Guest post by Joe H. Born,

Here we simulate a “test rig” for illustrating the difference between Christopher Monckton’s approach to projecting equilibrium climate sensitivity (“ECS”) and what he says climatology’s approach is.  (ECS is the change in equilibrium surface temperature that doubling carbon-dioxide concentration would cause, and we use climatology as Lord Monckton does to refer to proponents of high ECS values.)  We will see that failure to employ standard feedback theory is not the cause of the high ECS values we see bruited about.

In a series of WUWT head posts that began with in March 19, 2018, and have continued through May 8, 2021, Christopher Monckton has been describing his theory that climatology makes the “grave error” of basing equilibrium-climate-sensitivity (“ECS”) calculations on perturbations rather than entire quantities. The theory in question had been adumbrated at 39:17 et seq. in a March 23, 2017, video billed as a mathematical proof that ECS is low.  He has expended thousands of words on describing his approach, but a concise summary is what his August 15, 2018, WUWT post on the subject called “the end of the global warming scam in a single slide.”

The following plot illustrates that slide:

The $R_1$ and $R_2$ values in that slide are what the equilibrium temperatures that 1850’s and 2011’s carbon-dioxide concentrations would cause without feedback.  Or, rather, they’re what Lord Monckton tells us that climatology believes those values would be.  $E_1$ and $E_2$ are what those equilibrium temperatures supposedly would be with feedback.

Lord Monckton claims to have identified a “grave error” in climatology’s approach to inferring ECS (“$\Delta E_2$”) from those four values and the without-feedback equilibrium-temperature change $\Delta R_2$ that doubling carbon-dioxide concentration would cause.  Climatology’s error, he says, is that instead of entire quantities it uses “perturbations” $\Delta E_1=E_2-E_1$ and $\Delta R_1=R_2-R_1$, making the calculation $\Delta E_2=\Delta R_2\times\Delta E_1/\Delta R_1$.  Climatology’s result is the ordinate of the above plot’s green cross.

But according to Lord Monckton that’s not the right approach.  The proper approach according to Lord Monckton is dictated by standard feedback theory and infers ECS from “entire” values $E_1$ and $R_1$$\Delta E_2=\Delta R_2\times E_1/R_1$.  Standard feedback theory, he says, would result in the red cross’s ordinate.

The reader will recognize the green cross as the result of standard extrapolation, which assumes little change in the curve’s slope.  But Lord Monckton seems to believe that the feedback theory used in electronic-circuit design requires the abrupt slope change required to obtain the red cross.

We use the circuit below to test that proposition:

Without the feedback path in which the box at the bottom is disposed the circuit would be a linear amplifier, and, since we’re going to assume that R1 through R4 are all 1-kΩ resistors, its gain would be unity.  Without the feedback path, that is, the output voltage Vout would equal the input voltage Vin.  So Vin corresponds to Lord Monckton’s no-feedback values R, while Vout represents its with-feedback values E.

Note that the feedback path’s input is the entire output Voutvalue.  As Lord Monckton put it, that is, “such feedbacks as may subsist . . . at any given moment . . . perforce respond to the entire reference signal then obtaining, and not merely to some arbitrarily-selected fraction thereof.”  What we’ll see is that projecting from perturbations instead of entire values nonetheless yields a better estimate.

We could in principle use any nonlinear electronic component for the feedback element, but for the sake of expository convenience we’ll assume that the feedback component we’ve chosen conducts no current when the voltage $V_\mathrm{f}$ across it is negative and that its current $I_\mathrm{f}$ increases with positive voltage in accordance with $I_\mathrm{f}=KV_\mathrm{f}^a$.  Here $K$ and $a$ are parameters so chosen as to make the relationships between the overall circuit’s output and input numerically match the pre-industrial and current relationships between the with- and without-feedback temperatures in Lord Monckton’s numerical example.  Such relationships can be approximated by, e.g., a diode-resistor ladder:

The feedback element’s VI curve is as follows:

That feedback curve gives the overall circuit the following relationship of input to output:

In a June 22, 2018, video, Lord Monckton contended that a government laboratory’s electronic “test rig” has shown that Lord Monckton’s theory “checks out,” i.e., that the ECS calculation should be based on entire quantities instead of perturbations.  Before we use the “single slide” values in this circuit to show that they shouldn’t, we’ll apply a larger no-feedback change to it to show where Lord Monckton gets his extrapolation slope:

As the red dashed line illustrates, his use of entire quantities rather than perturbations means that his extrapolation line passes through the origin.  The green dashed line represents using perturbations instead and therefore does not pass through the origin.  This fact seems to be Lord Monckton’s basis for contending that climatology assumes the absence of a feedback response the sun’s radiation.

Now we’ll take a close-up view of the smaller, “single slide” change:

We see that the green cross, which represents what Lord Monckton tells us is climatology’s approach, projects the circuit’s output much better than his approach does.  This is true even though “such feedbacks as may subsist” in our circuit “at any given moment . . . perforce respond to the entire reference signal then obtaining, and not merely to some arbitrarily-selected fraction thereof.”  So nothing about feedback theory requires us to abandon ordinary extrapolation.

This isn’t to say that climatology is right.  It’s just that climatology’s error isn’t what Lord Monckton imagines.

Note from Anthony: Personally I believe BOTH arguments to be wrong, for a couple of reasons. But I’ve allowed this post strictly for the purpose of debate.

1. The atmosphere has a chaotic component, with both long and short periods. Linear and nonlinear circuits can’t come close to modeling the atmosphere without having a noise component. It’s just as over-simplistic as the claims by some that we can model any planetary temperature from gravity and atmospheric lapse-rate.

1. Electronic circuits have additional non-linearity built in. For example, operational amplifiers themselves are non-linear internally. They vary their gain with ambient temperature as well as induced temperature from operation. Resistors often have tolerances of 5-10% from their assigned value (in the example above, 1Kohm +/- 10% = 900-1100 ohms) which unless you use special resistors that are high tolerance and temperature stable can’t really represent true linear response in the first place.
2. Seasonal and diurnal variation in Earth’s atmosphere, combined with weather, create a situation where trying to model the Earth’s temperature with an electronic circuit a fools errand. Just look at the variance on Dr. Roy Spencer’s recent graph of the lower troposphere. Looks like a resistor blew out in March and April 2021, doesn’t it?

On a smaller scale, the USA looks even more highly varied in March.

I simply don’t believe ANY simple electronic circuit is capable of accurately modeling atmospheric behavior. Hell, even uber-complex climate models can’t get it right.

via Watts Up With That?

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May 12, 2021