Alan,

you beat me to it! It's like debating a brick wall!

RR,

point taken!

I would hazard a guess that EM is one of the " no surrender, not an inch" variety. He apparently has only one thought in mind and that is that the present and recent temperature increase is uniquely and solely the consequence of humans burning fossil fuels. It appears that his approach is " Don't confuse me with facts, my mind is made up."

That is why scientists are encouraged to use objective analysis tools rather than doing it by guess and by god.!

Now I'm going to discuss how we would look for a new law.

In general, we look for a new law by the following process. First we guess it. (...) Then we compute the consequences of the guess.(...) If it disagrees with experiment, it's wrong. (...)
It's therefore not unscientific to take a guess, although many people who are not in science think it is....

https://www.youtube.com/watch?v=EYPapE-3FRw

Paul Dennis

I have been living in Ulster too long.

I have become thran

Glebekinvara

Are you from Northern Ireland too? That is the sort of thing the Presbyterians say. They also tend to be thran.

EM - I pretty much agree with Paul Dennis's views on the futility of fitting polynomials to data where there little or no understanding of what is going on and particularly where any departure from a straight line is completely buried in the variability.

All the same, I thought I would play around a bit.

First, I found that the current LibreOffice Calc's function LINEST( ) will give the coefficients of polynomials, as well as doing ordinary straight line regression. (The documentation seems a bit coy about exactly how it does it for polynomials - maybe it assumes it's obvious.) LibreOffice Calc is an open source Excel alternative downloadable for free, so anybody who wanted to try fitting polynomials has the means to do so readily available.

I satisfied myself I could use LINEST( ) to recover the coefficients of a quadratic from values of the quadratic computed for a number of equally spaced values of its argument. Then I did some experiments with an alternative approach that I have always wondered about, as follows...

If you have a formula for a time series in form y(n) = a₀ + a₁.t(n) + a₂ t(n)², then it's a quadratic.

But if you make a new time series y'(n) by taking the first difference of the quadratic time series, y'(n) = y(n) - y(n-1), the new time series is a straight line y'(n) = b₀ + b₁.t(n) . There is a simple relation between the coefficients of the new (straight line) time series and the coefficients a₁ and a₂ of the quadratic time series:

a₂ = b₁/2

a₁ = b₀ - b₁/2

[E&OE --- I'll check what I wrote next week]

So you can find the coefficient of the quadratic terms either by direct regression polynomial computation *or* by fitting a straight line to the 1st difference of the data. In the case of noise-free data, the two methods give the same results - as they have to. In the case of noisy data, computations confirm that the results are not precisely identical, as would be expected.

If I get around to it next week, I'll see what happens when this is applied to the Central England January data. Here is the 1st difference of the January data: graph. It looks like trendless white noise to me. The very high value was where an exceptionally cold January (1795, -3.1°C), was followed by an exceptionally warm one (1796, 7.3°C).

EM

I'm not from Ulster but have a lot of friends there!

Martin A

Thank you. That looks like a very enjoyable piece of analysis.it has taken me an hour and a bit of research to understand it (oh for better maths)

If I understand correctly, you have shown that any trend in the data is probably linear rather than quadratic, which argues against my hypothetical cooling/ warming pattern.

You have also shown that the variations are mostly white noise, so any trend is likely to be obscured by the internal variability in the data.

This is bad news. CET is too noisy to give useful trend data.

Splitpin

I'm quite happy to accept guesses during the hypothesis generation stage. Objective analysis methods come into play when you are testing the hypothesis.

We are all prone to seeing what we expect or what we want to see. Proper statistical tests etc are tools for minimising this effect.

Paul Dennis

I was reading your paper Garnett et al(2003) on isotope temperature determination in a Holocene tufa.I found it fascinating and curiously nostalgic. It reminded me of Summers spent doing bog coring and pollen analysis for Peter Moore and David Bellamy in the early 1970s.

The paper gave me considerable help with the uncertainty problem. The paper mentions the 8.2kya event and estimated an 18O drop of 1o/oo was equivalent to a cooling of "about 1.7C". Later in the paper a 0.4o/oo change corresponded to a temperature change of 0.7C.

These put the sensitivity of your technique around 1.7C/ per 1o/oo or 0.59o/oo per 1C.

Earlier in the paper:-

Replication analyses of the laboratory standard gave a 2sigma of +/-0.11o/oo for oxygen and 0.19o/oo for carbon.

That is 18O based temperature 95% confidence limits of 0.11/0.59 = +/-0.19 C.

This is comparable with other sources such as Marcott et al(2013)whose data is +/- 0.25C for most of the Holocene.

