All posts by Paul_K

Data Comparisons

The Occam’s Razor Oscillatory Model

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I recently had a (very rare) intellectual difference of opinion with Lucia, related to the “Doug Keenan/Lord Donahue  vs the UK Met Office” kerfuffle.

I take some exception to the UK Met Office declaring that the rise in temperature from 1880 is “statistically significant”.   Given the application of inferential statistics by the UK Met Office, the question they are apparently seeking to answer  is:  Can we (use a statistical model to) show that the rise in temperature since 1880 is statistically significantly different from the expected?   This question  relates to detection rather than attribution – it asks if we can confirm that something strange is going on, not what is causing it, which comes later.

Let us also be very clear that  the UK Met Office was not trying to answer a different question i.e.  whether we can say with confidence that the temperature has really risen since 1880 – that was already a given, but even if it were not, the test applied by the UK Met Office would not be the correct test to answer this question;  such a test would need to focus on uncertainties in the estimates of average temperatures at the beginning and end of the temperature record, arising from observational measurement uncertainty, coverage and weighting;  the test actually applied does not address these sources of error  at all.

Continue reading The Occam’s Razor Oscillatory Model →

Climate models, Data Comparisons, Toy Physics

Observation vs Model – Bringing Heavy Armour into the War

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As I have noted before, most of the AOGCMs exhibit a curvilinear  response in outgoing global flux with respect to average temperature change.  One of the consequences of this is that there is a well-reported apparent increase in the effective climate sensitivity with time and temperature in the models; in particular, the effective climate sensitivity required to match historical data over the instrument period in the GCMs is less than the climate sensitivity reported from long-duration GCM runs.   This is not a small effect, although it varies significantly between the different GCMs.   In the models I have tested, it accounts for about half of the total Equilibrium Climate Sensitivity (“ECS”) reported for those models.   (Equilibrium Climate Sensitivity is defined by the IPCC as the equilibrium temperature in degrees C after a doubling of CO2.)  In general, models which show a more pronounced curvature will have a larger ratio of reported ECS to the effective climate sensitivity required to match the model results over the instrument period, and vice versa.

Kyle Armour et al have produced a paper, Armour 2012 , which offers a simple, elegant and coherent explanation for this phenomenon.   It comes down to geography.

Continue reading Observation vs Model – Bringing Heavy Armour into the War →

Data Comparisons

Pinatubo Climate Sensitivity Revisited

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I made a guest post here  on the subject of the estimation of climate sensitivity from the Pinatubo data.  The forcing data that I used were based on optical depth data taken from Douglass and Knox 2005  (“DK2005”) , which were reported to be from Amman et al 2003.  These values were converted to volcanic forcings using a conversion factor of 21 W/m2.

However, thanks to an observation made by Nic Lewis, we subsequently discovered that the optical depth values used by Douglass and Knox were different by a factor of about 0.87 from  global areally weighted values taken directly from source (Amman et al 2003).  For more detail, see the October 26th update addended to the original referenced post.

I brought this to the attention of Professor Douglass, and received a polite response, but the reason for the difference remains unexplained.  He confirmed the source of the data,  and suggested that any such difference in optical depth values, if it exists, would be absorbed into his estimation of the conversion factor from optical depth to forcing.  He has moved on to other things, and is evidently unenthusiastic about tracking down the discrepancy at the present time.

Continue reading Pinatubo Climate Sensitivity Revisited →

Data Comparisons

Pinatubo Climate Sensitivity and Two Dogs that didn’t bark in the night

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Gregory (Scotland Yard detective): “Is there any other point to which you would wish to draw my attention?”

Holmes: “To the curious incident of the dog in the night-time.”

Gregory: “The dog did nothing in the night-time.”

Holmes: “That was the curious incident.”

From The Memoirs of Sherlock Holmes (Arthur Conan Doyle)

 

Pinatubo was hailed by many climate scientists as a unique opportunity to test climate sensitivity.  It was the first major volcanic eruption during the satellite era.  For the very first time, we had top-of-atmosphere (TOA) measurements of radiative flux changes (from the ERBE) during a major eruption.

I would like to consider four papers here which deal with the estimation of climate sensitivity from the Pinatubo data;  they are:-

 

Douglass and Knox 2005  (“DK2005”);

Wigley et al 2005  (“Wigley2005”);

Forster and Gregory 2006  (“FG2006”);

Soden et al 2002 (“Soden2002 “) .

