Guest essay by George White
Feedback is the most misunderstood topic in climate science and this misunderstanding extends to both sides of the debate. This is disturbing because the theoretical support for substantial warming cause by man’s CO2 emissions depends exclusively on the ability of positive feedback to amplify something small (3.7 W/m2 of forcing from doubling CO2) into something large (a 3C surface temperature rise).
What makes a 3C temperature increase relatively large compared to the forcing asserted to cause it is the difference between the equivalent emissions of a black body surface at the approximate average temperature of the planet (287K) and the equivalent emissions of a surface 3C warmer. Based on the Stefan-Boltzmann Law, the difference in equivalent emissions exceeds 16 W/m2 and for that surface to emit this much more, it must be receiving an equal amount. Independent of the specific origin of the more than 12 W/m2 of required surface input in excess of the 3.7 W/m2 of input forcing, the amplification required exceeds a factor of 4. One thing that’s clear is that the atmosphere has no internal sources of power, thus all of the power driving the 12 W/m2 of additional surface emissions must be coming from feedback. This fact alone is sufficient to falsify claims of a high sensitivity since it’s impossible for 3.7 W/m2 of stimulus entering a passive system to result in more W/m2 of feedback than it provides as input unless Conservation of Energy is violated. Climate science obfuscates this contradiction by considering only temperature and not the equivalent emissions of a temperature, thus a sensitivity of 0.8C per W/m2 sounds plausible, yet in terms of joules, 4.3 W/m2 of incremental surface emissions per W/m2 of forcing does not, especially considering that each W/m2 of incident solar energy results in only 1.6 W/m2 of net surface emissions.
Theoretically, positive feedback can provide the required amplification, but only if the system being modeled conforms to the many assumptions that predicated Bode’s control theory, originally developed in the 1940’s as a tool for designing linear amplifiers using vacuum tubes.
Hansen was the first to apply Bode’s analysis towards quantifying climate system feedback in his 1984 paper. Schlesinger quickly followed with a paper to ‘correct’ some of Hansen’s errors but actually made it worse. This faulty analysis has been canonized by the IPCC since AR1 and the few related papers that followed simply restate Schlesinger’s analysis using different variable names. An example is Roe’s 2009 paper on climate feedback which will be referred to below.
While Bode’s analysis provides the framework to achieve the required amplification, it can only do so under the specific conditions outlined in the first two paragraphs of his book. One of these conditions is the requirement for linear behavior between the input and output of the modeled network and another is the presence of linear vacuum tube elements with an implicit power supply that provides active gain which add energy to the output above and beyond what’s supplied by the input stimulus.
It should be self evident that the Hansen/Schlesinger mapping to Bode violates both of these preconditions. First is that the input to the feedback network is forcing, expressed in W/m2 while the output is in temperature, expressed in degrees K and that the relationship between W/m2 and degrees K, as given by the Stefan-Boltzmann Law is very non linear. When the relationship between the input and output of an amplifier becomes non linear, Bode’s formulation no longer applies and the gain becomes a function of the input rather than being strictly a function of the open loop gain and feedback. An example of this is when an audio amplifier starts to clip. The open loop gain and feedback remain constant, yet the closed loop gain steadily decreases as the input increases.
If a stimulus is applied to a complex, yet completely passive RLC circuit, all the nodes will wiggle, but this can never be considered equivalent to the behavior of an active system. Bode’s assumption of active amplification is not relevant to the climate either. Many confuse the dynamics of weather as an indicator of an active system, but in the context of Bode, active and passive have very specific meanings. Passive means that there are no other sources of input other than the stimulus, which for the climate is the W/m2 of forcing arriving from the Sun, while active means the system has powered gain driven by an implicit, internal power source. An important result of Bode’s analysis is that a passive system is unconditionally stable which precludes the possibility of runaway positive feedback.
The difference between a passive system and an active system is like the difference between manual steering and power steering. Manual steering is a passive system that achieves force multiplication (gain) by a combinations of gears, levers and pivots as energy is conserved between the steering wheel and the tires. Power steering is an active system that positively reinforces arm muscles by adding energy to the system from a hydraulic power source driven by the engine. The climate is a passive system that manifests surface temperature amplification by delaying surface emissions and returning them to the surface some time in the future where they are combined with new incident power from the Sun. It’s these joules of energy being delayed and returned back to the surface that comprises the physical manifestation of climate system feedback. This feedback is tangible, which for the climate is expressed in W/m2 which are added to the new input from the Sun also quantified as W/m2. Watts are joules per second and first principles requires joules to be conserved.
Bode’s feedback model removes the requirement of Conservation of Energy between the input and output of the system. This is the result of assuming an external power supply will provide as much output as required. This isn’t valid for a passive system like the climate where solar input is the only source of power and thus COE must be accounted for. Unlike an active amplifier which measures the input and feedback to determine how much output to deliver from an unlimited source, a passive system consumes its input and feedback to produce its output. Disconnecting the input and output from the requirements of COE makes sensitivities that violate COE seem plausible and this is the only reason that such an unreasonably high sensitivity can be accepted. When COE is added to the analysis, the maximum possible sensitivity becomes less than the lower limit claimed by the IPCC.
Technically speaking, the model proposed by Hansen called the system input a change in forcing and its output a change in surface temperature. For the linear systems modeled by Bode’s equations, the absolute and incremental gain are the same and independent of the magnitude of the input or output. For the climate system feedback model, this is an invalid assumption owing to the non linearity between W/m2 of input and degrees K of output, where the ratio of a change in output temperature per change in input forcing depends on the starting temperature. To get around this, it’s asserted that the system is approximately linear, but the feedback formulation sets the reference temperature to 255K and while the relationship between power and temperature is approximately linear on either side of 255K, the current surface temperature of 287K is too far from the reference for the assumption of approximate linearity to be approximately true.
