Saturday, December 05, 2009

Climategate and Mediocre mathematics,A schoolboy howler

The Climategate saga continues to provide interesting revelations.Whilst the emails are deeply disturbing,a damning revelation that the code reveals problems of the simplest form are revealing of the standard of skill by these "modelers"

One of the simplest observations e have is the earth is a sphere,from the circumference we can deduce the surface area of the planet around 510,072,000 km2.

It seems an incorrect circumference measurement is used in the ?code of the UEA.

As was reported on BBC 2's Newsnight on Wednesday, UK programmer John Graham-Cumming has begun some analysis of the software code contained in the files released two weeks ago. So far, he has documented 4 bugs that he has found on his weblog here. It is impossible to ascertain at this time the effect those bugs would have on calculations performed with temperature records, but Graham-Cummings speculates:

"So some information is lost for data being plotted near the 180 degrees line. Admittedly, that's in the middle of the Pacific Ocean (although it does cut through some land mass). But if there are any ocean temperature measurements at the 'edge of the world' then bits of their data isn't being taken into account.

I wonder what, if any, impact these three bugs have on the output of this program.

PS. There's actually a fourth problem with this code. The number 110.0. It's being used to convert from kilometres to degrees of longitude and latitude. The same number is used for both even though the Earth isn't a perfect sphere.

The code is using a value of 39,600 km for the circumference of the Earth, whereas the mean value is actually 40,041 km. But, hey, what's an error of 1% between friends?"

I find it interesting that the software used to measure global warming has a 1% error in the Earth's circumference. I find it odd that they didn't adjust the numbers appropriately when converting kilometres to longitude and latitude.

Its worse then we thought.

Thursday, December 03, 2009

Nasa announces New Study adds to findings of life on ancient mars

As outlined in the previous post,Nasa has announced the findings of Thomas-Keprta et al 2009.

Johnson Space Center, Houston

RELEASE : J09-030

New Study Adds to Finding of Ancient Life Signs in Mars Meteorite

HOUSTON — Using more advanced analytical instruments now available, a Johnson Space Center research team has reexamined the 1996 finding that a meteorite contains strong evidence that life may have existed on ancient Mars.

The new research focused on investigating alternate proposals for the creation of materials thought to be signs of ancient life found in the meteorite. The new study argues that ancient life remains the most plausible explanation for the materials and structures found in the meteorite.

In 1996, a group of scientists led by David McKay, Everett Gibson and Kathie Thomas-Keprta of NASA’s Johnson Space Center (JSC) in Houston published an article in Science announcing the discovery of biogenic evidence in the ALH84001 meteorite. A newly published paper revisits that original hypothesis with new analyses. The paper, “Origin of Magnetite Nanocrystals in Martian Meteorite ALH84001,” by Thomas-Keprta and coauthors Simon Clemett, McKay, Gibson and Susan Wentworth, all scientists in the Astromaterials Research and Exploration Science Directorate at JSC, is in the November issue of the journal Geochimica et Cosmochimica Acta of The Geochemical Society and The Meteoritical Society.

Magnetite crystals in ALH84001 have been a focus of debate about the possibility of life on Mars. Magnetite is an iron-bearing, magnetic mineral. On Earth, some water and soil bacteria secrete the mineral within their cells. The 1996 study suggested that some magnetite crystals associated with carbonate globules in ALH84001 are biogenic because they share many characteristics with those found in bacteria on Earth. Other scientists have argued instead that the magnetite in ALH84001 was likely caused by inorganic processes, and that those same processes can be recreated artificially in the laboratory by heating carbonates in a process known as thermal decomposition, forming magnetite identical to that found in the Mars meteorite.

In this new study, the JSC research team reassessed the leading alternative non-biologic hypothesis that heating or shock decomposition produced the magnetites. The authors argue that their new results do not support the heating hypothesis for the formation of the magnetites. They conclude that the biogenic explanation is a more viable hypothesis for the origin of the magnetites.

“In this study, we interpret our results to suggest that the in situ inorganic hypotheses are inconsistent with the data, and thus infer that the biogenic hypothesis is still a viable explanation,” said lead author Thomas-Keprta, senior scientist for Barrios Technology at JSC.

“We believe that the biogenic hypothesis is stronger now than when we first proposed it 13 years ago,” said Gibson, NASA senior scientist.

There are full links to the paper and a review paper in the links above and here

In addition to the new paper on ALH84001, the JSC team has published a paper that identifies shapes or morphologies in Martian meteorites that resemble known microfossil and microbial shapes in samples from Earth. These new shapes, seen with a scanning electron microscope, are termed biomorphs because of their close resemblance to known, biologically produced features on Earth.

The morphology seems consistent with a biological origin,such as seen in hydrothermal vents such as thermophiles,which exudate high acidic residues,this will be a lively debate.

Saturday, November 28, 2009

ALH 84001 Discovery or Diversion ?

Nasa is to announce on Monday the 30th November "evidence of life on Mars" by reanalysis of the Antarctic Meteor ALH 84001.

