Errors of Global Warming Effects Modeling

Since 2006, in between promoting numeracy in education, and examples of simple statistics using topical issues from the theory of Anthropogenic Global Warming (AGW) to illustrate points, I asked the question “Have these models been validated?”, in blog posts and occasionally submissions to journals. This post summarizes these efforts.

Species Extinctions

Predictions of massive species extinctions due to AGW came into prominence with a January 2004 paper in Nature called Extinction Risk from Climate Change by Chris Thomas et al.. They made the following predictions:

“we predict, on the basis of mid-range climate-warming scenarios for 2050, that 15–37% of species in our sample of regions and taxa will be ‘committed to extinction’.

Subsequently, three communications appeared in Nature in July 2004. Two raised technical problems, including one by the eminent ecologist Joan Roughgarden. Opinions raged from “Dangers of Crying Wolf over Risk of Extinctions” concerned with damage to conservationism by alarmism, through poorly written press releases by the scientists themselves, and Extinction risk [press] coverage is worth the inaccuracies stating “we believe the benefits of the wide release greatly outweighed the negative effects of errors in reporting”.

Among those believing gross scientific inaccuracies are not justified, and such attitudes diminish the standing of scientists, I was invited to a meeting of a multidisciplinary group of 19 scientists, including Dan Bodkin from UC Santa Barbara, mathematician Matt Sobel, Craig Loehle and others at the Copenhagen base of Bjørn Lomborg, author of The Skeptical Environmentalist. This resulted in Forecasting the Effects of Global Warming on Biodiversity published in 2007 BioScience. We were particularly concerned by the cavalier attitude to model validations in the Thomas paper, and the field in general:

Of the modeling papers we have reviewed, only a few were validated. Commonly, these papers simply correlate present distribution of species with climate variables, then replot the climate for the future from a climate model and, finally, use
one-to-one mapping to replot the future distribution of the species,without any validation using independent data. Although some are clear about some of their assumptions (mainly equilibrium assumptions), readers who are not experts in modeling can easily misinterpret the results as valid and validated. For example, Hitz and Smith (2004) discuss many possible effects of global warming on the basis of a review of modeling papers, and in this kind of analysis the unvalidated assumptions of models would most likely be ignored.

The paper observed that few mass extinctions have been seen over recent rapid climate changes, suggesting something must be wrong with the models to get such high rates of extinctions. They speculated that species may survive in refugia, suitable habitats below the spatial scale of the models.

Another example of an unvalidated assumptions that could bias results in the direction of extinctions, was described in chapter 7 of my book Niche Modeling.

range_shift

When climate change shifts a species’ niche over a landscape (dashed to solid circle) the response of that species can be described in three ways: dispersing to the new range (migration), local extirpation (intersection), or expansion (union). Given the probability of extinction is correlated with range size, there will either be no change, an increase (intersection), or decrease (union) in extinctions depending on the dispersal type. Thomas et al. failed to consider range expansion (union), a behavior that predominates in many groups. Consequently, the methodology was inherently biased towards extinctions.

One of the many errors in this work was a failure to evaluate the impact of such assumptions.

The prevailing view now, according to Stephen Williams, coauthor of the Thomas paper and Director for the Center for Tropical Biodiversity and Climate Change, and author of such classics as “Climate change in Australian tropical rainforests: an impending environmental catastrophe”, may be here.

Many unknowns remain in projecting extinctions, and the values provided in Thomas et al. (2004) should not be taken as precise predictions. … Despite these uncertainties, Thomas et al. (2004) believe that the consistent overall conclusions across analyses establish that anthropogenic climate warming at least ranks alongside other recognized threats to global biodiversity.

So how precise are the figures? Williams suggests we should just trust the beliefs of Thomas et al. — an approach referred to disparagingly in the forecasting literature as a judgmental forecast rather than a scientific forecast (Green & Armstrong 2007). These simple models gloss over numerous problems in validating extinction models, including the propensity of so-called extinct species quite often reappear. Usually they are small, hard to find and no-one is really looking for them.

Hockey-stick

One of the pillars of AGW is the view that 20th-century warmth is exceptional in the context of the past 1200 years, illustrated by the famous hockey-stick graph, as seen in movies, and government reports to this day.