The reason its been so hard for climate science to get this right is that there are many co-dependent and reinforcing errors in the mapping from Bode to the climate system which confuses many into thinking that the model is reasonable. However; without these errors, Bode’s model simply can not support the required amplification. Without this support for substantial climate change caused by man, the IPCC and the self serving consensus driven by its reports collapses and to many on that side of the argument, this is an unfathomable consequence, especially given the political ramifications.
In addition to failing to honor the prerequisite assumptions made by Bode, there are other errors regarding how Bode’s variables were mapped into climate related variables. This led to an arithmetic error that provided faulty support for a potentially high sensitivity which was never questioned due to confirmation bias. This arithmetic error has to do Hansen’s failure to understand the difference between the what Bode calls the feedback fraction and what he calls the feedback factor and this 3 decade old error is still with us today.
The feedback fraction is the fraction of output fed back to the input and is a dimensionless fraction between -1 and 1 spanning a range from 100% negative feedback to 100% positive feedback. The 100% limits arise because you can not feed back more than is coming out of the system in the first place.
Bode defines the feedback factor as the reduction in the open loop gain that arises as the result of feedback. This arises from Bode’s gain equation which he states as,
ER = E0 μ/(1 – μβ)
Where E0 is the input to the system (forcing), ER is the output of the system (the surface temperature), μ is the open loop gain (reference sensitivity, λ0 per Roe, 2008) and β is the feedback fraction which corresponds to feedback coefficients expressed with units of W/m2 of feedback per degree K. Bode labels the closed loop gain eθ which is calculated as eθ = ER/E0 = μ/(1 – μβ) and calculates the feedback factor as eθ/μ = 1/(1 – μβ) which is the reduction in μ that results from the application β. The most important aspect of this equation is the μ on both sides of the equals sign. Bode then makes a simplification assuming that μ >> 1 and β < 0, both of which are true for linear amplifiers and asserts that μβ by itself can also be considered the approximate ‘feedback factor’. Modern amplifier design ignores this altogether as the effective μ of modern amplifiers is on the order of many millions and as μ approaches infinity, μ/(1 – μβ) approaches -1/β (the feedback fraction) and the feedback factor becomes infinite.
To adjust the gain equation for COE, the power applied as feedback, Erβ, must be subtracted from the output since feedback power can not also contribute to the available output. The gain equation that is applicable to the climate becomes,
ER = E0 μ/(1 – μβ) – Erβ
Climate science incorrectly considers λ0 times an empirical coefficient, c1, as the metric to quantify feedback, considers their product to be equivalent to Bode’s μβ and calls this the ‘feedback factor’. Again, Bode’s assumptions were not honored since the climate system μ is very close to 1, and in fact is exactly 1 for an ideal black body, thus the feedback factor would really be 1 – λ0 c1. While a compensating error added the 1 back to the equation, it didn’t fix the misunderstanding that led to the arithmetic error in the first place.
The arithmetic error arises when to get the units to line up and ostensibly conform to Bode, Roe defines the feedback factor f = λ0c1 (per Hansen and Schlesinger). If the sum of the input and feedback (the input to the gain block) is J, the output of the gain block is J*λ0. Roe’s assignment of the feedback factor infers that that c1 = f/λ0. Multiplying the output of the feedback network by f/λ0 (c1) produces a feedback term equal to Jλ0f/λ0. The λ0 cancels leading to a feedback term quantified as Jf, where f becomes equivalent to Bode’s β when μ is 1 and quantifies both the fraction of output and the fraction of J returned as feedback. The specific arithmetic error is assuming that the open loop gain is both λ0 and 1 at the same time. This is illustrated in figure 1.
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Figure 1
To illustrate the problem further, what μβ is actually quantifying is the post feedback influence of the input of the gain block, J, since the μ term amplifies the input while β takes a fraction of it and returns it as feedback. Conventional climate system feedback assumes that μβ is quantifying the effect feedback has on the output which is only true when μ is 1 and the input and output of the gain block are the same. A more accurate block diagram that represents the consensus climate science feedback model is shown in figure 2.
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Figure 2
Since the relevant open loop gain is a dimensionless 1, the output of the feedback network must be dimensionally the same as the input otherwise the input plus some fraction of the output can not be summed. The result is that what climate science calls the pre-feedback sensitivity, or the open loop gain, λ0, is no more than a scale factor applied to the required output in W/m2 converting it to a change in temperature. In other words, λ0 is outside of the feedback loop and unaffected by feedback, positive or negative. Calling λ0 the sensitivity before feedback is incorrect because it has nothing whatsoever to do with the feedback loop being modeled whose gain (sensitivity) is what’s being quantified.
This leads to another error which is with Roe’s calculation of the system gain, which he considers equivalent to Bode’s closed loop gain, eθ. He calculates this as the ratio of two sensitivities. The post feedback sensitivity divided by the zero feedback sensitivity. This implies that feedback amplifies the sensitivity which is not what Bode’s model is modeling. It models the amplification applied to an input stimulus to produce an output, where the input is forcing and the output is temperature. While feedback and gain are related, this is a fixed relationship and its the result of this fixed relationship that Bode is modeling. Climate science unfixes this relationship and considers Bode’s analysis to apply.
The justification for calculating the closed loop gain in this way comes from Schlesinger, who rationalized that gain could have dimensions because the ratio of gains is dimensionless. Of course, this assumed that the feedback network was modeling a sensitivity input and a sensitivity output, where feedback was modifying the resulting sensitivity while what is actually being modeled is how the surface temperature is affected by incremental forcing and not how feedback is affecting the sensitivity.
Had Hansen and Schlesinger gotten this right in the first place, CAGW would be a footnote warning about jumping to premature conclusions and not an extremely expensive and divisive political issue with either a for or against position in nearly every political platform in the world.
