Guest Post by Willis Eschenbach
I’ve been ruminating on the continuing misunderstanding of my position that a governor is fundamentally different from simple feedback. People say things like “A governor is just a kind of feedback”. Well, yes, that’s true, and it is also true that a human being is “just a bag full of organic chemicals, minerals, and water“ … but if you want to analyze humans, that’s far from sufficient.
Similarly, a governor is a kind of feedback … but if you want to analyze it, you can’t assume it’s just simple feedback.
For starters, let me offer my definition of a governor. A “governor” is a control system that uses both positive and negative feedback to maintain some system variable near a “set point” value. A common example in our daily lives is the cruise control on your car. It increases or reduces fuel flow (positive and negative feedback) to maintain the vehicle speed near some pre-set value.
I want to illustrate why you can’t analyze a governed system the same way you analyze an ungoverned system. Suppose I have a car, and I start out from a standstill on level ground. As I gradually add more and more gas by slowly pushing down on the gas pedal, the vehicle speeds up. I record the speed and the instantaneous fuel flow, and I get a graph like Figure 1. As is the usual custom, I’ve graphed the independent variable (fuel use) on the horizontal X axis, and the dependent variable (speed) on the vertical Y axis.
Figure 1. An illustrative graph of automobile fuel use versus speed, with no cruise control. Yeah, yeah, I know the shape of the curve won’t be exactly like that … which is why this is an “illustrative example”. [UPDATE: an alert reader has pointed out that the speed is of course in miles per hour (MPH) and not miles per gallon (MPG) … I can’t be bothered to redo all the graphs, so please just make the appropriate mental substitution.)
Figure 1 shows that the vehicle speed is some kind of function of fuel use. It’s not a straight line because as you speed up, the air drag on the car slows it down. And the drag increases by something like the cube of the speed. So as we add more and more fuel, the effect of each added unit of fuel decreases. You can see that at sixty miles per hour, the car uses 2 gallons of gas per hour.
The takeaway point from this analysis is that in terms of causation, we can see that a change in fuel flow causes a change in speed.
Now, let’s get the car going sixty miles an hour on level ground, turn on the cruise control, and once again measure the speed and the gas. Then, suppose the car goes uphill. It will start to slow down. As soon as it does, the cruise control will react to the reduction in speed by increasing the gas flow to keep the speed near to 60 mph. And when the hill steepens, speed goes down a bit more, and in response the governor further increases the fuel use to keep the speed up.
Then we crest the hill and start down the other side. The car starts to increase speed, and when it gets going faster than 60 mph, in response the cruise control will reduce the fuel flow.
This leads to a very curious situation—vehicle speed goes up as the fuel use goes down, and speed goes down as the fuel use goes up. Figure 2 shows an illustrative graph of the situation .
Figure 2. An illustrative graph of fuel use versus speed, with a cruise control set for 60 MPH.
I’m sure you can see the problem. If we analyze this situation in the exact same way as we analyzed the situation without the governor, we come to the ludicrous conclusion that if we increase the fuel use, it will reduce the speed of the car.
So how can we understand this change? The key to analyzing this system is to understand that the governor (cruise control) reverses the causation in the system. Without the governor, as mentioned above, a change in fuel flow causes a change in speed.
On the other hand, with the cruise control engaged the exact opposite is true—a change in speed causes a change in fuel flow. And as a result of this reversal of causation, our previous analysis method is useless because it incorrectly assumes that a change in fuel flow causes a change in speed.
But wait, it gets worse. Suppose we start up the car from a standstill as in Figure 1, but then when we get up to 20 mph we set the cruise control for sixty mph. The car will continue to accelerate as in Figure 1, but only until the car gets up to sixty mph. When it gets there, it doesn’t speed up any more. Instead, it takes up the pattern shown in Figure 2. So the complete graph of the run looks like Figure 3:
Figure 3. An illustrative graph of fuel use versus speed, with a cruise control that is set to 60 MPH just after the car starts moving.
Here we see that in the blue part of the graph, the change in fuel use causes a change in speed … but once it gets up to the set point speed of 60 mph, the causation reverses, and now the red line shows that a change in speed causes a change in fuel use. Note that this reversal does not require any change in the governor settings. When the situation is far from the set point, the causation goes fuel –> speed. But once it reaches equilibrium, causation reverses such that speed –> fuel.
How does this relate to the climate? Well, the underlying climate paradigm is that the forcing controls the temperature, such that a change in forcing causes a change in temperature.
On the other hand, I’ve proposed that there is a natural governing system regulating the temperature of the climate, a major part of which works as follows.
In the tropics, when it is warm, clouds form earlier and reflect away the sun to cut down the solar forcing. And when the tropics are cool, the clouds form later or not at all, which greatly increases the solar forcing.
What that means is that a change in temperature causes a change in forcing.
And that is why I say that the current method of analyzing the climate is totally incorrect, because it assumes the causation is going the opposite direction from what is actually occurring.
In closing, I can do no better than to post up this marvelous cartoon by Josh from five years ago showing my “Thundercloud” governor at work …
Best wishes to all,
w.
As Usual: If you disagree with someone, please quote the exact words you object to so that everyone can know both who you are addressing and just what it is that you disagree with.
Willis , you really need to find out what the terms mean if you want to discuss this kind of thing.
Positive and negative f/b does not relate to whether the thing being driven is going ‘up or down’. A negative f/b is one which acts to counter a deviation and a positive one is one which acts to increase it further.
If a hill slows the vehicle down, the cruise control acts as a negative feedback by increasing the gas.
Mike, fully agree.
Thanks, Joihn. It was a late-night exercise, I’ve struck out the one incorrect phrase.
All the best,
w.
Well being personally of the electronics persuasion, rather than mechanical, I use the term ” regulator ” rather than governor.
But I agree that there is a basic difference with just ” feedback ” in that with a regulagovernator you compare the system output parameter of interest (speed or other variable such as Temperature) with a fixed value (set point) and that output error variable becomes the source of the corrective input signal (via feedback). that will drive the output towards the set point.
In the case of say climate cloud feedback; there is no set point that we have control over.
The ” system ” has a preferred steady state (not equilibrium) that depends on zillions of variables,
For a given driving force such as TSI there will be some preferred steady state.
If some of the variables change, the system has a new preferred steady state.
Variables such as cloud cover; area, optical density, persistence, location directly alter the drive signal (TSI) and so change the preferred steady state.
Because the system is chaotic, we cannot always know what that adjustment might be.
If we add more CO2 and that reduces the output cooling rate, so Temperatures tend to rise, that Temperature rise, will cause more evaporation and lead to more clouds, which act to reduce that active part of TSI that reaches the surface.
So the net effect of increased CO2, would tend to be an increase in cloudiness, in all of its aspects, and an upward tweak of the Temperature.
That is NEGATIVE feedback, and with 7% increase in evaporation for a one degree C increase in Temperature, that seems like an extremely powerful feedback effect, that makes the effect of CO2 rather puny.
g
But the only set point in this feedback system is what all those myriad variable collectively vote on. Mother Gaia knows exactly what the Temperature and cloud cover need to be at all times.
Ditto.
The Stefan-Boltzmann law is a governor of sorts, increasing or decreasing radiation by the 4th power in an effort to maintain a temperature.
The missing energy may simply be increased outgoing-long wave radiation. As it gets warmer, more radiation/energy is emitted outward. Planck radiative feedback (or governor) is discounted by climate science but appears to be in the -4.0 W/m2/K range from the surface (measured by the missing energy) and -2.0 W/m2/K from the top of the armosphere (measured by Ceres).
Why this known science feedback is ignored and only positive ones like water vapor are counted in the climate change prophesy is beyond me but it reduces the global warming expected to 1.3C per CO2 doubling.
Amen. The use of the terminology is completely wrong.
On the other hand, Willis has the right instinct. Using control system theory to analyze the planet’s climate is seriously dodgy. Some other kind of analysis is probably much more appropriate.
Example: Consider a beaker of boiling water. The temperature will be maintained somewhere near the boiling point (until the water gone).
– Does that mean it’s a negative feedback control system? It is not.
– Might someone try to analyze it that way? They might.
– Would that analysis be valid? It might be “close enough”. Maybe.
– Could the system be more correctly analyzed without the use of control theory? Absolutely.
The climate is not a control system. Analyzing it that way is a gross simplification. People do that because they think they understand the mathematics. They are wrong to do so. We do not understand the climate well enough to justify the use of that simplification.
The climate IS a control system. Otherwise we would not be here to discuss it. ( Unless you believe that some deity is up there taking care the temp for us, and all the natural feedbacks are just noise put there to give us something to lbog about ).
commieBob,
Your analogy is only partway there. The beaker of boiling water would need a special coating that changes reflectivity and emissivity as the temperature of the water changes. If the beaker is close to a radiation source, that special coating will cause net radiative forces to go up or down, keeping the temperature of the water relatively constant for as long as the radiation source remains.
Using control system theory to analyze the planet’s climate is seriously dodgy. Some other kind of analysis is probably much more appropriate.
No., using control system theory is exactly right, that is not the problem, the problem is in using simple linear control system theory when you have a complex non linear climate.
Consider: You have a lump of ice the size of Greenland and you apply a certain excess watts per meter to it. The ice will start to melt, but the temperature of the remaining ice’ and indeed the meltwater, will not change They will hang around 0°C. At the melting point of ice, the relationship between energy input and temperature rise, is completely non linear.
Likewise at the boiling point.
The author has also identified a localised feedback system that works within a certain temperature range in the tropics. The albedo of tropical clouds which are full on negative feedback as well – until the clouds vanish, or its totally overcast.
At this point the cease to be feedback. They cease to govern. 100% cloud cover has the same albedo no matter how thick it is.
Handling these sorts of feedback systems is normal for engineers, and we understand that outside of the linear ranges we are into a very very hard bit of analysis, and there are no simple answer, just a selection of kludges and bodges and approximations that get us somewhere near. And most of our engineering is about designing systems that do NOT go into non linear ranges in normal operation, or if they do, do so in as predictable a way as possible.
And even then we know that its probably easier to e.g. take that race car with the rubber bump stops and the progressive rate shock absorbers out on the test track to optimise it, because calculations rapidly get horrendous.
The gaping hole in climate theory à la IPCC is that they assume a linear relationship between radiative forcing and temperature rise, multiplied by a positive feedback term bodged to fit a very short 20 year period of time.
Its so naïve its pathetic.
Firstly, what they don’t appreciate is the extreme non linearity of climate response to forcing, which makes their equations bound to fail. The water cycle that carries heat from the surface to the stratosphere and forms clouds, dumping terawatts of energy to space at night, and reflecting terawatts by day, is one such extremely non linear negative feedback system.
Secondly, what they don’t appreciate is that negative feedback delayed in time creates instability as much as positive feedback does. Taking the author’s cruise control, if it’s slow to respond, and then over reacts, the speed will oscillate about a mean : at times it will accelerate madly, then slow dramatically as the negative feedback tries to keep things to a mean, but fails to do it fast enough. The multi decadal ocean swings noted in the earth’s climate are just this sort of effect.
Add in some non linearity and you have a chaotic system with possibly multiple attractors. And that is precisely how the geologic climate appears to have behaved.
Sophisticatedsystem analysis can show that that is exactly what you would expect. The problem is, it also shows you how monumentally incalculable the solution may be, which makes nonsense of prediction à la IPCC!
Just because the warmists unbeleivably crude and naïve attempts at linear systems analysis have failed, doesn’t mean that system analysis is the wrong tool. Its just being used in a stupid and desperate way to prop up a pre-ordained commercial and political narrative, for profit and gain, not to actually represent the climate according to best practice
This would also be true if the water weren’t boiling, and it would be more like the actual climate. Geothermal heat is not boiling our oceans away.
@Leo Smith SPOT ON.
My 2007 GMC had to have a software change to the computerized transmission. The tech must have put in a wrong entry because my Cruse control did exactly like you described. Took it back, they claim they fixed it, but I still “feel” (cant see any change in speed or rpm) the vehicle slow down and then suddenly get pressed into the back of the seat.
You could indeed say that boiling water is a negative feedback, as the rate of boiling prevents the temperature from rising above 100 deg C; as the rate of heating rises, the rate of boiling rises. If you flash heat water, it can get above 100 deg C until it has a chance to convert to steam, suddenly.
Actually, I agree with everything you say except for “using control system theory is exactly right”. Practically, any attempt to do that will be either wrong or intractable. In fact, you eloquently make that point for me. Having said that, I am not proposing any viable alternative. 🙂
Exactly so.
“At this point the cease to be feedback. They cease to govern. 100% cloud cover has the same albedo no matter how thick it is.”
Convective clouds never reach 100% since there are always always areas where dry air is descending.
