Misplaced Pages

#171828

149-505: Investigations of paleoclimate date back to the 1930s, but quantitative methods were slow to come into use. In the 1960s, Hubert Lamb generalised from historical documents and temperature records of central England to propose a Medieval Warm Period from around 900 to 1300, followed by Little Ice Age . This was the basis of a "schematic diagram" featured in the IPCC First Assessment Report beside cautions that

298-434: A p -dimensional ellipsoid to the data, where each axis of the ellipsoid represents a principal component. If some axis of the ellipsoid is small, then the variance along that axis is also small. To find the axes of the ellipsoid, we must first center the values of each variable in the dataset on 0 by subtracting the mean of the variable's observed values from each of those values. These transformed values are used instead of

447-480: A climate sensitivity for the rest of the Phanerozoic which was calculated to be similar to today's modern range of values. The difference in global mean temperatures between a fully glacial Earth and an ice free Earth is estimated at 10 °C, though far larger changes would be observed at high latitudes and smaller ones at low latitudes. One requirement for the development of large scale ice sheets seems to be

596-464: A continually relatively warm surface during the complete early temperature record of Earth with the exception of one cold glacial phase about 2.4 billion years ago. In the late Archaean eon, an oxygen-containing atmosphere began to develop, apparently from photosynthesizing cyanobacteria (see Great Oxygenation Event ) which have been found as stromatolite fossils from 2.7 billion years ago. The early basic carbon isotopy ( isotope ratio proportions)

745-462: A data analysis procedure". Bloomfield as a statistician considered all the choices of data processing and methods to have been "quite reasonable" in a "first of its kind study". He said "I would not have been embarrassed by that work at the time if I'd been involved in it". In response to a question from Edward Wegman on the MBH use of principal components analysis, Bloomfield said this had been reviewed by

894-399: A data vector x ( i ) can therefore be given as a score t k ( i ) = x ( i ) ⋅ w ( k ) in the transformed coordinates, or as the corresponding vector in the space of the original variables, { x ( i ) ⋅ w ( k ) } w ( k ) , where w ( k ) is the k th eigenvector of X X . The full principal components decomposition of X can therefore be given as where W

1043-427: A data vector x ( i ) from an original space of p variables to a new space of p variables which are uncorrelated over the dataset. However, not all the principal components need to be kept. Keeping only the first L principal components, produced by using only the first L eigenvectors, gives the truncated transformation where the matrix T L now has n rows but only L columns. In other words, PCA learns

1192-487: A discussion of the differences between PCA and factor analysis see Ch. 7 of Jolliffe's Principal Component Analysis ), Eckart–Young theorem (Harman, 1960), or empirical orthogonal functions (EOF) in meteorological science (Lorenz, 1956), empirical eigenfunction decomposition (Sirovich, 1987), quasiharmonic modes (Brooks et al., 1988), spectral decomposition in noise and vibration, and empirical modal analysis in structural dynamics. PCA can be thought of as fitting

1341-544: A generally consistent picture of temperature trends during the preceding millennium", including the Medieval Warm Period and the Little Ice Age , "but the exact timing and duration of warm periods may have varied from region to region, and the magnitude and geographic extent of the warmth are uncertain." It concluded "with a high level of confidence that global mean surface temperature was higher during

1490-459: A graph of average hemispheric temperatures back to 1400 with shading emphasising that uncertainties (to two standard error limits) were much greater in earlier centuries. Jones et al. 1998 independently produced a CPS reconstruction extending back for a thousand years, and Mann, Bradley & Hughes 1999 (MBH99) used the MBH98 methodology to extend their study back to 1000. The term hockey stick

1639-403: A linear transformation t = W L T x , x ∈ R p , t ∈ R L , {\displaystyle t=W_{L}^{\mathsf {T}}x,x\in \mathbb {R} ^{p},t\in \mathbb {R} ^{L},} where the columns of p × L matrix W L {\displaystyle W_{L}} form an orthogonal basis for

SECTION 10

#1732793549172

1788-454: A new vector of principal component scores t ( i ) = ( t 1 , … , t l ) ( i ) {\displaystyle \mathbf {t} _{(i)}=(t_{1},\dots ,t_{l})_{(i)}} , given by in such a way that the individual variables t 1 , … , t l {\displaystyle t_{1},\dots ,t_{l}} of t considered over

1937-515: A once warmer climate, which he thought could be explained by a shift in Earth's axis. Fossils were, at that time, often explained as a consequence of a biblical flood. Systematic observations of sunspots started by amateur astronomer Heinrich Schwabe in the early 19th century, starting a discussion of the Sun's influence on Earth's climate. The scientific study of paleoclimatology began to take shape in

2086-457: A paper (since retracted) in 2008 in the journal Computational Statistics & Data Analysis where they suggested "that certain styles of co-authorship lead to the possibility of group-think, reduced creativity, and the possibility of less rigorous reviewing processes". They concluded they had provided "insight into the why certain fields of study may have migrated into a more politically driven framework." After computer scientist Ted Kirkpatrick of

2235-670: A paper claiming greater medieval warmth, and on this basis the Bush administration chief of staff Philip Cooney deleted references to climate reconstructions from the first Environmental Protection Agency Report on the Environment . The paper was quickly dismissed by scientists in the Soon and Baliunas controversy , but on July 28, Republican Jim Inhofe spoke in the Senate speech citing Soon and Baliunas to claim "that man-made global warming