Claims that 20th-century warming is ‘exceptional’ rely on selection of so-called temperature ‘proxies’ such as tree rings, and statistical tests of the significance of changes in growth. I modelled the proxy selection process here and showed you can get a hockey stick shape using random numbers (with serial correlation). When the numbers trend, and then are selected based on correlation with recent temperatures, the result is inevitably ‘hockey stick’ shaped: i.e. with a distinct uptick where the random series correlated with recent temperatures, and a long straight shaft as the series revert back to the mean. My reconstruction was similar to many other reconstructions with low variance medieval warm period (MWP).

from-clipboard-2

It is an error to underestimate the effect of ex-post selection based on correlation or ‘cherry picking’ on uncertainty. Cherry picking has been much criticised on ClimateAudit. Steve McIntyre and Ross McKitrick published in February 2009 a comment, cited my AIG article, in a criticism of an article by Michael Mann, saying:

Numerous other problems undermine their conclusions. Their CPS reconstruction screens proxies by calibration-period correlation, a procedure known to generate ‘‘hockey sticks’’ from red noise (4).

The response by Michael Mann acknowledged such screening was common, used in their reconstructions, but claimed it was ‘unsupported’ in the literature.

McIntyre and McKitrick’s claim that the common procedure (6) of screening proxy data (used in some of our reconstructions) generates ‘‘hockey sticks’’ is unsupported in peer-reviewed literature and reflects an unfamiliarity with the concept of screening regression/validation.

In fact, it is supported in the peer-reviewed literature, as Gerd Bürger raised the same objection in a Science 29 June 2007 comment on “The Spatial Extent of 20th-Century Warmth in the Context of the Past 1200 years by Osborn and Keith R. Briffa (29 June 2007)” finding 20th-Century warming not exceptional.

However, their finding that the spatial extent of 20th-century warming is exceptional ignores the effect of proxy screening on the corresponding significance levels. After appropriate correction, the significance of the 20th-century warming anomaly disappears.

The National Academy of Science agreed that uncertainty was greater than appreciated, and shortened the hockey-stick of the time by 600 years (contrary to assertions in the press).

Long Term Persistence (LTP)


Here
is one of my first php applications, a fractional differencing simulation climate. Reload to see a new simulation below, together with measures of correlation (r2 and RE) with some monthly climate figures of the time.

This little application gathered a lot of interest, I think because fractional differencing is an inherently interesting technique, creates realistic temperature simulations, and is a very elegant way to generate series with long term persistence (LTP), a statistical property that generates natural ‘trendiness’. One of the persistent errors in climate science has been the failure to take into account the autocorrelation in climate data, leading to inflated significance values.

It has been noted that there are no requirements for verified accuracy for climate models to be incorporated into the IPCC. Perhaps if I got my random model published it would qualify. It would be a good benchmark.

Extreme Sensitivity

“According to a new U.N. report, the global warming outlook is much worse than originally predicted. Which is pretty bad when they originally predicted it would destroy the planet.” –Jay Leno

The paper by Rahmstorf et al. must rank as one the most quotable of all time.

The data available for the period since 1990 raise concerns that the climate system, in particular sea level, may be responding more quickly to climate change than our current generation of models indicates.

This claim, made without the benefit of any statistical analysis or significance testing is widely quoted to justify claims that the climate system is “responding more strongly than we thought”. I debated this paper with Stefan at RealClimate, and succeeded in demonstrating they had grossly underestimated the uncertainty.

His main defense was that the end point uncertainty would only affect the last 5 points of the smoothed trend line with an 11 point embedding. Here the global temperatures were smoothed using a complex method called Singular Spectrum Analysis (SSA). I gave examples of SSA and other methods where the end point uncertainty affected virtually ALL points in the smoothed trend line, and particularly more than 5 end points. Stefan clearly had little idea of how SSA worked. His final message, without an argument, was:

[Response: If you really think you’d come to a different conclusion with a different analysis method, I suggest you submit it to a journal, like we did. I am unconvinced, though. -stefan]

But to add insult to injury, this paper figured prominently in the Interim Report of the Garnaut Review where I put in a submission.

“Developments in mainstream scientific opinion on the relationship between emissions, accumulations and climate outcomes, and the Review’s own work on future business-as-usual global emissions, suggest that the world is moving towards high risks of dangerous climate change more rapidly than has generally been understood.”

As time moves on and more data is available, a trend line using the same technique is regressing to the mean. It is increasingly clear that the apparent upturn was probably due to the 1998 El Nino. It is an error to regard a short term deviation as an important indication of heightened climate sensitivity.