In conclusion, there can be no doubt that the mapping from a Bode feedback system to the climate is irreconcilably broken. Without the ability to claim amplification from large positive feedback, the IPCC looses the only theoretical basis it has for its overstated sensitivity and unless someone invents new physics that transforms 1 W/m^2 of forcing into 4.3 W/m^2 of surface emissions and that doesn’t violate Conservation Of Energy, claims of catastrophic effects from CO2 emissions will become as quaint as an Earth centric Universe.
References
1) IPCC reports, definition of forcing, AR5, figure 8.1
2) Bode H, Network Analysis and Feedback Amplifier Design
assumption of external power supply and active gain, 31 section 3.2
gain equation, 32 equation 3-3
real definition of sensitivity, 52-57 (sensitivity of gain to component drift)
2a) effects of consuming input power, 56, section 4.10
impedance assumptions, 66-71, section 5.2 – 5.6
a passive circuit is always stable, 108
definition of input (forcing) 31
3) Hansen, J., A. Lacis, D. Rind, G. Russell, P. Stone, I. Fung, R. Ruedy, and J. Lerner, 1984: Climate sensitivity: Analysis of feedback mechanisms. In Climate Processes and Climate Sensitivity, AGU Geophysical Monograph 29, Maurice Ewing Vol. 5. J.E. Hansen, and T. Takahashi, Eds. American Geophysical Union, 130-163.
4) M. E. Schlesinger (ed.), Physically-Based Modeling and Simulations of Climate and Climatic Change – Part II, 653-735
5) Michael E. Schlesinger. Physically-based Modelling and Simulation of Climate and Climatic Change (NATO Advanced Study Institute on Physical-Based Modelling ed.). Springer. p. 627. ISBN 90-277-2789-9
6) Jerard Roe. Feedbacks Timescales and Seeing Red, Annual Review of Earth Planet Science 2009, 37:93-115
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I would like to offer another explanation of passive vs. active as this seems to be confusing for many of you.
If you have only an input stimulus and rectify it to supply power for an op amp, will you ever be able to get more power out of the op amp then it receives as stimulus? COE says NO
Now, replace the rectified input with an external supply, Yan more power come out than goes in now? COE no longer applies, so YES
In a nutshell, this describes the COE constraint that is not being honored by the climate science feedback model.
George
It’s been a lot time, but I disagree on what you call the input stimulus vs output drive power.
The Sun supplies output drive power directly, and indirectly into a high input impedance control input.
Consider no air asphalt on the equator at the max temp as full solar power, and the atm with albedo reducing it.
I say this not because I think they have correctly described climate as an electronic circuit, but because I believe you can replicate most any transfer function with electronics.
co2isnotevil, the Sun is a constant current source (W/m2)), not a constant power source (W hr/m2 or joules/m2).
Temperature is the amount of heat held in a substance times its “specific heat”. The amount of heat in a substance is the integral on the heat received (W hr/m2) minus the heat loss by conduction and radiation. When considering the Sun as a constant current source, the amount of heat absorbed is simply the integral of what the Sun provides. In this way, substances can be modeled as capacitors (where voltage is the integral of the current times a constant).
Assuming that heat is not loss via conduction or radiation, the maximum temperature a substance can obtain is infinite. It is the negative feedback, the loss of heat by various means, that limits the maximum temperature.
With respect to your model, op amps are powered by voltage sources, not current sources. Also, in the most general sense, they are voltage amplifiers, not current amplifiers – additional components are usually added to convert a control voltage to a current.
Perhaps a better way to explain (model) this is as a power supply. In this case the input current is used to power the supply and the output voltage is fed back (sampled) to control the output voltage. Obviously, the output power will be less than the input power, but the voltage could be anything. Using just a 12V battery, it is possible to create a power supply that outputs from much less than one volt to many hundreds of thousands of volts.
Not necessarily, if we consider the controlling element (The atm) A shutter, it could let more energy in, we know all of the Sun’s energy is not entering the system.
And for the same reason, the Sun is not a constant “current” source. You could consider it’s temperature a voltage and the difference between the Earth and Sun drives a current that is regulated by our atm, which regulates surface temp.
micro6500,
The shutter concept is albedo feedback. Albedo feedback must be specifically excluded from this feedback analysis since it’s already fully accounted for by how forcing is quantified. The IPCC defines forcing as a delta flux at TOA which already includes the effects of reflection by albedo. It’s a somewhat disingenuous metric since it obfuscates the apparent negative feedback from clouds and this is not the only problem with the way forcing has been defined.
Another problem with the IPCC metric of forcing is that an instantaneous W/m^2 of incremental, post albedo solar power is considered equivalent to an instantaneous W/m^2 reduction in LWIR emissions at TOA consequential to increased GHG absorption. In the former case, all of the W/m^2 affects the surface temperature of the planet, while in the later case, some fraction of the instantaneous absorption will be emitted from the planet in the steady state (about half) and not contribute to the surface temperature.
George
In this case, I don’t care what the ipcc say, they have no background in electronics (Or so it seems), nor do they have 15 years of making simulatable circuits and the models they require.
Both albedo, and cloudiness can make big differences in incoming power.
You could spend years arguing about how the ipcc does things. They do things that are self-serving, so don’t count on them being lucid.
“Both albedo, and cloudiness can make big differences in incoming power.”
Yes they do and this is another failure of the consensus feedback model which takes forcing as input and based on how forcing is defined, already includes the NET feedback effects from albedo variability. There’s so much wrong with the self serving climate science ‘consensus’ driven by IPCC reports its scientifically perplexing how any of this garbage ever got past peer review. That any of it did tells me that that there’s no science climate science and its peer review is about as effective as a boat with a giant hole in it. I doubt this is news to most here, even those on the warmist side, although I doubt any of them has the courage to admit this.
To be clear, the effects of clouds are LIKE positive feedback 0C. I emphasize LIKE because it’s not feedback in the Bode sense as should be pretty clear by now, but LIKE feedback where the equivalence of positive feedback is to warm the surface while negative feedback cools it.
