Random walks or how models drown in a sea of mathematical theory.

What I suggest is that in a persistent way, a system may exhibit historical behaviour, instead of recurrence.

David Ruelle a question to Yasha Sinai.

Another interesting paper from Demetris Koutsoyiannis shows the divergence of skill,between modelers and mathematical physicists.

According to the traditional notion of randomness and uncertainty, natural phenomena are separated into two mutually exclusive components, random (or stochastic) and deterministic. Within this dichotomous logic, the deterministic part supposedly represents cause-effect relationships and, thus, is physics and science (the “good”), whereas randomness has little relationship with science and no relationship with understanding (the “evil”). We argue that such views should be reconsidered by admitting that uncertainty is an intrinsic property of nature, that causality implies dependence of natural processes in time, thus suggesting predictability, but even the tiniest uncertainty (e.g., in initial conditions) may result in unpredictability after a certain time horizon. On these premises it is possible to shape a consistent stochastic representation of natural processes, in which predictability (suggested by deterministic laws) and unpredictability (randomness) coexist and are not separable or additive components. Deciding which of the two dominates is simply a matter of specifying the time horizon of the prediction. Long horizons of prediction are inevitably associated with high uncertainty, whose quantification relies on understanding the long-term stochastic properties of the processes.

http://www.hydrol-earth-syst-sci-discuss.net/6/6611/2009/hessd-6-6611-2009.pdf

"Long horizons of prediction are inevitably associated with high uncertainty,"

Indeed as DK cites the Kolmogorov-Chaiten problem of convergence-divergence due to slow-fast oscillators where relaxation times of the oscillator may be hiddem in the mists of time such as spin glasses etc. or randomness may be simply exhibiting recurrent behavior as rigorously proven by Yasha Sinai.

eg Ya G Sinai (1982) Limit behaviour of one-dimensional random walks in random environments,

Some more examination of this paper and the previous post is in order.

Models and muddles the divergence of science from theory.

It is inevitably necessary to think of all as contained within one
nature; one nature must hold and encompass all; . . . But within the
unity There, the several entities have each its own distinct existence.

Nalimov Faces of science p136

Models are abstracts of the real world (and are bounded by our understanding of natures laws).The models are formally experiments or measurements that unfold our understanding of real world process.If a model or experiment is published that violates natures laws and yet correlates with the experiment,we are left with a simple binary question (and answer).That either the model(experiment) is incorrect or the natural law is wrong.

One would think that this would be a significant barrier to publication in a kournal such as nature or science,but this seems not to be the case.

Ontogenetic growth: models and theory

Anastassia M. Makarieva, Victor G. Gorshkov and Bai-Lian Li

We re-analyze the assumptions underlying two recently proposed ontogenetic growth models [Nature 413 (2001) 628; Nature 417 (2002) 70] to find that the basic relations in which these models are grounded contradict the law of energy conservation. We demonstrate the failure of these models to predict and explain several important lines of empirical evidence, including (a) the organismal energy budget during embryonic development; (b) the human growth curve; (c) patterns of metabolic rate change during transition from embryonic to post-embryonic stages; and (d) differences between parameters of embryonic growth in different taxa. We show how a theoretical approach based on well-established ecological regularities explains the observations where the formal models fail. Within a broader context, we also discuss major principles of ontogenetic growth modeling studies in ecology, emphasizing the necessity of ecological theory to be based on assumptions that are testable and to be formulated in terms of variables and parameters that are measurable.

Evidently a problem but the continued repeating of the error in subsequent papers,suggests a significant failure of the peer review process.

eg Anastassia Makarieva

The validity of the fundamental laws of nature and of good theories based on them
has been tested on such a great amount of empirical data that it is a good theory that can tell you whether the empirical data are of good or bad quality rather than the data tell you something about the theory. For this reason, good theories can be used for making predictions, like the existence of many elementary particles was predicted in theoretical physics prior to their actual discovery. How justified is the use of models for making predictions?