More Droughts

The CSIRO Climate Adaptation Flagship produced a Drought Exceptional Circumstances Report (DECR), suggesting among other things that droughts would double in the coming decades. Released in the middle of a major drought in Southern Australia, this glossy report had all the hallmarks of promotional literature. I clashed with CSIRO firstly over release of their data, and then in attempting to elicit a formal response to issues raised. My main concern was that there was no apparent attempt demonstrating the climate models used in the report were fit for the purpose of modeling drought, particularly rainfall.

One of the main results of my review of the data is summed up in the following graph, comparing the predicted frequency and severity of low rainfall over the last hundred years, with the observed frequency and severity of low rainfall. It is quite clear that the models are inversely related to the observations.

image003

A comment submitted to the Australian Meteoreological Magazine was recently rejected. Here I tested the models and observation following an approach of Rybski of analyzing difference between discrete periods 1900-1950 and 1950-2000. The table belows shows that while drought decreased significantly between the periods, modeled droughts increased significantly.

p>Table 1: Mean percentage area of exceptionally low rainfall over time periods suggested by KB09. A Mann Whitney rank-sum test shows significant differences between periods.

1900-2007 1900-1967 1951-2007 P 1900-2007 vs. 1951-2007 P 1900-1950 vs. 1951-2007 Test
Observed % Area Drought 5.6±0.5 6.2±0.7 4.9±0.6 0.10 0.004 Mann-Whitney test
(wilcox.test(x,y) in R)
Modelled % Area Drought 5.5±0.1 4.8±0.2 6.2±0.2 0.006 <0.001 Mann-Whitney test
(wilcox.test(x,y) in R)

Moreover I showed that while similar results were reported for temperature in the DECR (where models and observations are more consistent), they were not reported for rainfall.

The reviewers did not comment on the statistical proof that the models were useless at predicting drought. Instead, they pointed to Fig 10 in the DECR, a rough graphic, claiming “the models did a reasonable job of simulating the variability”. I am not aware of any statistical basis for model validation by the casual matching of the variability of observations to models. The widespread acceptance of such low standards of model validation is apparently a feature of climate science.

Former Head of the Australian Bureau of Statistics Ian Castles solicited a review by ANU independent Accredited Statisticians, Brewer and Other. They concurred that models in the DECR required validation (along with other interesting points).

Dr Stockwell has argued that the GCMs should be subject to testing of their adequacy using historical or external data. We agree that this should be undertaken as a matter of course by all modelers. It is not clear from the DECR whether or not any such validation analyses have been undertaken by CSIRO/BoM. If they have, we urge CSIRO/BoM make the results available so that readers can make their own judgments as to the accuracy of the forecasts. If they have not, we urge them to undertake some.

A persistent error in climate science is using models when they have not been shown to be ‘fit for purpose’.

Miskolczi

Recently a paper came out potentially undermining the central assumptions of climate modeling. Supported by extensive empirical validation, it was suggested that ‘optical depth’ in the atmosphere is maintained at an optimal, constant value (in the average over the long term). Finding an initial negligible sensitivity of 0.24C surface temperature increase to doubling CO2 increase, it then goes on to suggest constrains that ensure equilibrium will eventually be established, giving no increase in temperature, due to reversion to the constant optical depth. The paper by Ferenc Miskolczi, (2007) called Greenhouse effect in semi-transparent planetary atmospheres, was published in the Quarterly Journal of the Hungarian Meteorological Service, January–March 2007.

I was initially impressed by the extensive validation of his theory using empirical data. Despite a furious debate online, there has been no peer-reviewed rebuttal to date. The pro-AGW blog site RealClimate promised a rebuttal by “students” but to date has made none. This suggests either that it is carefully ignored, or it is transparently flawed.

Quite recently Ken Gregory encouraged Ferenc to run his model using actual recorded water vapor data which declines in the upper atmosphere over the last few decades. While there are large uncertainties associated with these data, they do show a decline consistent with Ferenc’s theory, that water vapor (a greenhouse gas) will decline to compensate for increased CO2. The results of Miskolczi’s calculations using his line-by-line HARTCODE program are given here.

The theoretical aspects of Ferenc’s theory have been been furiously debated online. I am not sure that any conclusions have been reached, but nor has his theory been disproved.