The reason is that below 0C, the surface is covered in ice and snow and has the same reflectivity as the clouds (or perhaps even more reflective) thus the net effect of clouds is to hold heat at the surface making it warmer than it would be otherwise. Above 0C, clouds are more reflective than the surface and incremental clouds also reflect energy promoting cooling. When you quantify these two effects, they are nearly balanced across the planet and the net effective feedback from clouds is close to zero.
Robert.
Whether you treat the Sun as a voltage source or a current source is irrelevant. Volts and amps are linearly related to each other and in the final analysis a current is just a voltage drop across a resistance.
The basic problem with considering the Sun as the implicit power supply of Bode is that the energy from the Sun is already accounted for as contributing to the forcing input to the model and to consider it the power supply as well is to count it twice.
It’s crucially important to understand the difference between a passive system, like one containing only resistors, capacitors and inductors and an active system that contains tubes, transistors or op amps with their associated implicit power supplies which enables the system to manifest power gain, i.e. violate COE between the input and output. The climate system is the former and not the later as assumed by the feedback model adopted by climate science.
Yes it is critical. You seem to miss out that the atm is active, it isn’t just a passive system.
And the whole system is powered by the Sun, but the Sun isn’t the input into the active stage. The input is a summation of various surface effects(including a input signal based on solar), these can alter both cloudiness and albedo, both of which give it active control.
“You seem to miss out that the atm is active, it isn’t just a passive system.”
Bode has a very specific definition of passive and the climate system meets that criteria. NO INTERNAL SOURCES OF ENERGY. Refer to Bode page 108. The forcing input form the Sun is not an internal source of energy, while the implicit power supply of Bode is. It’s a subtle, but very important distinction.
Dynamic behavior must not be confused with active gain. Climate science has bungled this for far too long and when corrected, the whole CAGW concept crashes and burns in the fake heat it imagines.
As I requested before, please provide a link.
The following is from Active Versus Passive Devices
Since greenhouse gases and clouds affect the flow of IR radiation thru the atmosphere, it is proper to consider the system as “active”.
Robert,
You can download Bode’s book from here, or you can just google Bode for other sources.
https://archive.org/details/NetworkAnalysisFeedbackAmplifierDesign
Pay special attention to the first 2 paragraphs, page 32, page 108 and the pages around them.
SCR’s and TRIAC’s are switches that can select between 2 alternatives and do not provide active gain in the context of Bode. Tubes, transistors and op amps all have an implicit power supply that the climate lacks. In a strict sense, passive means that the accumulate output power is limited to the accumulated input power received. Feedback can contribute to the accumulated input power, but it can not also contribute to the output of the system. As Jeff pointed out, this partitioning is required to be consistent with Kirchoff’s Law, which I just consider another requirement of COE.
Only in a resister. Voltage across a capacitor is related to the integral of the current, with an inductor, to the derivative.
A battery can be modeled as a voltage source in series with a resister, or as a current source in parallel with a resister. However, a current source can not be modeled with a voltage source. Therefore, in this case, it does matter because matter stores heat like a capacitor stores electrons, and because the temperature of the Earth has no effect on the amount of electromagnetic radiation coming from the Sun.
It’s not a constant current source either, because changing the flow to earth also doesn’t alter the forcing to keep it constant.
But also it could be described as a voltage source with other parallel loads.
Robert,
“Only in a resister”
No. Capacitance and inductance have an imaginary component of resistance called reactance, where impedance is the magnitude of the real and imaginary components of resistance.
This is the whole point of doing the analysis in the S domain (or the discrete time Z domain) since capacitance and inductance becomes ohms of impedance which can be analyzed with Ohms Law rather than Farads or Henries which must be analyzed with simultaneous differential equations.
co2isnotevil, thank you for the link. I was not able to find that on my own.
Page 108 states
and I agree with that. However, he never defines an active network. The best I could find is that, on pages 5, 73, and others, for passive circuits the impedance is the same forward and backward thru the circuit, but for active circuits it is not. Therefore, by this definition, diodes SCR’s and TRIAC’s would be active.
On page 188 he implies that devices with poles in the right hand plane are active and are modeled as passive networks with either a voltage or a current source on the output. Notice, these active components do not actually contain a power source, only their models do. (I have had to paraphrase this, the text is not that clear.) As a result, and by analogy, anything that emits thermal radiation would be considered to be an active device.
This is actually a powerful concept – it means that circuit modeling programs could be used to model the planet.
Yes. While you could use it to add clarity and rigor, it would just be way to slow.
Now, you might be able to use it to create a more validated abstraction of a circuit model.
More interesting is that you could build it in hardware. Where hardware because a problem is it would be hard to make adjustments
Robert,
“he never defines an active network”
Active is the opposite of passive.
In the first paragraph of his book he states:The first sentence in chapter 1 of Bode’s book states,
“The networks to be considered consist of ordinary lumped
inductances, resistances and capacities, together with vacuum tubes.”
It goes on to say,
“For purposes of discussion the tubes will be replaced by equivalent
structures consisting of ordinary circuit elements connected between
the accessible terminals, together with a source of current or voltage
to represent the amplification of the tube.”
The key phrase here is “together with a source of current or voltage to represent the amplification of the tube.” This is absent from his definition of passive.
My argument regarding your position is about this topic. BTW, op-amp transfer functions didn’t originally include a power supply, later it was added to model it’s load on the supply, and at some point to put a limit on output voltage, but the transfer function doesn’t care.
But, you keep saying it can’t be active because there is no supply, I disagree, there is very obviously a supply, it’s only when defining circuit topology you draw it outside the circuit. But the Sun is the power supply, and the atm is one of the possible “valves” regulating power to the planets surface.
When you define the circuit like this, the feedback and bias signals can be amplified in some function into the output, how much the ground and surface air warms.
The whole type of supply is immaterial, consider it a battery tossed into a saltwater pool, and the planet is in the current path, it basically doesn’t matter.