The modern temperature record has 95% confidence limits of +/-0.1C. If paleo has 95% confidence limits of +/-0.2C your profession is doing excellent work. Your concern about large uncertainties in the paleo temperate record seems excessive.

EM,

You misunderstand me. I have said repeatedly here that at single locations, with a good understanding of the local hydrology and hydrogeology, that good records are achievable. I cited the example of Soreq and Pequin Caves in Israel. I was far too modest to cite my own work!

However, I believe you are mixing up our laboratory analytical uncertainty with precision for temperature estimates.

Since you have brought up the Wateringbury Tufa we worked on if you read the discussion carefully you will see that the controls on the oxygen isotopic composition of the carbonate is complex: (i) the thermodynamic partitioning of 18-O between water and calcite; (ii) The effect of local temperature on precipitation isotope composition and (ii) possible precipitation amount effects, and (iv) a combination of all of these. We discounted (i) as the sole casue of the isotopic variation because it implied a large Holocene climate shift of more than 6 degrees C. We suggested the dominant control was a smaller change in local mean air temperature that affected the isotopic composition of precipitation and the local groundwater. This led to an estimated temperature change of 1.7 degrees C. This is entriely based on a study by Kazimierz Rozanski and others at the IAEA who show that fro modern rainfall the isotopic composition of precipitation in north west Europe varies by about 0.58 per mille per degree C. Using this data and ignoring the effect of temperature on 18-O partitioning between calcite and water we arrived at the temperature change above. However, the temperature change is an approximate guide. It is NOT accurate but is consistent with what we know of Holocene change in this part of the UK. In fact, from memory we state that temperature effects on the the thermodynamic partitioning of 18-O between calcite and water also should impact on this temperature. If we take these into account as well we could well end up with a larger temperature change. I might do the calculation later tonight for you.

You then go on to take our laboratory analytical uncertainty and use our estimate of temperature change to estimate confidence intervals of just +/-0.19 degrees C on our method, I think this is wrong! Our estimate of the 1.7 degree C temperature change likely has an error of +/- 0.5 degrees as a minimum.

Thank you for the compliment about how well we are doing but because the systems are so complex our estimates are just that - ESTIMATES.

Paul Dennis

Thanks for that +/-0.5C. Still sounds good considering the complexities.

Getting numbers out of the others here is like squeezing blood from a stone.

I get a lot of flack here for my apparent obsession with confidence limits. They fail to appreciate that, as you say, all sampled data are estimates. Confidence limits tell you what the estimates are worth.

Paul Dennis, thank you for the refresher course in Confidence Limits. It does seem that Global Warming experts only remember them, when it suits their purpose.

In a field remote from global warming, I have witnessed the damage caused by a 'well respected expert' giving an off the cuff, ' rough guide approximation' figure for something. This figure was then hijacked, and presented as the ' expert's definition', and quoted in professional reports and legal arguments, for years. Maybe it still is.

EM,

the Wateringbury study is a good example of how difficult it is to recover temperatures and temperature changes from freshwater isotope records. The range in d18O values at Waterningbury is about 1.5 per mille from -6 to -4.5 from about 10,000 to 8000 years ago. If we consider that this reflects a change as a result of the effect of temperature on the fractionation of 18-O between calcite and water this represents a temperature change of about -6 degrees C.This is unlikely as it would require groundwater temperature changes without any accompanying change in air temperature! If we consider that the change is due to a change in the oxygen isotope composition of precipitation as a result of changes in air temperature and that the groundwater remained at a constant temperature then the isotope shift represents a change of +2.6 degrees C. This is possible with a lag between groundwater and air temperature changes. If we consider that the air and groundwater temperature covary (a more likely possibility in my opinion) then we would estimate a temperature change of +4.5 degrees C. We should have explored this in more detail in the paper. On re-reading it is not written very well because we just say that the isotopic signal associated with temperature of precipitation would dampen (reduce) the 'climatic temperature signal'. We didn't say by how much. It is nearly 2 degrees C!

So you see our estimate of temperature change varies from -6 degrees C through +2.6 to +4.5 degrees C depending on the model we choose. To resolve this we'd need very detailed study of the relationship between: (i) air temperature and precipitation isotope composition at Wateringbury; (ii) the relationship between air temperature and groundwater temperature at Wateringbury etc. This is typical of the problems associated with freshwater oxygen isotope records. There are other complexities as well. So the confidence I have in the temperature estimates is low. My +/-0.5 degrees C I posted yesterday is too optimistic. It is based on the assumption of a model for which we don't have the necessary validation. Now I would say that the isotope record represents a change in temperature of a minimum of +2.6 to a maximum of +4.5 degrees C over the period 10,000 to 8,000 years ago.