2384-416: A particular area. On a longer time scale, geologists must refer to the sedimentary record for data. On a longer time scale, the rock record may show signs of sea level rise and fall, and features such as "fossilised" sand dunes can be identified. Scientists can get a grasp of long-term climate by studying sedimentary rock going back billions of years. The division of Earth history into separate periods

2533-526: A search for some basis on which to discredit these particular scientists and findings, rather than a search for understanding." He stated that MBH had given out their full data and descriptions of methods, and were not the only evidence in the IPCC TAR that recent temperatures were likely the warmest in 1,000 years; "a variety of independent lines of evidence, summarized in a number of peer-reviewed publications, were cited in support". Thomas Crowley argued that

2682-415: A sequence of p {\displaystyle p} unit vectors , where the i {\displaystyle i} -th vector is the direction of a line that best fits the data while being orthogonal to the first i − 1 {\displaystyle i-1} vectors. Here, a best-fitting line is defined as one that minimizes the average squared perpendicular distance from

2831-535: A shift from a reducing atmosphere to an oxidizing atmosphere. O 2 showed major variations until reaching a steady state of more than 15% by the end of the Precambrian. The following time span was the Phanerozoic eon, during which oxygen-breathing metazoan life forms began to appear. The amount of oxygen in the atmosphere has fluctuated over the last 600 million years, reaching a peak of 35% during

2980-540: A special "Committee on Surface Temperature Reconstructions for the Past 2,000 Years" was assembled by the National Research Council to quickly prepare a concise report. The NRC Committee, chaired by Gerald North , consisted of 12 scientists and statisticians from different disciplines. Its task was "to summarize current scientific information on the temperature record for the past two millennia, describe

3129-411: A spin machine." The report opened with a statement that its remit was to provide "an independent verification of the critiques" of MBH98 and MBH99 by McIntyre and McKitrick (MM), "as well as the related implications". They produced a social network analysis to imply problems of peer review not being independent, suggested that climatologists worked in isolation from statisticians, and alleged that there

SECTION 20

#1732793549172

3278-399: A two-dimensional diagram; whereas if two directions through the data (or two of the original variables) are chosen at random, the clusters may be much less spread apart from each other, and may in fact be much more likely to substantially overlay each other, making them indistinguishable. Similarly, in regression analysis , the larger the number of explanatory variables allowed, the greater

3427-467: A very useful step for visualising and processing high-dimensional datasets, while still retaining as much of the variance in the dataset as possible. For example, selecting L  = 2 and keeping only the first two principal components finds the two-dimensional plane through the high-dimensional dataset in which the data is most spread out, so if the data contains clusters these too may be most spread out, and therefore most visible to be plotted out in

3576-409: A wide variety of techniques to deduce ancient climates. The techniques used depend on which variable has to be reconstructed (this could be temperature , precipitation , or something else) and how long ago the climate of interest occurred. For instance, the deep marine record, the source of most isotopic data, exists only on oceanic plates, which are eventually subducted ; the oldest remaining material

3725-459: Is 200 million years old. Older sediments are also more prone to corruption by diagenesis . This is due to the millions of years of disruption experienced by the rock formations, such as pressure, tectonic activity, and fluid flowing. These factors often result in a lack of quality or quantity of data, which causes resolution and confidence in the data decrease over time. Specific techniques used to make inferences on ancient climate conditions are

3874-412: Is a linear dimensionality reduction technique with applications in exploratory data analysis , visualization and data preprocessing . The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified. The principal components of a collection of points in a real coordinate space are

4023-542: Is a p -by- p matrix of weights whose columns are the eigenvectors of X X . The transpose of W is sometimes called the whitening or sphering transformation . Columns of W multiplied by the square root of corresponding eigenvalues, that is, eigenvectors scaled up by the variances, are called loadings in PCA or in Factor analysis. X X itself can be recognized as proportional to the empirical sample covariance matrix of

4172-415: Is a disadvantage to this method. Data of the climate only started being recorded in the mid-1800s. This means that researchers can only utilize 150 years of data. That is not helpful when trying to map the climate of an area 10,000 years ago. This is where more complex methods can be used. Mountain glaciers and the polar ice caps / ice sheets provide much data in paleoclimatology. Ice-coring projects in

4321-442: Is analyzing how the varying concentrations of CO2 affect the overall climate. This is done by using various proxies to estimate past greenhouse gas concentrations and compare those to that of the present day. Researchers are then able to assess their role in progression of climate change throughout Earth’s history. The Earth's climate system involves the atmosphere , biosphere , cryosphere , hydrosphere , and lithosphere , and

4470-414: Is generally reflected by a greater or lesser thickness in growth rings. Different species however, respond to changes in climatic variables in different ways. A tree-ring record is established by compiling information from many living trees in a specific area. This is done by comparing the number, thickness, ring boundaries, and pattern matching of tree growth rings. The differences in thickness displayed in

4619-521: Is largely based on visible changes in sedimentary rock layers that demarcate major changes in conditions. Often, they include major shifts in climate. Coral “rings'' share similar evidence of growth to that of trees, and thus can be dated in similar ways. A primary difference is their environments and the conditions within those that they respond to. Examples of these conditions for coral include water temperature, freshwater influx, changes in pH, and wave disturbances. From there, specialized equipment, such as