What does matter more is it’s a dynamic system, and the 240W/m^2 averages does not do the circuit any justice, nor the analysis of what is actually happening.
“But, you keep saying it can’t be active because there is no supply”
No this is not what I am saying. I’m saying that its not active because is has no power supply that can add joules to the output above and beyond the joules supplied as input. In other words, the climate does not exhibit POWER GAIN.
You do understand that there is no requirement for COE between the input and output of an op amp, so why do you think this also applied to the climate?
Because you are misidentifying the input, vs the power source input powering the circuit.
The input into the climate “circuit” is not toa, the power supply input to the circuit is toa.
Circuit input and output is near the surface, not near space.
micro6500,
you said,
“The input into the climate “circuit” is not toa, the power supply input to the circuit is toa.”
Incorrect, at least relative to how Bode was mapped to the climate system by Hansen, Schlesinger, Roe and a few others. The input to the model is forcing which is defined at TOA and the output is temperature. If you can only think about it as no signal input and only a power supply input, fine, or even a power input connected to the signal input, but that’s not what the climate system feedback model is modelling and its not what Bode is modelling, moreover; the requirement for COE relative to the output is still present and its this COE requirement that climate science is ignoring.
You can think of the Bode model as having a second, implicit input which is the power supply input to the amplifier. In its basic form, the Bode model assumes that this implicit connection can supply all of the power required by the output as dictated by the open loop gain time the input across a arbitrary load impedance (even zero!).
obviously not how I would do it.
But that said it is fundamentally acceptable. They are still using energy from the Sun to power the gain in the output. No COE violation.
I know you want to show they are wrong and exclude this point from them, but the circuit topology is not flawed because there isn’t energy to provide gain. There is a way to provide the required power, it just lets more of the Suns power into the system, I don’t know that it actually does this, but it could, you can’t just exclude it for the “no power” reason.
micro6500,
Please explain the physical process in the climate system that provides the infinite power gain assumed by Bode’s model. If you can identify this and patent it, you will become rich as the inventor of free energy. If you don’t see how Bode’s model is assuming infinite power gain, then you don’t understand his model.
It’s only an approximate model that makes many, many simplifying assumptions to make the analysis easier and among these simplifying assumptions is that of infinite power gain. Most of these simplifying assumptions do not apply to the climate system. How else do you think the consensus can get away with a sensitivity that is such an obvious violation of COE? That is, the absurd claim that positive feedback amplifies 3.7 W/m^2 of forcing into more than 16 W/m^2 of incremental surface emissions to manifest the claimed 3C rise.
You also seem to be confusing the modelled behavior with the actual behavior. Of course COE must be observed in the real system and this is my point, the model used does not. The Bode model assumes that COE is not applicable between the input (forcing) and output (temperature) of the model because it assumes an implicit power supply that can provide more joules of output than are provided as input.
And it does, the Sun provides any required additional power. Enough to easily make desert temps +130F
“Sun provides any required additional power”.
You didn’t answer my question, so let me ask again in terms of your recent response.
How does the Sun provide additional power beyond what it provides as stimulus?
Also, do you understand the difference between the stimulus, which the Bode model EXPLICITLY accounts for and the power supply which the Bode model IMPLICITLY assumes?
Here, http://www.analog.com/library/analogDialogue/archives/35-02/avoiding/index.html
Pick any of the single supply options and substitute the Sun for VS
I made my living explaining how to model circuits like this 30 years ago to EE’s.
“Pick any of the single supply options and substitute the Sun for VS”
OK. If the Sun is VS, then what is Vin? If you think its both, then how can Vout deliver more output power than arrives to the combination of Vin and VS?
If the load on Vout demands more power than is available as Vin, even if rectified and turned into VS, the system goes non linear operation and Bode no longer applies because VS is no longer constant and the gain becomes dependent on the input. It seems that the problem with simplifying assumptions is that they can be misinterpreted as being unconditionally true.
My point is not that you can’t rectify the stimulus to power the op amp, but that the result will not produce power gain and infinite power gain is assumed by the Bode model used to represent the climate and that infinite power gain is required to support runaway effects and the absurdly high sensitivity claimed by the IPCC.
Vin are the various effects of absorbed SW, for instance water evaporates and turns into clouds which alter the amount of SW that makes it to earth.
Stop worrying about the input power, no one is trying to get power from the signal.
“Stop worrying about the input power, no one is trying to get power from the signal.”
Except that this is what the Bode model, as applied to the climate system, is doing. You can’t ignore the limitations imposed by conserving power and energy. This is what climate science is doing and is why it is so wrong and you are just extending this same flawed approach.
I can’t speak to what anyone else is doing or not. But, there is 30 to 50% of the Sun’s energy that is not being used that is available to provide power while preserving COE.
There is no power/COE issue.All of this unused energy can be tapped to drive the climate.
I’ve even given you real circuits that are self biased, all active circuits, all powered by a single power input, the signal could be any type of internal feedback, ie water evaporating and becoming a cloud. The energy evaporating the water could regulate a much larger amount of energy, circuit gain.
And we know this process in nonlinear, another sign of an active circuit.
Remember I did exactly this sort of thing for almost 15 years evangelizing circuit simulation.
micro6500,
You said,
“it’s a dynamic system”
A dynamic system is not an active system, even though you perceive activity. Bode is very specific about what passive means and very specific that his analysis ASSUMES an IMPLICIT power supply that can provide joules to the output in excess of the joules provided as input and that the Bode amplifier assumes active power gain that is not a property of the climate system. Why is this so hard accept?
Consider an RC circuit with a resistive load attached. If the impedance is low enough and voltages high enough, you can drive this with megawatts of sine wave input power, but the power delivered to the load will always be less than the power driving the circuit. Is this an active circuit or a passive circuit?