Conclusions

What often happens is that a publication appears which gets a lot of exciting attention. Then some time later, rather quietly, subsequent work gets published that questions the claim or substantially weakens it. But that doesn’t get any headlines, and the citation rate is typically 10:1 in favor of the alarmist claims. It does not help that the IPCC report selectively cites studies, and presents unvalidated projections as ‘highly likely’, which shows they are largely expert forecasts, not scientific forecasts.

All of the ‘errors’ here can be attributed to exaggeration of the significance of the findings, due to inadequate rigor in the validation of models. This view that this is an increasing problem is shared by new studies of rigor from the intelligence community, but apply even more to data derived so easily from computer modeling.

The proliferation of data accessibility has exacerbated the risk of shallowness in information analysis, making it increasingly difficult to tell when analysis is sufficient for making decisions or changing plans, even as it becomes increasingly easy to find seemingly relevant data.

I also agree with John P. A. Ioannidis, who in a wide-ranging study of medical journals found that Most Published Research Findings Are False. To my mind when the methodologies underlying AGW are scrutinized, the findings seem to match the prevailing bias. To make matters worse, in most cases, the response of the scientific community has been to carefully ignore, dissemble, or ad hom dissenters, instead of initiating vigorous programs to improve rigor in problem areas.

We need to adopt more practices from clinical research, such as the structured review, whereby the basis for evaluating evidence for or against an issue is well defined. In this view, the IPCC is simply a review of the literature, one among reviews by competing groups (such as NIPCC REPORT 2008 Nature, Not Human Activity, Rules the Climate). In other words, stop pretending scientists are unbiased, but put systems in place to help prevent ‘group-think’ and promote more vigorous testing of models against reality.

If the very slow, to no rate of increase in global temperature continues, we will be treated to the spectacle of otherwise competent researchers clinging to extreme AGW, while the public become more cynical and disinterested. This would have been avoided if they had been confronted with “Are these models validated? If they are, by all means make your forecasts, if not, don’t.”

Redoubt now Ultraplinian

The rumbling Alaskan volcano Redoubt has exploded producing a stratosphere-reaching plume in excess of 60,000 ft (17 km). An eruption is termed ‘ultraplinian’ if its ejecta reaches the stratosphere, about 10km in height. Dust and gases in the stratosphere are known to depress the global temperature for up to a few years after the eruption. The extent of cooling depends on the amount and type of material, the size and duration of ultraplinian eruption, and the latitude (high latitude eruptions like Redoubt are less effective than lower ones).

The plume could be seen easily on infrared here (top center of first radar).

Continue reading Redoubt now Ultraplinian

Climate Flagship Response

A number of familiar tests, often used to evaluate the performance of models: R2 correlation, Nash-Sutcliffe efficiency and similarity of trends and return period, were reported here, noting not much evidence of skill in the DECR models compared with observations at any of these. I also said what a better treatment might entail but left that for another time:

The percentage of droughted area appears to be a ’bounded extreme value, peaks over threshold’ or bounded POT statistic. The distribution resembles a Pareto (power) law, but due to the boundedness where predicted extent of drought approaches 100% becomes more like a beta distribution (shown for SW-WA on Fig 2). Recasting the drought modeling problem into known statistical methods might salvage some data from the DEC report. Aggregating the percentage area under drought to the whole of Australia might reduce the boundedness of the distribution, and might also improve the efficiency of the models.

Aware that the tests I applied were not the last word due to the idiosyncratic nature of the data, the conclusion in the summary was slightly nuanced: that as there was no demonstration of skill at modeling drought (in both the DECR and my tests), and as validation of models is necessary for credibility, there is no credible basis:

Therefore there is no credible basis for the claims of increasing frequency of Exceptional Circumstances declarations made in the report.

What is needed to provide credibility is demonstrated evidence of model skill.

Andrew Ash, of the CSIRO Climate Flagship sent a response on 12/18/08. This was to fulfill an obligation he made on 16 Sep 2008, to provide a formal response to your review of the Drought Exceptional Circumstances report (dated 3 Sep 2008), after my many requests to provide details of the validation to skill at modelling of droughts.

I must say I was very pleased to see there was no confidentially text at the end of the email. I feel so much more inclined to be friendly without it. I can understand confidentiality inside organizations, but to send out stock riders to outsiders is picayune. The sender should be prepared to stand by what they say in a public forum and not hide behind a legal disclaimer. Good on him for that.