Also 100% cloud cover does not always have the same albedo. Thin clouds have lower albedo than thick ones. All clouds are translucent to some degree, otherwise it would be completely dark when the sky is cloud-covered.
yes. makes total nonsense of the article.
He’s correct, Willis.
Doesn’t negate your point, but misuse of some terms may turn off certain folks and that would be unfortunate.
Correct. There is no positive feedback in a cruise control. None. Zero.
Thanks, Mike. I wrote this late last night, I’ve struck out the offending phrase.
w.
Good man, Willis. Glad to have you back on board.
Shouldn’t speed in the graphs be MPH (miles per hour) rather than MPG (miles per gallon)?
Good catch, Jeff. I’ve put a note up in the head post, no time for changing it, gotta go.
w.
governor/feedback – seems to be essentially mass-spring behavior = simple to make with complicated inertial-motive responses whether these are thunderclouds or human skeletal muscle tissues
“It increases or reduces fuel flow (positive and negative feedback) … ” That is where you are going wrong. Fuel flow can be increased and decreased and both situations can be negative feedback.
The feedback signal is subtracted (negative!) from the set point – your 30mph, say. If the difference is positive that means that we are not getting enough negative feedback yet so we add fuel. The speed increases so the negative feedback increases until the difference between the feedback and the set point is zero.
If when the feedback is subtracted (negative!) the result is negative then you are getting too much negative feedback. To reduce it we will need to reduce the speed and so a reduction in fuel is required. This will reduce the speed and reduce the negative feedback until the difference with the set point is zero.
Negative, as in negative feedback, just means that the signals are subtracted. The result of that subtraction can be either positive or negative but that is after the feedback loop. The resulting positive or negative signal will be fed into the forward part of the control system.
The spring in a traditional light switch is an example of postive f/b. Once it passes the mid-point in the movement, ( the tipping point as our freinds would likely call it ) the spring acts to accelerate the movement. A small displacement will cause it snap to the on position. It will then meet a strong negative f/b in the form of the rigid body of the switch. This is a very common situation where a positive feedback is eventually bounded by a dominant negative feedback. Any system without this kind of effect would be completely unstable and would only exist fleetingly.
It amazes me how many people do not understand the concept of set point and diff!
The red and blue lines do not represent the same environment for the car. The comparison is false.
What does the blue line look like if you put the same hill into the storey?
I’ll answer my own question: as the car climbs the hill the blue line will deviate to the right of the cubic relationship, having a slower equilibrium speed for a given fuel consumption . As it approaches the brow of the hill it will fall back to rejoin the original blue line. As it begins to descend the other side, the fuel graph will veer off in the other direction accelerating to a higher equilibrium speed than the blue line. Finally returning to level ground it will return to the cubic relationship.
If we explore the graph while on a steady upward climb it will have a similar curvature but lie below the level ground, blue line. Conversely, on a downward slope the curve would be above the original blue line. Mathematically, they would both be linear + cubic as fuel is converted into gravitational potential energy, on one case and in the other some fuel is substituted by recovering gravitational potential energy.
So we see the whole curve is shifted in a way similar to the way the red dot of the cruise control point moves to describe the locus shown as the red line in Willis’ fig. 2.
The comparison is classic apples and oranges.
The blue line without hills compares to the red dot: cruise control point on level ground. The red dot is ON the blue line. The red line should be compared to a 2D surface swept out as the coeff of the linear term ( reflecting the gradient of the hill ) is varied and the curve is shifted to one side then the other.
Willis has confused the issue by introducing a third variable into the discussion but only applying it to one of the cases he was discussing.
The cruise control does not change the behaviour from the blue line to the red line, it locks it to one red dot ON the blue line. If you introduce a hill the cruise control red dot with still be on the NEW blue line corresponding to the same conditions.
The red line represents the set of all possible dots on all possible blue lines at 60 mph.
I do not understand this fuss. I understand perfectly (I think) what is being portrayed.
I consider a control system to use negative feedback but is not itself negative feedback.
I agree that a lag in the control system feedback makes it unstable and it will probably oscillate or even self-destruct (think of “Galloping Gertie”).
http://www.wsdot.wa.gov/tnbhistory/connections/connections3.htm
The question of lag was described by someone else very well below. However, that is irrelevent to the article which considering fuel consomation after settling to an equilibrium speed. This is not discussing transient behaviour.
No, the cruise control introduces an effect with the opposite sense ( negative feedback ) which reduces the original variability. It does remove it totally, nor reverse it.
The red line is due to introduction of a third variable which would also have moved the blue line in a similar way had it been discussed.
The idea that the cruise control changes behavious A ( blue line ) into behaviour B ( red line ) is erroneous. They are not the same thing.
The cruise control will only control the speed when going downhill if it is also coupled to the [braking] system otherwise the car will continue to accelerate (until other mechanical factors contribute).
GIL – depends on your vehicle. Some vehicles apply engine braking to maintain speed on the downhill leg, disengaging over drive and gearing down. Depends on how sophisticated your automobile cruise control is. I have two vehicles that will control speed on both uphill and downhill very well, and one older one that indeed will accelerate downhill unless I drop it our of drive then it works fine, both uphill and downhill.
I’m not sure I’m seeing the complexity here.
Using the analogy the sun forces temp rise and the petrol forces speed increases, and the clouds provide negative feedback on the sun in response to temp and the governor provides negative feedback on the petrol flow in response to speed. .
So in the first case beyond a certain temp the clouds provide negative feedback so that as temp increases the impact of the sun reduces (to the point where temp starts to drop), and if under the certain temp it increases the impact of the sun.
In the second the governor also provides negative feedback so that as the speed increases it constrains fuel flow (to the point where speed starts to drop), and if under the certain speed it increases the fuel flow.
In both cases causality exists between forcing/petrol and temp/speed, it is just that the clouds/governor acts as a damping control over the relationship.
If you treat both as black boxes, continued forcing without a governor causes the systems to be unstable within the systems’ constraints, with a governor they both become stable (but within limits no doubt).
“and the governor provides negative feedback on the petrol flow in response to speed”
Not quite the same thing. A governor enforces a set-point, using a LOT of feedback to achieve “lock”. A phase-locked loop is another example.
Mere negative feedback reduces the effect of a change in input in a linear way. 50 percent negative feeback reduces climate sensitivity 50 percent.
An effective control system changes the negative feedback dynamically. Around the set point, the negative feedback will be minimal or zero; as the velocity (in this example) increasingly deviates from the setpoint, more negative feedback is utilized; but it might not actually be “negative feedback”.
What, exactly, is being “fed back” in the automobile example? Velocity is being measured, not “fed back”. The difference of measurement from setpoint will cause movement of the control input but it must be damped or it will oscillate.
A governor may be thought of as a specialized form of feedback, focused more on maintaining a more or less constant setpoint rather than trying to follow a control signal. Governors also have a connotation of enforcing limits, e.g. an engine governor may be set up to limit maximum speed. Governors also have the connotation of responding to variations in load as opposed to changing the settings on the control knob.
Willis is right in that CO2 is an external forcing to climate, NOT a control knob.
FWIW, the “feedback” from tropical thunderstorms sounds more like a limiter to me. Limiters have a very non-linear response to input. In the case of thunderstorms, the vapor pressure of water roughly doubles for every 20F increase in temperature and this vapor pressure is independent of the partial pressure of CO2.
Micheal 2
I hadn’t really intended to get into the “negative feedback” issue but the problem is there are a number of specialist definitions that means one can argue over whether a governor is or isn’t.
At its heart however a governor is both a feedback mechanism and negative.
It takes a signal (temp/speed) and uses it to modify it (hence “feedback”). It is “negative” because it dampens the signal, accelerating when below the set point or accelerating when below it.
The fact that we use language like “it was the negative feedback that caused the oscillation” shows that if the result is oscillation we don’t still call the process negative feedback.
“What exactly is being ‘fed back’ in the automotive example?” Information about the speed is being used to modify the fuel flow.
Erik Magnuson
I was going to add in my earlier comment that in the analogy the hill is misrepresented (others have said this on this thread). The hill is part of the environment that equally has a separate influence on the signal (speed). In this sense it is the equivalent of the concentration of CO2 in the analogy. Just as the governor will respond to hitting a downhill run and is blind to the fact that the increase in speed wasn’t due to an increased flow of fuel, so the clouds will respond to an increase of CO2 in the atmosphere and be blind to the fact it had nothing to do with the sun hotting up.
Sorry – should read
“…. accelerating when below the set point or decelerating when above it.”
A governor is a governor. Feed back is feedback. Totally different animals. Next thing you know , people will be saying that CO2 is a control knob
A governor is a control device that applies a negative feedback.
“A governor is a control device that applies a negative feedback”
A governor is a control device that applies a negative or positive feedback depending on which side of the set point it is on.
No Roy, you are making the same mistake as Willis did. See comment #1 . You also need to read up on what ‘negative feedback’ means. If the control variable is dropping below the control point, a negative feedback will act to bring it back UP.
I disagree. A governor can produce either a positive or negative feedback, depending on how it is tuned. Excessively turning up the gain or derivative on a PID controller (governor) may produce positive feedback and an unstable system. In some systems such as level control, this is not the case, in fact a very high gain is ideal. Temperature control needs PI, with I, Integral, to prevent reset windup, although with simple systems, P is sufficient.
That’s correct if you want to extend the definition of “governor” to include every kind of control system including PIDs. What was wrong is the idea that positive feedbacks drive things up and neg. f/b drive them down. That is NOT what negative means in this context.
A governor always applies a negative (counter-deviation) feedback.
I have decided a pox on both of your houses. This is not feedback. Negative feedback, often used in amplifier circuits, simply inverts the output and feeds it back to the input to stabilize it. The proportion of feedback is not dynamic.
A control system measures something, then commands a control input in a non linear way to seek the setpoint. By non-linear I mean the strength of the control change will vary depending on distance from the setpoint and how aggressive it is designed which itself takes into account inertia of the system response as otherwise it becomes unstable and will oscillate (I mention Galloping Gertie above).
Feedback is directly applied to the input. A control system measures a thing (velocity) and controls something (fuel flow) seeking a setpoint using an algorithm that might not be, and probably isn’t, a simple mathematical function.
I once built a cruise control for my UV (long before SUV). It was too simple and would surge way over the setpoint, then throttle back to idle nearly coming to a stop, then surge.
Mike is right. A governor always tends to drive the system controlled variable towards the set point.
If the speed / Temperature / whatever, is below the set point, the drive is increased to move it towards the set point, I. e. increase.
If the speed / temperature / whatever is above the set point, the drive will decrease to move it towards the set point I. e. decrease.
The ” restoring force ” is always in the direction opposite to the error from set point.
Now that presumes the system is designed to be stable over all possible variable values.
So if (x) is the displacement from the equilibrium value (set point), the restoring force is given by : fF= -kx where k is a transfer function value.
In a mechanical system, we have that F = m a = m d^2x / dt^2
So we get m d^2x /dt&2 = – kx
This is well recognized as the differential equation of simple harmonic motion and has solutions of the form x = A sin (omega t) + B cos (omega t)
In a practical system, there will be damping that ensures that the amplitudes A and B do not steadily increase, and in fact a designer would seek to get the fastest settling time to a new value, whenever something changes, without overshoots or long time delays to reach within an acceptable error band.
But the restoring forcing is always towards the set point, so opposite to the displacement from the set point. And that makes it negative feedback.
With positive feedback, the feedback forcing, would drive the operation further away from the set point and increase the error.
That does not mean it will explode; but it will be more unstable.
Michael 2:
You’re virtually alone here in correctly recognizing that negative feedback–in the rigorous scientific sense–is the instantaneous addition of the INVERTED output signal to the input. Inasmuch as the input into the planetary climate system is SW solar radiation and the output is the OLWR at TOA, it should be apparent that we have a feedTHROUGH, not a feedBACK, system! Nor is that system any “governor,” in the sense of limiting the system output to the vicinity of some predetermined “set-point,” irrespective of the input.
That quasi-steady response is the consequence of the virtually constant energy of TSI provided to the system as excitation. Variations of surface temperature due to internal changes in trace GHGs are negligible compared to the those produced daily or seasonally by changes in cloud-modulated insolation. All the GHGs, including water vapor, are simply capacitive/inductive components that effect cannot heat storage in the convectively-heated atmosphere beyond their very minor mass.
In the last sentence, it should read “…cannot affect heat storage…”
You guys are missing the point. A governor is a switch, a feedback is an effect.
IMHO, you guys are quite correct, but are all missing real point of Willis’ post, that the cause and effect of the fuel and speed is reversed by the ‘cruise control’, and that this is not understood (or is ignored) by many when discussing AGW. Hence the false assumption (among many I’m sure) that CO2 drives global temperature, when the reverse is the case. Thanks everyone, and especially Willis.