During model development the priority is given to reaching a satisfactory agreement
between the data and the mathematical structure of the model. On the basis of theavailable sets of data points taken from the general ensemble of all empirical evidence the modelers determine linear and non-linear correlations between the chosen measurable variables, including their temporal changes. The resulting time dependence of model variables allows one to make a forecast for the future. Such a forecast, however, is nothing but a limited extrapolation of what has been observed in the past. With changing the empirical datasets the model structure and forecasts change. With inclusion of ever growing amounts of observations the models become more and more complex, while their agreement with the available observations naturally improve. Thus, an ideal model ultimately comes as an exact and convenient, i.e. mathematically formalized, representation of all the available data. However, to the degree the model is a model and not a theory, it lacks the predictive power. Because of the obvious fact that it cannot be expected that the calibrations made on the basis of the knowndata will remain valid in the domain of predicted (i.e. still unknown) data. This is a conceptual, fundamental problem with the modeling approach. The universal laws of nature predict things

Based on our own scientific expertise, we can illustrate the above points with specific examples of models that were judged to be most successful based on their agreementwith the data and claimed derivability from a "universal" theory, yet shown to confront the fundamental laws of nature. As one can see, the problem transcends across the natural science as a whole. The biological model of organismal growth (West et al., 2001) misinterpreted the energy conservation equation and replaced it with the one conflicting with the energy conservation law. Despite that, the model showed perfect agreement with the data. After the error was identified (Makarieva et al., 2004) it took the model’s authors four years to explicitly admit it (Moses et al., 2008) and re-formulate the model. The re-formulated model re-calibrated using the same data as the original (wrong) one showed equally good agreement with the data and got equally well published (Hou et al., 2008). Thus, irrespective of conflicting with the energy conservation law or not, the model agreed with the data, was widely cited and raised little concern in the reading audience

One could reflect on Alven Tofflers suggestion that the illiterate of the future will not be an inability to read and write.but to learn and think.

Reality Clouds climate crystal balls

It is obvious that in any real-life activity it is impossible to wholly rely on such deductions. The reason is at least that the parameters of the studied phenomena are never known absolutely exactly and a small change in parameters (for example, the initial conditions of a process) can totally change the result. Say, for this reason a reliable long-term weather forecast is impossible and will remain impossible, no matter how much we develop computers and devices which record initial conditions.

In exactly the same way a small change in axioms (of which we cannot be completely sure) is capable, generally speaking, of leading to completely different conclusions than those that are obtained from theorems which have been deduced from the accepted axioms. The longer and fancier is the chain of deductions ("proofs"), the less reliable is the final result.

Vladimir Arnold..

In what could be perceived as an about turn in reporting the BBC has separated the "forecasts" for climate to the "reality" that the observations have shown that global warming has stopped

.

This headline may come as a bit of a surprise, so too might that fact that the warmest year recorded globally was not in 2008 or 2007, but in 1998.

But it is true. For the last 11 years we have not observed any increase in global temperatures.

And our climate models did not forecast it, even though man-made carbon dioxide, the gas thought to be responsible for warming our planet, has continued to rise.

So what on Earth is going on?

Climate change sceptics, who passionately and consistently argue that man's influence on our climate is overstated, say they saw it coming.

They argue that there are natural cycles, over which we have no control,

As we see with quasiperiodic systems the return to a “previous climate” state is regularly seen in the NAO.,PDO and IPO. These are sates with long periodicity for a climate regime of warmer then normal or cooler then normal climate states.

The ability for a recurrent periodic state such as the PDO or an inverse temperature “state” is in essence a binary transformation or bifurcation.. The transformation as a velocity inversion has the same effect as a time inversion, (v to - v ) (t to - t )

A fundamental consequence of the aperiodicity of the atmospheric and climate dynamics is the well-known difficulty to make reliable predictions.Contrary to simple periodic or multiperiodic phenomena(such as eclipses,tides ets) for which a long term prediction is possible, predictions in meteorology and climate are limited in time.

The most plausible (and currently admitted) explanation is based on the realization that a small uncertainty in the initial conditions used in a prediction scheme (usually referred as error") seems to be amplified in the course of the evolution. Such uncertainties are inherent in the process of experimental measurement, The uncertainty being in the “closeness of the boundary to the point of bifurcation, and the error in linear equations.” An important aspect discussed by Arnold and Shulinov.

