D’Arcy Thompson in his “On Growth and Form”  remarked “Numerical precision is the very soul of science”  The main point of scientific laws is to be able to calculate from them.

When there is a project to send a man to the moon, the trajectory of the rocket has to be calculated using a complex set of  mathematical equations with substituted parameters. The equations are based on scientific laws which have been established and tested, to known standards of accuracy. The parameters have been measured to known standards of accuracy. In this way it is possible to predict exactly where the moon module will land, with a known measure of its accuracy.

The complex series of mathematical equations is a computer-based mathematical model. Before it can be used there must be  statistically based studies on the accuracy of each part of the system, and comprehensive tests to prove that its predictions actually work within  known limits.

Computer-based mathematical models have many applications. It is possible to simulate an entire industrial process and use the model to predict the effect of changes in the process.

The whole point is, that a computer-based mathematical model of any process or system is useless unless it has been validated.  Validation of such a model involves the testing of each equation and the study of each parameter, to discover its statistically based accuracy using a range of numerically based probability distributions, standard deviation, correlation coefficients, s and confidence limits. The final stage is a thorough test of the model’s ability to predict the result of changes in the model parameters over the entire  desired range.

No computer climate model has ever been validated.  An early draft of Climate Change 95  had a Chapter titled “Climate Models - Validation” As a response to my comment that no model has ever been validated, they changed the title to “Climate Models - Evaluation” and changed the word “validation” in the text to “evaluation” no less than fifty times. There is not even a procedure in any IPCC publication describing what might need to be done in order to validate a model.

Without a successful validation procedure, no model should be considered capable of providing a plausible prediction of future behaviour of the climate.

This same point, made more politely, so as to make its way through the hazards of peer review, is made in a recent paper by Soon et al. (1)

Instead of validation, and the  traditional use of mathematical statistics, the models are “evaluated” purely from the opinion of those who have devised them. Such opinions are partisan and biased. They are also nothing more than guesses.

Attempts have been made to attach spurious measures of precision to these guesses. The following footnote appears on page 2 of the “Summary for Policymakers” of Climate Change 01 (2)

“In this Summary for Policymakers and in the Technical Summary, the following words have been used where appropriate to indicate judgmental estimates of confidence: virtually certain (greater than 99% chance that a result is true); very likely  (90-99% chance): likely (66-90% chance); medium likelihood ( 33-66% chance); unlikely ( 10-33% chance);  very unlikely (1-10% chance); exceptionally unlikely (less than 1% chance)."

As might be expected,  there are no models or correlations falling into the medium likelihood, , unlikely or very unlikely categories.

Chapter 8 of Climate Change 01  “Model Evaluation”  (3) evades the problem. A paragraph headed “What is meant by evaluation?” (4)  never answers the question. They talk about “an approach” to evaluation. They confess “We fully recognise that many of the evaluation statements we make contain a degree of subjective scientific perception and may contain much “community” or “personal” knowledge. For example, the very choice of model variables and model processes that are investigated are often based upon the subjective judgement and experience of the modelling community”

In truth, all of their evaluation is subjective, and since it is made by the modelling community itself,  suspect.

The Executive Summary of the Chapter (5) consists entirely of  vague subjective opinions.

“Coupled models can provide credible simulations”

“Confidence in model projections is increased by the improved performance….”

“ There is no systematic difference..”

“ Some modelling studies suggest that…

“The performance of coupled models …. has improved..”

“Other phenomena previously not well simulated in coupled models are now handled reasonably well”

“Analysis of, and confidence in, extreme events ..is emerging”

“Coupled models have evolved and improved significantly…”
 (but we never get a numerical measure of “significant”)

“ Confidence  in the ability of models to project future climates is increased by the ability of several models to reproduce the warming trend in the 20^th century surface air temperature when driven by radiative forcing due to increasing greenhouse gases and sulphate aerosols”

This statement illustrates the imperfect character of the IPCC “confidence”

Firstly, as explained in our Chapter 3, the warming trend of the combined weather station temperature measurements is most plausibly explained by their biased proximity to human habitation, and by such phenomena as volcanic eruptions, ocean and sun variability, none of which effects are incorporated in the models

Secondly,  model parameters, particularly those due to sulphate aerosols, are so uncertain, that it is possible to simulate almost any climate sequence, including a temperature fall, by suitable choices of parameters.