Right! I was waiting for someone to recognize this. A governor limits the allowable range of system. If climate were controlled by a governor the temperature would stop rising when it gets to a certain point (the IPCC turns off the sun when it gets 2C above nominal).
Boyfromtottenham & BobJ
No, Willis doesn’t show anything about the cause and effect of fuel and speed (or sun and temp). In all cases the former causes the latter.
The impact of the introduction of a control is to change the amount of fuel/sun in response to speed/temp.
The point is that an increase in CO2 (say) causes an increase in efficiency of the sun that causes an increase in temp that causes a change in the clouds that causes a decrease in the efficiency of the sun that causes the temp to decline. The observed relationship between CO2 and final temp in any such system is contingent, but in this case there is nothing to suggest that change in temp causes a change CO2.
That is the simple case. Consider now the case where you press the gas pedal and car decelerates. Then you release the gas and the speed starts to accelerate and goes faster and faster even though you use the brakes. Then you release the brakes and the car slows down. Where were the hills and valleys?
Humans have an anticipating central governor: http://runnersconnect.net/running-training-articles/central-governor-theory. Your running slows down before you run out of fuel.
Another BIG difference is Ramp bias ,measured in time and % of rated motor load in response to a deviation of set point
“It increases or reduces fuel flow (positive and negative feedback) to maintain the vehicle speed near some pre-set value.”
As already mentioned, this statement is completely wrong. Servomechanisms are specifically designed to use negative feedback. If the fuel flow is increased in order to maintain the correct speed then it is still negative feedback.
As an electronics design engineer I had a lot of experience with all kinds of electronic and mechanical servomechanisms. Particularly with mechanics, inertia means that, as frequencies increase, the response lags more and more until negative feedback becomes positive feedback. Result: oscillation. The whole point of servomechanism design is to ensure that it remains a negative feedback system over the frequency domain where there is significant system gain.
Chris
Very nicely put: clear, concise and simple. 😉
Yes, unfortunately Willis’ apparent misuse of the term “positive feedback” has caused many to miss his actual point. All he is trying to point out is that the climate is operating in a feedback control regime where it is being controlled within limits by many factors, and that confuses people observing those factors. The cloud factor that he described is a negative feedback control mechanism for the temperature in the tropics. As long as the dominant feedback is negative, the climate system will operate within a stable control regime. However, while operating in that controlled regime things will seem backwards to an observer. If temperature is forced up by something, then the negative feedback adjusts to force it back down. Therefore, one will observe more clouds as well as higher temperatures. Determining what or which came first can become confusing. Simply, in a controlled system the controller uses a manipulated variable to maintain a controlled variable at a set point. While operating in a negative feedback controlled regime, the controller’s actions literally reverse the apparent relationship between the manipulated and the controlled variables, potentially confusing folks on cause and effect. That is Willis’ point.
No Willis has confused the issue by comparing a two variable problem to a two dimensional projection three variable problem. He’s comparing apple to oranges. The relationship appears reversed because there is another factor that is not shown on the graph : gravitational potential energy. One graph is level ground the other is not.It is the new “fuel” which is changing the relationship not the governor.
I explained this is some detail above, but several people just jump in and start commenting without reading.
http://wattsupwiththat.com/2015/08/02/problems-with-analyzing-governed-systems/#comment-1999034
The neg. slope results from the fact that the regulation provided by the governor is not perfect and there is a small residual of the effect or the external input ( gravity )
Mike, I agree with you wholly here. But, how is that different from what goes on in Climate Science anyways? While I appreciate the engineering pedants deeply, it doesn’t detract from Willis sketch of the epistemic problem and the failures that can arise from within it.
Mike, I was discussing Willis’ point about the climate, not cruise control. Although the comments on the use of terminology in his post were correct (and he modified the post to take out those references) the issue that Willis was driving at is that introducing negative feedback in a system changes the system operation. The “Main Stream” climate scientists are intent on ignoring any negative feedbacks and focus instead on every possible or imagined positive feedback. They completely ignore the negative feedback control that is operating daily in the climate system, which is a major reason why their estimates of CO2 sensitivity are so high and that their models are failing so miserably. The entire premise of Catastrophic Global Warming is based on and requires the imagined positive feedback of increased CO2 causing an increase in water vapor in the atmosphere, which has not happened based on actual measurements.
You got it Mike.
Please provide metric graphs for the rest of the world outside of the USA…
It is especially helpful to have Amps and Volts in metric units.
Amps and volts are already metric units.
+1
And, perhaps you just don’t want to do the conversions yourself..
+1
According to alexa 60% of the vistitors to this site is non-US
No ! The metric (SI) units are : amp and volt .
No caps and no plurals. But the symbols are : A and V .
g or G
English is way more fun:
Poppyseed, Line, Barleycorn, Digit, Finger, Inch, Nail, Palm, Hand, Shaftment, Link, Span, Foot, Cubit, Yard, Ell, Fathom, Rod, Chain, Furlong, Mile, League.
🙂
“Suppose I have a car, and I start out from a standstill on level ground. As I gradually add more and more gas by slowly pushing down on the gas pedal, the vehicle speeds up.”
Cringe.
A diesel engine is moderated by fuel, a gasoline engine is moderated by air. Your analogy is fine for a diesel engined car, not gas.
Gasoline engines are controlled by air flow, the fuel system reacts to changes in air flow. Sorry to confuse you, Dean.
Dean says “So I can go faster and faster simply by adding more air, which is free, and no more fuel, which costs money? Please tell me more!”
More is coming… wait for it…
Open the hood, look inside. The “gas pedal” goes to the throttle plate. That’s the only place it goes. You can operate the throttle plate by hand if you wish, grab it and turn it, let more air into the engine.
In most (maybe all) fuel injected engines, an air velocity measuring device measures how much air is entering your engine and squirts the appropriate amount of fuel into the intakes at the appropriate time. In older carbureted systems, the airflow itself pulls fuel at is flows through a venturi, increasing velocity but also reducing pressure.
So the control input in either case is adjusting how much air enters the engine.
PS: Air may soon no longer be free, not the CO2 part of it anyway.
The y axis of each graph says MPG. Should be MPH.
Thats fascinating Willis. Have you got any thoughts on what a governor forcing might look like? Because if it is possible to define a governor “fingerprint”, you could predict the characteristics of that signal, then see if a forcing matched that fingerprint. I know the current thinking is albedo – does that fit the fingerprint?
I think Willis’ governor is the tropical cloud band over the Pacific.
Couple nit pickies here. On the charts, the ordinate label should be MPH rather than MPG, and the abscissa should be Fuel Flow, rather than Fuel Use (fuel use would be in gallons only). In Fig. 3, the blue line should extend beyond where it ends.
The red and blue lines describe different items. The red line describes governor response; its slope is set by the manufacturer, tuned to the engine-vehicle combination. A whole set of roughly parallel red lines would describe settings for different speed settings. The blue line describes flat terrain vehicle performance.
If this is climate, replace y axis ( speed ) by temperature and x-axis ( fuel consumption ) by incoming SW in the tropics. The hypothesised ‘governor’ acting via regulation of the timing, extent and duration of cloud cover.
The negative slope of the fig.2 is the proposed negative cloud feedback. This will act to reduce the slope of the overall δT vs δrad relationship which has a positive slope. That slope is climate sensitivity.
No problem with that part of climatology and feedbacks.
It’s interesting to learn how engineers define and use “positive” and “negative” when discussing feedback but for laymen Willis’ example is clear no matter how feedback is defined: a changing temperature can change forcing to one which acts to reverse the temperature change. At least that’s how I see it.
Paul, perhaps you should read comment-1999034 and state clearly ( ie QUOTE me ) where you think I am incorrect, before declaring me “lost”.
http://wattsupwiththat.com/2015/08/02/problems-with-analyzing-governed-systems/#comment-1999034
Sorry Paul , that was supposed to be a reply to “Cube” below.
Once you start using systems analysis, you are firmly in the domain of engineers, and it behoves you to use the terms as they do, or else time will be wasted arguing definitions.
Negative feedback acts against the sign of the amplitude change. That is the definition. It does not become positive feedback because the amplitude of the change reverses sign.
Nice analogy Willis. Mike, I think you’re lost in the details and completely miss the point.
“Cube”, perhaps you should read comment-1999034 and state clearly ( ie QUOTE me ) where you think I am incorrect, before declaring me “lost”.
http://wattsupwiththat.com/2015/08/02/problems-with-analyzing-governed-systems/#comment-1999034
I think what Mike is trying to say is that the reverse illusion the author refers to isn’t necessarily caused by the cruise control, rather it is caused by the hills COMBINED with the cruise control. If it were level ground there would be no inverse relationship to fuel consumption and speed with or without the cruise control. The author’s point is that it is mostly the cruise control that causes the inverted curve. The way I see it is the hills are the primary cause, and in that particular environment cruise control inverts the curve. Same thing would happen if a person where driving. I don’t see there is much of a point to make about this.
Or I suppose another way to look at it is that a phantom reverse correlation is created between fuel consumption and speed, due to the correlation between the slope of the hill (up or down) and throttle position, i.e. fuel consumption rate, that is forced by the cruise control (or a person driving at a constant speed which is really just cruise control). If you account for this forced correlation and subtract it out you do not get the phantom inverted curve. But if you don’t account for it, as this example doesn’t, then you get the phantom inverted curve. Moral of the story is that failure to account for correlations such as this can lead your results astray. I guess that is a strong point from that perspective.
Tony:
“Temperature control needs PI, with I, Integral, to prevent reset windup, although with simple systems, P is sufficient.”
Most systems these days are PI, however, the ‘I’ can cause windup!
With P only, there is no integral in use, therefore no windup/lockup is possible, but the downside is that without ‘I’, you will always get an offset ( a difference between what you want and what you get).
Governors (PID controller plus actuator) always operate with negative feedback.
Many controlled systems are adjusted to have as much gain (P) and as much integral (I) as they can tolerate whilst remaining stable. We call this Quarter decay tuning.
Willis, should the Y-axis in your graphs show MPH rather then MPG?
A common example in our daily lives is the cruise control on your car. It increases or reduces fuel flow (positive and negative feedback) to maintain the vehicle speed near some pre-set value.
No, that is all negative feedback.
At this point I lost the will to live.
NEGATIVE feedback is feedback that opposes the tendency of the system to do what it start to do. So if the car starts to slow. NEGATIVE feedback opposes the deceleration and speeds it up. Conversely for if it speeds up downhill. NEGATIVE feedback opposes the acceleration.
Please Mr Watts, do not accept articles that start and are based entirely on a misconception of what clear and well define engineering terms actually mean.
Positive feedback is ‘runaway instability’. The tendency of a pencil balanced on its point to fall over. The tendency of an atomic reaction over critical mass to degenerate into an atomic explosion. The tendency of a microphone coupled to an amplifier and loudspeaker to go into full volume howlround.
A governor is a simple negative feedback system.
End of.
“The tendency of a microphone coupled to an amplifier and loudspeaker to go into full volume howlround.”
Which is of course a positive feedback, bounded by a dominant negative f/b: to power available to the amp.
That is exactly what I said. Why do you comment as if it negates it?
Positive feedback is ‘runaway instability. ….The tendency of a microphone coupled to an amplifier and loudspeaker to go into full volume howlround’.
“A governor is a simple negative feedback system.”
I disagree. A governor contains intelligence and maintains a setpoint exactly, negative feedback merely resists a control input producing an output change than is less than would be the case without the negative feedback.
A governor can maintain 60 mph exactly. Negative feedback cannot since there must ALWAYS be at least some error signal for the feedback mechanism to operate.
But a governor measures the velocity and makes corrections to land exactly on 60. It can even have attitude measuring inputs to sense when the vehicle is starting an ascent and add fuel/air in advance of measured speed drop using previously calibrated tables of how much energy is needed for any particular situation. The governor could also use accelerometers with vastly quicker response time than the drop in speed of the vehicle itself.
A governor does not maintain a speed, it limits the speed to some set point. Governor usually have upper and lower droop settings which control how the speed will vary above and below the set point on road grades. A governor is a hard limiter which is a negative feedback system with non linear feedback. In fact, a governor is often called a “vehicle speed limiter“.
To suggest the governor will “maintain 60 mph exactly” is absurd as there will always be some variation in the speed. In fact you admit it does when you state “But a governor measures the velocity and makes corrections to land exactly on 60”. When a vehicle starts down a hill the speed will increase and the governor will reduce the fuel appropriately.
Well Leo you don’t have it correct either.
Positive feedback is certainly going to increase the instability, but that does not mean it becomes ” runaway instability ” That is only if the loop gain exceeds 1.