Continue reading Pinatubo Climate Sensitivity and Two Dogs that didn’t bark in the night →

Climate models, Data Comparisons

Ocean Heat Uptake Efficiency, Chicken-laying Eggs and Infinite Silliness

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In a recent post here, I discussed the nonlinearity of the Earth’s radiative flux response to temperature change exhibited in most of the GCM results, and the application of an incompatible linearised model to those results for the purpose of analyzing climate feedbacks.

The conversation in the comments section, perhaps inevitably,  got onto the subject of “ocean heat uptake efficiency”, and more specifically onto the 2008 paper by Gregory and Forster, (“GF08”).  The assumption underpinning ocean heat uptake efficiency is that you can characterize the net flux imbalance as a simple linear function of temperature change,  with a constant of proportionality, κ.  I expressed the view in the comments section that the concept was inelegant, ultimately unnecessary and founded on a mathematical fallacy.  With Lucia’s permission, I would like to try to defend this comment, and take the opportunity to address some of the questions which arose.

 

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Climate models, Data Comparisons

The Arbitrariness of the IPCC Feedback Calculations

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Introduction

Professor Isaac Held recently published a blog article  here with the title “The arbitrariness in feedback analyses”.   The title refers to the arbitrary selection of a reference response against which to assess feedbacks.   I agree with much of  Professor Held’s paper  on the issue of the arbitrariness of the starting point, which is a definitional issue, but I also believe that the paper leaves a very large elephant under the table.

I wish here to discuss the elephant.  The elephant is the application of a linearised response function to the nonlinear response observed in the GCMs when a large forcing is applied, and which gives rise to a quite different source of arbitrariness in the feedback analyses  reported by the IPCC .

The IPCC feedbacks calculated for each GCM are highly case-sensitive as well as being sensitive to the choice of the run-time over which they are estimated.  In particular, these values, which are based on large forcings applied in future scenarios, cannot be reconciled with the feedbacks effective (in the same GCM) over the historic instrumental temperature period.

Not only do the calculated values  have  little explanatory value outside the specific cases examined, but, even within those specific cases, the assumption that all individual feedbacks are linear with temperature, and therefore additive, makes the relative attribution between feedbacks within any model, quite fundamentally flawed.

Continue reading The Arbitrariness of the IPCC Feedback Calculations →

Climate models, Data Comparisons, Statistics

More Blue Suede Shoes and the Definitive Source of the Unit Root

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Introduction

In a previous article here, I showed  that it was possible to invert the instrumental temperature series into the flux domain, and that the incremental flux series could then be decomposed into three bandwidths yielding a Very Low Frequency component (the “SURE”), a Low Frequency component (represented here by just two cycles of 60.8 years and 21.3 years approximately) and a High Frequency component.

The SURE curve – which controls the  average trajectory of the temperature series – is seen to be a relatively smooth curve, tailing over at late time, when expressed as incremental flux.  The signal shows no obvious evidence of any CO2 effect.  I concluded in my previous article that it is impossible to quantify the effects of AGW from the temperature series alone, notwithstanding that various authors have claimed so to do.

I also stated that this approach – that of inverting the temperature signal to net flux – explains why statistical tests on the temperature series “fail to reject” a unit root in the temperature series.  I will show in this article where the unit root comes from, but before I do so, I would like to clear up three questions which were left outstanding from the first article.

Continue reading More Blue Suede Shoes and the Definitive Source of the Unit Root →

Data Comparisons, Statistics

Noisy Blue Ocean, Blue Suede Shoes and AGW Attribution

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Q. What do Blue Suede Shoes have to do with the temperature series?
A. Both Elvis and an AGW signal have been sighted there with equal credibility.
 