Thirdly a correlation, however successful, does not necessarily imply a cause and effect relationship.

Fourthly, the models are never applied to the more reliable temperature record in the lower atmosphere, which shows no warming for the past 23 years

Despite these entirely qualitative, inevitably prejudiced “assessments” -

“We consider coupled models, as a class, to be suitable tools to provide useful projections of future climates” (5)

All this, despite the fact that no model has ever provided a successful prediction of a future climate.

The Chapter continues with similar qualitative opinions which are too numerous to mention.

A number of spurious statistical procedures are used for “evaluation”

For example, it is comment to provide a “range” of results, and consider this as somehow equivalent to an uncertainty figure. Of course this is nonsense. Each modellist will choose what he thinks are the best parameters and equations, but the “range” of results is not a fair measure of the probability distribution that would result if a proper statistical study were made.

An example is the treatment of “Climate Sensitivity”, the predicted global mean temperature rise for a doubling of atmospheric carbon dioxide concentration, derived from many models. The “range” of results for the global temperature rise is quoted as between 1.5°C and 4.5°C. This figure was, apparently, originally derived by a “show of hands”, a typically unscientific procedure. But this “range” does not begin to characterise the true uncertainties of model results.

Another dubious statistical procedure is “pattern analysis” where a pattern of climate data are compared with those predicted by a model. Invariably, no account is taken of the uncertainties of both components.

In a recent paper (6) Reilly et al put it this way:

“it is preferable to derive parameter uncertainty from observations, but the needed data often do not exist. Distributions of input parameters then must be selected by expert elicitation….. Care must be taken in applying expert elicitation for well-known biases in human judgement”

Surely, when the “experts” are the modellists themselves the “well-known bias” immediately applies.

This article was followed by another by Allen et al (7) which concluded

“results are only of practical value when the factors responsible for the uncertainty are reasonably well documented and understood, which is certainly not the case for climate change in the late 21^st century”

Perhaps the best illustration of the huge uncertainties associated with all the climate models is Figure 5.1 (8,9,10) which shows the global and annual mean radiative forcing for some of the model parameters

This diagram appears three times in Climate Change 01,  each with a different caption. The caption in Chapter 6 is slightly more honest about the uncertainties.

First it should be noted that several of the most important contributors to radiative forcing are not even included. The most important greenhouse gas, water vapour, and the clouds that results from it, have been relegated to the status of a “feedback”, where the large uncertainties in their estimation can be concealed.

The caption (10) says

"The forcing associated with stratospheric aerosols from volcanic eruptions is highly variable over the period and is not considered for this plot”

Then, indirect effects of tropospheric aerosols are left out, because they are “poorly understood”, despite a statement in Chapter 5 (11) that shows that they are well enough understood to say:

“The largest estimates of negative forcing due to the warm-cloud indirect effect may approach or exceed the positive forcing due to long-lived greenhouse gases”

The caption to Figure 6.6 (10) states

“The uncertainty range specified here has no statistical basis….”  Meaning that the uncertainties are larger than indicated. The use of the term “Level of Scientific Understanding” also implies much larger uncertainties.

The caption warns that an overall figure for radiative forcing cannot be obtained by merely adding and subtracting the figures in the diagram. But it is surely obvious that with the admitted uncertainties, a very large range of possible net radiative forcings are possible, including zero and negative values.

Figure 5.1 surely shows that the uncertainties associated with the parameters commonly incorporated into climate models are so uncertain that the results of the models are completely worthless.