As the “natural variability” and inverse regimes are often accompanied by inverse temperature states always and everywhere(except in gcm predictions) explanations are clearly in order.

Solar recession causes global cooling.

Our calculations provide the maximum semi-annual value of W in cycle 23
equal to 110–122 and the epoch of maximum in the first half of 2000. Hence, the
present cycle is not as high as was expected and predicted several years ago, nor as low as forecasted by some authors. This shows that the Gnevyshev–Ohl–Kopecký rule fails in this cycle. The end of the cycle is expected at 2006–2007. Proceeding from the current CGL brightness (the second half of 1999), we can predict a low cycle 24 with the maximal W not exceeding 50 (similar to cycles 5–6) and the epoch of maximum at 2010–2011. Thus, as inferred by our results, we are on the eve of a deep minimum of solar activity similar to that at the beginning of the 19th century.

BADALYAN et al 2000

One of the conundrums of the IPCC and the pro-contra arguments of AGW verses natural variability is with the sensitivity to Greenhouse gases,and the proportion of natural variability such as solar forcing.

There are many arguments, with the measurement problem ,solar variance such as TSI , volcanism, PDV etc

The main argument has been there is no trend in TSI(in the instrumental record) and if solar flux has not increased ,.Therefore the presumed causal mechanism is GHG..

One could then ask what happens if the sun enters a period of “Solar recession” an extended period of “inactivity” such as was seen during the maunder minimum and the little ice age of the 18-19th centuries.

As we observe in the botton graph, global temperatures have plateued and moved slightly negative in the last decade,and solar cycle 23 involved a decrease in TSI and a deep continuous minimum from which it is now possible to construct for the first time a trend in TSI which is negative and correlates to a decrease of 0.2w.

Evidence of a long-term trend in total solar irradiance
C. Fröhlich 2009

ABSTRACT
Aims. During the solar minimum of 2008, the value of total solar irradiance at 1AU (TSI) was more than 0.2Wm−2 lower than during the last minimum in 1996, indicating for the first time a directly observed long-term change. On the other hand, chromospheric indices and hence solar UV irradiance do not exhibit a similar change.
Methods. Comparison of TSI with other activity parameters indicates that only the open solar magnetic field, BR, observed from satellites at 1AU show a similar long-term behaviour. The values at the minima correlate well and the linear fit provides a direct physical relationship between TSI and BR during the minimum times.
Results. This correlation allows an unambiguous reconstruction of TSI back in time, provided the open solar magnetic field can be determined from e.g. geomagnetic indices or cosmogenic radionucleides. Since the solar UV irradiance has no long-term trend, the mechanism for the secular change of TSI must differ from the effect of surface magnetism, as manifested by sunspots, faculae, and network which indeed explain well the intra-cycle variability of both total and spectral irradiance. Conclusions. The long-term trend of TSI is most probably caused by a global temperature change of the Sun that does not influence the UV irradiance in the same way as the surface magnetic fields.

One might ask what is the rate of viscosity or contraction for an inverse forcing?

Carbon emissions fall by steepest in 40 years

The IEA is to announce a decrease in anthropogenic emissions by 2.6% in the last 12 months in early October,the announcement has been brought forward for the UNFCC meeting in Thailand.

Reuters report

Global emissions of the commonest man-made greenhouse gas carbon dioxide will fall by the sharpest rate in 40 years in 2009 following tumbling factory output, the International Energy Agency said on Monday.

The world must use the drop of about 2.6 percent to drive a global fight against climate change, rather than allow emissions to rise again as after previous recessions, Fatih Birol, IEA chief economist, told Reuters in an interview.

"The biggest fall (in about 40 years) was in 1981, at 1.3 percent, after oil price shocks and economic troubles," Birol said. "We estimate this year the fall will be around twice that."

As these are significant numbers(and the IPCC) tell us they can calculate the manmade proportion in the observations to 4 significant muners to the right of the decimal point,one would expect the "signal" will be observable in the Mauna loa record,singularities which as in essence a velocity inversion are a good test of the accuracy of measurements.

Evidence of Abiogenic Hydrocarbons

One of the paradoxes of hydrocarbons is they are ubiquitous in the universe,eg Titan.The mechanism of their production has been a matter of some robust debate(in the west,)it is important to also note that this is an additional source.