Wiki gives us a general outline.

Allan Hills 84001 (commonly abbreviated ALH 84001[1]) is a meteorite that was found in Allan Hills, Antarctica on December 27, 1984 by a team of US meteorite hunters from the ANSMET project. Like other members of the group of SNCs (shergottite, nakhlite, chassignite), ALH 84001 is thought to be from Mars. On discovery, its mass was 1.93 kg. It made its way into headlines worldwide in 1996 when scientists announced that it might contain evidence for microscopic fossils of Martian bacteria.

The Times has a hyped story on this.

Nasa scientists have produced the most compelling evidence yet that bacterial life exists on Mars.

It showed that microscopic worm-like structures found in a Martian meteorite that hit the Earth 13,000 years ago are almost certainly fossilised bacteria. The so-called bio-morphs are embedded beneath the surface layers of the rock, suggesting that they were already present when the meteorite arrived, rather than being the result of subsequent contamination by Earthly bacteria.

“This is very strong evidence of life on Mars,” said David Mackay, a senior scientist at the Nasa Johnson Space Centre , who was part of the team of scientists that originally investigated the meteorite when it was discovered in 1984.

In a 1996 study of the sample, Dr Mackay and others argued that the microfossils were evidence of life, but sceptics dismissed the claims, saying that similar-shaped structures might not be biological. The new analyses, the product of high resolution electron microscopy, make a strong case for the Allan Hills 84001 Meteorite having carried Martian life to Earth. The microscopes were focused on tiny magnetite crystals present in the surface layers of the meteorite, which have the form of simple bacteria. Some argued that these could be the result of a carbonate breaking down in the heat of the impact.

The abstract of the paper reads.

The Martian meteorite ALH84001 preserves evidence of interaction with aqueous fluids while on Mars in the form of microscopic carbonate disks. These carbonate disks are believed to have precipitated 3.9 Ga ago at beginning of the Noachian epoch on Mars during which both the oldest extant Martian surfaces were formed, and perhaps the earliest global oceans. Intimately associated within and throughout these carbonate disks are nanocrystal magnetites (Fe3O4) with unusual chemical and physical properties, whose origins have become the source of considerable debate. One group of hypotheses argues that these magnetites are the product of partial thermal decomposition of the host carbonate. Alternatively, the origins of magnetite and carbonate may be unrelated; that is, from the perspective of the carbonate the magnetite is allochthonous. For example, the magnetites might have already been present in the aqueous fluids from which the carbonates were believed to have been deposited. We have sought to resolve between these hypotheses through the detailed characterization of the compositional and structural relationships of the carbonate disks and associated magnetites with the orthopyroxene matrix in which they are embedded. Extensive use of focused ion beam milling techniques has been utilized for sample preparation. We then compared our observations with those from experimental thermal decomposition studies of sideritic carbonates under a range of plausible geological heating scenarios. We conclude that the vast majority of the nanocrystal magnetites present in the carbonate disks could not have formed by any of the currently proposed thermal decomposition scenarios. Instead, we find there is considerable evidence in support of an alternative allochthonous origin for the magnetite unrelated to any shock or thermal processing of the carbonates.

This suggests an ecological connection in so far as geological process seem to be eliminated.The paper has been online since June,and one might wonder if this is a 'good news" balance of the climategate problem.

Saturday, November 21, 2009

Climate Mafia,Mediocre Mathematicians and the Mind Projection Fallacy

The strength of a government depends on the people’s ignorance.Moreover, he said, the government is aware of this and would therefore always fight against the people’s education


The release of emails and other data exposing the mindset of climate scientists in resisting dissent by distorting or withholding of datasets, will bring questions,however the main uncertainty that needs to be asked is why global warming has stopped.

The fact is that we can’t account for the lack of warming at the moment and it is a travesty that we can’t. The CERES data published in the August BAMS 09 supplement on 2008 shows there should be even more warming: but the data are surely wrong.
- Kevin Trenberth, head of the Climate Analysis Section at the National Center for Atmospheric Research and a lead author of the 2001 and 2007 IPCC Scientific Assessment of Climate Change

This is a clear case of the mind projection fallacy (My own ignorance) - (Nature is indeterminate)eg Jaynes Probability as Logic,

It seems that mankind has always been occupied with the problem of how to deal with ignorance.Primitive man, aware of his helplessness against the forces of Nature but totally ignorant of their causes, would try to compensate for his ignorance by inventing hypotheses about them. For educated people today, the idea of directing intelligences willfully and consciously controlling every detail of events seems vastly more complicated than the idea of a machine running; but to primitive man (and even to the uneducated today) the opposite is true. For one who has no comprehension of physical law, but is aware of his own consciousness and volition, the natural question to ask is not:What is causing it?", but rather:Who is causing it?"

The answer was to invent Gods with the same consciousness and volition as ourselves, but with the additional power of psychokinesis; one in control of the weather, one in control of the seas, and so on. This personication of Nature must have been going on for thousands of years before it started producing permanent written records, in ancient Egypt and Greece. It appears that the adult citizens of those times really believed very literally in all their local Gods This oldest of all devices for dealing with one's ignorance, is the firrst form of what we havecalled the Mind Projection Fallacy".