Now, consider an RF amplifier that requires 100 W of input to produce 10KW of output. The input is 100 W, but absent the IMPLICIT power supply, the amplifier can not deliver more than 100 W to its load. Turn on the power and voilà, the output jumps to 10 KW and the load on the implicit supply is > 10 KW.
The feedback model explicitly accounts for its input, but the power supply is ASSUMED and with regard to the basic Bode gain equation is ASSUMED to be infinite. Yes, you can put limitations on the available supply power, but this is not accounted for by Bode’s basic gain equation which climate science incorrectly applies to justify the idea that positive feedback can amplify something small into something big.
It has an implicit supply.
Just to give a bit of background, I spent from 1983 to 1997 explaining circuit simulation to EE’s, proving they worked, even with their quirky analog circuit they all had to try and trick the simulator up. It also included supporting them as they were designing their products, and had a question on why it did whatever it was doing. I spent 14 years doing this, even when they couldn’t actually show me the circuit, I helped them.
You’re messing up your circuit, it is active, it has a power source.
co2isnotevil,
And the reactance is frequency dependent and produces a phase lag. At near DC, we use differential equations and time constants.
However, you have a point – when modeling a few thousand years at a time, the reactance model might give very good results. On the other hand, my current focus is trying to model a single day and (in my opinion) reactance is the wrong approach.
You shouldn’t, there is definitely a multi-month delay as heat is stored in exposed surfaces (dirt, concrete, buildings, etc).
But I laud your studying the daily solar input, and the planet’s response (you are studying they daily response aren’t you?)
“trying to model a single day … reactance is the wrong approach”
Consider the input from the Sun to be a periodic signal and the sum of sin waves representing diurnal and seasonal periodicity (Fourier tell us that any periodic signal can be decomposed in to the sum of sin waves). Superposition must apply in the power domain a consequence of COE, so Laplace transforms and the rest of the math applied to analyzing systems by impedance can be leveraged forward as long as the input and output of the system is expressed in units linear to joules (i.e. W/m^2).
micro6500 and co2isnotevil, your comments with respect to cycles and phase delay are correct. However, the response time of a cloud passing over is much shorter than a 30yr climate model. In particular, I want a model the explains the long wave radiation seen at the surface and from orbit. To put it bluntly, in my opinion, the models currently available (that I’ve seen) don’t! In fact, they are not even close.
Consider a centrifugal governor – When the engine spins too fast, the governor reduces the input power and the engine slows down. When it moves too slow, the governor increases the input power and the engine speeds up. This is basic negative feedback – the governor tries to keep the engine speed constant.
In the climate, when the Earth heats up more greenhouse gases enter the atmosphere causing the Earth to cool down. When the Earth cools, there is less water vapor and the planet warms (except at the poles). If adding more greenhouse gases caused the Earth to warm, then we would have had runaway a long time ago. In this way, greenhouse gases act as a governor providing negative feedback.
Except … the Stefan-Boltzmann relation also provides negative feedback. As a result, it is possible for the greenhouse gases to actually provide positive feedback which is overpowered by the SB feedback.
What I am trying to develop is a collection of short term models to determine what is actually happening. It is absolutely clear that the overall system is dominated by a negative feedback. And I have extremely good evidence that the greenhouse gas feedback is negative, but that partly depends on what the system “output” is. In fact, there are many possible “outputs” – temperature of the surface, the temperature of the atmosphere, the lapse rate, and many other parameters.
I’ve watched they both come and go, but and we get days that start off completely clear, grow lots of cumulus clouds, then they disappear during the evening.
As I’ve mentioned other places, something slows radiative cooling on clear breezeless nights, as air temps near dew points. Then cooling rates drop by 80%. This is what controls night time cooling, not co2.
Robert,
Take a look at the plots here. They represent the measured transfer functions between various climate variables as reported or otherwise extracted from the ISCCP data set.
http://www.palisad.com/co2/sens
The smaller dots are monthly measurements of one attribute against another for constant latitude slices of the planet. The larger dots are the averages of all monthly measurements spanning about 3 decades for the same slices. Connect the larger dots together to form the measured LTE transfer function. This does not imply which is causal to which, although in general, everything is causal to the input stimulus arriving from the Sun.
Nearly all of this information gets cancelled out of anomaly analysis which is a significant obfuscation since observing how the planet responds to very large seasonal changes is trivially extrapolated to the LTE response to smaller changes once you can determine the relevant time constants.
co2isnotevil,
Thanks for the definition – I had read that but was not able to find it again – paragraph 1, exactly where it should be. (I was searching for “current source” not “a source of current”.)
I think the following supports my position that active models have an internal power source.
When a rock has heat, it radiates IR. In my opinion, that is enough to qualify it as an active component. Granted, the heat originally came from somewhere else – just like a battery is charged via a power supply. And just like the battery supplies power for an active circuit, the rock supplies energy to the Earth’s climate system.
I think our disagreement is related to power (W/m2) vs heat (work, energy – joules). Heat is related to the integral of power – temperature is related to heat, not power. My idea is to model everything that can store heat as a capacitor and the transfer of heat with a transfer function. For conduction of sensible heat, a resister makes sense. Latent heat (phase change) is a resister (to reach the transition temperature) and a capacitor plus a transfer function (rate of phase change) I can’t find a reference for. For Stefan-Boltzmann radiation, the function would be modeled as a custom temperature-controlled current source, ie, an active component. And so forth (yes, there is more).
At any rate, the purpose is to determine which parameters CO2 affects and to run the model with different values.
“that is enough to qualify it as an active component. ”
The rock in this context is just a black body radiator. Energy stored in the rock by absorption is no different than the energy stored in a charged capacitor. In the context of Bode, both are passive.
There’s no internal source of energy in the rock. If there was and you took the input power away, it would stay hot and perhaps even get warmer, but instead, it will eventually radiate all of its energy away and its temperature will drop to 0K.
http://www.palisad.com/co2/sens
Thanks – but way too much data without a guide or tutorial. Also, each chart needs a description explaining how to reproduce it. They are probably obvious to you, but I have no clue.
