I keep making this argument in bits, and have been meaning to put it together but have never had the time. So rather than putting it off again, I’ve decided to put my assessment of the impact of CO2 on global temperature in this very quickly prepared post. Note, because it is quick, I’m assuming a reasonable competence by you the reader.
First we look at the ubiquitous “global warming graph”.
Second we do what any decent engineer would do and look at the frequency components of this graph:

As you will see it rises almost linearly which is typical of 1/f noise. And it is so suspiciously straight line that it looks like 100% random noise. The only “deviation” is at lower frequencies (higher periods >50yr) which is because you only get one or two cycle of 50/100year periodic noise in a 150years of data. This is to be expected. (As is the way you see more “detail” at higher frequencies – which is because there are more such cycles in the dataset)

Initial conclusion: It is consistent with pure noise.

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The initial assessment of the global instrumental data the signal shows that the signal has the appearance of being noise. There this must be the “working hypothesis” or “null hypothesis”.

The next step is to look at the CO2 signal.

What we see here is that the measured CO2 fro 1958 onward. It shows a very smooth curve (albeit with yearly fluctuation). Also before accurate measurements were available in 1958, we see massive “error bars” and virtually no growth in the available measurements we have.
Anyone who does frequency analysis will understand that this type of smoothly increasing signal shown by CO2 is very difficult to discriminate from 1/f type noise. This is because 1/f noise has increasing noise when looking at longer periods. So, the longer we look, the bigger the error. Or to put that another way, 1/f noise will show significant trends which are impossible to distinguish from induced slow change such as that expected from CO2.

Conclusion 2: It is very difficult to distinguish in the global temperature signal between any slow change affect and background 1/f noise.

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In other words, given our null hypothesis “that it is noise”, the slowly increasing CO2 warming signal is not sufficiently different from 1/f noise that we can distinguish any such signal within that noise with any degree of certainty.

Is there anything abnormal in the later 20th century?

We know CO2 was rising far more rapidly at the end of the 20th century than the beginning. That temperature record starts about 1960s (the decade of the global cooling scare). We know there was a sharp rise in temperature from the 1970s. Is this rise significantly larger than anything we see in the earlier part of the temperature record that we can say the post 1960s section is “unusual”?

The above graph shows that the 1970-2000 warming (after which we get the pause) was absolutely indistinguishable in length and magnitude from the 1910-1940 rise.

Conclusion 3: There is nothing unprecedented about the post 1960 rise (the period we know there was a sharp rise in CO2)

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Conclusion 4: There is nothing in the available global temperature record that would suggest we need to modify the initial hypothesis that the temperature signal is natural variation in the form of 1/f type noise.

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Can we discern anything from any available temperature record?

Whilst we do not have a global temperature record before the 1850s, we do have a record called the “Central England Temperature” record that goes more than another century. If this shows unprecedented warming in the latter halve when we know CO2 was rising, then this would be strong evidence (but not conclusive) that CO2 had caused global warming which was then being seen in this regional record.
This shows the CET (from John Daly’s Blog ). The good thing is that we can see the 1970-2000 warming (marked Global Warming Scare begins). The bad news is that in this record this warming is about 1C over 30 year (0.33C/decade). But there is clearly a massive warming period from 1690 to 1740 is 2C (0.4C/decade). As this is bigger, it shows the late 20th warming is far from unprecedented. We also have cooling from 1660- 1690 of -0.33/decade. So, we are beginning to see a pattern of both warming and cooling of around the same magnitude. The earlier cooling/warming is natural, so this is strong evidence the latter 20th warming is also (largely) natural. The post 1960 warming is far from unusual.

Conclusion 5: there is nothing in the Central England Temperature record to suggest the post 1960 warming is unusual.

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The instrumental temperature record is unable to show anything unusual about the global temperature in the period we know CO2 is rising.

Is it possible that the Central England Temperature record fails to capture global temperature changes?