Early radio receivers used positive feedback to increase the signal gain, but they stopped short of runaway gain increases, which lead to “squegging” where the gain increased until the system ran into one of the stops, either full on or full off. And once at the limit the loop gain drops to near zero and it starts all over again
BDTP beat me to it. Y axis should be MPH. (Ot M/S for you SI bigots. You know who you are.)
The terms “Negative feedback” and “Positive feedback” are misused/misdefined. Traditionally, the +/- notion of feedback defines whether the feedback term is added or subtracted at the summing junction.
Negative feedback will cause an increase in output if the output is less than the set point.
Mike
Hello Willis,
Off topic here, but you have marine experience so—-
Are you or anyone else with access to the historic data interested in attempting to do an analysis of the current flow to find a possible location for the crash of flight 370. I expect that the search area they used was a bit off.
You will also need to account for sea surface movement over the period the floating debris was in the ocean. IIRC the sea surface moves downwind at about 10% of the surface wind speed.
Gerald, the problem is that the ocean is chaotic in the sense that if you go out into the ocean and drop two floats, one on each side of the boat, most of the time they’ll end up in very, very different locations … not good.
w.
Are you sure it’s chaotic and not random? Why/why not? Use math. Thanks.
Still waiting for math. Tell us the difference between chaotic and random. Double dog dare you.
Dinostratus August 3, 2015 at 4:51 pm Edit
Dinostratus August 4, 2015 at 8:21 pm Edit
Thanks for the question, Dinostratus, but I fear that your manner of trying to get your way doesn’t work with me. I don’t respond well to that kind of ragging.
However, your luck is amazing. As it happens I’ve been looking at that very question for a couple of months now. I have the post half written. However, you’ll have to wait, because I plan to finish it on my schedule, not yours.
All the best,
w.
‘I don’t respond well to that kind of ragging.”
Or poorly for that matter.
“As it happens I’ve been looking at that very question for a couple of months now. I have the post half written. However, you’ll have to wait, because I plan to finish it on my schedule, not yours.”
It’s a fairly simple answer. It has a lot to do with f(t+tau) but nothing to do with auto correlations….. be warned.
Dinostratus August 5, 2015 at 4:06 pm
So you know the answer? That’s great! Are you going to tell us?
Or are you going to be a prince among men and dance around the subject and play games and withhold your supposed knowledge for personal aggrandizement?
If you know the answer then why on earth are you asking me? If you think the issue is important then stop playing silly buggers and give us the damn answer. If it’s all that important, I’m sure that I’m not the only one that’s interested, so how about you give us your explanation?
w.
I’m withholding my supposed knowledge for personal aggrandizement. That and chicks. Never forget the ladies.
Okay, new question….. What’s the difference between linear feedback and nonlinear feedback? The answer doesn’t take more than once sentence.
Looking qualitatively at the known current field I would say that the find pretty much supports the choice of search area. The fact that the arrival in Réunion was in 16 months or less, which is slightly less than expected might indicate that the crash site was somewhat further west, where the gyre is stronger.
His analogy may be bad and his terminology wrong. But what he’s saying about climate is that rising temperatures cause rising albedo and other heat loss events, whereas cooling temperatures cause lowered albedo and a decline in heat loss, the result of this being a temperature that is stable within some fairly narrow limits.
He may be right or wrong about the analogy to the car, and right or wrong about his use of negative and positive. The interesting and independent question is whether he’s right about the relationship between rising heat and heat loss events.
If he is wrong, its the other way around. The heat loss, whether through albedo or decline in storms or perhaps from CO2 insulation, causes a rise in temperature and that does not trigger any mechanism to reverse or limit it.
The question is whether that is how it works, or whether he is right that the underlying first cause is the rise. He does then need to explain what causes the rise or fall in the first place. I guess it might be the persistence of one of the correcting mechanisms? We have a rise in albedo, that was caused by warmup, and this rise then causes cooling, so we are always oscillating around a central value with rises or falls in the cooling mechanisms.
Many commenters here are missing the point. Willis is correct, and thinking clearly.
He has a point to make, and its a very good point, but it is not helped by simply redefining standard terms to mean their opposite.
IF he had bothered to study feedback and control systems properly, he would have both discovered that the situation he describes is known, understood, nothing special (to engineers), and had a correct and precise vocabulary with which to express it.
This isn’t skepticalscience.com. Here we try to get things right.
Tropical clouds are a fast reacting non linear localised negative feedback system that act to govern tropical maritime temperatures.
That is ALL he is saying, plus the data to support that statement.
Its a very significant and important statement to make, especially with evidence to support it, and I happen to think its true as well, but that doesn’t make it a very COMPLICATED statement to make.
He may be correct about the dynamics, but if you call a watt a farad, we’re going to have problems.
This disagreement is a trivial semantics squabble.
The “It’s all negative feedback” folks are insisting that the governor always acts counter (thus negatiove feedback) to the second derivative (or acceleration) of the motion to keep the system near a set point. Willis is using the term “positive feedback” for the application of fuel to increase the velocity (first derivative) in the positive direction of motion. Since the vehicle is slowing this application of fuel is counter “or negative” to the now negative acceleration of the motion but it is positive, or still in the same direction as the velocity, Hence Willis’ use of the term “positive” feedback.
Pendants are tedious.
.
No, pedants are necessary.
If we do not agree what terms mean, we cannot communicate effectively.
If I tell you its OK to drive through red lights and stop at green because I am using the term red, as you would use green, and vice versa, we have a problem, Houston.
Engineers have been here before, and mapped and defined this territory. It is not down to anyone else to come charging in and redefine the vocabulary of it according to personal taste.
Because the discipline and the vocabulary allow for concise and precise statements. ‘It’s all just negative feedback’ is one such.
Once you have appreciated that that is in fact the correct statement, according to current engineering terminology, you can then access the whole body of what is known about negative feedback systems to help describe and understand the phenomenon.
If all people were engineers , you would be 100% correct . Clearly , all people are not engineers . These people may insist that their terminology is correct and yours is not … so how do we best communicate with them ?
(A problem engineers face ….daily ?..whether or not they realize it …(8>))
Bob wrote:
You don’t do it by completely breaking the conventions used throughout the field. Or are you suggesting that we re-educate every engineer and rewrite every textbook on the subject? Perhaps we can do the same with medicine and finance.
The only way to deal with it is to educate the non-engineer on the proper use of the terminology.
A forcing implies a temperature setpoint. The earth works to maintain that setpoint. That’s a governor—a governor that employs feedback to approach the setpoint.
If the temperature (read speed) exceeds the forcing-dictated setpoint, net top-of-the atmosphere downward radiation (read fuel use) decreases to reduce it. (Not that radiation imbalance is a different animal from forcing.) If the temperature exceeds the forcing-dictated setpoint, net top-of-the atmosphere radiation decreases. “This leads to a very curious situation”: as the temperature goes up the net radiation goes down.
In other words, we say potato, Mr. Eschenbach says potahto. Distinction without a difference. Let’s move on.
Well another way of looking at what he is saying is simply this.
“Systems with negative feedback can contain their own causes for change.”
In other words the climate changes all by itself. No need for radiative forcing from excess CO2 or anything. Given enough non linear feedback and time delay inherent in it, the climate will wobble around unpredictably even if the sun shines constantly and the CO2 never budges a single ppm.
The other way of saying this is this.
‘Observed climate change is fully consistent with no external forcing at all‘
Think about how much more radical that statement sounds than the original…
Excellent point!……. very minor addition to your summary statment.
‘Observed climate change is fully consistent with no change in external forcing at all‘
It’s difficult to explain to non-engineers (or at least those without a solid college level mathematics background) and especially anybody who hasn’t formally studied control theory how excessive delay in the response of any simple negative feedback system will cause oscillation about the set point of the system.
Should have been “Note that radiation imbalance is a different animal from forcing.”
I’m not celebrating yet, but offer my congrats. The otherwise tainted Wikipedia offers insight ranging from plain language for the lay person, to in-depth complex math for those who prefer abstract symbols, into control system theory in their “PID Control” article. Beware, their terminology isn’t perfect either.
One simple comment is all that was needed to point out Willis’ slight error in terminology. Any ADULT could make note of the issue and move on. All the extremely small people piling on here strike me as Antonio Salieri wanna be’s to Willis’ Mozart.
Please people, lets get back to the point of the article.
Actually, it’s BECAUSE Mike, Leo and others were willing to go into in depth description and the workings of control systems (a thing I know little about) that I now understand how Willis’ cloud governor theory could be right even though his use of terminology was wrong. Now if Willis can use this to rewrite his theory with the correct terminology and a good understanding of control system, his idea will be able to spread quickly among those who work with them.
Thanks Dave, that was the only reply so far and very valid and why doesn’t any one see that ? I have followed Willis and his observations of the Tropical thunderstorm and cloud formation as a typical day happens for years no. Maybe to some it was not filled with graphs, journals and eons of data. To me it had the most important thing.
Logic!
Dang, should have read” Thanks Dave, that was the only reply so far I agree with”.
When I think of governors I think of limiting devices. When growing up in NY state, our school bus had a governor that limited the speed of the bus to 50 mph, in college at a factory, the centrifuges had governors on them. In these example, control would always be negative.
“What that means is that a change in temperature causes a change in forcing”
…
Your “model” is useless in explaining the advance and retreat of glaciers.
Someone wrote to me and asked me if I had written this on Anthony’s blog. A was astonished and had to answer “no.”
If that’s your authentic name, congratulations. If it isn’t, please pick another pseudonym. Thanks!
Brian G Valentine
Arlington, Virginia
US DOE & OAEE UMCP
Willis,
Keep up the good work.
Looks like you need to use smaller words and more verbosity to keep highly focused, but blinkered, folk on the reservation.
I view that your statements and meaning are clear.
……”for over speed, the governor applies a feedback negative, i.e. to slow down, the system,
……for under speed the governor applies a feedback positive, i.e. to speed up, the system”
“feedback positive to the speed” vs “positive feedback” in clear context?
On tropic climate, there is “a feedback that is negative to change”:
….when the temperature is higher than the set point, clouds form
….when the temperature is lower than the set point, few clouds form.
-> one is ” negative” to the temperature, and one is “positive” to the temperature.
Ignoring “negative to change” feedback in the “pursuit of money” is…..
Willis
Think you have missed the obvious. The control system (governor) didn’t changed, the feedback did. The hill is a negative feedback when the car is going up the hill (fighting gravity). The engine must overcome friction, wind resistance and gravity. But it becomes a positive feedback when the car tops the hill and starts down the other side (assisted by gravity). The engine + gravity must now over come only friction and wind resistance.
Look at your analysis again and see if that makes a difference.
Basic process control uses PID (Proportional, Intergral and Derivative), or some variation (P+I, P+D {rare} or P+I+D). More advanced algorithyms are used to address more extreme systems, such as highly exothermic processes. The typical cruise control on cars is P+I.
Systems dominated by positive feedbacks will eventually saturate at one extreme or the other. Systems dominated by negatived feedbacks will fluctuate within an envelope of acceptable conditions but rarely stay in a saturated state. Think about a bowl and a ball. If the bowl is upside down with the ball on top, once the ball goes over the edge, it will roll or fall to the table. If the bowl is right side up, the ball will roll around inside the bowl but will always eventually come back to the bottom. The ball will only leave the stable condition if acted upon an unusual outside forcing, such as a gamma ray burst that adds a great deal of energy to our contained climate system in a relatively short period of time.
Earth’s climate exhibits all the character traits of a system dominated by NEGATIVE feedbacks. The AGW crowd assume it is dominated by positive feedbacks. Although we have seen “Snowball Earth” twice in our geologic history, Earth’s climate has never displayed runaway warming even when CO2 concentrations reached 7,000 ppm. If it didn’t do it then, it sure as hell won’t do it at 400, 500 or even 1,000 ppm now.
AGW is about “Control” and “Fear”, not about science!
Love your posts.
Bill
Sorry I am with the “It’s all negative feedback” and Engineers. You start using the term positive feedback and as they said you are describing a system that will go into runaway either to destruction or some other stable state. That is a system that has a tipping point that the climate catastrophe true believers will tell you about. A cruise control on a car should ideally contain no tipping unless it’s a jeep that has been hacked.
A governor operates purely by negative feedback, however in any real-world system a problem we encounter is that there is a measurable time lag between applying a corrective change and the the correction appearing at the output. Thus if the corrective change is applied too rapidly or to too large an extent, the result will be an overshoot, because the correction cannot be withdrawn fast enough to keep the output from exceeding the desired level. In extreme cases the output may keep on overshooting alternately above and below the required value, in a process termed ‘hunting.’