I agreed with that in my previous post.
The same can be said for a transistor or vacuum tube, but you have a good point.
I originally tried to model the system using only passive components, but I couldn’t figure out how. By implementing the Stefan-Boltzmann relation as a current source “solved” part of the problem. Therefore, the system is active … unless you can suggest a completely passive method to solve that problem. One technique I tried was to use the difference in two temperatures (each to the 4th power, of course). I dropped that because I thought it would be easier to model a capacitor and current source as a single 3-pin component than to model a special non-linear 2-pin resister, assuming a constant emissivity.
I guess the point is – Can the climate system be modeled using only passive 2-terminal devices?
If it can – then “passive” is the answer.
Perhaps the real question is – How should we model the components related to the greenhouse gases? Their emissivity depends on temperature, pressure, and the number of available molecules. Since the emissivity is the parameter defining the non-linear SB resister, the only way I can think of to make it a variable requires a 3-terminal device. Can you suggest a passive configuration to model these?
I don’t see anyway to do it without active devices.
My thoughts were to do it like they do for gcm’s, make a multi-input summer/amp for each layer on your grid.
You’d have one for oceans, different surface types, then the first layer of air, followed by more air layers until space. Then you can turn the transfer functions for the outputs for each layer, then stack and connect them all up and see if it will initialize, if you can get numerical stability.
But it’ll be hard, and you might be better off just writing in FORTRAN or whatever. You should also really study up on gcm’s, probably a lot you can learn from them.
Also, I believe the temperature series are corrupt, and making a model based on them isn’t useful, though you will get people applauding you if you do, I just think it’s already wrong if you do.
On that note I can provide data on what was measured for the various surface stations, and will help you if I can, so if you need something specific from the surface data, I’ll try and generate it for you.
” I believe the temperature series are corrupt”
I do as well, so I don;t rely on GISS temp or other reconstructions based on surface measurements and only rely on temperatures extracted from satellite data.
Robert,
“The same can be said for a transistor or vacuum tube”
It’s only passive until you connect it to an implicit power supply, then it becomes an active amplifier that can provide power gain.
The best you can do to model the climate with passive devices is to consider the planets energy storage as a capacitor. You can think of energy stored as being stored between the warm surface water ‘top plate’ and the deep ocean cold ‘bottom plate’ where the thermocline is the dielectric. You need an asymmetric charge/discharge path since the planet’s charging time constant seems to be longer than its discharge time constant (a consequence of net negative feedback) and which you can implement with diodes, but what this really shows is that the time constant is not a constant, but has a dependence on the surface temperature. A better approach to leverage circuit analysis techniques is to apply a Laplace transform to the RC circuit like differential equation quantifying COE at the planet scale and then consider how the time constant is a function of Ts (surface temperature), as opposed to be constant for the typical RC circuit. In a way, its like a voltage variable capacitor, which BTW, is also a passive component per Bode because it can not provide power gain.
To model the climate, start with this DE:
Pi = Po + dE/dt
Pi is the post albedo power arriving from the Sun (total forcing), Po is the power leaving the planet. Pi and Po are instantaneous functions of time and Po lags Pi owing to time constants. Their difference, dE/dt is the sensible heat that either adds to the solar energy stored by the system, E, when Po Pi.
Pi is actually Psun(1-a), where a is the albedo, but accommodating this can be deferred, especially since the feedback model takes forcing input and the IPCC definition of forcing already includes the effects of albedo on the incident solar energy.
If we define an arbitrary amount of time, tau, such that E can be exhausted at the rate Po in tau time,
we can rewrite this as,
Po = E/tau
Pi = E/tau + dE/dt
This is the same form as the LTI DE that describes the charging and discharging of a capacitor, where tau is the time constant given as the product of the resistance and capacitance. The difference is that tau is not constant and decreases as Ts increases. We can recognize this by considering that Po has a T^4 dependency on the surface temperature. This brings up an important point, which is that conventional climate science requires feedback to modulate the exponent in T^4 relationship between Po and Ts (Ts == surface temperature), when in fact all it can do is apply is a linear scale similar to an emissivity since due to quantum mechanical considerations, the T^4 component of this relationship is immutable.
Since 1 calorie increases 1 CC of water by 1C, we can say that Ts is linearly proportional to E, but Po is some constant times Ts^4 (the SB constant times a scale factor < 1). Rewrite the relationships between Po, E, Ts and tau and it becomes clear that tau has a strong temperature dependence.
E/tau = Po = k1*Ts^4
E = k2*Ts
substituting,
tau = (k1/k2) / Ts^3
which as you should expect is the same form as the derivative of the SB relationship (its slope, or dTs/dPi).
I’m confused by
I think that that should be the total energy, not the energy emitted as radiation in the previous equation. I think the following is what you meant.
Robert,
E is the total energy stored by the system and since temperature is linear to stored energy (not emissions or to the forcing that results in incremental emissions), the ratio of E to Ts is the same as the ratio of dE to dTs. Keep in mind that dTs is a change in the surface temperature while dE/dt is the rate at which the surface is warming or cooling. The units of E are joules/m^2 while the units of dE/dt are W/m^2 and in the steady state, the long term integration over time of dE/dt == 0.
In that case, what does E mean in the first equation. I don’t think it can have the same meaning.
E is the solar energy stored by the planet per m^2. In the first equation, the instantaneous difference between Pi and Po either adds to or subtracts from the stored energy, E, depending on the sign of the difference. In the second equation, E is represented as being linear to Ts while Po is proportional to Ts^4.
