By Christopher Monckton of Brenchley

Judge Alsup, in the California global warming trial, has accepted the amicus curiae brief from my eight distinguished colleagues and me. The brief now becomes an official part of the court documents. The judge may yet ask all parties to respond to it.

The initial reaction of the two California cities that brought the case against five oil companies, demanding that they should fork out billions to fend off sea-level rise, was to use the traditional totalitarian tactic of attacking our personal reputations. So much easier, that, than producing a scientific argument. The judge was unmoved.

A simple feedback amplifier circuit from Bode (1945, page 31). Note that the input and output signals are not deltas but entire values. Numerous climate papers cite the feedback math in Bode as the basis for climate feedback analysis.

Meanwhile, my account here at WUWT of the grave error that we have discovered right at the heart of climate physics has attracted 1000+ comments – not unprecedented, but rare. The high level of activity shows that the climate fanatics are worried – very worried.

But not worried enough to work out a credible line of attack. I have seldom seen so many feeble arguments in one place. On countless occasions, those who so often try to disrupt comment threads here with a melange of spiteful ad-hom attacks and half-baked pseudo-science (one of them even sent me a vile email offering gratuitous and profoundly offensive medical advice, though he was not a medic, a sure sign of extreme desperation on his part) found themselves attacking official climate science.

To these I felt like replying: “Comrade, do you realize you are criticizing the Party Line? Do you not know the penalty for that?” Instead, I suggested they should address their concerns to the climate clique, not to me.

Official climatology’s error is grave. It has hitherto been assumed that, while a change in temperature, such as the small warming from adding the non-condensing greenhouse gases to the atmosphere, can induce a feedback response, the Earth’s far larger emission temperature somehow cannot.

The most significant objection to our argument came from Roy Spencer, who said official climatology defines a temperature feedback as an extra forcing induced by a change in temperature, but not by the original temperature itself.

That is indeed the definition. But merely because official climatology says white is black, we should not be too hasty in bidding farewell to white.

With respect, the question is not whether official climatology defines feedbacks in such a way as to exclude from the account the large feedback response to the Earth’s emission temperature, but whether in reality the emission temperature actually induces that large feedback response.

When I was in Moscow recently, presenting our result to members of the Russian Academy of Sciences, Professor Mojib Latif, an IPCC lead author, recommended a paper by several NASA authors, Lacis et al. (2010), who had run a general-circulation model in which they had removed all non-condensing greenhouse gases from the atmosphere and had studied how the climate would evolve over 50 years.

Their conclusion was that after 50 years with no greenhouse gases the Earth’s albedo would have risen from today’s 0.293 to 0.418, and that mean surface temperature would have fallen from 288 K to 252 K, a drop of 36 K, of which 9 K, they imagined, was the loss of directly-forced warming from the non-condensing greenhouse gases and the remaining 27 K was the loss of feedback response to that directly-forced warming.

What would the emission temperature be if the albedo were 0.418? The answer, assuming today’s insolation, is 243.3 K. Yet Lacis et al. said the equilibrium temperature with no non-condensing greenhouse gases would be 8.7 K higher than that, at 252 K. That is manifestly a feedback response to emission temperature, albeit an unrealistically low one.

Since we shall want to compare the pre-industrial and industrial-era values of the feedback fraction f, we shall take the 287.5 K surface temperature in 1850 as the equilibrium temperature for the pre-industrial calculation. And, when we come to the industrial-era calculation, we shall bend the argument rather too far in favor of official climatology.

Lacis says one-quarter of the [35.5 K] difference between 252 K and [287.5 K] [i.e. 8.9 K] is directly-forced warming from the non-condensing greenhouse gases, while three-quarters of the [35.5] K [i.e. 26.6 K] is the feedback response to that [8.9 K] of greenhouse-gas direct warming. Thus, Lacis takes the feedback fraction f to be three-quarters, or 0.75.

