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THE HURST PHENOMENON by Professor Will Alexander February 17, 2009

Posted by honestclimate in Discussions.
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By Professor Will Alexander

Received via email, February 16, 2009

Dear all,


The attached memo on the Hurst Phenomenon is very important.

Major anomalies in the climatic processes, particularly floods and droughts, have been recorded since biblical times.

In this memo I describe the problems that engineering hydrologists and mathematicians had in describing these anomalies mathematically. They gave up.

I then demonstrate the undeniable causal linkage with predictable variations in received solar energy.

Once this is appreciated it explains the observed anomalies from biblical times through to the present. They can now be described mathematically.

This completely undermines climate change theory and all the alarmist predictions based on it.

Two questions remain. How long will it take for the nations of the world to appreciate that they have been misled? And how much damage will be caused to national economies, international relationships and the image of science as an honourable profession by the time that this realisation occurs?

All my calculations and conclusions can be replicated by others who have the necessary expertise, patience and perseverance.

Please circulate.

Memo 12/09

Climate change – the Hurst Phenomenon [VERY IMPORTANT PLEASE]

Monday 16 February 2009

How can you tell the difference between ignorance, dishonesty and fraud? Ignorance is when you innocently omit something. Dishonesty is when you deliberately omit something that weakens your case, or when you include something that you know is false. The Oxford English Dictionary defines fraud as the use of false representations to gain an unjust advantage..

In 2001 the IPCC published its third assessment reports. The report of Working Group 1: the Scientific Basis, included the infamous ‘hockey stick’ graph. It showed changes in global air temperatures since 1000 AD. These were shown as departures from those of the 1961 to 1990 period. The earlier temperatures were determined from proxy data derived from analyses of tree rings, corals and ice cores.

Figure 1. The infamous hockey stick graph (bottom panel) in the IPCC’s 2001 assessment report of Working Group I.

It was claimed that the rapid increase in global temperatures since 1900 was clear and irrefutable evidence of the consequences of human activities. There was an uproar when it was discovered that this was a fraudulent graph. The graph failed to show the well-known ice age and warm periods during the past 1000 years. The IPCC offered no apology or explanation for this deliberate mistake.

This graph no longer featured in the IPCC’s fourth assessment report that was distributed in 2007 but a graph for the period 1800 to 2000 remained.

In this memo I describe for the first time, yet another fraudulent error that demonstrates the dishonesty of the whole IPCC process. It relates to the Hurst Phenomenon that climate alarmists deliberately ignore, and its linkage with periodic variations in received solar energy which they also refute.

The Hurst Phenomenon

You may recall that in my memo on the Joseph Effect I described how, given a long record of river flow, the minimum capacity required to sustain the specified demand from a dam without interruption is determined. A little thought will show that this depends on the most severe drought sequence (the Joseph Effect) in the period of record.

Continuing on this line of thought, it must be obvious that a long record is likely to contain a more severe drought sequence than a short record. It is also obvious that the greater the variability of the flow in the river the greater the storage capacity required to meet the specified demand.

The range R is the required storage capacity ignoring all evaporation and other losses. Assuming a record length of n years and a standard deviation of the time series of S, then

Rn / Sn ~ nh

Theoretically, h should have a value of 0.5 for normally (or log-normally) distributed sequences of independent random values.

Rodda Nilometer

In 641 AD – more than a thousand years ago – a water level gauging structure was built on Rodda Island in the Nile River at Cairo. The record from the Rodda Nilometer is the longest available hydrological record in the world. In 1950 the civil engineer R.E. Hurst analysed 1080 years of data from the Rodda Nilometer recorded during the period 641 to 1946. He then used this to determine the required storage capacity of the proposed new Aswan High Dam.

He applied the Rippl method to successive segments of equal length, i.e. n=10, 20 etc and found an unexplained anomaly in the data. The value of the coefficient h for the Nile River was approximately 0.75. He then analysed other long geophysical records, where he found the same anomaly.

The information in Table 1 was published 60 years ago. What does it tell us?

It is important to note that the same multiyear anomalies that were present in the flow records of the Nile River were also present in other climatological and geophysical processes. Surely it must be very obvious that all these processes must be related to a single cause. The only conceivable cause is variations in received solar energy.

Table 1. Values of the Hurst coefficient for various geophysical phenomena.




Nile maxima



Deposits in lakes



Tree rings












Wheat prices



Figure 2 is from Klemes’ paper The Hurst Phenomenon: A Puzzle? My copy of his paper has faded over the years. In particular I draw your attention to the phrase ‘— nonstationarity of the mean — ‘ in the introduction to his benchmark paper. This is the crux of the matter. This nonstationarity is the Joseph Effect which in turn is related to the variations in solar activity, although Klemes and others did not make the connection.

Figure 2. Synthetic 1000-year sequences using different time series generation models.

Notice the general similarity of these graphs with the historical graph for the past 1000 years in Figure 1 above. Notice in particular the similarity in the output of the ARIMA (auto-regressive moving average) model with the hockey stick graphs in Figure 1.

These are purely synthetic sequences unrelated to historical events yet they show remarkable similarities with the historical data sequences. Perhaps you will now understand why experienced water resource engineers shrug their shoulders and considered this whole climate change issue as nothing more than an unverified hypothesis.