The gist of the whole email is that he felt less compelled to respond due to an ongoing review I sent to the Australian Meteorological Magazine on 23 Sep 2008. As it was, I was still waiting for the review from the AMM on the 18th December when I received this response. Kevin Hennessy relayed some advice from Dr Bill Venables, a prominent CSIRO statistician, and the following didn’t add anything:

However, we have looked at the 3 Sep 2008 version of your review. The four climate model validation tests selected in your analysis are inappropriate and your conclusions are flawed.

* The trend test is invalidly applied because (i) there is a requirement that the trends are linear and (ii) the t-test assumes the residuals are normally distributed. We undertook a more appropriate statistical test. Across 13 models and seven regions, there are no significant differences (at the 5% level) between the observed and simulated trends in exceptionally low rainfall, except for four models in Queensland and one model in NW Australia.

Its well known that different tests can give different results, depending on the test. It is also true that some tests may be better or more reliable than others. Without more details of their more test its hard to say anything, except to say that lack of significance does not demonstrate skill. The variability of the climate model outputs could be so high that they allow ‘anything to be possible’, as often seems to be the case.

* The correlation and efficiency tests are based on an assumption that the climate models are being used to hindcast historical weather. This assumption is incorrect. As a result, the tests selected are inapplicable to the problem being addressed. This in turn leads to false conclusions.

This would be true if these were the only tests and if correlation and efficiency were dependent entirely on ‘short-term-fluctuations’. They are not as they will capture skill at modeling both short AND long term fluctuations. This is also why I placed more emphasis skill on modelling trends over climatically relevant time scales. He is also not specific about which conclusions. The conclusion of ‘no credible basis’ is not falsified by lack of evidence.

It should also be noted that the DECR also considered return periods (Tables 8 and 10) so any criticism of returns periods applies equally to the DECR.

* The return period test is based on your own definition of ‘regional return period’, which is different from the definition used in the DEC report. Nevertheless, your analysis does highlight the importance of data being collected or produced at different resolutions and the effect this has on interpretations of the frequency of drought. The observed data have the shortest return period as they have the finest spatial resolution and the model based return regions have increasingly larger mean return periods, inversely related to the spatial resolution at which they are reported. We were well aware of this issue prior to the commencement of the study and spent a considerable amount of time designing an analysis that would be robust to take this effect into account.

I appreciate the explanation for the lack of skill at modelling return period, which measures drought frequency, as opposed to drought intensity measured by efficiency. Nevertheless, lack of demonstrated skill at modelling drought frequency stands.

Note they continue to be unresponsive to requests for evidence the climate models have skill at modelling droughts. Where we stand at the moment is, that irrespective of the reliability of my tests, there is still no evidence of skill to be seen, at the short term, long term, or at drought intensity or frequency and so my claim of “no credible basis for the claims of increasing frequency of Exceptional Circumstances declarations” still stands. The Climate Flagship has steadfastly abjured presenting validation evidence. While the concerns expressed have relevance to the quality of the tests (which are widely used, but problematic due to the strange data), they were not precise about the conclusions or claims they were trying to rebut.

Further Work

I came across a recent drought study that also finds no statistical significance between models and drought observations. This was actually in Ref 27 of the DECR: Sheffield, J. &Wood, E. F. Projected changes in drought occurrence under future global warming from multi-model, multi-scenario, IPCC AR4 simulations. Climate Dynamics 13, 79-105 (2008).

Although the predicted future changes in drought occurrence are essentially monotonic increasing globally and in many regions, they are generally not statistically different from contemporary climate (as estimated from the 1961-1990 period of the 20C3M simulations) or natural variability (as estimated from the PICNTRL simulations) for multiple decades, in contrast to primary climate variables, such as global mean surface air temperature and precipitation.

Below is a plot of the observations for the drought statistic, area experiencing less than 5% exceptionally low rainfall (leading to an Exceptional Circumstances drought declaration). You can see how ‘peaky’ it is, even when the average is taken (black).

image002

In some ways it might have been better to just knuckle down and develop a POT model right from the start, as it might have allowed me to produce a less nuanced response. I have been doing that, but have had to upgrade R. A recompilation is needed, that took all night and lost my graphic interface to R. Even then, the package VGAM doesn’t compile for some reason, so I have to look for other packages.