An interesting paper on this has been released in nature.

Researchers at KTH have been able to prove that the fossils of animals and plants are not necessary to generate raw oil and natural gas. This result is extremely radical as it means that it will be much easier to find these energy sources and that they may be located all over the world.

“With the help of our research we even know where oil could be found in Sweden!” says Vladimir Kutcherov, Professor at the KTH Department of Energy Technology in Stockholm.

Together with two research colleagues, Professor Kutcherov has simulated the process of pressure and heat that occurs naturally in the inner strata of the earth’s crust. This process generates hydrocarbons, the primary elements of oil and natural gas.

According to Vladimir Kutcherov, these results are a clear indication that oil supplies are not drying up, which has long been feared by researchers and experts in the field.

He adds that there is no chance that fossil oils, with the help of gravity or other forces, would have been able to seep down to a depth of 10.5 kilometres in, for example the US state of Texas, which is rich in oil deposits. This is, according to Vladimir Kutcherov, in addition to his own research results, further evidence that this energy sources can occur other than via fossils - something which will cause a lively discussion among researchers for a considerable period of time.

“There is no doubt that our research has shown that raw oil and natural gas occur without the inclusion of fossils. All types of rock formations can act as hosts for oil deposits,” asserts Vladimir and adds that this applies to areas of land that have previously remained unexplored as possible sources of this type of energy.

This discovery has several positive aspects. Rate of success as concerns finding oil increases dramatically – from 20 till 70 percent. As drilling for oil and natural gas is an extremely expensive process, costs levels will be radically changed for the petroleum companies and eventually also for the end user.

“This means savings of many billions of kronor,” says Vladimir.

Nikolai Kudryavtsev formulated the discussions in the early 1950's,and the Russian oil company has around 350 deep wells in production after first drilling in 1970 (a wildcat well)

The nature paper is here

Methane-derived hydrocarbons produced under upper-mantle conditions

Anton Kolesnikov1,2, Vladimir G. Kutcherov2,3 & Alexander F. Goncharov1

Abstract

There is widespread evidence that petroleum originates from biological processes1, 2, 3. Whether hydrocarbons can also be produced from abiogenic precursor molecules under the high-pressure, high-temperature conditions characteristic of the upper mantle remains an open question. It has been proposed that hydrocarbons generated in the upper mantle could be transported through deep faults to shallower regions in the Earth's crust, and contribute to petroleum reserves4, 5. Here we use in situ Raman spectroscopy in laser-heated diamond anvil cells to monitor the chemical reactivity of methane and ethane under upper-mantle conditions. We show that when methane is exposed to pressures higher than 2 GPa, and to temperatures in the range of 1,000–1,500 K, it partially reacts to form saturated hydrocarbons containing 2–4 carbons (ethane, propane and butane) and molecular hydrogen and graphite. Conversely, exposure of ethane to similar conditions results in the production of methane, suggesting that the synthesis of saturated hydrocarbons is reversible. Our results support the suggestion that hydrocarbons heavier than methane can be produced by abiogenic processes in the upper mantle.

Temperature trends in the South Pacific, some ordinary observations of interest..

“Fear feeds ignorance” said James Lovelock in the Ages of Gaia,*and a great niche was opened for fear when science became incomprehensible to those who were not its practitioners”

Mathematical theory tells us there is am infinite way of describing the average statistic of temperature in a set of observations. Peterson and Vose.(1997) An Overview of the Global Historical Climatology Network Temperature Database found over 100 different averages of temperatures have been used in meteorology and climate studies.

The standard or arbitrary axiom is to use the anomalies (variation) from some arbitrary set of observations (a temporal set of usually around 30 years) and “picture” the variations from today’s weather (usually on a monthly basis) with the moving averages. and explain that this is proof of forthcoming cataclysm.

In reality this is not proof in a mathematical sense, as the mathematical theory of climate (and its variations) is yet to be published

The complexity of both the science and the mathematical description is often perplexing to the “ordinary person” so the graphs pictured are more readily comprehensible we used the set of observations for the New Zealand Airports, stations Auckland, Wellington, Christchurch and Invercargill. Data is from the WMO reported series.