Introduction

 

Just occasionally, I come across something which makes my subjective world reel for a moment. This is one of those occasions. I have come to the very serious conclusion that, if there is an AGW signal in the temperature series, then it is unquantifiable by any known methodology. I have also decided that all the attribution arguments which I have seen to date, which are based on analysis of the temperature series – or the change in slope of the temperature series – are fundamentally flawed. I also hope that, after reading this article, anyone who picks up a pencil and ruler to draw a straight line through a temperature plot will think very carefully about what they are going to do with the result. I will show that a straight line through the temperature series is based on a non-physical assumption. Using a trend line for comparison of models may be justified. Doing so for attribution arguments is not.
I am going to demonstrate here that there is no evidence of any unusual change in the instrumental temperature series. None at all. In logic terms, the absence of evidence is not the same thing as the evidence of absence; so let me make clear at the outset that what I am presenting here does not prove that there is no AGW signal in the temperature series. It does prove that, if there is one, we cannot quantify it.
The recent intellectual dispute between Lucia and Doug Keenan here over the structural form of the temperature series led me to wonder whether we might gain some insight into the most appropriate structural form by considering the input signal rather than the output.
What input signal, you may ask? Well, the physics problem is normally modeled forwards. A climate model typically generates a temperature profile from a given set of exogenously imposed flux perturbations (forcings), conditioned by assumptions and parameters. To find the input signal then, we need to reverse this process i.e. find the imposed flux perturbations (radiative forcings plus any non-radiative forcings into or out of the mixed layer) which reproduce the given temperature series exactly. Mathematically, this is equivalent to finding the inverse transform to go from temperature to the input flux perturbations, rather than the other way around.
The solution to the inversion problem is given in Appendix A.
Here are the resulting calculated values of the annual (incremental) flux forcings which control the global temperature series (derived in this instance from annualized HADCRUT3):-
Continue reading Noisy Blue Ocean, Blue Suede Shoes and AGW Attribution →

Data Comparisons

Equilibrium Climate Sensitivity and Mathturbation – Part 2

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The late great Spike Milligan used to tell a story about coming across his young
daughter drawing.  He asked her what she was doing, and she replied “I’m drawing a picture of God.”  Spike laughed and said “But no-one knows what he looks like.”  With a pained look,  his daughter snapped back “Well they will when I’ve finished the drawing!”

In Part 1 here I got as far as the application of this energy balance equation to 34 years of OHC data from GISS-E.

dH/dt = F(t) -   λ1ΔT – λ2 ΔT2 – λ3 ΔT3 – λ4 ΔT4 + (error order  ΔT5 )     … B.3

I demonstrated that it wasn’t possible to estimate ECS uniquely from this short-run data and I promised to develop two additional models to allow further tests using the GISS-E temperature and OHC data series.   However, before I do so, there is something I must do for humanitarian reasons.  At the end of Part 1, I left Steven Mosher chewing his fingernails and chain-dropping valium.  I was touched by the simple, heart-rending sincerity of his anguished crie de cœur in the comments section: “Crap, the suspense is killing me.”

Steven is waiting for the answer to a key question.  For his mental health, I will sacrifice dramatic literary effect and give the answer to the key question upfront.

The Question:  Can you or can you not estimate Equilibrium Climate Sensitivity (ECS) from  120 years of temperature and OHC data  (even) if the forcings are known?

The Answer is:  No.  You cannot.  Not unless other information is used to constrain the estimate.

An important corollary to this is:- The fact that a GCM can match temperature and heat data tells us nothing about the validity of that GCM’s estimate of Equilibrium Climate Sensitivity.

This fact arises from the mathematical properties of the problem.

The models I am going to develop today to complete the proof of this will solve for temperature, as well as heat gain, and to do that I must now make some assumptions about the distribution of heat.   Since I am looking at the world through the lens of a GCM, I am going to assume that all energy arriving through radiative imbalance ends up as heat;  i.e. there is no other long-term energy storage in, for example, biomass or planetary kinetics. Continue reading Equilibrium Climate Sensitivity and Mathturbation – Part 2 →

Data Comparisons

Equilibrium Climate Sensitivity and Mathturbation – Part 1

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Introduction

On 4th May, SteveF  posted  A-simple-analysis-of-equilibrium-climate-sensitivity.  I made a number of critical comments targeted on SteveF’s methodology, while stating that I had no serious problem with the magnitude of his final answer.   This led to a friendly challenge from SteveF where he suggested that instead of throwing rocks at his approach, I should show my approach to equilibrium climate sensitivity.

Lucia graciously offered me some rope in the form of column-space with which to mix metaphors. 