Creating a Statistical Model with a Cherry-picking Process

Steve McIntyre, always gracious in his acknowledgments, mentioned my note in the Australian Institute of Geologists newsletter (AIG News No 83 Mar 2006 pp14) in a post yesterday “The Full Network“.

We’ve discussed on many occasions that you can “get” a HS merely from picking upward-trending series from networks of red noise (David Stockwell had a good note on this phenomenon on his blog a couple of years ago. My first experiments of this type were on the cherry picks in the original Jacoby network.)

This note published way back in May 2006 (citeable but not peer reviewed) was probably the first of my posts that got picked up in other blogs, such as the American Thinker. The graph shows reconstructed temperature anomalies over 2000 years, using completely random numbers with autocorrelation, has a strong resemblance to other published reconstructions, particularly the prominent ‘hockey-stick’ shape, the cooler temperatures around the 1500s and the Medieval Warm Period around the 1000s. This demonstrates that the method from dendroclimatology of choosing proxies based on correlation with the reference period, (aka cherry-picking) will generate plausible climate reconstructions even on random numbers.

This undermines the credibility of reconstructions using this process from proxies, particularly where this source of uncertainty has not been recognized, and confidence intervals have not been expanded to incorporate the additional uncertainty.

What is environmental modeling?

How many narcissists does it take to change a light bulb?
Just one — but he has to wait for the whole world to revolve around him.

Blog watchers would have noticed a post at ClimateAudit where Steve has reprinted a comment by Ian Jolliffe on the form of PCA (decentered) used way back in 1998 by Mann et al. in the original hockey stick papers. (If you don’t understand all that you have some background reading at CA for homework.)

In a numerate science, statistical methods are standard, commonly applied and understood. Instead, Mann and cohorts represent at trend in environmental modeling that believes environmental science consists of creating and promoting the most obtuse methods to further their theories. Hence the joke above.

Apologies if this is not the correct place to make these comments. I am a complete newcomer to this largely anonymous mode of communication. I’d be grateful if my comments could be displayed wherever it is appropriate for them to appear.

It has recently come to my notice that on the following website, tamino.wordpress.com/2008/03/06/pca-part-4-non-centered-hockey-sticks/ .. , my views have been misrepresented, and I would therefore like to correct any wrong impression that has been given.

An apology from the person who wrote the page would be nice.

In reacting to Wegman’s criticism of ‘decentred’ PCA, the author says that Wegman is ‘just plain wrong’ and goes on to say ‘You shouldn’t just take my word for it, but you *should* take the word of Ian Jolliffe, one of the world’s foremost experts on PCA, author of a seminal book on the subject. He takes an interesting look at the centering issue in this presentation.’ It is flattering to be recognised as a world expert, and I’d like to think that the final sentence is true, though only ‘toy’ examples were given. However there is a strong implication that I have endorsed ‘decentred PCA’. This is ‘just plain wrong’.

The link to the presentation fails, as I changed my affiliation 18 months ago, and the website where the talk lived was closed down. The talk, although no longer very recent – it was given at 9IMSC in 2004 – is still accessible as talk 6 at www.secamlocal.ex.ac.uk/people/staff/itj201/RecentTalks.html
It certainly does not endorse decentred PCA. Indeed I had not understood what MBH had done until a few months ago. Furthermore, the talk is distinctly cool about anything other than the usual column-centred version of PCA. It gives situations where uncentred or doubly-centred versions might conceivably be of use, but especially for uncentred analyses, these are fairly restricted special cases. It is said that for all these different centrings ‘it’s less clear what we are optimising and how to interpret the results’.

I can’t claim to have read more than a tiny fraction of the vast amount written on the controversy surrounding decentred PCA (life is too short), but from what I’ve seen, this quote is entirely appropriate for that technique. There are an awful lot of red herrings, and a fair amount of bluster, out there in the discussion I’ve seen, but my main concern is that I don’t know how to interpret the results when such a strange centring is used? Does anyone? What are you optimising? A peculiar mixture of means and variances? An argument I’ve seen is that the standard PCA and decentred PCA are simply different ways of describing/decomposing the data, so decentring is OK. But equally, if both are OK, why be perverse and choose the technique whose results are hard to interpret? Of course, given that the data appear to be non-stationary, it’s arguable whether you should be using any type of PCA.