This covers a geographic slice of increasing latitudes of around 1200 kilometers and the trends (station specific) get progressively cooler towards the higher(polar) latitudes.

Auckland 0.0086c/yr (extrapolating to 120 yrs + 1c)
Wellington 0.0016c/yr (extrapolating to 610 yrs+ 1c)
Christchurch -0.00649c/yr (extrapolating to 160 yrs- 1c)
Invercargill -0.076c/yr (extrapolating to 13 yrs -1c)

Climate Cooling natural variability outweighs AGW

Why, all the Saints and Sages who discuss'd
Of the Two Worlds so wisely — they are thrust
Like foolish Prophets forth; their Words to Scorn
Are scatter'd, and their Mouths are stopt with Dust.

Rubaiyat of Omar Khayyam

In an interesting reversal of projections since the IPCC AR4 report was released,9and how natural variation was significantly downplayed0 as the trend or flat lining of the positive anomalies is now apparent,we see a remarkable "hedging of positions" ny authors of the IPCC,

New Scientist reports

Forecasts of climate change are about to go seriously out of kilter. One of the world's top climate modellers said Thursday we could be about to enter "one or even two decades during which temperatures cool.

"People will say this is global warming disappearing," he told more than 1500 of the world's top climate scientists gathering in Geneva at the UN's World Climate Conference.

"I am not one of the skeptics," insisted Mojib Latif of the Leibniz Institute of Marine Sciences at Kiel University, Germany. "However, we have to ask the nasty questions ourselves or other people will do it."

Few climate scientists go as far as Latif, an author for the Intergovernmental Panel on Climate Change. But more and more agree that the short-term prognosis for climate change is much less certain than once thought.

Latif predicted that in the next few years a natural cooling trend would dominate over warming caused by humans. The cooling would be down to cyclical changes to ocean currents and temperatures in the North Atlantic, a feature known as the North Atlantic Oscillation (NAO).

Another is from lEAN AND RIND 2009

How will Earth's surface temperature change in future decades?

Abstract

Reliable forecasts of climate change in the immediate future are difficult, especially on regional scales, where natural climate variations may amplify or mitigate anthropogenic warming in ways that numerical models capture poorly. By decomposing recent observed surface temperatures into components associated with ENSO, volcanic and solar activity, and anthropogenic influences, we anticipate global and regional changes in the next two decades. From 2009 to 2014, projected rises in anthropogenic influences and solar irradiance will increase global surface temperature 0.15 ± 0.03°C, at a rate 50% greater than predicted by IPCC. But as a result of declining solar activity in the subsequent five years, average temperature in 2019 is only 0.03 ± 0.01°C warmer than in 2014. This lack of overall warming is analogous to the period from 2002 to 2008 when decreasing solar irradiance also countered much of the anthropogenic warming. We further illustrate how a major volcanic eruption and a super ENSO would modify our global and regional temperature projections.

This suggests that we have entered into a period or transformation from solar maxima to solar minima,there is some evidence that the transformation is yet to occur ie a greater decrease lies ahead .

eg Lockwood et al

ABSTRACT. We use geomagnetic activity data to study the rise and fall over the past century of the solar wind flow speed V SW, the interplanetary magnetic field strength B, and the open solar flux F S. Our estimates include allowance for the kinematic effect of longitudinal structure in the solar wind flow speed. As well as solar cycle variations, all three parameters show a long-term rise during the first half of the 20th century followed by peaks around 1955 and 1986 and then a recent decline. Cosmogenic isotope data reveal that this constitutes a grand maximum of solar activity which began in 1920, using the definition that such grand maxima are when 25-year averages of the heliospheric modulation potential exceeds 600 MV. Extrapolating the linear declines seen in all three parameters since 1985, yields predictions that the grand maximum will end in the years 2013, 2014, or 2027 using V SW, F S, or B, respectively. These estimates are consistent with predictions based on the probability distribution of the durations of past grand solar maxima seen in cosmogenic isotope data. The data contradict any suggestions of a floor to the open solar flux: we show that the solar minimum open solar flux, kinematically corrected to allow for the excess flux effect, has halved over the past two solar cycles.