The simple cure for hunting is to make the governor’s responsiveness slower than that of the process it controls. (in the tried and tested principles of cowboy electronics, slap a honkin’ great capacitor across the input sensor lead) The problem with this approach is that it also makes the governor rather slow to respond to errors.
The proper solution is to design ‘lead/lag’ compensation which tailors the governor’s response to not only the amount of error but also to the rate at which the error is being corrected. Thus, a large static error will result in a large correction, a small and reducing error will be given only a very small correction. A small error which is reducing too rapidly may even be given a reverse correction so as to prevent an overshoot.
An interesting area of engineering, and one in which achieving excellent results is not a trivial exercise.
What Ian said.
it’s called phase and gain margin. You design the loop to cross unity gain at something other than 180deg phase shift or vice versa.
I’m not an engineer, so I don’t know what the actual definition of positive or negative feedback comes from, but I’ve always loved operational amplifiers (OA) and they work by taking some of the output of a system and feeding it back to an input of the OA. This can be done either at a positive feedback terminal or a negative one, and I think that’s what Mike and others are talking about. But for everyday people they’re worried about whether the voltage inputted to the OA is positive or negative. So the actual source of confusion is not which input the signal is entered at (I agree it will be the negative feedback input), but whether the signal entered is a positive or negative value.
BTW, I knew “OA” didn’t look quite right. The usual abbreviation is “Op-amp”. And if I recall correctly, “negative feedback input” is usually called the inverting input.
An interesting thing about control loops is that you cannot troubleshoot a closed loop system. Also, as long as a system is within its control range, you cannot see the limits of that control range. What are the limits of the control range on the climate system? You cannot know, unless you can drive the system out of the control limits. IF you do that, the system will drive to one side (high or low) extremely rapidly.
Additionally, in a dynamic system, the feedback path will appear nonsensical. It’s kind of like watching a craps game without knowing any of the rules… the feedback signal really doesn’t appear to make sense (if you even know how to observe it), because the error amplifier behavior will be unknown (unless it was previously quantified). Thus, you can’t understand what you’re seeing in the feedback path, because you do not have the cognitive ability to understand the signal even if you know what the error amplifier is doing. And this is on a simple first or second order system. That’s why control loops are described mathematically.
This is a classic troubleshooting problem. As my mentor used to hammer me (repeatedly) you must open the loop to troubleshoot it. This allows you to inject static stimulus and observe deviation from the closed loop performance. It allows you to measure the behavior of the individual sections.
In some closed loop systems you can “ping” the system with a known stimulus and observe response behavior which will tell you certain things, but I would not expect most academicians to understand those methods. This is one reason it is alternately entertaining and frustrating to watch “climate scientists” attempting to rediscover control theory.
Despite this, control loops are fairly trivial… (eh, well, it is painfully difficult to learn the theory), but are so well understood that a competent engineer can design one without much difficulty. So if you’ve designed it, you know what it’s doing and what the limits are by design.
To me the term governor does not sound appropriate for a natural process. A governor implies that it is there by design. It also implies that the system goes to a set point but history shows there is no set point.
I think looking at this system as being stable, neutral or unstable makes more sense. History again seems to show that the system is quite stable but it does move to different equilibrium points over time. The idea that the system might be unstable and will be sent off into terrible conditions at some tipping point seems hardly possible. The question then might be how stable is the system.
There are ways to evaluate stability in physical systems and maybe this has been already done or tried with the climate.
Also a “governor” sound too political but the idea of natural stability seems far from a political concept. 🙂
Hi Erik,
Systems can have more than one stability point. Think of it like a rubber sheet with a couple of indentations in the sheet, the depth of which is related to the stability at that location (the deeper the indentation, the more stable at that point). So in a system like that, you can displace the current stability location given a large enough stimulus to push the thing over the hill into the next stability region. Then it will tend to stay near that until displaced again by a large enough input.
Gerry, very true but I would not expect that normal disturbances would push the climate into such a new stability point.
But even a relatively stable system, can have values move about the stability point depending on the disturbances and responses and even change the stability point as things are added and taken away from the system. Complicated for sure but not necessarily chaotic.
One of the few things I remember about Thermodynamic in university was that in general the final steady state conditions of a closed system were dependent on the net input/outputs to the system and were independent of any of the processes within the system. And I am not even sure I remember this correctly. 🙂
[snip -fake commenter using assumed name -mod]
Yes, the cruise control directly controls the throttle – for the purpose of controlling the fuel flow – for the ultimate purpose of controlling vehicle speed. To be consistent, you should not say the ECS computer controls the fuel flow either, as it actually only directly controls a certain voltage… If you allow yourself to say the ECS computer controls the fuel flow, you should allow Willis to say the cruise control controls the fuel flow.
SR
Confusing positive and negative feedback is as ridiculous as saying that when you drop something it will fall upwards because of gravity. Claiming that everything is right apart from the terminology does not help!
In my view the car analogy could be improved. Firstly, most people know about speedometers but to keep to a set point we do not need a speedometer. We just need to know whether we need more gas or less. So we need a meter with a centre zero.
Secondly, instead of using speed which has inbuilt notions of positive being faster and negative being slower it would be more educational to use steering. Our centre zero meter would indicate left or right. Maybe one would be positive in some sense but that would not be relevant.
The point would be to keep the meter at the zero (set) point, then, when you get blown off course to the right, the meter says “go left” so you steer left. The feedback itself is agnostic, it has no concept of positive or negative. The point is that you need to restore the centre zero meter back to zero – negating the change hence negative feedback.
OK, this is where this whole thread starts to make sense to me. Everything is negative feedback if it drifts from the setpoint. So there really is no such thing as positive feedback unless the goal of the setpoint is to “change the current state.”
Is this right give what you’ve just said?
And if it’s right then from a climate modeling standpoint there can be no positive or negative feedback, since the climate system has no given setpoint. All you can have is various processes that change at changing rates. So maybe it’s the use of the term “feedback” that is getting a lot of people hung up. Further, the notion of “regulation” doesn’t make a lot of sense to me either.
@MftMW: Following my steering example, imagine the wiring to the centre zero meter to be swapped over. So, if you were blown off course to the right the meter would say turn right. So rather than correcting the change you would be compounding it.
This is why positive feedback is “not sustainable” to coin a phrase. It is why people argue that whatever positive feedbacks there are in the earth system they have probably already been tripped sometime in the last 4.5 billion years.
explain night
When the sun goes around to the other side of the earth.
:slow clap:
To jump on the pedantic wagon 🙂 more technically when the observer side of the earth is turned away from the sun.
Steven Mosher August 2, 2015 at 7:55 am
Explain your comment.
w.
The problem with the ‘Governor’ affect is that it only applies to a portion of the system. The system is more like a bunch of cars going down the roads. Some of the cars are idling at stop lights, some are coasting to a stop, some are accelerating, most are going at a steady speed or stopped altogether.
If the supply of gasoline goes up, what happens to the average speed on the highways? That is similar to what happens if the supply of CO2 goes up, what happens to the average temperature.
OK maybe the critics would be happier if the article contained “…creates the illusion of…”
Then the graphs would be interesting without offending the engineers.
Andrew, the problem with engineers is that we are held accountable for our designs. Thus, we cannot just publish crap claiming it represents truth. This leads to a certain discipline of thinking and intolerance of sloppiness or (willful error, particularly politically driven willful error). By the way, none is harder on an engineer than his fellow engineers (and we all make mistakes btw). It’s still a field where respect is earned.
“Thus, we cannot just publish crap claiming it represents truth.”
Was not a swipe at Willis. I was thinking of climate scientists. Willis makes a real effort to understand things and publish thoughtful articles.
Willis is also usually willing to rethink something if an error is explained in a way that he can Grok, which I expect is why he’s been so quiet in this thread. Maybe reading up on control systems and PID like I’ve just been doing. Always fun to learn a new way of looking at the world. ^¿^
schitzree August 2, 2015 at 10:38 am Edit
Dear heavens, why are peoples’ speculations on my inner mental state and my actions often so far from reality? schitzree, I was “quiet in this thread” because I wrote it on six hours sleep in two days, and then I went to bed. And strange as it may seem, when I’m sleeping I’m usually “quiet” on all threads.
When I got up (late of course) I read the thread, saw my error, and I acknowledged it and corrected it immediately. So your unpleasant suppositions about me are all you, nothing to do with me. Which should lead you to reflect on whether you assuming the worst interpretation of my actions is something you might want to re-examine …
w.
A governor is a mechanism, circuit, or algorithm that uses feedback to maintain a certain output.
I think some further confusion exists regarding what these regulators do. For example, some regulators sense rate of change and respond. Others, notably older marine autopilots, sense a compass point and try to hold that. Rate systems can be used in marine autopilots but they also need a fixed reference (compass, magnetic or gyro) because there’s no point in reducing rate of change of heading through rudder angle if the heading walks off over time.
The automobile speed controller is necessarily imperfect in holding speed and that is because the error between actual speed and intended speed can never be reduced to zero. Zero error equates to no input change of throttle. So when going up a hill a car’s speed is necessarily less than desired because if it were not there would be no throttle input to compensate for the hill and the car would slow. In fact in vacuum powered throttle position actuators this happens in worn engines. The actuator opens the throttle, the manifold vacuum drops, the actuator can no no longer respond linearly, and the car slows to the point the transmission will downshift in a sudden lurch that both increases the manifold vacuum and causes the throttle position to go to the floorboard.
Humans get around this by intelligently applying appropriate throttle for the conditions, and people can anticipate because of complex inputs what will be needed for throttle under varying conditions (down hill, sharp corner). Humans also have access to braking which is not available to speed controllers.
Faulty nomenclature, otherwise all good…
Thanks, gymnosperm. While I understand why my error in nomenclature has people concerned, some folks like yourself are able to look past that.
w.
Willis,
A number of others have already made these points verbally, I’ll put them in the form of equations. Consider a simple energy balance model of the atmosphere (yes, this is oversimplified, I use it to illustrate the principle). We have
dH/dt = R
where H is the enthalpy of the system measured relative to some reference state and R is radiative imbalance. H can be written as a product of a suitably averaged heat capacity, C, and a suitably averaged temperature, T, measured relative to the same reference state as H. Since C is constant, our equation becomes
C*dT/dt = R.
Let’s suppose that the reason that R differs from zero is due to some exogenous change, like a change in the solar constant. We call that exogenous change the forcing, F. If the change happens instantaneously at time t=0, we have
C*dT/dt = F at t=0
But T now starts to change and that causes a change in the radiative balance. For small enough changes in T, we can assume a linear response. Then the change in R due to the change in T can be written as
delta_R = -lambda*T
where lambda is a constant and the minus sign is included to indicate that an increase in T causes a reduction in net incoming radiation (most directly via an increase in outgoing radiation); i.e., a negative feedback. Including this in our equation, we now have
C*dT/dt = F – lambda*T.
This is exactly analogous to your example, with T instead of speed and R instead of fuel use. Stepping on the gas (increasing F) increases T and R. But increasing T reduces R. Exactly the same reversal of sign as in your example. That is a general property of a negative feedback control system.
You wrote: “What that means is that a change in temperature causes a change in forcing”.
A change T causes a change in R. You could call that “forcing” if you like, but in that case you have to be careful to distinguish between the exogenous forcing, F, and the response forcing, lambda*T. You have not done so.
“And that is why I say that the current method of analyzing the climate is totally incorrect, because it assumes the causation is going the opposite direction from what is actually occurring.”
No, you are totally incorrect since you have used forcing to mean two different things, without realizing it.
I suppose someone will respond to this by saying “but climate models have positive feedback”. I’ll explain that misunderstanding when the time come.
Mike M. (period) August 2, 2015 at 8:37 am
Thanks for the math, Mike. I am in total agreement with you except for the part above, where I’m not seeing the difference.
Exogenous forcing is composed of the solar input minus the cloud reflections.
Response forcing is is composed of the solar input minus the cloud reflection.
I’m not clear about the difference you are pointing to. Not saying you are wrong, just saying I don’t understand the difference you are pointing out between the two, since both seem to me to be the same phenomena.
Regards,
w.
Willis,
“Response forcing is is composed of the solar input minus the cloud reflection.”
The response forcing depends on T, so it certainly does not include the solar input. It could include cloud reflection if there is a T dependent cloud cover. But it will mainly be a change in IR emission.
Thanks for the clarification, Mike. You say:
I have demonstrated through several independent datasets that there is indeed T dependent cloud cover, one which is strong enough to drive the temperature down in the face of increasing TOA solar input.
Since the change in incoming solar due to T dependent cloud cover is typically on the order of hundreds of watts, while the change in IR emission is typically on the order of watts, I’m not sure why you say the response is “mainly” a change in IR emissions. What am I missing?
w.