Wegman Report - Misplaced Pages Continue

4768-745: Is likely the warmest in the last millennium", and added that "This doesn't change the scientific landscape in terms of the greenhouse warming debate". In its summary, the NRC committee noted the development of large-scale surface temperature reconstructions, especially MBH98 and MBH99, and highlighted six recent reconstructions: Huang, Pollack & Shen 2000 , Mann & Jones 2003 , Hegerl et al. 2006 , Oerlemans 2005 , Moberg et al. 2005 and Esper, Cook & Schweingruber 2002 . Its main findings were; 20th century instrumentally measured warming showed in observational evidence, and can be simulated with climate models, large-scale surface temperature reconstructions "yield

4917-436: Is not being questioned." A Nature editorial commented on the implication that the plagiarised material in the retracted paper was likely to also be present in the earlier "infamous" Wegman Report, including allegations against Mann and his co-authors which had frequently been cited by climate-change deniers. The George Mason University's policies indicated that its initial inquiry should have been completed within 12 weeks of

5066-596: Is not replenished anymore and starts decaying. The proportion of 'normal' carbon and Carbon-14 gives information of how long the plant material has not been in contact with the atmosphere. Knowledge of precise climatic events decreases as the record goes back in time, but some notable climate events are known: The first atmosphere would have consisted of gases in the solar nebula , primarily hydrogen . In addition, there would probably have been simple hydrides such as those now found in gas giants like Jupiter and Saturn , notably water vapor, methane , and ammonia . As

5215-404: Is of limited use to study recent ( Quaternary , Holocene ) large climate changes since there are seldom discernible in the geomorphological record. The field of geochronology has scientists working on determining how old certain proxies are. For recent proxy archives of tree rings and corals the individual year rings can be counted, and an exact year can be determined. Radiometric dating uses

5364-430: Is sensitive to the scaling of the variables. If we have just two variables and they have the same sample variance and are completely correlated, then the PCA will entail a rotation by 45° and the "weights" (they are the cosines of rotation) for the two variables with respect to the principal component will be equal. But if we multiply all values of the first variable by 100, then the first principal component will be almost

5513-412: Is the chance of overfitting the model, producing conclusions that fail to generalise to other datasets. One approach, especially when there are strong correlations between different possible explanatory variables, is to reduce them to a few principal components and then run the regression against them, a method called principal component regression . Dimensionality reduction may also be appropriate when

5662-705: Is the greatest hoax ever perpetrated on the American people". Later in 2003, Stephen McIntyre and Ross McKitrick published McIntyre & McKitrick (2003a) disputing the data used in Mann, Bradley & Hughes (1998) paper. They were given extensive publicity, and met Inhofe as well as making a presentation sponsored by the George C. Marshall Institute and the Competitive Enterprise Institute . In 2004 Hans von Storch published criticism of

5811-601: Is the scientific study of climates predating the invention of meteorological instruments , when no direct measurement data were available. As instrumental records only span a tiny part of Earth's history , the reconstruction of ancient climate is important to understand natural variation and the evolution of the current climate. Paleoclimatology uses a variety of proxy methods from Earth and life sciences to obtain data previously preserved within rocks , sediments , boreholes , ice sheets , tree rings , corals , shells , and microfossils . Combined with techniques to date

5960-419: Is the square diagonal matrix with the singular values of X and the excess zeros chopped off that satisfies Σ ^ 2 = Σ T Σ {\displaystyle \mathbf {{\hat {\Sigma }}^{2}} =\mathbf {\Sigma } ^{\mathsf {T}}\mathbf {\Sigma } } . Comparison with the eigenvector factorization of X X establishes that

6109-492: Is to study relict landforms to infer ancient climates. Being often concerned about past climates climatic geomorphology is considered sometimes to be a theme of historical geology . Evidence of these past climates to be studied can be found in the landforms they leave behind. Examples of these landforms are those such as glacial landforms (moraines, striations), desert features (dunes, desert pavements), and coastal landforms (marine terraces, beach ridges). Climatic geomorphology

Wegman Report - Misplaced Pages Continue

6258-525: The Carboniferous period, significantly higher than today's 21%. Two main processes govern changes in the atmosphere: plants use carbon dioxide from the atmosphere , releasing oxygen and the breakdown of pyrite and volcanic eruptions release sulfur into the atmosphere, which oxidizes and hence reduces the amount of oxygen in the atmosphere. However, volcanic eruptions also release carbon dioxide, which plants can convert to oxygen. The exact cause of

6407-474: The Great Oxygenation Event , and its appearance is indicated by the end of the banded iron formations . Until then, any oxygen produced by photosynthesis was consumed by oxidation of reduced materials, notably iron. Molecules of free oxygen did not start to accumulate in the atmosphere until the rate of production of oxygen began to exceed the availability of reducing materials. That point was

6556-779: The L features (the components of representation t ) that are decorrelated. By construction, of all the transformed data matrices with only L columns, this score matrix maximises the variance in the original data that has been preserved, while minimising the total squared reconstruction error ‖ T W T − T L W L T ‖ 2 2 {\displaystyle \|\mathbf {T} \mathbf {W} ^{T}-\mathbf {T} _{L}\mathbf {W} _{L}^{T}\|_{2}^{2}} or ‖ X − X L ‖ 2 2 {\displaystyle \|\mathbf {X} -\mathbf {X} _{L}\|_{2}^{2}} . Such dimensionality reduction can be

