Dim Sun Anyone?

MSimon · Post by **MSimon** » Fri May 22, 2009 11:12 am

I believe you said:

Anyway the point is that you can get amplification from a positive feedback with gain < 1 (any electronic engineer will tell you the same thing).

Now it is possible the "<" was in error. If so I'd like you to correct the record and we can go from there.

tomclarke · Post by **tomclarke** » Fri May 22, 2009 11:18 am

If the climate system does not have infinite gain (very large will do) at a tripping point there will be no runaway greenhouse effect. Because below the tripping point the system would drive itself to some lower bound dependent on the system. i.e. at the tripping point the system goes from large negative gain to large positive gain. We don't see that. If you want to learn more about tripping points may I suggest a study of Schmidt Triggers. That is the electronic analogy of what you suggest. In fact these days most control problems and mechanical systems are described in terms of electronic analogies. I'd love to see the electronic analog of the climate system. With the right scaling you can make an analog computer that should do a nice job of quickly simulating the climate system. If you get the parameters right. And they are much faster than digital computers when it comes to solving some classes of problems.

I was playing with BJT Schmidt triggers when I was 12 years old. (At the time for some reason I was preoccupied with making electronic telephone answering systems).

There is an issue with the climate system which is related to differing time constants.

The GCM people distinguish between "feedbacks" - e.g. H2O vapour effects - and "forcings" e.g. anthropogenic CO2. But actually it is a matter of residency time. H2O equilibrates in the atmosphere within a few days, so at timescales longer than this it is considered a feedback. CO2 equilibrates in the atmosphere with timescale of several 100 years, so it is considered a forcing. But the distinction is somewhat arbitrary.

When we talk about "gain" of the climate system we need to specify timescale and include variables which equilibrate within the given timescale as feedbacks. Having done that we have the (direct) sensitivity to a given forcing and the (equilibrium) sensitivity to said forcing taking into account any feedbacks. The ratio being the "closed loop" gain.

This model which linearises the whole system is only approximate - with significant perturbations the linear approximation may break. In particular if the linear approximation predicts instability (unbounded exponential or oscillatory exponential solutions, or loosely and rather unhelpfully close loop gain of infinity) - this does not mean indefinate runaway behaviour since the system will behave nonlinearly and away from the initial conditions the feedback parameters will be different.

In the case of the climate system you are thinking that any unbounded exponential would be non-oscillatory and would drive the system into a new (stable) regime - as with a Schmidt trigger. This is quite possible I agree although the presence of multiple time constants of different lengths means that in principle the system could just become oscillatory or more likely chaotic.

But all of this is not relevant to the initial question, which was David's statement about the effect of H2O feedback on CO2 forcing. Here the time constant is a few days, we can ignore other feedbacks, and we consider only whether the sensitivity to CO2 forcing is made large, smaller or infinite by the presence of H2O feedback. And under these assumptions I agree infinite gain is equivalent to a Schmidt trigger - and this means that what happens depends on behviour outside the original linear approximation.

David argues that the (open loop) sensitivity must be either made less (negative feedback) or we have unbounded feedback (equivalent to infinite closed loop gain). Which is not true, as my equations up above make much clearer than all these words!

Analog computer simulating climate - we work on VLSI sub-micron analog computers, which are much more efficient than digital ones. But they are not very accurate. You can't get away from the multivariate nature of the problem (and the smaller your grid size, hence the more accurate, the more variables you have). With such a very large number of variables you need an awful lot of analog circuitry - though the plus point is that the connectivity is all local. The great advantage of digital is that you can multiplex calculations and need only have a few bits (well maybe 32 or 64) stored for each different variable.

Best wishes, Tom

tomclarke · Post by **tomclarke** » Fri May 22, 2009 11:30 am

I believe you said:

Quote:
Anyway the point is that you can get amplification from a positive feedback with gain < 1 (any electronic engineer will tell you the same thing).

Now it is possible the "<" was in error. If so I'd like you to correct the record and we can go from there.

No problem Simon, on record. As follows:

If open-loop gain g satisfies 0 < g < 1 then closed loop gain will be:

g/(1-g)

this leads to amplification.

From electronics an example would be any "fast" op-amp e.g. TLC071 when used in unity gain negative feedback configuration. At high frequency (20MHz or so) the open-loop gain will be less than one and phase 180 degree, hence overall feedback is positive. The result is a peak in frequency response with gain > 1.

This is not an exact analog of the climate system because we are dealing with non-zero frequency, but it illustrates principle.