I am planning on presenting some analysis here, which involves the development of four mathematical models, although in this Part 1, I will only consider the first two models.   Since the turgid mathematical details will make it very easy to lose sight of my main line of argument, it will probably help everyone if I offer a road-map in advance:-

1)      The IPCC AR4 states that Equilibrium Climate Sensitivity (ECS) from a doubling of CO2 is ” “likely to be in the range 2 to 4.5°C with a best estimate of about 3°C, and is very unlikely to be less than 1.5°C. Values substantially higher than 4.5°C cannot be excluded, but agreement of models with observations is not as good for those values.” 

2)      The source of the IPCC range of estimates is the CMIP4 model suite – the GCMs, and only the GCMs.  Paleo evidence provides no corroborative evidence for a high climate sensitivity, in fact, quite the contrary.  

3)      I will show that the current estimates of climate sensitivity in the GCMs are (a) mathematically arbitrary and (b) biased high.   Climate sensitivity in any GCM is “structurally input” to the model in the sense that the model developer must make a series of critical choices about (a) what exogenous forcings he will account for, and (b) how to model temperature-dependent feedback processes.  Once those choices are made, the ECS is largely fixed in the model, apart from some tuning parameters.  Once the ECS is fixed,  it is then possible to match surface temperature and OHC data to the GCM, using the total forcing as a variable input, rather than finding the ECS which best matches  the data.   I will defer to  Kiehl 2007 to prove that  this is, in fact,  what is actually happening in practice.  Loosely summarizing: – The ECS value associated with a GCM is not derived  from information content in the observed temperature (and heating) data; the GCM can be forced to match that data for any ECS value.   The ECS is predetermined by the model builder and then forcing data is adjusted until the model is ‘not inconsistent with’ the temperature (and heating) data.   If the adequacy of model fit to temperature and heating cannot be used as a discriminant, it follows that, in order to meet a minimum necessary (but not sufficient) condition for credibility in its estimate of ECS, the GCM must then demonstrate its ability to match other critical data simultaneously.  None of the GCMs manage to do this. 

4)      There is increasingly convincing evidence from quite separate lines of enquiry that the indirect effects of solar (via UV amplification and albedo modulation) are greater than the direct forcing effects of TSI variation.   Climate variation historically can be more consistently explained using a low climate sensitivity and a larger indirect solar forcing.  This explanation avoids the many paradoxes which arise from a strained over-attribution of temperature control to CO2 forcing.

 Whether one accepts the evidence supporting indirect amplification of solar effects or not, it is a simple fact that to achieve the history matches for AR4, the GCMs have all replaced SW heating with LW suppression in the critical heating period post -1980 when we have the satellite data to compare with.  This SW deficit in the models comes from an underestimate (by the models) of albedo reduction during this period.

 

The above IPCC graphic (taken from Chapter 9 of WG1) shows  a substantial  cumulative error (deficit) in SW heating amounting  to around 2 W/m2 over this period.  (This uses the relatively conservative estimates of Wong et al and Zhang et al for comparative purposes. There are larger estimates of the error even within the IPCC references.)  One is left with the inevitable conclusion that the GHG heating effect has been overestimated.  Since the magnitude of radiative forcing from a doubling of CO2 is reasonably secure science, this strongly suggests that the estimates of climate sensitivity in the models are all too high.

5)      If we reverse the problem, and fix the forcing data, we find that direct estimation of ECS from  short-run temperature and heat data is mathematically ill-conditioned i.e. a large range of ECS values can be found to match the same time-series even with the forcing data fixed.   I will illustrate this with a series of successively higher-order energy balance models, and we will see why this is so.      

6)      The obvious route forwards is to recognize that we have a lot more data than just mean surface temperature and OHC data with which to constrain a solution.   It seems that the modelers have sacrificed the need to match  these other critically important data in favour of retaining a structurally high ECS.  Where significant differences are apparent between observed and modeled data, those differences show a warm bias.  

Eventually, but perhaps not in my lifetime, we will develop a super -GCM that can provide a reasonable match to all of the data and constrain the ECS within credible bounds.  In so doing,  it must increase the total SW heating effect relative to heating by atmospheric capture of LW, and must therefore land on a lower climate sensitivity than the current GCM-derived range of estimates.  My best guess is that it must land somewhere between 1.2 and 2 deg K for a doubling of CO2.

A little more history
Continue reading Equilibrium Climate Sensitivity and Mathturbation – Part 1 →