6705-599: The National Academy of Sciences , and Jay Gulledge of the Pew Center on Global Climate Change . The hearing also heard testimony from Wegman and McIntyre. In an interview, North stated that the politicians at the hearing at which the Wegman Report was presented "were twisting the scientific information for their own propaganda purposes. The hearing was not an information gathering operation, but rather

6854-519: The Simon Fraser University read the "Deep Climate" website allegations of plagiarism, he made a formal complaint to the journal. On 16 March 2011, Wegman sent an email to the journal saying that a student "had basically copied and pasted" work by other authors into the Wegman Report, and this text had been used in the journal paper without acknowledgement. He said that "We would never knowingly publish plagiarized material". In May 2011

7003-688: The United States House Energy Subcommittee on Oversight and Investigations wanted expert opinion on the validity of criticisms of the Mann, Bradley & Hughes 1999 reconstruction. Wegman set up a team of statisticians, and over the next nine months Barton's staffer provided them with material to review. The team included Wegman, Yasmin H. Said who had been his graduate student, and statistician David W. Scott, all statisticians with no expertise in climatology or other physical sciences . They were assisted by two others; Wegman testified that one of his graduate students did

7152-511: The carbon cycle . The weathering sequesters CO 2 , by the reaction of minerals with chemicals (especially silicate weathering with CO 2 ) and thereby removing CO 2 from the atmosphere and reducing the radiative forcing. The opposite effect is volcanism , responsible for the natural greenhouse effect , by emitting CO 2 into the atmosphere, thus affecting glaciation (Ice Age) cycles. Jim Hansen suggested that humans emit CO 2 10,000 times faster than natural processes have done in

7301-420: The cross-covariance between two datasets while PCA defines a new orthogonal coordinate system that optimally describes variance in a single dataset. Robust and L1-norm -based variants of standard PCA have also been proposed. PCA was invented in 1901 by Karl Pearson , as an analogue of the principal axis theorem in mechanics; it was later independently developed and named by Harold Hotelling in

7450-801: The n rows represents a different repetition of the experiment, and each of the p columns gives a particular kind of feature (say, the results from a particular sensor). Mathematically, the transformation is defined by a set of size l {\displaystyle l} of p -dimensional vectors of weights or coefficients w ( k ) = ( w 1 , … , w p ) ( k ) {\displaystyle \mathbf {w} _{(k)}=(w_{1},\dots ,w_{p})_{(k)}} that map each row vector x ( i ) = ( x 1 , … , x p ) ( i ) {\displaystyle \mathbf {x} _{(i)}=(x_{1},\dots ,x_{p})_{(i)}} of X to

7599-509: The "most knowledgeable" of his contributors on the topic. Following the GMU inquiry, the student issued a statement that she had been "Dr. Wegman's graduate student when I provided him with the overview of social network analysis, at his request. My draft overview was later incorporated by Dr. Wegman and his coauthors into the 2006 report. I was not an author of the report." She had met with a GMU misconduct committee, and said that "My academic integrity

SECTION 50

#1732793549172

7748-702: The (CSDA) article, as a result of poor judgment for which Professor Wegman, as team leader, must bear responsibility", and Wegman was to receive an "official letter of reprimand". The investigation reports were to be sent on to federal authorities, but would not be made public. Bradley described the split result as "an absurd decision" which would encourage GMU students to think it acceptable to copy work without attribution. 1965 1978 1979 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Paleoclimate Paleoclimatology ( British spelling , palaeoclimatology )

7897-502: The 1930s. Depending on the field of application, it is also named the discrete Karhunen–Loève transform (KLT) in signal processing , the Hotelling transform in multivariate quality control, proper orthogonal decomposition (POD) in mechanical engineering, singular value decomposition (SVD) of X (invented in the last quarter of the 19th century ), eigenvalue decomposition (EVD) of X X in linear algebra, factor analysis (for

8046-516: The 22 years he had been a government scientist; he thought it could "have a chilling effect on the willingness of people to work in areas that are politically relevant." Benjamin D. Santer told the New Scientist "There are people who believe that if they bring down Mike Mann, they can bring down the IPCC." Congressman Boehlert said the investigation was as "at best foolhardy" with the tone of

8195-486: The 91 pages in the Wegman Report were plagiarized, and "often injected with errors, bias and changes of meaning." Wegman responded that he was "very well aware of the report", but at the university's request would not comment further until all issues were settled. Reviews by outside experts contacted by USA Today found plagiarism from textbooks which was obvious and inappropriate; the social network analysis section had also been partly copied from Misplaced Pages. Wegman said there

8344-519: The Advanced Very High Resolution Radiometer (AVHRR) instrument, can be used to derive the sea surface temperature and water salinity from the past few centuries. The δ O of coralline red algae provides a useful proxy of the combined sea surface temperature and sea surface salinity at high latitudes and the tropics, where many traditional techniques are limited. Within climatic geomorphology , one approach

8493-540: The Earth's current oxygen level. At the end of the Proterozoic, there is evidence of global glaciation events of varying severity causing a ' Snowball Earth '. Snowball Earth is supported by different indicators such as, glacial deposits, significant continental erosion called the Great Unconformity , and sedimentary rocks called cap carbonates that form after a deglaciation episode. Major drivers for