Willis,
“Since the change in incoming solar due to T dependent cloud cover is typically on the order of hundreds of watts”
No way is that possible, at least if you mean the usual W/m^2. Average reflected solar from clouds is only about 45 to 50 W/m^2, variations due to global T change are not more than a fraction of that. In fact, there is no real evidence that the change is different from zero. Instantaneous, local variations in incoming solar might be very large, but you can not compare that to numbers that are averaged globally and annually.
“I’m not sure why you say the response is “mainly” a change in IR emissions. What am I missing?”
Anthropogenic forcing, F, is about 2.3 W/m^2 (for brevity, I am not going to bother with error bars) and the imbalance, R is about 0.5 W/m^2, so lambda*T is around 1.8 W/m^2. The “Planck response (Stephan-Boltzmann)” is about (0.85 K)*(3.3 W/m^2/K) = 2.8 W/m^2, so the other response (water vapor, lapse rate, albedo, cloud “feedbacks”) contribute combined about -1.0 W/m^2 (net positive). So the direct IR response seem to dominate.
Note: There are two ways that people use the term “feedback”. One includes the Planck response, in which case the feedbacks are net negative. The other refers only to the non-Planck responses, which are net positive. The first is the one that is consistent with the terminology being used here.
Mike M. (period) August 2, 2015 at 12:38 pm
Thanks, Mike, I think we may be talking about different things. I’m talking about the strength of the governor, which operates on a daily basis, not on an annual average basis. Here’s daily data from the TAO buoys:
As you can see, cloud variations easily can cut 100-200 W/m2 out of the incoming solar.
Regards,
w.
Willis I am glad to see you have responded to my many post on this subject to a varied degree with this article.
I am interested in solving the climate puzzle as you must be. This is why as I have suggested before I think it would be of value to have a subject about what possibilities or combination of factors can come about in such a way to over come the governor on the climate to a point which is strong enough to take the earth from an Inter- glacial state to a glacial state and vice versa.
Willis you must be thinking about this and I think it is a topic that would be very is worth while.
Salvatore Del Prete August 2, 2015 at 8:37 am
Since I’ve never seen a single post from you on this subject, your idea that I am “responding to” your posts is just your self-importance speaking …
w.
Is this really an issue?
Negative feedback attenuates deviations. Positive feedback amplifies deviations.
BTW, I posted this before, but here is some fun video feedback. I used to love playing with it.
We know the climate has a regulator of sorts but what we do not know are the influences which can overcome this regulator enough which allows the climate of the earth to vary enough to bring it into different climatic regimes although the extreme boundaries warm or cold do have a limit.
Why ? That is the question and it is elusive. Very elusive.
Any natural regulatory system has bounds on the variations it can control, and there are events that could alter or destroy the regulation.
A quote from Willis, (the above sentence) which is one of the most important things ever to be said when it comes to the climate. It is spot on and the heart of the problem.
Hasn’t happened in 4 billion years, so probably not a concern. I’d be more worried about ebola.
Question:
Does the current obsession with “selfies” produce positive or negative feedback loops?
My answer would be “positive” — they tend to amplify narcissism — thus making selfies NOT governors.
Haven’t you heard? Selfies are passé. The latest narcissistic obsession are “dronies”: a selfie from a drone.
Don’t ask me to explain…
This whole argument breaks down into one of perspective. It reminds me of several years ago they were interviewing a geologists on television. While standing somewhere near the middle of Wyoming, he said: ” The equator use to run right through here” as he pointed at the ground beneath his feet. ** Wrong *** The place where he was standing use to be located on the equator. It is all a matter of perspective.
Willis is merely looking at the system from the standpoint of how much fuel is necessary, more/less equals positive/negative feedback. The engineers are looking at the system from the set point (i.e., intended speed). When the speed varies either plus or minus, it takes a negative feedback to return it to the set point. A positive feedback increases the deviation from set point.
Actually, Will’s point of view is probably more easily understood by the non-engineers in the crowd. It is also just as valid from a systems point of view. You can tell by the reactions of the poor control engineers that they have had he “negatives” of “positive feedback” drilled into them so hard, and for so long, just the mention of the words causes a “valvie”.
No, these are accepted, well-defined terms with a precise meaning. It is not a case of ‘ oh I think I’ll redefine for the layman’ , the use was wrong. W has corrected the article. If you also imagined it meant something else, you have once again learnt something from visiting WUWT.
How does this relate to the climate? Well, the underlying climate paradigm is that the forcing controls the temperature, such that a change in forcing causes a change in temperature.
On the other hand, I’ve proposed that there is a natural governing system regulating the temperature of the climate, a major part of which works as follows.
Willis further says which again is the heart of the problem for why nevertheless the climate changes.
Why why why????
It deals with a general epistemic problem in the sciences. Specifically that of dealing with assigning causes and analyzing them. This is just a specific case of ‘correlation is not causation’ with an illustration of how and why that can be.
I teach Physics and Environmental Science. I will use this article as well as the Comments this year in class.
Also, climate is, of course, very complex. To make things even more complicated, there are undoubtedly mechanisms that not only vary with temperature in the intensity of their effects, but there are also some mechanisms that only work over certain temperature ranges, thus turning on and off as factors in climate. Nothing can be assumed to be a constant factor, even the Sun, as ingenuously assumed by the IPCC.
For starters, let me offer my definition of a governor. A “governor” is a control system that uses both positive and negative feedback to maintain some system variable near a “set point” value. A common example in our daily lives is the cruise control on your car. It increases or reduces fuel flow (positive and negative feedback) to maintain the vehicle speed near some pre-set value.
There are “self-organized” systems, “evolved” systems (random variation and natural selection, as with biological organisms; also human success with “trial and error”), and “designed systems”. Your argument incorporates the ideas of the Reverend William Paley’s “argument from design” about the existence of God, and the modern arguments about “intelligent design”. That is, it does so if it is an “argument” instead of a bald “assertion”. Designed systems are explicitly teleological, with parts and attributes selected in advance to achieve a goal or improve upon the system as it is. Evolved systems have been modified with at least some randomness (independence of the goal or function), and selected post hoc when they are better than their predecessors. Self-organized systems are observed to operate with describable characteristics or within bounds because of the properties of locally-acting processes; they are also systems with “emergent properties”, but have not been explicitly designed or selected in order to achieve those describable characteristics and bounds.
Random variation and natural selection can be observed in every population of living things that has yet been studied. Intelligent design can be observed in the design and manufacture of automobiles and aircraft (though they are not completely deterministic — some ideas work better than others and are selected for more development), and self-organization can be observed in a lot of chemical systems such as “reaction-diffusion” reactions (and in some “deterministic” computational systems such as high dimensional non-linear dissipative systems, where the equations are not selected to achieve any particular behavior in phase space.)
When I questioned your use of the word “thermostat” I was not questioning your analysis of how it works (that may have been separate, though I think your analysis of clouds is basically sound), I was questioning the teleology implied by calling it a “thermostat”. What evidence have you that any of the properties of the system were designed or selected to produce any of the regularities of the observed system? Did some agent place the Earth within a range of distances from the sun to produce life (contrary to Mars and Venus), either by design or by trial an error (the “Goldilocks position” after the inadequacies of Mars and Venus). Did that agent create oxygen with the capacity to make ozone to protect us from too much sunlight and also to permit our biological energy processes? Did the agent create metals so that the process of random variation and natural variation could evolve enzymes like hemoglobin and chlorophyll? Some people answer those questions in the affirmative: Christians, Deists and more. But to paraphrase a famous aphorism, the invocation of the Agent adds nothing to the understanding of how the system works.
I appreciate and understand the engineering wonks and pedants getting their knickers up about ‘positive feedback’ and ‘governors’ precisely because Willis is using some of their terms. This despite that Willis could have, and did, call his terms anything and define them for the purposes of his argument.
What I do not appreciate are people in a deep search for problems that they can answer with their pet religious views. People such as yourself. When Willis moves on from descriptives to origin myths, please have my every encouragement to jump in and postulate your own. Indeed, feel free to rebut any origin myth that Willis or anyone else raises at that time.
Until then, be happy that your religious zealotry has been duly noted; and put a sock in it.
Matt, I generally value what you say, but you lost me here. What is your point, exactly? You are free to question the teleology of calling what is going on a “thermostat”, but I don’t understand just what word you might want to replace it with.
It seems that your objection is that you think there could not be a natural thermostat … despite the fact that there are natural heat engines.
So I’m just not getting what you’re trying to say. Could I ask you to boil it down into the “elevator speech” version, and make your point clearer?
Like I say, I ask because your thoughts are usually interesting.
w.
Willis: You are free to question the teleology of calling what is going on a “thermostat”, but I don’t understand just what word you might want to replace it with.
“clouds”
using a thermostat to explain the workings of the cloud feedbacks has the same conceptual problem as using “greenhouse” and “blanket” as analogies of the CO2 effects. Understanding greenhouses and blankets does not actually illuminate the discussion of how the CO2 produces its effects, and causes some people endless confusion. (e.g. [Adding an extra blanket can not “cause” additional body warming because the blanket is cooler than the body, so adding CO2 can not cause additional Earth surface warming .])
The thermostat and the cruise control have another important property in their workings that is absent in the clouds: somebody can “set” and “reset” the thermostat or cruise control. It isn’t at all clear that anyone can set the clouds, and the idea that we can set the clouds by controlling the CO2 is at the heart of the policy debate. If we could set the clouds by controlling the CO2, then the clouds might be like a thermostat. But your basic argument is that the cloud system is self-organized, and can not be set. At least I think that is your basic argument.
Thresholds, thresholds and thresholds are a big factor in a non linear, chaotic, random system such as the climatic system is. This if/when reached puts the governor on the climate system to the test.
For those who missed my statements on individual threads, I agree totally with those who have said that a generator uses just negative feedback … my bad, written on six hours sleep in two days. I have changed the two incorrect statements in the head post to reflect the correct terminology, and they have my thanks for pointing it out.
Let me add that this doesn’t change either the other statements or my conclusions in the post.
Regards to everyone, this is the beauty of the web. My mistakes don’t last long without being revealed … not always with the kindest of intentions and words, but that is the way of life, and I’m happy to have been corrected.
w.
Hi Willlis
This post brought to mind Le Chatelier’s Principle I was exposed to in chemistry classes. I am sure you can make an interesting post discussing Le Chatelier’s Principal and climate “change”…
kalya22,
This does indeed *resemble* Le Chatelier’s Principle but it is not a result of Le Chatelier’s Principle. That rule only applies to systems at thermodynamic equilibrium. Systems not at equilibrium might or might not respond as expected from Le Chatelier’s Principle, so it provides no predictive power in such cases.
Mike M. (period) August 2, 2015 at 10:33 am
Mike, what evidence do you have that the earth is NOT at thermodynamic equilibrium? It only heats or cools a tiny amount over centuries (± 0.3°C over the 20th century). How is that not thermodynamic equilibrium?
w.
Willis,
The temperature is not the same everywhere, therefore not at thermodynamic equilibrium.
The earth is in something approximating a steady state, if you don’t get too picky. Some people call that “equilibrium”. But that is certainly not “thermodynamic equilibrium”, which has a very specific meaning.
Brian,
“With swings of +/- 5 degrees C, with the associated glaciation and retreat in the long term (800K yrs) it’s hard to characterize it as “steady”.
I tend to agree, which is why I said “if you don’t get too picky”. And, of course, on time scales under a year, it is not at all steady.
Brian G Valentine August 2, 2015 at 12:19 pm
Thanks, Brian. You are correct. While the earth is thermodynamically stable, it is not in thermodynamic equilibrium.
However, let me add that that I don’t think that Le Chatelier’s Principle only applies at thermodynamic equilibrium as you said above. Le Chatelier said:
For example, the ocean is a buffered system which is (generally speaking) at chemical equilibrium. but far from thermal equilibrium. Le Chatelier’s principle operates there regarding the chemical species of the ocean.
As to whether the global climate system obeys Le Chatelier’s Principle, I’d say likely not … but instead, it obeys the dictates of the Constructal Law, which often amounts to the same thing. You might enjoy my posts on the subject, here and here.
Best regards,
w.
Willis,
“For example, the ocean is a buffered system which is (generally speaking) at chemical equilibrium. but far from thermal equilibrium. Le Chatelier’s principle operates there regarding the chemical species of the ocean.”
Actually, the ocean is not at chemical equilibrium. For example the pH varies from place to place and with depth.
In the real world, thermodynamic equilibrium only occurs on limited scales of time and place and within some limited range of accuracy. I might have liquid acetone at dry ice temperature in a Dewar flask and have it be usefully close to equilibrium for the duration of some experiment, but if I come back in a week I will likely find it to be at room temperature. Similarly, I might be able to treat some finite chunk of the ocean as being in thermal and chemical equilibrium even though the ocean as a whole is not. An example is measuring temperature; that is something that can technically be only done in a system at equilibrium.