Note that based on measurements, dE/dt has a seasonal variability of about about 170 W/m^2 peak to peak in the N hemisphere and over 200 W/m^2 p-p in the S hemisphere, both of which are centered around zero. It is positive in the spring and summer (warms) and negative in the fall and winter (cools). The asymmetry results in the dE/dt signature of the S hemisphere appearing in the global response, even as the dTs/dt signature of the N hemisphere dominates the global response. The larger variability in the S hemisphere is indicative of a longer time constant owing to a relatively larger fraction of ocean and the asymmetry between hemispheres contributes to a confusing global response that only starts to make sense when the hemispheres are treated as mostly independent of each other.
But one is a change in energy with respect to time, and the other is the change in energy with respect to temperature and that is why I was having trouble with this.
On the other hand, hyperphysics derives pretty much the same equation.
Thanks for helping.
Are you saying that even though op-amps have a power supply, they are not passive?
Respectully disagree.
wreckafire,
“Are you saying that even though op-amps have a power supply, they are not passive?”
Op amps are not intrinsically passive devices. Based on Bode’s definition of passive and active, an OP amp without an external power supply would be considered passive, but add the implicit power supply and it provides active gain and Bode’s analysis ASSUMES active gain.
Oh crap.
That “not” was not supposed to be in that sentence above. I meant to say
“Are you saying that even though op-amps have a power supply, they are passive? Respectfully disagree”.
“Oh crap.’
And as I said, with a power supply connected, an op amp is an active amplifier. Without a power supply it’s a brick.
Another point of confusion seems to be related to equivalent modelling which is something that EE’s understand intuitively, but climate science does not. There’s no such thing as an exact model, except as the representation of an unrealizable system. All models are idealized equivalent models and by that, the model exhibits the behavior of what is being modelled, but is not necessarily reflective of the exact internals of the system, or any deviations from ideal behavior. For example, you can have a 3-terminal, passive system (input, output and reference) containing millions of resistors in a complex configuration, but you can always simplify it to a system containing only 3 resistors, either as a Thevenin or Norton equivalent circuit and the result will have the same behavior between its terminals (transfer function) as the more complex system. A gray body representation of the climate, where T is the surface temperature and the EQUIVALENT emissivity is the ratio between planet emissions and surface emissions and equal to the reciprocal of the closed loop gain is just such a model.
When you plot the surface temperature (input pin) vs. planet emissions (output pin), the correspondence to this EQUIVALENT model at the observable ‘pins’ of the feedback model (top and bottom of the atmosphere) is undeniable and yields an EQUIVALENT emissivity of about 0.62 and a corresponding open loop gain of 1/0.62 = 1.6 which means that each W/m^2 of forcing results in 1.6 W/m^2 of surface emissions. How is it possible for anyone to legitimately claim that the next W/m^2 of forcing will result in 4.3 W/m^2 of incremental surface emissions?
Note that the relationship between the surface temperature and planet emissions that the Hansen feedback model models is reflective of the relationship between the surface temperature and input forcing because in LTE, the planet emissions == total input forcing.
Here’s some measured data demonstrating that a gray body EQUIVALENT model of the planet accurately reflects the transfer function.
http://www.palisad.com/co2/tp/fig1.png
Each small red dot is 1 month of average temperature vs. average emissions by the planet for a 2.5 degree slice of latitude, where all slices and months covering about 3 decades are represented. The green line represents the idealized gray body relationship between the surface temperature and planet emissions. The blue line is representative of the nominal sensitivity claimed by the IPCC and it should be clear from this how the assumption of approximate linearity was bungled. The magenta line is representative of the sensitivity relative to the input power (instead of the output power), which turns out to be equivalent to the sensitivity of an ideal BB at the surface temperature! If you replace fig1 with fig2 in the above link, the relationship between the surface temperature and incident power is superimposed on the relationship between surface temperature and output emissions. Note that the incident power is measured directly, while the output power is calculated based on a presumed radiative model of the atmosphere driven by a surface temperature given as the color temperature of the planets emissions. These two transfer functions cross at the intersection of the current average surface temperature (287K) and current average input/output power (239 W/m^2).
When reverse engineering any system, including the climate, the first thing you do is model the transfer functions between the inputs and outputs and only then can you start to try and figure out what’s inside that resulted in the measured transfer function. Climate science has skipped this first, crucial step and instead presumes CO2 drives the climate and then attempts to figure out what’s inside than can have this presumed influence.
This is an eloquent testimonial about how much more sensible it is to let observations and hard data show us what the Earth system is actually doing than it is to develop sophisticated but imperfect models of how we think Earth is really behaving.
IMO, at the origin of this is not really a violation of COE itself, but a violation of basic physical logic in terms of what should be the most accurate and realistic way to map the climate system into a feedback network. The way to whole feedback issue is framed and being applied is flawed, because it’s more akin to a static steady-state system whose behavior upon a change in response to an energy imbalance is unknown or big mystery. The climate system and the net effect of its operating feedbacks, especially those from clouds and water vapor (the two most dynamic components of the whole atmosphere), are already mostly physically manifested and are acting to dynamically maintain the energy balance from the forcing of Sun.
Where mainstream climate science goes wrong has more to do with what they consider the ‘no-feedback’ starting point than perhaps anything else.
“Where mainstream climate science goes wrong has more to do with what they consider the ‘no-feedback’ starting point than perhaps anything else.”
Yes, this has been bungled big time. What they consider the no feedback sensitivity of 0.3C per W/m^2 is actually the post feedback sensitivity for the next W/m^2 of solar input. They adjust lambda0 up from the sensitivity of an ideal BB at 255K to the current sensitivity of a surface at 287 K being heated by only 239 W/m^2 without really understanding what they did and then claim the ‘feedback’ that is already accounted by the lambda0 adjustment further ‘amplifies’ the sensitivity. They don’t understand that the gain, or what they call the sensitivity of the model they specified amplifies the forcing input to produce an output temperature and instead, they craft a nonsense model around it that considers feedback to be amplifying the sensitivity.
The mapping from Bode to the climate is so broken, it’s astounding that it has survived as long as it has, but then again, confirmation bias provides a powerful mechanism to fabricate apparent truth out of obvious lies.