8642-430: The Earth's surface. Dependent on the radiative balance of incoming and outgoing energy, the Earth either warms up or cools down. Earth radiative balance originates from changes in solar insolation and the concentrations of greenhouse gases and aerosols . Climate change may be due to internal processes in Earth sphere's and/or following external forcings. One example of a way this can be applied to study climatology

8791-478: The Earth’s climate system. These estimates include the evidence for systems such as long term climate variability (eccentricity, obliquity precession), feedback mechanisms (Ice-Albedo Effect), and anthropogenic influence. Examples: On timescales of millions of years, the uplift of mountain ranges and subsequent weathering processes of rocks and soils and the subduction of tectonic plates , are an important part of

8940-687: The MBH statistical methods were discussed in Chapter 11 in the context of more recent research which explored ways of addressing these problems, and showed greater amplitude of temperature variations over 1000 to 2000 years. Recent papers cited included Wahl & Ammann 2007 . On McIntyre and McKitrick's criticism of principal component analysis as tending to bias the shape of the reconstructions, it found that "In practice, this method, though not recommended, does not appear to unduly influence reconstructions of hemispheric mean temperature", and reconstructions using other methods were qualitatively similar. Some of

9089-676: The McIntyre and McKitrick methodology. In June 2005 Rep. Joe Barton launched what Sherwood Boehlert , chairman of the House Science Committee , called a "misguided and illegitimate investigation" into the data, methods and personal information of Mann, Bradley and Hughes. At Boehlert's request a panel of scientists convened by the National Research Council was set up, which reported in 2006 supporting Mann's findings with some qualifications, including agreeing that there were some statistical failings but these had little effect on

SECTION 60

#1732793549172

9238-687: The National Research Council panel that had produced the NRC report, Tom Karl , director of the National Climatic Data Center , and Hans von Storch . Wegman and Steve McIntyre also testified at the hearing. A second hearing was arranged on 27 July 2006, and heard testimony from Mann, John Christy , a climate scientist at the University of Alabama in Huntsville , Ralph J. Cicerone , president of

9387-587: The PCA. PCA is defined as an orthogonal linear transformation on a real inner product space that transforms the data to a new coordinate system such that the greatest variance by some scalar projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. Consider an n × p {\displaystyle n\times p} data matrix , X , with column-wise zero empirical mean (the sample mean of each column has been shifted to zero), where each of

9536-522: The Precambrian climate is difficult for various reasons including the low number of reliable indicators and a, generally, not well-preserved or extensive fossil record (especially when compared to the Phanerozoic eon). Despite these issues, there is evidence for a number of major climate events throughout the history of the Precambrian: The Great Oxygenation Event , which started around 2.3 Ga ago (the beginning of

9685-622: The Proterozoic) is indicated by biomarkers which demonstrate the appearance of photosynthetic organisms. Due to the high levels of oxygen in the atmosphere from the GOE, CH 4 levels fell rapidly cooling the atmosphere causing the Huronian glaciation. For about 1 Ga after the glaciation (2-0.8 Ga ago), the Earth likely experienced warmer temperatures indicated by microfossils of photosynthetic eukaryotes, and oxygen levels between 5 and 18% of

9834-546: The Wall Street Journal announced that a report commissioned by the Energy and Commerce Committee was due to be released that day. It gave a preview of the conclusions of the report, which had been prepared by three statisticians. The committee chairman U.S. Rep. Joe Barton issued a press release giving a summary of the report's findings, with quotations from the report. The Wegman Report was not peer reviewed in

9983-513: The aim was intimidation of climate researchers in general, and Bradley thought the letters were intended to damage confidence in the IPCC during preparation of its next report. A Washington Post editorial on 23 July which described the investigation as harassment quoted Bradley as saying it was "intrusive, far-reaching and intimidating", and Alan I. Leshner of the AAAS describing it as unprecedented in

10132-613: The arrangement of continental land masses at or near the poles. The constant rearrangement of continents by plate tectonics can also shape long-term climate evolution. However, the presence or absence of land masses at the poles is not sufficient to guarantee glaciations or exclude polar ice caps. Evidence exists of past warm periods in Earth's climate when polar land masses similar to Antarctica were home to deciduous forests rather than ice sheets. The relatively warm local minimum between Jurassic and Cretaceous goes along with an increase of subduction and mid-ocean ridge volcanism due to

10281-503: The auspices of International Partnerships in Ice Core Sciences (IPICS), defined a priority project to obtain the oldest possible ice core record from Antarctica, an ice core record reaching back to or towards 1.5 million years ago. Climatic information can be obtained through an understanding of changes in tree growth. Generally, trees respond to changes in climatic variables by speeding up or slowing down growth, which in turn

10430-542: The authority of the House Commerce Committee, is probably not the best way to resolve a scientific issue, and a focus on individual scientists can be intimidating", and proposed that the NAS should appoint an independent panel to investigate. Barton dismissed this offer. Mann, Bradley and Hughes sent formal letters giving their detailed responses to Barton and Whitfield. On 15 July, Mann wrote emphasising that