I've gone into some detail to illustrate how complex unravelling these systems is and actually how imprecise some of our estimates are. In practise many of these same caveats apply to all isotope proxy systems, especially those based on terrestrial freshwater deposits such as tufas, speleothems etc.

Paul Dennis

Now I would say that the isotope record represents a change in temperature of a minimum of +2.6 to a maximum of +4.5 degrees C over the period 10,000 to 8,000 years ago.

That sets the 95% confidence limits at +/-0.95C.

Thinking aloud, that allows you to confidently resolve temperature differences larger than 2C. This includes the three main default climate states. The Eocene style hothouse earth, the icehouse interglacial and the icehouse glacial periods are easy to distinguish They are ~5C apart and statistically significantly different.

The Younger Dryas is more marginal. It would need to be at least 2C cooler than the periods before and after for you to be 95% confident of its existance.

Heinrich events, the 8.2kya event, the more recent cooling from the Holocene Optimum, the "Minoan Warm period", the "Roman Warm Period", the Mediaeval Warm Period", the "Little Ice Age" and the 1880 to 2015 warming in the modern temperature record are all too small for you to confidently resolve.

Would that be a reasonable summary of your position?

Paul, REMEMBER THE BRICK WALL. Such inanities as EM's last offering, I strongly suggest you ignore for all our sakes. As if such climatic intervals would rely only upon isotopic data from terrestrial carbonates. EM is only getting worse.

Alan Kendall

I was invited to interact with paleo professionals. I am doing so, and learning.

What is your take on paleo uncertainties?

If +/-0.95C is towards the top end of the uncertainty range for paleotemperature, what accuracy would you expect for other techniques such as oxygen isotopes in ice cores or beryllium isotopes in corals?

Which paleo events would you regard as well established and which are scientifically dubious?

These are genuine questions. I always welcome new information, but I know bullshit like the Glacier Girl comment when I see it.

You complain about my wall. Each brick is evidence that supports my world view.

Briefly, I think that past temperatures are mediated by continental position, then orbital cycles and solar insolation. CO2 acts sometimes as a forcing, but mostly as a feedback. Other factors such as meltwater lakes, shield volcano's or impacts perturb the system. Modern warming is mostly due to CO2 from fossil fuels acting as a forcing.

If you want my view to change, show me good evidence, especially good numbers.
I present my view to those here willing to debate the science and read their responses. Occasionally they correct my errors. Occasionally I correct theirs.

Neither side is likely to convert the other. In the meantime, the debate is fun.

Martin A

Browsing around I found two other bloggers discussing CET, one from Clive Best and one from Ed Hawkins.

EM,

In answer to your last question to me NO!

I was talking about a single record where the evidence is of a warming over a temperature interval of the early Holocene between 2.6 and 4.5K. At other sites where there is better understanding of the controlling factors then better estimates are possible. Please see my previous notes.

You have an uncanny knack of moulding whatever information is available to suit your worldview. Your insistence on trying to take my statements about the Wateringbury tufa deposit and extrapolate these into some sort of confidence interval for isotope studies is but an example of this. Similarly, as Martin A has pointed out your estimates of confidence intervals on the Argo data are just wrong. They do however, give you a comfort blanket.

That this is so is betrayed by your next reply to Alan where you talk about supporting your world view. Please take the blinkers off and approach data with an open and enquiring mind. Be realistic about how precise and accurate records are and above all be cognisant of the fact that our understanding of past climates, as Alan has explained, is based on a very wide range of different types of evidence.

One final point what the has Beryllium isotopes in corals got to do with palaeoclimate reconstructions? I don't know who Glacier Girl is but as for bullshit you can sometimes give her a run for her money.

Alan Kendall, Paul Dennis & Radical Rodent

it is normally at this point, that true believers in the one and only faith of Global Warming through Anthropogenic CO2 emissions, will want to divert and refocus attention onto the precise details of the BRICK WALL. Composition of the bricks, wall thickness, bonding pattern, age, condition, lime or cement mortar, weather conditions during construction etc

Alan and Paul, thank you for all your contributions on this blog so far. This thread was started by Dung, and it matched my curiosity about what could be 'revealed' from paleo and geological records. I have had some involvement with archaeology, geology, forensics etc, and not at the same time either. I have enjoyed programmes such as Timewatch, and how modern techniques and technologies can reveal stuff not possible 10/20/30 years ago.

It does seem that the quest for a quick easy and cheap win for AGW, is not to be found under the earth's surface. Perhaps they should dig tunnels in the air, to look for more compliant rocks.

I hope you appreciate that Radical Rodent does also have a slightly mischievous sense of humour.