I am by no means a climate change denier. My strong impressive is that the evidence rests on much much more than the hockey stick. It therefore seems crazy that the MBH hockey stick has been given such prominence and that a group of influential climate scientists have doggedly defended a piece of dubious statistics. Misrepresenting the views of an independent scientist does little for their case either. It gives ammunition to those who wish to discredit climate change research more generally. It is possible that there are good reasons for decentred PCA to be the technique of choice for some types of analyses and that it has some virtues that I have so far failed to grasp, but I remain sceptical.

Ian Jolliffe

Steve continues:

As an editorial comment, the validity of Mannian PCA is only one layer of the various issues.

For example, Wahl and Ammann approach the salvaging of Mann overboard from a slightly different perspective than Tamino. Their approach was to argue that Mannian PCA was vindicated by the fact that it yielded a high RE statistic and thus, regardless of how the reconstruction was obtained, it was therefore "validated". I don't see how this particular approach circumvents Wegman's: "Method Wrong + Answer 'Right' = Incorrect Science", but that's a different argument and issue. Also if you read the fine print of Wahl and Ammann, the RE of reconstructions with centered PCA are much lower than the RE using incorrect Mannian PCA, but, again, that is an issue for another day.

It would be nice if Jolliffe's intervention were sufficient to end the conceit that Mann used an "alternate" centering convention and to finally take this issue off the table.

Niche Modeling. Chapter Summary

Here is a summary of the chapters in my upcoming book Niche Modeling to be published by CRC Press. Many of the topics have been introduced as posts on the blog. My deepest thanks to everyone who has commented and so helped in the refinement of ideas, and particularly in providing motivation and focus.

Writing a book is a huge task, much of it a slog, and its not over yet. But I hope to get it to the publishers so it will be available at the end of this year. Here is the dustjacket blurb:

Through theory, applications, and examples of inferences, this book shows how to conduct and evaluate ecological niche modeling (ENM) projects in any area of application. It features a series of theoretical and practical exercises in developing and evaluating ecological niche models using a range of software supplied on an accompanying CD. These cover geographic information systems, multivariate modeling, artificial intelligence methods, data handling, and information infrastructure. The author then features applications of predictive modeling methods with reference to valid inference from assumptions. This is a seminal reference for ecologists as well as a superb hands-on text for students.

Part 1: Informatics

Functions: This chapter summarizes major types, operations and relationships encountered in the book and in niche modeling. This and the following two chapters could be treated as a tutorial in the R. For example, the main functions for representing the inverted ‘U’ shape characteristic of a niche — step, Gaussian, quadratic and ramp functions – are illustrated in both graphical from and R code. The chapeter concludes with the ACF and lag plots, in one or two dimensions.

Data: This chapter demonstrates how to manage simple biodiversity databases using R. By using data frames as tables,
it is possible to replicate the basic spreadsheet and relational database operations with R’s powerful indexing functions.
While a database is necessary for large-scale data management, R can eliminate conversion problems as data is moved between systems.

Spatial:
R and image processing operations can perform many of the
elementary spatial operations necessary for niche modeling.
While these do not replace a GIS, it demonstrates that generalization of arithmetic concepts to images can be implemented simple spatial operations efficiently.

Part 2: Modeling

Theory: Set theory helps to identify the basic assumptions
underlying niche modeling, and the relationships and constraints between these
assumptions. The chapter shows the standard definition of the niche as
environmental envelopes is equivalent to a box topology. It is proven that when
extended to infinite dimensions of environmental variables this definition
loses the property of continuity between environmental and geographic spaces.
Using the product topology for niches would retain this property.

Continue reading Niche Modeling. Chapter Summary

Rings of Noise on Hockey Stick Graph

Finally, one journalist has the message right: Duane Freese in his article — “Hockey Stick Shortened?” — at TechCentralStation reports on the National Academy of Sciences report “Surface Temperature Reconstructions for the Last 2,000 Years“. Repetition of the consensus view of strong evidence of recent global warming is not newsworthy. Increase in the uncertainty of the Millennial temperature record is. He says:

The most gratifying thing about the National Academy of Science panel report last week into the science behind Michael Mann’s past temperature reconstructions – the iconic “hockey stick” isn’t what the mainstream media have been reporting — the panel’s declaration that the last 25 years of the 20th Century were the warmest in 400 years.

The hockey stick, in short, is 600 years shorter than it was before and the uncertainties for previous centuries are larger than Mann gave credence. And when the uncertainty of the paleoclimatogical record increases with time, the uncertainty about human contribution is likewise increased. Why? For a reason noted on page 103 of the report: climate model simulations for future climates are tuned to the paleoclimatogical proxy evidence of past climate change.