PS - the g/(1-g) factor is the exact analog of the amplification that the CO2 forcing gets from H2O feedback - and is clear from my equations above.

tomclarke · Post by **tomclarke** » Fri May 22, 2009 11:37 am

Sorry - in my last message the exact factor depends where in the feedback loop you take the output from - I am thinking here electronics not control - i can be more precise if you like? Tom

ravingdave · Post by **ravingdave** » Fri May 22, 2009 5:28 pm

tomclarke wrote:David,

The equations are quite clear. You are right they are a simplification but any complex system can be linearised for small perturbations. Equally all the other feedbacks (if fast) can be subsumed in the given coefficients.

Anyway the point is that you can get amplification from a positive feedback with gain < 1 (any electronic engineer will tell you the same thing).

The temperature rises in accordance with this, as the equations say, until there is a new equilibrium. The effect is to amplify the original forcing.

If you don't agree with this we had better leave it - I can't make it any clearer.

Best wishes, Tom

I remember many years ago in high school we were told to calculate the path of a ball thrown into the air. We had an equation that described this situation. Of course, some of us, (just for fun) decided to use a negative time value. We discovered that the ball which had been thrown into the air was plotted as some distance below the surface of the ground. Likewise, if time were allowed to be greater than that required for the ball to hit the ground, the equation predicted the ball would again be beneath the ground.

This was a good learning day for me because it made me realize that equations may be perfectly reasonable and valid, but sometimes people can make mistakes when they are trying to apply an equation to real world events.

In any case, my point is that we are currently the beneficiaries of the equilibrium that you are referring to. The Current temperature IS the equilibrium. It is the point where the positive and negative feedback characteristics of water vapor in the atmosphere balance each other.
(of course this is oversimplified)

At any rate, I don't find this subject particularly interesting, and I am constantly surprised that other people do. With that in mind, I think I shall let those of you who like to discuss this continue on without distraction from me. I think you sort of understand my point, and I don't see any further need to belabor it.

Have fun.

David

ravingdave · Post by **ravingdave** » Fri May 22, 2009 5:40 pm

MSimon wrote:The gain of the climate system could be positive 1,000,000 and it would not run away if the feedbacks are negative.

I deal with this in op amps all the time. Us electronicers love high gain amps. They do not imply runaway (i.e. rail to rail) systems. It all depends on the feedback and a few more esoteric points which I'm not going to deal with here - like overall gain vs phase - as they are not necessary to make my point.

A gain of 1million is pretty much a standard assumption for op amps. The amplifications is actually pretty independent of the gain, as long as the gain is pretty large. The gain is of course set by the ratio of the feedback resister to the input resistor with the input resistor serving the function of a load from the previous stage. The inverting input pin on the chip is effectively equivalent to ground as far as the preceding stage is concerned.

Op amps are awesome!

David

tomclarke · Post by **tomclarke** » Fri May 22, 2009 6:50 pm

Op-amp technology has got much better. The latest stock op-amps (e.g. TLC072) have essentially infinite input impedance (10^12 ohm), low quiescent current, high slew-rate and output drive current and 10MHz GBP. And 7nV/Hz^(1/2) noise, 60uV offset. And DC gain 10^6. All from 5V supply. Extraordinary!

The only problem with these devices is that faster is not always better. They are less stable then the old slower devices - partly because they sacrifice some phase margin at high frequencies to boost the GBP at working frequencies.

Best wishes, Tom

MSimon · Post by **MSimon** » Sat May 23, 2009 3:36 pm

Three IPCC climate models, recent NASA Aqua satellite data, and a simple 3-layer climate model are used together to demonstrate that the IPCC climate models are far too sensitive, resulting in their prediction of too much global warming in response to anthropogenic greenhouse gas emissions. The models’ high sensitivity is probably the result of a confusion between forcing and feedback (cause and effect) when researchers have interpreted cloud and temperature variations in the real climate system. (What follows is a brief summary of research we will be submitting to Journal of Climate in January 2009 for publication. I challenge any climate researcher to come up with an alternative explanation for the evidence presented below…I would love to hear it…my e-mail address is at the bottom of the page.)

http://www.drroyspencer.com/research-ar ... -evidence/

MSimon · Post by **MSimon** » Sat May 23, 2009 3:42 pm

AD4898

http://www.analog.com/en/amplifiers-and ... oduct.html

* Ultralow noise:
0.9 nV/√Hz
2.4 pA/√Hz
1.2 nV/√Hz @10 Hz
* Ultralow distortion: −93 dBc at 500 kHz
* Wide supply voltage range: ±5 V to ±16 V
* High speed:
−3 dB bandwidth: 65 MHz (G = +1)
Slew rate: 55 V/μs