I never heard of the Constructal Law before. At first glance it sounds both fascinating and crackpot; I will have to set aside the latter impression until I learn more. I seriously doubt that it has any meaningful connection to thermodynamics, but that does mean it is not useful.
But I would think that the Constructal Law is not useful if you can not predict a priori what the correct quantity is to extremize. You might suppose that a flowing river tries to maximize length, but I am pretty sure that it tries to minimize length (or maximize slope). Meanders occur when the slope is small as a result of a positive feedback loop that drives the flow away from the optimum, until it snaps back. The point here is not which view is correct; it is that you can’t get a reliable result until you know what extreme is “sought”. Maybe when I learn more, I will learn how to answer such a question.
A question for Willis:
Your proposed governor mechanism would tend to maintain a given “level state” of the climate system, as I understand your position. You point out that this is consistent with the evidence to within a decent tolerance (ie a very small percentage variation in average temperature pretty much throughout Earth’s history). My question is, what in your opinion determines what that level is in the long run? I apologize if you’ve been over this before, I can’t recall reading anything you’ve written to that effect.
Good question, Andrew. I doubt that there is a simple answer. The climate temperature control system is quite complicated. It includes many emergent climate phenomena, including inter alia clouds, thunderstorms, El Nino/La Nina pump, and dust devils. Some complex combination of these determines the global average temperature but I don’t think disentangling them is possible at this time.
w.
Andrew_FL says “My question is, what in your opinion determines what that level is in the long run?”
Pardon my jumping in here… The phase transitions of water are the boundaries over which the control system can operate. Exceed either boundary and it can “lock up” as for instance “snowball Earth”. The Earth remarkably has all three water phases (vapor, liquid and ice) concurrently and climate regulates, and is regulated by, the proportions of these phases. Weather is heat trying to reach the ice from the tropics.
Earth appears to have more than one stable state; the long glacial periods (100 thousand years or so) and the interglacials (ten thousand years or so). It also has a snowball state (very bad for life) and a hypothesized-by-warmists Venus state exactly the opposite of snowball.
I very much appreciate Leo Smith’s contributions here to the discussion. I have been thinking for some time that the real issue is whether or not climate has overall negative or positive climate feedback systems. The warming crowd have fixated on one potential variable in CO2 and decided that it is positive to warming and there are no offsetting negative variables This seems to me to be extremely unlikely given that earth has had a fairly stable environment for most of 3 billion years. This in spite of significant variation in CO2 levels. Additionally, Leo Smith mentions the tremendous amounts of heat transported upwards ( and outwards) by water vapour. This heat transport mechanism is a powerful and pure negative feedback on temperature, aided by the ability of warmer air to hold and therefore transport greater amounts of heat as temperatures rise. It seems to me that climate change has become an intellectual industry that consumes a fantastic amount of human effort in what I fear is a very wasteful pursuit of a solution to a problem that doesn’t exist. Can it be that hard to actually measure earth’s heat input versus output from space?
John Harmsworth,
“The warming crowd have fixated on one potential variable in CO2 and decided that it is positive to warming and there are no offsetting negative variables”.
That is simply not the case. All climate models, even the simplest as in my post above, include the “Planck feedback” (which I called “Planck response” above). If you change the radiative balance (say, with a change in solar output, or a big volcanic eruption, or by changing CO2), the temperature changes in response. That causes IR emission to change, via the Stephan-Boltzmann law. And that restores the radiative balance, at a slightly lower or higher T. So there is negative feedback that makes the climate system stable, in the sense that it does not run away.
The confusion comes from the fact that there are knock-on effects, such as changes in water vapor and clouds. Some people reserve the term “feedback” for those additional effects, excluding the primary Planck response. If you use that terminology, then a “positive feedback” means an overall response that is less stabilizing than the Planck response alone and a “negative feedback” means more stabilizing than the Planck response. Personally, I find that very confusing.
Congrats to Willis for knowing when to back down. The difference between positive and negative feedback isn’t trivial semantics; it’s the difference between systems that are inherently unstable and inherently self-stabilizing. Big, huge, important difference.
If you’re interested in a discussion of terms I suggest Otto Mayer, “The Origins of Feedback Control”, MIT Press, 1970. He opens with a discusssion of the feedback theory of Watt’s centrifugal governor. Both feedback and governor are in one sentence since there’s no real distinction between them.
His definition of feedback is
1. The purpose of a feedback control system is to carry out commands; the system maintains the controlled variable equal to the command signal in spite of external disturbances.
2. The system operates as a closed loop with negative feedback.
3. The system includes a sensing element and a comparator, at least one of which can be distinguished as a physically separate element.
In terms of the earth’s climate the input is obviously sunlight but exactly what is the output? Temperatures, clouds, precipitation, wind, local or global values,…, exactly what?
The “feedbacks” are obviously albedo and radiation to space since they subtract from the net solar input of energy to the oceans and atmosphere. The top of the atmosphere might be considered the comparator since the “difference” of input and output energy occurs there. But in a standard feedback loop the difference is with respect to the set point, the desired value of a variable, e.g., the speed. What’s that here? Is there some desired net energy input to the climate system with the interals just natural fluctuations?
The use of feedback terminology in climate science is a complete misuse of the concept. What they actually have is a system of coupled nonlinear partial differential equations with nonlinear couplings. Good luck with solving that.
Perhaps then you’d appreciate this cartoon.
http://www.maxphoton.com/straight-talk-on-art/
paullinsay August 2, 2015 at 1:05 pm
Thank, Paul, but “No real distinction between them”??? The governor is what he is calling the “feedback control system”. A “feedback control system” is most assuredly different from “feedback”. A governor is a control system which USES feedback, which means the control system and the feedback are not the same.
The “comparator” is provided by the tropical cloud system, which forms clouds when the local temperature (more properly ∆T, but in any location that averages out) exceeds a certain value. As a result, more clouds form when it is warm, and less clouds form when it is cool, and the “set point” is the local temperature at which the clouds form. See my post “The Thermostat Hypothesis” for a discussion of the issues.
Thanks,
w.
I say tomato, you say tamato, … ;-). It should be Mayr.
I think that your mechanism, which I’m not disputing, is subsumed in albedo and radiation as a combination of both, though black cloud tops absorb sunlight rather than reflect it.
The real issue is that the climate system is too complicated to be described by a simple one variable “feedback” system. There is no single control knob in CO2 that adjusts the global temperature, which is a meaningless unphysical concept anyway.
Nobody has mentioned what I believe is the real problem with Willis’ example yet so here’s my take on it. I’m also puzzled as to why nobody else has mentioned it yet because I know there are some experts in control system theory who watch this blog. Perhaps others commented on this above but I missed it?
SYSTEM IDENTIFICATION.
Go read up on the topic of system identification in control system theory as well as what the “state” of a control system is. For example, here:
https://en.wikipedia.org/wiki/System_identification
or
http://controltheory.org/
and many other places on the internet as well as any undergradutate text in control theory.
In Willis’ example, the system input is the desired speed. System output is the actual speed. The “plant” in this case consists of the engine computer, engine, transmission and speedometer. The input to the plant is a desired throttle setting — which is determined by the cruise control based on the difference between desired and actual speeds (that’s the feedback part). Fuel flow is an internal system variable that is indirectly driven by the engine computer.
Target Speed ==> Difference ==> Throttle ==> Engine Computer ==> Fuel Flow ==> Car ==> Speedometer
^ |
|———————————————–<– Feedback —-<———————————–|
When you look at fuel flow, it does not make a lot of sense in the example because you have started with the idea that fuel flow directly determines speed — and it does not. You have not correctly identified/modeled the system. Instead, if you make a proper model of the system:
1) Plant takes a throttle setting input.
2) Plant output is actual speed.
3) Speed is compared to desired speed to compute a new throttle setting (feedback).
Then it all makes sense. Now you can analyze the relationship between fuel flow and speed if you realize there is some internal transfer function that relates speed to fuel flow. This transfer function includes the concept that the car has a "state" which among other important variables includes the current speed or kinetic energy. Failing to include kinetic energy as part of the "state" will yield an inaccurate model of the plant and you are back to a state of confusion.
Here's a grossly oversmplified example of an equivalent analogy in the climate system. Say that temperature is what's being regulated — that means there's a desired temperature and an actual temperature. For the climate, desired temperature would be an inherent part of the overall system, not something that could necessarily be changed at will. The "plant" here would take water vapor as an input and through various processes yield an actual climate temperature. The feedback system would vary the amount of water vapor as a function of the difference between actual and desired temperatures. So, to translate Willis' example to this, it would be like trying to analyze temperature as a function of water vapor. What you would wind up with is how the climate's temperature responds to changes in water vapor. However if the climate system is not properly identified (e.g. not all of the input variables have been discovered), then your analysis will fail.
In summary, I don't know if the difference between a governor and a control system (whatever that might be as I'm confused on the point) is relevant here. Proper system modeling seems more relevant to me.
Another attempt a the little pictorial:
Target Speed ==> Difference ==> Throttle ==> EC ==> Fuel Flow ==> Car ==> Speed
^ |
| |
|———————————————–<– Feedback —-<—————–|
wxobserver August 2, 2015 at 5:40 pm
Fuel flow definitely determines speed … when cruise control is not turned on. Which was the condition in the first example, and which was why I mentioned it.
When the governor is engaged, causation reverses, and speed determines fuel flow.
Are you disputing either of those statements?
I ask because I read your links on “System Identification” and I don’t see anywhere that I misidentified any systems. So where is it that my example is incorrect?
w.
Thanks for the clarification Willis. Now I see that some of this is about semantics and not physics/control systems.
I was looking at this from the point of view of the open loop plant (cruise control off). From that perspective, fuel flow is a determining factor in speed but does not actually set the speed. Your example of a headwind illustrates this point.
Once the control loop is closed (cruise control is on), then you can still analyze behavior as before but only IF you still use the same definition of “plant”. In other words, the speed will still respond to fuel flow as before, but you can no longer directly set fuel flow as the cruise control is doing that.
Here’s where the semantics comes in. Once the loop is closed, it’s all circular. You can define any point in the loop as an “input” or “forcing” and any other point as an output. That’s what you’ve done in your example. I’ll try to say this again in different words.
Input is throttle setting, output is speed and fuel flow is an intermediate value set by the engine computer. From my viewpoint this is true whether the cruise control is on or not. With cruise off, it is my foot that sets the throttle (at my whim). With cruise on, the throttle is set by feedback from the speed. In both cases, the same relationship exists between fuel flow and resulting speed.
If I’m correctly understanding your viewpoint (correct me if I’m wrong), with cruise on you have changed the definition of the system input to be the speed and the system output is now fuel flow. You are free to do this of course because the loop is closed and you may pick your inputs and outputs. Realize though that you have changed the definition of “plant” in doing so.
For a different twist, you could define the input to be fuel flow and the output is throttle setting. Because the loop is closed, changes in fuel flow eventually change the speed, which changes the throttle setting requested by cruise control. You wound indeed find a relationship here but it would be quite odd and hard to understand.
To recap, I think what you’ve done is to define the “plant” as fuel flow ==> speed when cruise controls is off. When cruise is on, you’ve changed the “plant” to be speed ==> fuel flow. The second plant definition of course does not work when cruise is off because there is no relationship between speed and fuel flow in that case (well, there is but it’s the human driver acting as feedback in that case).
I’ve tried to show that you can pick any two points in a closed loop system and declare them to be input/output pairs but in doing so you are really changing the definition of the “plant”. As a result, you wind up with an apples to oranges comparison. I hope this makes sense…?
After thinking about this a bit more I realized another good way to look at this. Yes, causation is reversed, but you are the one who reversed it by redefining what the inputs and outputs are. The relationship between how fuel flow affects vehicle speed is still unchanged even with cruise on.
Positive Feedback
aka: The Star Spangled Banner
by Jimi Hendrix (the Ungoverned)
Gosh, … while we’re here …
Voodoo Child
by Jimi Hendrix
Considering the ocean and clouds in the equatorial Pacific, which is the control variable? As Eschenbach notes, you get a different slope for each:
Current science has CO2 as the control variable but if it’s a minor control other factors could cancel some or all of it out. Temperature seems more likely to the be control variable signaling each molecule to do a certain thing. Water to assume a certain form, rise or sink. I would not assign every last thing to temperature as all the other factors do impact it but it’s probably the predominate factor. That gives us a controlled stable situation as in the Temp/Cloud graph. Eschenbach’s figure 3 is informative. The blue line is the climate scientists view of things, and the red line is the pause that may have been caused by the governor that is not part of their understandings. The slope changed signs at the intersection and the CO2 is not doing what they expected. The blue line is on the way to equilibrium and once there the slope changes perhaps revealing CO2s true effect. CO2 is supposed to work longer but at the pause equilibrium, temperature showed its power. Theory sort of says CO2 can hijack temperature’s power and become the control variable. It could just be a minor player.