This conclusion is enhanced by reading Chapter 7, ‘"Physical Climate Processes and Feedbacks” (12) of  Climate Change 01  which gives a detailed discussion of each of the processes, invariably concluding that the uncertainties are greater than is usually  assumed by the models. But, of course, they decline to quantify any conclusion.

Figure 6.1  Global annual mean radiative forcings (in watts per square metre)
  for a number of agents since 1750 (8,9,10)

So far, the discussion has been mainly concerned with the general climate models; but exactly the same considerations apply to carbon cycle models (13). We have some actual measured values for the carbon emitted by combustion of fossil fuels, and for the carbon in the atmosphere (if you accept that the Mauna Loa and other measurements can be considered representative). The other components of the cycle, are however, without known numerical value. There is a theoretical treatment of carbon dioxide absorption by the ocean, but no reliable measurements, apart from very rough “estimates” from isotope studies.  The missing link is the carbon absorbed by the land surface, for which there are no reliable measurements, and also no reliable theory. Indeed, it used to be thought that there was a net outflow from the land, due to “deforestation.”  The uncertainties in carbon cycle projections are thus without any numerical value for their uncertainties. Yet the IPCC has the effrontery to extrapolate "Stabilisation scenarios" as far ahead as the year 2300 (14) with no indication of uncertainty. This is science fiction, not science.

Although models showed some success in predicting the temperature effects of the eruption of Mount Pinatubo in June 1991, the models have failed to successfully predict any other climate change. On the contrary:

·  All the models predict that the Arctic should warm much faster than the rest of the earth. This is just not happening.

·  The models predict a temperature increase in the lower atmosphere. Measurements for the last 23 years show that this is not happening.

·     The models predict a steady increase in global surface temperature. The combined weather station record has changed in a fashion which is far from steady. Between 1940 and 1975 it showed a fall in temperature. Models can only cope with this by addition of arbitrary quantities of aerosols.

·     Models predict that the Northern Hemisphere should warm at a slower rate than the Southern Hemisphere, because most aerosols are produced in the North. The combined weather station record shows greater warming in the North than in the South, and so does the satellite record in the lower troposphere.

·     Models are unable to explain why most of the warming of the combined weather station record took place at night, or in the winter.

Despite the very great emphasis on models by the IPCC they have yet to show that their use, either to simulate climate, or to predict future climate, can be justified.

References

1       Soon, W, S Baliunas, S B Idso, K Y Kodratyev and E S Posmentier 2001 “ Modelling climatic effects of anthropogenic carbon dioxide emissions: unknowns and uncertainties.”  Climate Research 18  250-275

2       Climate Change 01  “Summary for Policymakers” , page 2, footnote 7

3       Climate Change 01  Chapter 8 “Model Evaluation”

4       Climate Change 01  Chapter 8, page 474

5       Climate Change  Chapter 8 Executive Summary, page 473

6       Reilly J, P H Stone, C E Forest, M D Webster, H D Jacobs, R G Prinn. 2001.”Uncertainty and Climate Change Assessments”. Science  293 430-433

7       Allen M, S Raper, J Mitchell 2001 “Uncertainty in the IPCC’s Third Assessment Report“ Science 293 430-433

8       Climate Change 01  “Summary for Policymakers”, Figure 3, page 8

9       Climate Change 01  “Technical Summary”, Figure 9. Page 37

10     Climate Change 01  Chapter 6 “Radiative Forcing of Climate Change”, Figure 6.6 page 392

11    Climate Change 01  Chapter 5 “Aerosols, Their Direct and Indirect Effects”, page 334

12    Climate Change 01  Chapter 7 “Physical Climate Processes and Feedbacks”, 417-70

13    Climate Change 01  Chapter 3  “The Carbon Cycle and Atmospheric Carbon Dioxide”. 3.6. Carbon Cycle Model Evaluation, pages 213-218

14    Climate Change 01 Chapter 3 page 223

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