Then the 44.2 K difference between emission and 1850 temperatures comprises 8.7 K feedback response to emission temperature; 8.9 K directly-forced greenhouse warming; and 26.6 K feedback response to direct greenhouse warming.

According to our corrected method, f is a lot less: 1 – (243.3 + 8.9) / 287.5, or 0.123. In that event, the 44.2 K comprises 243.3 f / (1 – f) = 34.0 K feedback response to emission temperature; 8.9 K directly-forced greenhouse warming; and 8.9 f / (1 – f) = 1.3 K feedback response to direct greenhouse warming. That seems a more reasonable apportionment.

Now for the industrial-era value of the feedback fraction. Lacis says that for “the entire terrestrial greenhouse effect” and also for “current climate” the feedback fraction is 0.75. Not much nonlinearity there, then. But many commenters worry about nonlinearities, so we shall go overboard to accommodate them.

For our corrected method, we begin by noting that from 1850-2011 the IPCC’s estimate of total net anthropogenic forcing was 2.29 Watts per square meter; that the Planck parameter is 0.313 Kelvin per Watt per square meter; and that, therefore, anthropogenic reference warming before accounting for feedback was 2.29 x 0.313 = 0.72 K. Yet, since 0.76 K warming was observed over that period, our industrial-era feedback fraction, to first approximation, is 1 – 0.72 / 0.76 = 0.05.

However, commenters have asserted that the equilibrium warming will be perhaps 40% greater than the 0.76 shown in the temperature record, because some of the warming will have gone into the ocean, and may return to warm the atmosphere in a few decades.

In that event, our industrial-era feedback fraction becomes 1 – 0.72 / (0.76 x 1.4) = 0.32, or more than two and a half times the pre-industrial feedback fraction. That should handsomely allow for the nonlinearities in feedbacks whose omission from the original calculation several commenters complained of. In reality, the nonlinearity will be far less than this.

Armed with the probably much inflated industrial-era feedback fraction 0.32, we can derive Charney sensitivity (equilibrium sensitivity to doubled CO 2 concentration) by noting that the CMIP5 estimate of the CO 2 radiative forcing is 3.5 Watts per square meter, which, when multiplied by the Planck parameter 0.313 Kelvin per Watt per square meter, gives reference warming 1.1 K. Charney sensitivity is then 1.1 / (1 – 0.32) = 1.6 K, and not the 3.3 K that is the CMIP5 models’ current mid-range estimate.

Now for some questions which, in our submission, anyone who wishes to adhere to official climatology’s notion that emission temperature induces no feedback response must credibly answer.

Question 1: If, from Lacis’ model, the 8.7 K difference between emission temperature 243.3 K and equilibrium temperature 252 K with no non-condensing greenhouse gases is not a feedback response to emission temperature, then what on Earth is it?

Question 2: How is it that emission temperature of 243.3 K induces a feedback response of only 8.7 K (or 0 K if, notwithstanding Lacis’ result, you think emission temperature cannot induce any feedback response at all), and yet that the 27-times-smaller 8.9 K direct warming from the presence of the naturally-occurring, non-condensing greenhouse gases induces as much as a 26.6 K feedback response?

Question 3: Would it not be more likely that, as we find, the feedback response to emission temperature of 243.3 K is 34.0 K, while the feedback response to directly-forced greenhouse warming of 8.9 K is only 1.3 K, rather than Lacis’ 8.7 K and 26.6 K respectively?

Question 4: Since feedbacks are denominated in Watts per square meter of the temperature that induces them, how do the feedbacks know that they should not respond at all to the emission temperature of 243.3 K but that they should suddenly respond very strongly by quadrupling the 8.9 K directly-forced reference warming from the non-condensing greenhouse gases?

We have here made the most generous allowance for the points raised by commenters, and yet Charney sensitivity, at 1.6 K, is not a lot greater than the 1.2 K in the original article.

In my submission, then, there will simply not be enough global warming to require any mitigation measures at all. If we are right, this really is game over.

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