* Unity gain stable
* Low input offset voltage: 150 μV maximum
* Low input offset voltage drift: 1 μV/°C
* Low input bias current: −0.1 μA
* Low input bias current drift: 2 nA/°Cq
* Supply current: 8 mA

MSimon · Post by **MSimon** » Sat May 23, 2009 3:49 pm

Since computerized climate models are the main source of concern over manmade global warming, it is imperative that they be tested against real measurements of the climate system. The amount of warming these models predict for the future in response to rising concentrations of carbon dioxide in the atmosphere is anywhere from moderate to catastrophic. Why is this?

It is well known that most of that warming is NOT due to the direct warming effect of the CO2 by itself, which is relatively weak. It is instead due to indirect effects (positive feedbacks) that amplify the small amount of direct warming from the CO2. The most important warmth-amplifying feedbacks in climate models are clouds and water vapor.

Cloud feedbacks are generally considered to be the most uncertain of feedbacks, although all twenty climate models tracked by the Intergovernmental Panel on Climate Change (IPCC) now suggest cloud feedbacks are positive (warmth-amplifying) rather than negative (warmth-reducing). The only question in the minds of most modelers is just how strong those positive feedbacks really are in nature. This article deals with how feedbacks are estimated from satellite observations of natural climate variability…and describes a critical error in interpretation which has been made in the process.

http://www.drroyspencer.com/research-ar ... -evidence/

MSimon · Post by **MSimon** » Sat May 23, 2009 4:16 pm

Tom,

The change in sign of the feedback in the amplifier situation you mention does not turn an amplifier into a Schmidt trigger.

tomclarke · Post by **tomclarke** » Sat May 23, 2009 8:10 pm

Well I was conscious of being inexact, I did not give precise circuit and when talking about control I specified loop gain but not what was the forward and what the reverse component of this.

The thing about feedbacks is when you first think about it it is difficult to be clear. Suppose we work out a circuit with (optional) feedback where the effect of the feedback is the H2O feedback.

We have an inverting op-amp with virtual earth node ve and output Tout, with CO2 forcing input CO2in. Conductances g1, gf, etc as follows:

CO2in g1 ve

Tout gf ve

So sensitivity, excluding feedbacks, is g1/gf

We then have unity gain inverting stage input Tout and output Tout'

Adding in H2O feedback is just like putting a conductance gh from Tout' to ve.

Loop gain is gh/gf, if this is >1 we have a system with hysteresis which will move quickly to Tout = Vmax or Tout = -Vmin when input is < -ghVmax/g1 and input > ghVmin rspectively. (Assume both op-amps outputs saturate at Vmax or -Vmin).

And it is an op-amp schmidt trigger. (For a bipolar Schmidt trigger you need a slightly more complex circuit).

Best wishes, Tom

MSimon · Post by **MSimon** » Sat May 23, 2009 8:26 pm

Loop gain is gh/gf, if this is >1 we have a system with hysteresis which will move quickly to Tout = Vmax or Tout = -Vmin when input is < -ghVmax/g1 and input > ghVmin rspectively. (Assume both op-amps outputs saturate at Vmax or -Vmin).

But that does not comport with reality. Which argues for net negative feedback. We do not see rail to rail slams (at least in the short term - centuries).

Spencer in the article I quoted argues for a over all gain of about .6 i.e. a CO2 forcing with no feedback that would give a temp rise of about 1 deg. C actually gives a temp rise of .6 deg. If I read the article correctly.

tomclarke · Post by **tomclarke** » Sat May 23, 2009 8:57 pm

MSIMON!

rail to rail only if loop gain is >1. the real situation corresponds to loop gain < 1 so the feedback amplifies the original but the output remains linearly (in this approximation) dependent on forcing input.

The circuit is nice because with gh/gf < 1 you can see exactly how the amplification works.

MSimon · Post by **MSimon** » Sat May 23, 2009 9:33 pm

tomclarke wrote:MSIMON!

rail to rail only if loop gain is >1. the real situation corresponds to loop gain < 1 so the feedback amplifies the original but the output remains linearly (in this approximation) dependent on forcing input.

The circuit is nice because with gh/gf < 1 you can see exactly how the amplification works.

What is this tipping point re: climate I keep hearing so much about?