# Toward a new theory of iceages VI (Climate stability)

The last article discussed negative and positive feedbacks in the climate. Now I want to see how these impact the stability of the climate and also how the stability of the climate can tell us what kinds of feedback are present.

## Climate stability

I introduced the idea in the overview of feedbacks that negative feedbacks are rather like a driver on a road constantly correcting any small veer to one side or the other. I then suggested that positive feedbacks produce the kind of effect that would occur if an ordinary driver got into a car where the steering wheel acted in reverse. So that as they turn to the right to correct a drift to the left, rather than the car going right as intended, the car goes further and further to the left. As a result almost all normal drivers getting into such a car will go off the road and so would a climate with large positive feedbacks.

In general climates with positive feedback tend to be unstable and the higher the feedback the more unstable they become.

To illustrate the idea of positive feedback I used the analogy of a driver in a dodgem car, which rather than behaving as normal, so that the driver would tend to act to reduce any error in the direction, the steering wheel is geared in reverse. This means that as they veer to one side, they turn the steering wheel so as to increase the error.

I showed in the last article that small levels of positive feedback can be stable. The example I used was a feedback of 1/10 so that a 1C rise in temperature resulted in 1.11111C.. total rise above what it would have been without the feedback.

But too large and always when the feedback is above 1, then the climate is unconditionally unstable and like the dodgem car with the reversed steering wheel, the climate tends to veer “off the road”.

In other words, simply having large positive feedbacks results in a situation that cannot possibly last because even a very small change will be amplified by the feedback and then as it causes more change (1c → >+1C = >2C) the increase due to feedbacks will be larger than the original change and so that in addition will cause even more change (1c → >+1C = >2C → >+2C = >3C). And so if the positive feedback introduces more change than the original change, the climate will just “go off the road”.

In contrast, if we have modest positive feedback such the increase is 1/10 of the initial change. Then we get: (1c → >+0.1C = >1.1C) then that additional 0.1 C will itself cause more change so (1c → >+0.1C = >1.1C → >+0.11C = >1.11C) and it can be shown that the total increase from something that tended to increase the temperature by 1C will be a totaly change after time from positive feedback of 1.11111111111… C

So, we can conclude as a matter of simple maths, that a climate that is stable has feedbacks which are either negative, or if they are positive, the feedback must be smaller than the original change.

So, no climate that has been relatively stable can have high levels of positive feedback. And if a climate did have very high levels of positive feedback it would have “gone off the rails” a very long time ago either leading to runaway warming or runaway cooling until the climate had so changed that the positive feedback mechanism disappeared and it became stable again but with an entirely new temperature or state.

## Climate Oscillations

However, whilst no climate can be stable over any length of period with high levels of positive feedback on their own, if the climate has some kind of “buffers” or threshold beyond which negative feedbacks dominate, then this is rather like the car I discribe above with the reverse geared steering wheel, but only this time they are not on an open road, but instead they are in a bumper car with large crash barrier to keep them on the road.

Here, almost all drivers initially heading down the track would tend to veer to one side. They would turn the wheel in the way they expect to self correct and find that instead they turn more and more sharply toward the side.

When the hit the side, (assuming it continues forward) the car would eventually end up heading slightly away from that side. Then because of the nature of the steering, the driver would tend to veer to the middle over-compensate and hit the other side. Then they would veer away from that side and hit the other. So, the driver would go down the track veering sharply from side to side and only stopping from going further by hitting the “buffer”.

So, climates can in principle have large positive feedbacks present. But in order to prevent them “going off the road”, there must be mechanisms that impose a threshold so that the effect of the positive feedback is eliminated and forms of negative feedback (buffers always push toward the middle) come into play.

So, we can also say, that unless there is an external driver such as the day length or yearly change in the climate where the sun imposes a daily or yearly cycle on the climate, if the climate is subject to oscillations, then at least within the range of the oscillation there must be high levels of positive feedback (such that a 1C changes leads to a further increase of >1C) AND there must be large negative feedbacks or very reduced levels of positive feedback at the limits of oscillation.

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### 4 Responses to Toward a new theory of iceages VI (Climate stability)

1. Rud Istvan says:

You might want to rethink this a bit. There are two points to be made.
First the Bode sum of feedbacks model used by Linzen (1/(1-f) for ECS is stable and well behaved up to the inflection at f~0.75. The AR4 implicit f is almost exactly 0.65; 0.5 water vapor and 0.15 clouds. Those are too high. WV is more likely 0.25-0.3, and clouds ~0. See my extensive comments to Montkton’s post on his irreducibly simple model at WUWT, also in last weekends open thread at Climate Etc. See also three essays in most recent book.