The above graph shows that whilst the CET record has more variation (as one would expect from an unaveraged signal), CET and the global temperature closely match each other in trends and have the same general ups and downs over longer periods.

Conclusion 6: The Central England Temperature record appears to be a good proxy for century scale global climate change. Therefore the lack of any unprecedented warming in the Central England record is a strong indicator that there has been no unprecedented warming globally Therefore we cannot reject the null hypothesis that the changes we see in global temperature are natural variation.

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Can we use any other proxies?

• Tree rings – whilst an individual tree will respond to climatic conditions, over long periods the “forest” will adapt. So that if conditions get worse, there will be less trees, and if conditions improve there will be more. These trees will change the competition between trees. So in worsening conditions, over time the canopy will become more sparse, allowing those trees that survive to grow better. Depending on the species, this “forest adaptation” will significantly change the response after a few decades. This means that whilst an individual tree may respond to climate change for a few decades, after the forest as a whole adjusts to the change, the impact on the remaining trees may be significantly less than expected. As a result the tree-ring response to long term climate change (time for the trees to grow/die) will be significantly different from the shorter year-to-year change. Until this problem is resolved, tree-ring data and similar “natural proxies” are only reliable for short term changes. In my opinion they are wholly unreliable as an absolutely proxy for temperature. They are only suited to the evaluation of climate change when comparing very similar period such as one century to the next or one decade to another. THEY CANNOT BE COMPARED TO INSTRUMENTATIONAL DATA.
  
• Ice cores – strong evidence that there are significant problems with this proxy (See Salby)
• Sea level The above graph shows how the observed sea level is not a good proxy for temperature. (Note. The IPCC have a figure for sea level which incorporates an introduced rise. This is not credible as a proxy).
• Other proxies – with so many bogus reconstructions (only uncovered by skeptics and not those doing the reconstructions), there may be others, but none have so far shown to be compiled with the necessary rigour to suggest they provide any reason to challenge the available temperature data.

Is there another way to predict the effect of CO2

Rather than trying to work out what effect CO2 has had on a system which is dominated by natural variation, can we instead work from first principles and estimate the degree of warming.
Various attempts have been made to estimate the effect of increasing CO2. I personally think the most credible estimate is from Hermann Harde who is an expert in the radiative absorption properties of gases and who unlike most other estimates (which produce higher figures) has used the latest spectroscopic data for CO2. As a result he came up with a figure “30% lower than the IPCC”. This is the most credible estimate I have seen.
The IPCC however, don’t make that figure obvious. From memory the IPCC figure for doubling CO2 is around 1C (it may be 1.2C). That makes the best estimate of the radiative effect of doubling CO2 around 0.7C – 0.8C

Conclusion 7: based not on the climate signal, but on the properties of CO2, we expect around 0.7 – 1.2C of warming for a doubling of CO2.

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What about positve feedbacks?

Climate researchers try to force the their models to match the late 20th century warming, and they do so by assuming (without good grounds) massive positive feedbacks to take the 1C of CO2 warming up to delusional levels of around 6C warming for a doubling. What they are in effect doing is scaling an almost linear rise in projected CO2 warming to fit a largely linear rise in temperature from 1970-2000. A six year old could do the same thing by drawing a line through the 1970-2000 warming and the projected warming is in reality just an extension of this crayon line. I have never seen any justification for this scaling up of the CO2 warming and in my opinion the resultant figures from doing so are bogus.

This is amply shown by the way models using such feedbacks fail in practice:

This shows that the predicted warming (orange area) is now well above the actual temperature even after a very short time period. That it takes such a short period (in terms of climate) for the projected global warming from models including feedbacks to be far too high is very strong evidence these scaled up warming projections are way too high.

Conclusion 8: Models including positive feedback vastly overestimate the impact of CO2.