Continue reading Rings of Noise on Hockey Stick Graph

In Praise of Numeracy

Mathematical shapes can affect our lives and the decisions we make.

The
hockey stick graph
describing the earths average temperature over the last millennia has been the subject of a controversial debate over reliability of methods of statistical analysis.

hockey stick.jpg
From this to this …
Long_tail.PNG

The long tail is another new icon, described in a new book, developed in the Blogosphere, by Chris Anderson called “The Long Tail”:

Forget squeezing millions from a few megahits at the top of the charts. The future of entertainment is in the millions of niche markets at the shallow end of the bit stream. Chris Anderson explains all in a book called “The Long Tail”. Follow his continuing coverage of the subject on The Long Tail blog.

As explained in Wikipedia:

The long tail is the colloquial name for a long-known feature of statistical distributions (Zipf, Power laws, Pareto distributions and/or general Lévy distributions ). The feature is also known as “heavy tails”, “power-law tails” or “Pareto tails”. Such distributions resemble the accompanying graph.

In these distributions a low frequency or low-amplitude population that gradually “tails off” follows a high frequency or high-amplitude population. In many cases the infrequent or low-amplitude events—the long tail, represented here by the yellow portion of the graph—can cumulatively outnumber or outweigh the initial portion of the graph, such that in aggregate they comprise the majority.

Continue reading In Praise of Numeracy

AIG Article

The Australian Institute of Geoscientists News has published online my article “Reconstruction of past climate using series with red noise” on page 14. Many thanks to Louis Hissink the editor for the rapidity of this publication. It is actually a very interesting newsletter with articles on the IPCC, and a summary of the state of the hockey stick (or hokey stick). There are articles on the K-T boundary controversy and how to set up an exploration company.

Reconstructing the hokey stick with random data neatly illustrates the circular reasoning in a general context, showing the form of the hokey stick is essentially encoded in the assumptions and proceedures of the methodology. The fact that 20% of LTP series (or 40% if you count the inverted ones) correlate significantly with the temperature instrument record of the last 150 years illustrates that (1) 150 years is an inadequate constraint on possible models to base an extrapolation of over 1000 years, and (2) the propensity of analogs of natual series with LTP to exhibit ‘trendiness’ or apparent long runs that can be mistaken for real trends. And check back shortly for the code, I have been playing around with RE and R2 and trying some ideas suggested by blog readers to tighten things up.

With the hokey stick discredited from all angles, even within the paleo community itself with recent reconstructions of Esper and Moberg showing large variation in temperature over the last 1000 years, including temperatures on a par with the present day, one wonders why it is taking so long for the authors of the hokey stick to recant and admit natural climate variability. While the past variability of climate may or may not be important to the attribution debate, it is obviously important on the impacts side, as an indicator of the potential tolerances of most species.

A new temperature reconstruction

In honor of the National Research Council of the National Academies committee to study “Surface Temperature Reconstructions for the Past 1,000-2,000 Years” meeting at this moment, I offer my own climate reconstruction based on the methods blessed by dendroclimatology. The graph below shows reconstructed temperature anomolies over 2000 years, with the surface temperature measurements from 1850 from CRU as black dots, the individual series in blue and the climate reconstruction in black. I think you can see the similarity to other published reconstructions (see here), particularly the prominent ‘hockey-stick’ shape, the cooler temperatures around the 1500s and the Medieval Warm Period around the 1000s. What data did I use? Completely random sequences. Reconstruction methods from dendroclimatology will generate plausible climate reconstructions even on random numbers!

Continue reading A new temperature reconstruction

Peer-censorship and scientific fraud

The major scientific journals are often regarded as the touchstones of scientific truth. However, their reputation has been tarnished with yet another major scientific fraud unfolding over South Korean researcher Hwang Woo-suk’s peer-reviewed and published Stem Cell research. Should the publication of these results be viewed as simple ‘mistakes’, a crime by a deviant individual, or a broader conspiracy aided by lax reviewing and journal oversight? Blogs were apparently instrumental in uncovering the inconsistencies in Hwangs publications. Here I look at peer-censorship in environmental sciences and its role in concealing scientific waste and fraud, and uncover the emerging solutions from pre-print archives and blogs.

Continue reading Peer-censorship and scientific fraud