A little amused by this “fuel flow” business, Willis. Surely a cruise control is maintaining constant road speed regardless of engine load. You might argue that’s just splitting hairs but some of us have manual shift cars with cruise that allow you to shift gear (up or down) without resetting. You still need to dip the clutch though 🙂
A simpler example is a Watt type centrifugal governor on a steam engine or lawn mower. Constant RPM regardless of load.
A governor mechanism is inverse feedback. In the case of a cruise control, as road speed tends to increase above a set point, output power is decreased and visa-versa. And crucially, it’s proportional.
Don’t much like this positive/negative terminology, it just confuses the issue. Maybe that’s at the root of your ruminations; terms like forcing imply positive or negative exclusively and do not speak of proportionality.
Maybe saying a governor is an example of inverse proportional feedback is the way to go.
Feedback for either a single control loop of an entire dynamic system can be defined as follows:
1) If one unit of forcing results in one unit of response, feedback is “zero”.
2) If one unit of forcing results in more than one unit of response, feedback is “positive”
3) If one unit of forcing results in less than one unit of response, feedback is “negative”
A speed governor typically consists of several control loops. Some of those control loops employ positive feedback and some employ negative feedback. The “system” compares actual speed with desired speed and produces an output designed to produce one of three effects:
1) Hold existing speed.
2) Increase speed.
3) Reduce speed.
The amount of “system feedback” in a speed governing system is called “speed droop” in the speed governor ‘bidness. It may be varied from “zero” to various negative feedback values, the units of which are given in “percent”. In no case is speed governor “system” feedback “positive” (except for very brief transitions). Such a “positive feedback” system would go unstable at the first variation in “actual speed”.
A speed governor set with “zero droop” is called an “open governor” in the electric utility business. That governor will do whatever it takes (within the mechanical limits of the controlled prime mover) to match actual speed with desired speed. With a speed governor set at 5% droop, a fully loaded electric generator (prime mover at full throttle) running at desired speed will settle out at 105% of desired speed when that load is suddenly removed (load rejection).
AGW theory postulates that one unit of CO2 forcing results in more than one unit of climate system temperature response. That would be, by definition, “positive system feedback” to CO2 forcing. AGW theory makes that preposterous claim by postulating that attendant variations other atmospheric greenhouse constituents, primarily water vapor, cause CO2 forcing to be multiplied.
The question I’ve never been able to answer is the following:
If climate system feedback to temperature changes induced by atmospheric CO2 variations were positive, how could we all still be walking the face of the earth?
Don’t know where you got your definitions.
Most people would consider your # 1 to be more a definition of ” gain ” rather than feedback, or more generally of ” Transfer Function “.
I got my definitions in the course of designing control systems for some 40 years, including systems involving speed-governors. You confuse signal input versus signal output (gain) with system forcing and response functions. I do take your point, however, in that the speed-governor with a set-point is not the best analogy for what is meant by positive and negative system feedback in general. Let me try another approach using the definitions I laid out:
1) If a straightforward greenhouse calculation showed that a 5% increase in some gas constituent should yield a 1% rise in temperature and if measured results confirmed that 1% rise, then the conclusion would be that system feedback to temperature forcing by that gas was “zero”.
2) If temperature rose more than 1%, the conclusion would be that system feedback was positive.
3) If temperature rose less than the calculated 1%, system feedback was “negative”.
I’ll say again, the heart of AGW theory and the source of all the hysteria is the erroneous claim that atmospheric system feedback to an increase in CO2 greenhouse temperature forcing is “positive”.
Recall that Olavi Karner has demonstrated negative feedback in several atmospheric data series.
http://www.aai.ee/~olavi/
For instance:
http://www.aai.ee/~olavi/ISPM-app4f.pdf
http://www.aai.ee/~olavi/EE2007-ok.pdf
http://www.aai.ee/~olavi/cejpokfin.pdf
http://www.aai.ee/~olavi/2001JD002024u.pdf
I realize that this stuff is highly non-comprehensible for for non-experts on the matter, but with the large amount of experts on feedback here, it’s sad that all this never took off to refute the positive feedback alarmists.
“In the tropics, when it is warm, clouds form earlier and reflect away the sun to cut down the solar forcing. And when the tropics are cool, the clouds form later or not at all, which greatly increases the solar forcing.
What that means is that a change in temperature causes a change in forcing.”
This depends, as so often does, on definitions.
I suggest that the forcing in this case above is the suns input to earth, and does not change in this example.
Clouds form at a height and time dependant upon temperature, humidity, air pressure and other variables I am unaware of.
They also rain on us for the same reasons as above.
We know the genius of water, ice and water vapour, how is is able to transport a large amount of energy, and how very small changes in temperature/height/humidity causes clear sky, cloudy sky and rainy skies.
I would suggest that physics of clouds will hold the majority of information of how our climate works.
Could we ever understand ‘Global climate’? I suspect not in the near future.
Hi Willis,
As others have pointed out, a governor has a set point which is independtly determined. A simple negative feedback system hs no such set point. There are strong negative feedbacks in the climate system, with T^4 Stefan-Boltzman being the most obvious. The response of tropical cloud cover to changes in sea surface temperature is another. The formation of thunder storms or dust devils may be others. We know that negative feedbacks, in total, dominate the system, because the Earth’s temperature does not “run away”. But none of those negative feedbacks is a governor; they have no set point. They are temperature (and humidity) based atmospheric responses to local conditions.
If solar output were to change by a few percent (up or down) the Earth would either warm or cool on average, it would not remain at the same temperature. There would be a multitude of non-linear responses, of course, but the temperature would go in the expected direction: more solar energy, higher temperature, less solar energy, lower temperature. It is why we see seasonal temperature changes. The change in average temperature for a specific change in solar output would tell us the net sensitivity to external solar forcing. It seems to me that is pretty clear. Do you agree?
If we were to dump a huge quantity of sulfur hexafluoride (a strong and very long lived infrared absorber) into the atmosphere, then the loss of infrared energy from the Earth’s surface would be somewhat reduced, so we could reasonably expect that this would increase the average surface temperature. Just as with a change in solar intensity, there would be a multitude of non-linear responses, but the change in surface temperature, on average, would tell us the sensitivity of Earth to ‘forcing’ by sulfur hexafluoride.
The basic argument in climate science is about the relative importance of negative and positive feedbacks, and the resulting net sensitivity to ‘forcing’ by CO2, methane, etc, not about whether Earth has a set point temperature; the Geological record shows us there is no set point. I think there is strong evidence that the overall sensitivity to infrared forcing is relatively weak, and almost certainly far lower than GCMs suggest. But at the same time, I think it is incorrect (or at least very, very confused) to describe Earth’s climate as a governed system; it is just a complicated system with multiple negative and positive feedbacks.
Steve Fitzpatrick August 3, 2015 at 5:38 am
Thanks, Steve. Looking at the TAO buoy data, it’s clear that the strength of the climate response is greater in warmer conditions than in cooler. This argues that whether we understand how it happens, there is a set point. Otherwise, we’d see the same response at all temperatures.
SOURCE: Daily Albedo Cycle
You continue:
From our knowledge of the life cycles of stars, it is generally agreed that the luminosity of the sun has increased by about 5% over the last half billion years. This is the time that life has been popular on the planet.
However, we have absolutely no evidence of any such change in the temperature of the planet. Instead, over the time that the sun has warmed by about 5%, instead of warming by a percent or so as you suggest, the earth seems to have cooled by a percent or so.
As a result, I fear that your claim flies in the face of the evidence.
Next, if there is no “set point”, then why does the temperature return to the same level after something like a volcanic eruption?
And finally, if there is no “set point”, then why did the global temperature vary by only ± 0.3°C over the entire 20th century?
Best regards,
w.
Steve Fitzpatrick:
While agreeing that there’s no “set-point temperature,” I hasten to point out that there are no genuine “feedbacks,” negative or positive, operating in the climate system. “Climate science” has egregiously misappropriated that word from rigorous system analysis to mean a mélange of complicated responses and effects that have nothing to do with the output signal of the system being fed back as input without any delay. Even more egregiously, the frequency-dependent transfer function of linear feedback systems has been oversimplified to the static gain 1 / (1 +/ f) and applied to a system that is demonstrably nonlinear. As the widely scattered empirical results show, the attendant estimates of static “climate sensitivity” are physically quite meaningless.
Moderator:
Please correct the formula to read (1 +/- f) in the denominator.
I think there is more then one climate governor or regulator. One is terrestrial bound as Willis has suggested(tropical governor for example) , which is subject to terrestrial changes such as land/ocean arrangements, volcanic activity, ice dynamics and clouds to name a few.
The other climate regulator I think is extra -terrestrial due to Milankovitch Cycles, which is subject to solar variability, extra terrestrial impacts to name a few.
The dynamics of how all this relates then determines how effective the climate governors are which can vary from being able to maintain a stable climate lasting 1000’s of years to one that can change from an inter-glacial state to a glacial state over a rather short time period, but nevertheless will still be range bound to a degree in that the climate will not keep going in a warm/cold direction indefinitely.
The big unknown are climatic thresholds due to all of the above which are very likely to occur due to the fact the climatic system of the earth is chaotic, random and non linear and when it changes it does so in step fashion rather then in a slow gradual fashion.
All of that is evidence of thresholds in the climatic system which is not being addresses enough in my opinion.
Why? Probably because the essence of it is so elusive and beyond the capabilities of climate science to address in any real proper comprehensive manner. What confirms that statement is the fact there is still no real explanation as to why the climate at times changes abruptly and goes from a glacial to inter- glacial state, while at other times is relatively stable.
Till this is solve we will remain in climatic darkness as far as being able to predict when /how the climate may change going forward.
I expect that we will know the cause of the next step change due to all of the monitoring now in place. Lets hope the data is not massaged too much to prevent a good analysis…..
This time I only made it to this sentence, “Well, yes, that’s true, and it is also true that a human being is “just a bag full of organic chemicals, minerals, and water.“ Like poison ivy, my resistance is fades over time.
The terms you are discussing have mathematical definitions. If you don’t understand the math then you can argue by analogy all day long and you still will not understand. Do us all a favor and learn the math.
Dinostratus August 3, 2015 at 4:46 pm Edit
Dino, it appears that there is some unknown “mathematical definition” which you think I’ve not agreed with, or don’t know about, or something.
But since all you quoted was my statement about humans, along with a bunch of handwaving and insults, I don’t have a clue which “mathematical definition” you might be talking about, what you might think said definition is, or how I may have transgressed in whatever I said.
As I have requested many, many times,
QUOTE THE WORDS YOU DISAGREE WITH AND TELL US WHY YOU DISAGREE WITH THEM!
Is that so hard to do? Well, I guess if you don’t actually have a point and your intention is to just throw mud at me, it might be …
w.
I disagree with the part where you use words and arguments by analogy rather than mathematical definitions. Write the mathematical definitions. If you can’t, just say so.
Lots of people don’t know control theory, even simple linear control theory. There’s nothing shameful about that.
Dinostratus August 4, 2015 at 8:25 pm Edit
That’s your answer to a request for a direct quote?
Sorry, Dino, but I was serious. As I said:
As you have not done that, I fear I still don’t know what you are referring to.
In any case, if you wish to provide the math, please do so, as I have no interest in doing so. Me, I’m interested in the concepts. I’m not trying to explain how to do the math. I’m trying to explain the concepts to a lay audience. And the problem with writing for a lay audience is that as a rule of thumb, every number I put in the post loses me one reader, and every equation I put in there loses me ten readers. So I generally err on the side of explanation rather than math.
So if you wish to bring up the math, please go ahead, and I’m happy to discuss it. However, I don’t understand what the math would show that is different than my explanation … but hey, if you can disprove my work mathematically I’m more than interested.
Up to you,
w.
Two words: “Snowball Earth”.
Three words: “Tub a guts”. (Gimme’ some mathematical definitions, Dinostratus!)
The climate of science is much more about concepts then math especially if one thinks the GHG effect is bogus.
It’s precisely because math elucidates concepts unequivocally that makes it the language of bona fide science.
Good post. I’ve tried to illustrate what may be happening:
Let’s say CO2 equals Temperature until equilibrium. Then as Eschenbach suggests, there is a slope reversal. Missing a slope reversal if one exists, could be a major thing.
Full post here:
https://chaosaccounting.wordpress.com/2015/08/15/climate-set-point/