Second, overall feedback in climate terms gets misunderstood. It is the rate of change in a change. Best example is clouds. No one doubts that they have a net negative feedback, through the mechanisms of albedo and precipitation (which removes atmospheric water vapor). They massively damp climate. The climate feedback to CO2 question is, does this feedback get stronger (negative feedback to the cloud feedback) or weaker (positive cloud feedback in the IPCC/GCM sense). The current best evidence suggests perhaps no net change at all, f=0.

There is a linking mechanism that also fits the statements of your last two paragraphs. This is Lindzens adaptive IR iris hypothesis (2001). Higher SST and air temp gives rise to more tropical convection (thunder storms in the ITCZ) which in turn cools by releasing latent heat of evaporation high in the troposphere where it has an easier time escaping the ‘greenhouse effect’, and reducing atmospheric water vapor via precipitation. GCM grid scales are incapable of modeling this massively sub grid process. Smallest CMIP5 grid is 110KM; most are 250. Current weather models get structural features like fronts on a 30km grid scale, then drop down to 1.5 or 2 to do convection cells.

And the computational impossibility of a GCM doing tropical convection means they have to be parameterized for that process. And all CMIP5 GCMs selected parameter sets that best hind cast to the period from 2005 back to about 1975. That was explicitly part of the ‘near term’ experimental design, and a required submission for inclusion. So they were parameterized to a period of warming, under the assumption that all the observed warming was driven by CO2. It wasn’t. There was a natural variation component, just like warmunists are now realizing there must be a natural variation component to the pause the models did not project.

2. Scottish-Sceptic says:

Without getting too technical, I was trying to explain that a oscillations like an ice-age cycle imply high levels of feedback, but they also require negative feedback mechanisms in order to limit the scale of the oscillation (otherwise the signal would just fly off to either + or – infinity).

In the general sense, this means that near the middle of the swing we should be in a regime where the loop feedback is > 1. But it also means that near the top and bottom the feedback MUST drop substantially to well below 1. However, that in itself is not enough, because in such a system the signal will tend to head toward either the top or bottom and then stick there.

So, there must be some form of timing element such that it tends over time to force the signal away from either extreme.

One mechanism for this is a “relaxation oscillation”. Here one extreme triggers some kind of event which causes the signal to rise … and then slowly decline. This is symptomatic of the kind of sawtooth we find in the ice-age cycle.

Another possibility is that we have out of phase or delayed feedback. Here, the signal reaches one or other extreme, and then after a delay it starts to be pushed back toward the central region where positive feedbacks come into play and the signal then suffers “catastrophic” swing to the other extreme. However, such a system would tend to have a symmetric waveform.

Other similar form of oscillator is a bi-stable one. Here the system exists in two stable states. But for some reason, the system has feedbacks which over time tend to push it toward the other state and then it “flips”.

On the level of feedbacks in climate models. My moment of “revelation” was when I told myself to stop thinking about the temperature signal as something global and just look at it as if it were any other signal that I had dealt with in my life designing and running temperature control systems.

And from the moment I started treating it like just another temperature control unit which I’m trying to diagnose I realised that the massive variation was very likely natural in origin.

But worse for the idea of massive positive feedbacks because the system is going through a cycle it must be experiencing changing levels of feedback and as I said above, this is almost certainly very much less than +1.

Moreover, if you are experience with such systems you get a feel for the level of feedback. This is because the changing level of feedback will show itself in how the natural variation is magnified.

In other words, as feedback moves toward high levels of positive feedback, we should see increases levels of natural variation, and visa versa as negative feedback increases and the system become stable, the expressed natural variation in the temperature signal must decrease.

I’ve looked at the temperature signals both long-term and short-term and I just don’t see the type of symptoms I would normally see in a system with high gain (except obviously in the actual ice-age cycles themselves).

So, given that the level of natural variation shown in CET has not changed and continues almost seamlessly from the beginning to end of the series and that 20th century warming is not abnormal within that series, I have to reject the models that falsely omit the obvious huge levels of natural variation. The problem is that once you exclude this obvious natural variation, you are then forced to include massive positive feedbacks in order to make the small CO2 forcing result in a much larger change in temperature than can be easily physical explained.

But, worst of all … if such massive positive feedbacks existed, there would be no “buffer” to have halted warming at the end of the last ice-age and so it would be very likely that either in this cycle or some other cycle that the warming would have continued increasing to a much level so that the world did experience a massive change to negative (or very small positive) feedbacks. This would be obvious in the temperature signal … as a threshold (like the current interglacial level) which was hard to exceed.