Lindzen & Choi (2011)||300 mb||0.310 K W–1 m2||–1.80 W m–2 K–1||0.2 K||0.4 K|
|Spencer & Braswell (2011)||300 mb||0.310 K W–1 m2||–1.80 W m–2 K–1||0.2 K||0.4 K|
|M of B lower bound||1013 mb||0.215 K W–1 m2||–1.60 W m–2 K–1||0.2 K||0.3 K|
Table 2. 100-year (ΔTS,100) and equilibrium (ΔTS,∞) climate sensitivities to a 50% increase in CO2 concentration, applying Eq. (1) at the characteristic-emission altitude (300 mb) and, boldfaced, at the surface (1013 mb).
Once allowance has been made not only for the IPCC’s reduction of the feedback sum f from 2.05 to 1.5 W m–2 K–1 and the application of Eq. (1) to the relationship between TS and FS but also for the probability that f is not strongly positive, for the possibility that a 50% increase in CO2 concentration is all that can occur before fossil-fuel exhaustion, for the IPCC’s estimate that only half of equilibrium sensitivity will occur within the century after the CO2 increase, and for the fact that the CO2 increase will not be complete until the end of this century, it is difficult, and arguably impossible, to maintain that Man can cause a dangerous warming of the planet by 2100.
Indeed, even one ignores all of the considerations in the above paragraph except the first, the IPCC’s implicit central estimate of global warming this century would amount to only 1.1 K, just within the arbitrary 2-K-since-1750 limit, and any remaining warming would come through so slowly as to be harmless. It is no longer legitimate – if ever it was – to maintain that there is any need to fear runaway warming.
Quid vobis videtur?