One asserts that the creations of his own imagination are real properties of Nature, and thus in effect projects his own thoughts out onto Nature. It is still rampant today, not only in fundamentalist religion, but in every field where probability theory is used Of course, we are not arguing against a scientist's practice of formulating hypotheses about what is happening in Nature. Indeed, we see it as the highest form of creativity { far transcending mere mathematical manipulative skill { to conceive the right hypothesis in any field, out of one's educated imagination. Copernicus, Newton, Faraday, Darwin, Mendel, Pasteur, Wegener, Einstein are our heroes for having done this The difference between an imaginative scientist on the one hand, and primitive man and religious fundamentalists on the other, is that the scientist clearly recognizes the creations of his imagination as tentative working hypotheses to be tested by observation; and he is prepared to test and reject a hundred different hypotheses in order to find the right one.

Indeed as see the interbreeding of ideas of a small community of very ordinary scientists,has seen a field stagnate into a toxic cesspool that controls peer review and browbeats editors and censors ideas plausible or otherwise as a heresy.

Tommy Gold spoke of this at Nasa.

Another area where it is particularly bad is in the planetary sciences where NASA made great mistakes in the way in which they set up the situation. NASA made the grave mistake not only of working with a peer review system, but one where some of the peers (in fact very influential ones) were the in-house people doing the same line of work. This established a community of planetary scientists now which was completely selected by the leading members of the herd, which was very firmly controlled, and after quite a short time, the slightest departure from the herd was absolutely cut down. Money was not there for anybody who had a slightly diverging viewpoint. The conferences ignored him, and so on. It became completely impossible to do any independent work. For all the money that has been spent, the planetary program will one day be seen to have been extraordinarily poor. The pictures are fine and some of the facts that have been obtained from the planetary exploration with spacecraft - those will stand but not much else.

Indeed the decrease of scientific diversity (interbreeding) is akin to an Appalachian mining town.

Clearly these limitations are skill based and one could conjecture that this western phenomena is a result of the antiscientific mathematical cnstraint as outlined by Vladimir Arnold.

In the middle of the twentieth century a strong mafia of left-brained mathematicians succeeded in eliminating all geometry from the mathematical education (first in France and later in most other countries), replacing the study of all content in mathematics by the training in formal proofs and the manipulation of abstract notions. Of course, all the geometry, and, consequently, all relations with the real world and other sciences have been eliminated from the mathematics teaching.

Define the multiplication of natural numbers by the long multiplication rule. The
commutativity of the multiplication (ab = ba) becomes then a difficult theorem, which
one can however deduce logically from the definition. Forcing poor students to learn such proofs, the left-brained criminals had inevitably created the present negative opinion, of society and governments, of mathematics.

But the left-brained ill people have succeeded in breeding generations of mathematicians,who understand no other approach to mathematics and are able only to continue to teach it the same way. The aversion to mathematics of the ministers who have suffered through the humiliating teaching of this type in high school is a normal and healthy reaction.

Unfortunately, their aversion to mathematics is acting indiscriminately on all of it and can kill it completely. One of the dangerous trends is to eliminate the proofs from the high-school mathematics.The role of the proof for mathematics is similar to that for orthography or even calligraphy for poetry. A person, who had not mastered the art of the proofs in high school, is as a rule unable to distinguish correct reasoning from that which is misleading Such people can be easily manipulated by the irresponsible politicians. Mass hypnosis and the disastrous social events may result.

The continuity of the dumbing down of mathematics and science is criticized in the Royal society of Chemistry on the UK examination standards.

The question ran: 'A solid cube has sides of length 5 cm. Work out the total surface area of the cube. State the units of your answer.'

Dr Pike said, 'The correct answer can be arrived at within seconds, by noting that the area of each face of the cube is 5 x 5, or 25 square centimetres, and there are six faces to a cube, so that the result is 150 square centimetres.'

He added, 'Two important issues emerge from this. Firstly, schools in the independent sector are moving increasingly to International GCSEs (IGCSEs), which are seen as more demanding, and prepare pupils more effectively for A-Level. This is creating a two-tier system in education, since these are not recognised in the state sector, and is further attractive to schools because the curriculum is relatively stable, unlike for GCSEs where some observers see the incessant modifications as principally an income source for those involved in producing educational materials.

'Secondly, it raises the questions: Who is in charge of GCSEs? Who monitors? Who challenges? Why is it that, with dozens of agencies, authorities, boards, institutes and quangos, these extraordinary outcomes still surface?

Dr Pike said, 'Until we all get to grips with this fiasco, with some tough talking, this country risks sliding down the road to mediocrity'.

The last word returns to Tolstoy.

I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth, if it be such as would obliged them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives.

Tuesday, November 17, 2009

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.


"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 historical in stead of 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.

Saturday, October 10, 2009

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.

Wednesday, October 07, 2009

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

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?

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