10579-617: The breakup of the Pangea supercontinent . Superimposed on the long-term evolution between hot and cold climates have been many short-term fluctuations in climate similar to, and sometimes more severe than, the varying glacial and interglacial states of the present ice age . Some of the most severe fluctuations, such as the Paleocene-Eocene Thermal Maximum , may be related to rapid climate changes due to sudden collapses of natural methane clathrate reservoirs in

10728-527: The climate and how they affected the surrounding species. Older intact wood that has escaped decay can extend the time covered by the record by matching the ring depth changes to contemporary specimens. By using that method, some areas have tree-ring records dating back a few thousand years. Older wood not connected to a contemporary record can be dated generally with radiocarbon techniques. A tree-ring record can be used to produce information regarding precipitation, temperature, hydrology, and fire corresponding to

10877-634: The code for them, and another of his graduate students provided a section of the report in draft, but was not an author of the report. Lacking Barton's agreement, Boehlert's Science Committee independently requested the NAS in November to commission the National Research Council Report . On 10 February 2006 the Wall Street Journal revealed Barton's contact with Wegman when it reported that "people familiar with

11026-450: The committee along with other statistical issues, and "while the issues are real, they had a very minimal effect, not a material effect on the final reconstruction." Barton dismissed the offer of a joint investigation with an independent panel appointed by the U.S. National Academy of Sciences (NAS), and on 1 September 2005 statistician Edward Wegman was contacted about giving testimony. Bardon's staffer then met Wegman, and explained that

11175-476: The committee finds it plausible that the Northern Hemisphere was warmer during the last few decades of the 20th century than during any comparable period over the preceding millennium", though there were substantial uncertainties before about 1600. It added that "Even less confidence can be placed in the original conclusions by Mann et al. (1999) that 'the 1990s are likely the warmest decade, and 1998

11324-435: The conclusion that climatic warming is occurring in response to human activities, and they are not the primary evidence." At the press conference, North said of the MBH papers that "we do roughly agree with the substance of their findings. There is a small disagreement over exactly how sure we are." All three from the NRC committee panel said it was probable, though not certain, that current warming exceeded any previous peak in

11473-427: The conclusion that, in the Northern Hemisphere, the 1990s was likely to have been the warmest decade and 1998 the warmest year during the past 1,000 years. The graph was featured in publicity, and became a focus of dispute for those opposed to the strengthening scientific consensus that late 20th century warmth was exceptional. In 2003, as lobbying over the 1997 Kyoto Protocol intensified, Soon and Baliunas published

11622-512: The corresponding singular value. This form is also the polar decomposition of T . Efficient algorithms exist to calculate the SVD of X without having to form the matrix X X , so computing the SVD is now the standard way to calculate a principal components analysis from a data matrix, unless only a handful of components are required. As with the eigen-decomposition, a truncated n × L score matrix T L can be obtained by considering only

11771-511: The criticisms of validation techniques were more valid than others, these issues and the effect on robustness of the choice of proxies contributed to the committee's view of increased uncertainties. They called for further research into methods and a search for more proxies for earlier periods. At the press conference the three NRC panellists said they found no evidence supporting the allegations of inappropriate behaviour such as data manipulation, or "anything other than an honest attempt to construct

11920-410: The data matrix. PCA is the simplest of the true eigenvector-based multivariate analyses and is closely related to factor analysis . Factor analysis typically incorporates more domain-specific assumptions about the underlying structure and solves eigenvectors of a slightly different matrix. PCA is also related to canonical correlation analysis (CCA) . CCA defines coordinate systems that optimally describe

12069-877: The data set successively inherit the maximum possible variance from X , with each coefficient vector w constrained to be a unit vector (where l {\displaystyle l} is usually selected to be strictly less than p {\displaystyle p} to reduce dimensionality). The above may equivalently be written in matrix form as where T i k = t k ( i ) {\displaystyle {\mathbf {T} }_{ik}={t_{k}}_{(i)}} , X i j = x j ( i ) {\displaystyle {\mathbf {X} }_{ij}={x_{j}}_{(i)}} , and W j k = w j ( k ) {\displaystyle {\mathbf {W} }_{jk}={w_{j}}_{(k)}} . In order to maximize variance,

12218-432: The data. This choice of basis will transform the covariance matrix into a diagonalized form, in which the diagonal elements represent the variance of each axis. The proportion of the variance that each eigenvector represents can be calculated by dividing the eigenvalue corresponding to that eigenvector by the sum of all eigenvalues. Biplots and scree plots (degree of explained variance ) are used to interpret findings of

12367-402: The dataset X . The sample covariance Q between two of the different principal components over the dataset is given by: where the eigenvalue property of w ( k ) has been used to move from line 2 to line 3. However eigenvectors w ( j ) and w ( k ) corresponding to eigenvalues of a symmetric matrix are orthogonal (if the eigenvalues are different), or can be orthogonalised (if

12516-433: The dataset is not too large, the significance of the principal components can be tested using parametric bootstrap , as an aid in determining how many principal components to retain. The principal components transformation can also be associated with another matrix factorization, the singular value decomposition (SVD) of X , Here Σ is an n -by- p rectangular diagonal matrix of positive numbers σ ( k ) , called

12665-527: The distinction of being the optimal orthogonal transformation for keeping the subspace that has largest "variance" (as defined above). This advantage, however, comes at the price of greater computational requirements if compared, for example, and when applicable, to the discrete cosine transform , and in particular to the DCT-II which is simply known as the "DCT". Nonlinear dimensionality reduction techniques tend to be more computationally demanding than PCA. PCA