Given this information how on earth can climatologists claim that the multi-year irregularities in the data are caused by human activities? Putting it the other way round, how can they distinguish between natural variability that has been observed since biblical times, and the superimposed human-related consequences? I have undertaken diligent studies of long hydro-climatological data series for the past 30 years. If present, trends related to human activities are undetectable while the solar signal is very clear.

It also confirms the important conclusion in an earlier memo that the solar signal is more than 17 times the strength of the human activities signal. This conclusion was based on calculated variations in received solar energy, not hypotheses.

For more than two decades these anomalies were studied by hydrologists and mathematicians. The studies included the effects of serial correlation. When this could not be identified in the data, the assumption had to be made that no meaningful serial correlation existed. However, once the records became long enough to identify the presence of 21-year serial correlation and its synchronous linkage with sunspot activity then everything fell into place.

Ignorance, dishonesty or fraud?

There you have it. Nearly 60 years ago the civil engineer R.E. Hurst demonstrated that the proxy data used by the IPCC to determine past global temperatures possessed anomalies that are related to the Joseph Effect. This in turn is related to concurrent variations in solar activity.

Now let us put all this together. The very essence of this whole climate change issue is that human activities cause global temperatures to increase with a whole range of consequences including increases in floods, droughts and threats to water supplies. This temperature increase is the foundation on which climate change theory is built.

In order to press this message home, the IPCC cooked the books. They fraudulently omitted the well-known historical ice-age and warm periods in their hockey stick graph.

Most important of all, they also fraudulently denied the influence of variations in solar activity on variations in climate. There is abundant evidence of its presence in long climatological and geophysical records.

They dishonestly omitted to inform the public that there were serious anomalies in the proxy as well as the measured temperature data in the IPCC publications, (the Hurst Phenomenon).

Given the emphasis in the IPCC documents on the postulated (i.e. unproven) claims of intensification of the hydrological processes – floods, droughts and threats to water supplies – and the large research expenditures, I do not for one moment believe that climate change scientists were unaware of these well documented anomalies in the climate-related data. The omission of this information in their reports is thoroughly dishonest.

I can go even further.

This is the 12th memo that I have distributed this year. I have tried to produce them in a digestible format so that I could bring you to this very important point.

In 1978 Klemes, a leading stochastic hydrologist, produced his detailed overview paper The Hurst Phenomenon: A Puzzle? In it he addressed the most puzzling problem that faced academics and practitioners alike. It was very clear that the properties of the hydrological and geophysical time series could not be replicated in mathematical models that assumed random variability about a constant mean. It was clear that the mean was not constant with time.

The next problem was to quantify the behaviour of the mean and its causes. Mathematicians and stochastic hydrologists were eventually forced to give up. They could not describe the changes in the mean values either mathematically or causally.

I was one of the few who travelled an altogether different route. My point of departure, also in 1978, was to determine whether or not a predictable linkage existed between solar activities (using sunspot numbers as proxies) and the hydrological processes. Following this route I succeeded where mathematicians and stochastic hydrologists failed. The mean is not constant but varies from year to year in 21-year sequences.

These sequences are closely but not exactly, synchronous with the double sunspot cycle. My co-author Fred Bailey discovered and quantified this relationship. It is the consequence of the sun’s wobble as it moves through galactic space under the influence of the orbiting planets.

This leaves the whole IPCC position in total disarray. The public are being misled by the IPCC and its followers (either through ignorance, dishonesty or fraud) with their claim that under natural conditions the climatological processes are sensibly constant and that human activities will result in steady changes in time all the way through to 100 years into the future. They then claim that by controlling greenhouse gas emissions we can prevent this from happening.

This is simply impossible. All global climate model projections are based on unchanging mean values as their point of departure. Are climate modellers completely ignorant of all these anomalies in climate that have been observed since biblical times? If so, then they are incredibly ignorant of the processes that drive climate.

The attempts by climate alarmists to suppress the truth and denigrate all those who disagree with them, can only lead to one conclusion — their behaviour is fraudulent, unscientific and unethical.

Two of the sessions at the Midrand Summit presentations will be on the publications of the IPCC’s Working Groups I and II. Will these fundamental deficiencies be discussed? I doubt it. The deliberate omission will be dishonest at the very least.

Penalties and incentives

Last Wednesday our Minister of Finance announced his budget for 2009. It included some mild green taxes but more importantly he announced tax incentives for energy reduction by industries. This is in contrast with the tax penalties imposed by many Western nations. The costs and benefits of both incentives and penalties will be passed on to the consumers. Obviously, the introduction of incentives is the way to go.

Am I dreaming when I believe that South Africa may even provide an example to other countries in seeking optimum solutions to the conflicting objectives of reducing dangerous emissions while maintaining a healthy economy?

This can only be achieved in an atmosphere of multidisciplinary cooperation, truth and honesty. All these requirements are absent in the climate change literature.

There is nothing more that I can do.


[For those who would like a more detailed background to the problem of time series analyses, I strongly recommend that you obtain a copy of Klemes’ benchmark paper The Hurst Phenomenon: A Puzzle? It was published in Water Resources Research Vol 10, No 4, in August 1978. Consider this memo as an unofficial appendix to his paper! ]


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