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What about negative feedbacks

In a system where strong negative feedbacks come into play we expect the signal to be damped down so that any perturbation to the system has very impact. One type of such feedback is found in a bath. At first, as the water flows in, the water levels rises roughly in proportion to the amount of water that has gone into the bath. But when the level reaches a point where it starts overflowing, even a vast increase in water input will have very little affect on the water level. This is a system where strong negative feedback comes into play. Such negative feedback constrain the system within strict limits and vastly overpower any positive feedbacks present.
In a system with strong negative feedbacks, we expect there to be a “line”, like that of the drain hole on a bath, beyond which it will not go.

The above graph shows several proxies for global temperature over the period of the last few ice-ages. Each one shows a signal, which changes markedly up to a certain point (particularly well shown on the lowest plot). This is the “drainhole” effect. Any one used to dealing with signal should immediately recognise this as a form of limiting at a particular level. Something is preventing the system rising higher.
This means, that in an inter-glacial, whilst it is possible that there exist positive feedbacks that may enhance any cooling effect, any further warming is strongly resisted by the system. It can get colder, but it is extremely difficult for the climate system to get much warmer.
These “drainhole” effects come into play in the inter-glacials warm periods. We are currently in such an inter-glacial and therefore:

Conclusion 9: In an inter-glacial as at present, the global climate system has some mechanism that introduces massive negative feedbacks which work to prevent further temperature rise.

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Now putting these altogether this is what I get:

Conclusion (10): There is no evidence showing human impact through rising CO2 on the climate. The direct effect of CO2 is estimated at about 0.8-1.2C for a doubling of CO2. This figure will be modified by feedbacks. Models using positive feedbacks have proven invalid in a relative short time period, strongly suggesting these positive feedbacks are vastly overstated. There is strong evidence that high levels of negative feedbacks are present in inter-glacial periods preventing temperature rise. As such it is very likely the direct CO2 warming of 0.8 to 1.2C will be reduced.

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And finally, if I were personally asked to predict the impact of rising CO2 this is what I would say:

Based on the available evidence negative feedback is dominant and therefore it is very likely warming will be less than 1C for a doubling of CO2.

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Addendum

Stewgreen has reminded me I was going to put in a section as follows:

Even if we cannot distinguish the 20th century warming from noise, is there anything to suggest we should be concerned?

A good doctor (who’s really just a good engineer), wouldn’t just rely on what they can prove to be wrong with the patient. Even if all the clinical tests showed no conclusivel problem, they would also look out for “worrying” symptoms.
As such, I’ve kept an eye open for any worrying symptoms of the climate. One of the most persuasive documents I read was an report by Trenberth. Trenberth is a capable researcher, well “connected” and also a global warming zealot. Therefore I think it is reasonable to say that if anyone had found anything of concern it would be in his report.
I read his report, and whilst it was full of computer predictions (the equivalent of a hypochondriac exaggerating the slightest thing and thinking they must be ill) I found only one “symptom” in addition to those expected as a result of a warmer climate after the little ice-age.
This “worrying symptom” was something like the most intense rainfall within heavy rainfalls had gone up. It did not take me long to realise this was probably because modern instrumentation takes measurements more often and so is more likely to pick up short-term intense periods within a downfall. So even this one single figure might easily be due to improvements in equipment.
There have been other reports, such as the researchers who were “surprised” to find that there had been no trend in the main measures of extreme weather.
So, apart from some melting ice (something we expect after a little ice-age), there is NOTHING to be concerned about.
I would even go as far as to say, I am surprised that there are not more “worrying” trends, because in a system with natural variability, some things should appear to be getting worse.
This may actually be the effect of rising CO2. E.g. I think the number of hurricanes (or is it tornadoes) has decreased (something I think that Trenberth failed to mention). This may actually be the only visible impact of rising CO2 (these storms need hot and cold sinks – rising CO2 may be stopping the cold sink and therefore reducing storm intensity)
The other impact, is that I understand there has been an increase in plant growth (presumably due to CO2) and a predictable impact of rising CO2 is that plants will be able to tolerate drier conditions – and indeed we are seeing a reduction in deserts.