12814-660: The early 19th century, when discoveries about glaciations and natural changes in Earth's past climate helped to understand the greenhouse effect . It was only in the 20th century that paleoclimatology became a unified scientific field. Before, different aspects of Earth's climate history were studied by a variety of disciplines. At the end of the 20th century, the empirical research into Earth's ancient climates started to be combined with computer models of increasing complexity. A new objective also developed in this period: finding ancient analog climates that could provide information about current climate change . Paleoclimatologists employ

12963-607: The environment and biodiversity often reflect on the current situation, specifically the impact of climate on mass extinctions and biotic recovery and current global warming . Notions of a changing climate most likely evolved in ancient Egypt , Mesopotamia , the Indus Valley and China , where prolonged periods of droughts and floods were experienced. In the seventeenth century, Robert Hooke postulated that fossils of giant turtles found in Dorset could only be explained by

13112-410: The first i − 1 {\displaystyle i-1} principal components that maximizes the variance of the projected data. For either objective, it can be shown that the principal components are eigenvectors of the data's covariance matrix . Thus, the principal components are often computed by eigendecomposition of the data covariance matrix or singular value decomposition of

13261-411: The first k  − 1 principal components from X : and then finding the weight vector which extracts the maximum variance from this new data matrix It turns out that this gives the remaining eigenvectors of X X , with the maximum values for the quantity in brackets given by their corresponding eigenvalues. Thus the weight vectors are eigenvectors of X X . The k -th principal component of

13410-500: The first L largest singular values and their singular vectors: The truncation of a matrix M or T using a truncated singular value decomposition in this way produces a truncated matrix that is the nearest possible matrix of rank L to the original matrix, in the sense of the difference between the two having the smallest possible Frobenius norm , a result known as the Eckart–Young theorem [1936]. The singular values (in Σ ) are

13559-456: The first few principal components compared to the same noise variance, the proportionate effect of the noise is less—the first few components achieve a higher signal-to-noise ratio . PCA thus can have the effect of concentrating much of the signal into the first few principal components, which can usefully be captured by dimensionality reduction; while the later principal components may be dominated by noise, and so disposed of without great loss. If

13708-430: The first principal component of a set of p {\displaystyle p} variables is the derived variable formed as a linear combination of the original variables that explains the most variance. The second principal component explains the most variance in what is left once the effect of the first component is removed, and we may proceed through p {\displaystyle p} iterations until all

13857-415: The first weight vector w (1) thus has to satisfy Equivalently, writing this in matrix form gives Since w (1) has been defined to be a unit vector, it equivalently also satisfies The quantity to be maximised can be recognised as a Rayleigh quotient . A standard result for a positive semidefinite matrix such as X X is that the quotient's maximum possible value is the largest eigenvalue of

14006-491: The full data and necessary methods information was already publicly available in full accordance with National Science Foundation (NSF) requirements, so that other scientists had been able to reproduce their work. NSF policy was that computer codes "are considered the intellectual property of researchers and are not subject to disclosure", as the NSF had advised McIntyre and McKitrick in 2003, but notwithstanding these property rights,

14155-411: The growth rings in trees can often indicate the quality of conditions in the environment, and the fitness of the tree species evaluated. Different species of trees will display different growth responses to the changes in the climate. An evaluation of multiple trees within the same species, along with one of trees in different species, will allow for a more accurate analysis of the changing variables within

14304-707: The ice caps of Greenland and Antarctica have yielded data going back several hundred thousand years, over 800,000 years in the case of the EPICA project. A multinational consortium, the European Project for Ice Coring in Antarctica (EPICA), has drilled an ice core in Dome C on the East Antarctic ice sheet and retrieved ice from roughly 800,000 years ago. The international ice core community has, under

14453-488: The instrumental and proxy records, statistical procedures, paleoclimate models, and the synthesis of large scale temperature reconstructions with an assessment of the "strengths, limitations, and prospects for improvement" in techniques used. The NRC committee's report (the North Report ) was published on 22 June 2006. Committee member John Michael Wallace said that "Our conclusion is that this recent period of warming

14602-704: The issue was demonstrated when, on 23 June 2005, Rep. Joe Barton , chairman of the House Committee on Energy and Commerce wrote joint letters with Ed Whitfield , Chairman of the Subcommittee on Oversight and Investigations , referring to issues raised by the 14 February 2005 article in the Wall Street Journal and demanding full records on climate research. The letters were sent to the IPCC Chairman Rajendra Pachauri , National Science Foundation Director Arden Bement, and to

14751-473: The journal's editor, Stanley Azen of the University of Southern California , announced that the journal was retracting the paper, because it used portions of other authors' writings without sufficient attribution. John Dahlberg of the United States Office of Research Integrity indicated that plagiarism could result in sanctions. A George Mason University spokesman declined to comment and said it

14900-525: The last few decades of the 20th century than during any comparable period during the preceding four centuries", justified by consistent evidence from a wide variety of geographically diverse proxies, but "Less confidence can be placed in large-scale surface temperature reconstructions for the period from 900 to 1600", and very little confidence could be assigned to hemispheric or global mean surface temperature estimates before about 900. The NRC committee stated that "The basic conclusion of Mann et al. (1998, 1999)

15049-423: The last thousand years. When asked if they could quantify "less confidence" and "plausible", Bloomfield explained that their wording reflected the panel's scientific judgements rather than well defined statistical procedures, and "When we speak of 'less confidence' we're more into a level of sort of 2 to 1 odds, which IPCC, they interpreted 'likely' as that level, roughly 2 to 1 odds or better." Various criticisms of

15198-447: The left shows the temperature change over the past 12,000 years, from various sources; the thick black curve is an average. Climate forcing is the difference between radiant energy ( sunlight ) received by the Earth and the outgoing longwave radiation back to space. Such radiative forcing is quantified based on the CO 2 amount in the tropopause , in units of watts per square meter to

15347-676: The letters and saying he had "failed to hold a single hearing on the subject of global warming" during eleven years as chairman, and had "vociferously opposed all legislative efforts in the Committee to address global warming .... These letters do not appear to be a serious attempt to understand the science of global warming. Some might interpret them as a transparent effort to bully and harass climate change experts who have reached conclusions with which you disagree." The U.S. National Academy of Sciences (NAS) president Ralph J. Cicerone wrote to Barton that "A congressional investigation, based on

15496-423: The letters showing the committee's "inexperience" in relation to science. Barton was given support by global warming denier Myron Ebell of the Competitive Enterprise Institute , who said "We've always wanted to get the science on trial ... we would like to figure out a way to get this into a court of law", and "this could work". In his Junk Science column on Fox News , Steven Milloy said Barton's inquiry

15645-462: The main areas of uncertainty and how significant they are, describe the principal methodologies used and any problems with these approaches, and explain how central is the debate over the paleoclimate temperature record to the state of scientific knowledge on global climate change." The NRC report went through a rigorous review process involving 15 independent experts. The report provided a summary and an overview, followed by 11 technical chapters covering

15794-409: The matrix, which occurs when w is the corresponding eigenvector . With w (1) found, the first principal component of a data vector x ( i ) can then be given as a score t 1( i ) = x ( i ) ⋅ w (1) in the transformed co-ordinates, or as the corresponding vector in the original variables, { x ( i ) ⋅ w (1) } w (1) . The k -th component can be found by subtracting

15943-401: The matter" said that Barton had already requested an analysis of the hockey stick from statistician Edward Wegman. It said that the deputy staff director for Barton's committee had made a statement that closer study was needed because of anticipated costs of mitigating climate change, and that Barton's concerns were "unlikely" to be fully addressed by the NAS. In an editorial dated 14 July 2006,

16092-870: The medieval warming might not have been global. The use of proxy indicators to get quantitative estimates of the temperature record of past centuries was developed, and Bradley & Jones 1993 introduced the "Composite Plus Scaling" (CPS) method used by most later large scale reconstructions. Their study was featured in the IPCC Second Assessment Report , and in the United States House Committee on Science its findings were disputed by Pat Michaels . In 1998 Michael E. Mann , Raymond S. Bradley and Malcolm K. Hughes developed new statistical techniques to produce Mann, Bradley & Hughes 1998 (MBH98), which showed global patterns of annual surface temperature, and included

16241-538: The oceans. A similar, single event of induced severe climate change after a meteorite impact has been proposed as reason for the Cretaceous–Paleogene extinction event . Other major thresholds are the Permian-Triassic , and Ordovician-Silurian extinction events with various reasons suggested. The Quaternary geological period includes the current climate. There has been a cycle of ice ages for

16390-486: The one investigating the 2006 Wegman Report gave a unanimous finding that "no misconduct was involved". Stearns stated that "Extensive paraphrasing of another work did occur, in a background section, but the work was repeatedly referenced and the committee found that the paraphrasing did not constitute misconduct". He said that the 2008 social network analysis paper was investigated by a separate committee which unanimously found "that plagiarism occurred in contextual sections of

16539-607: The original complaint, and although 14 months had passed without this being resolved, there were loopholes for extensions. It said that the university should "take the initiative to move investigations along as speedily as possible while allowing time for due process. Once an investigation is complete, the institution should be as transparent as it can about what happened", especially where public funds were involved. George Mason University provost Peter Stearns announced on 22 February 2012 that charges of scientific misconduct had been investigated by two separate faculty committees, and that

16688-415: The original observed values for each of the variables. Then, we compute the covariance matrix of the data and calculate the eigenvalues and corresponding eigenvectors of this covariance matrix. Then we must normalize each of the orthogonal eigenvectors to turn them into unit vectors. Once this is done, each of the mutually-orthogonal unit eigenvectors can be interpreted as an axis of the ellipsoid fitted to

16837-425: The original variables can be written The empirical covariance matrix between the principal components becomes where Λ is the diagonal matrix of eigenvalues λ ( k ) of X X . λ ( k ) is equal to the sum of the squares over the dataset associated with each component k , that is, λ ( k ) = Σ i t k ( i ) = Σ i ( x ( i ) ⋅ w ( k ) ) . The transformation T = X W maps

16986-514: The past 2.2–2.1 million years (starting before the Quaternary in the late Neogene Period). Note in the graphic on the right the strong 120,000-year periodicity of the cycles, and the striking asymmetry of the curves. This asymmetry is believed to result from complex interactions of feedback mechanisms. It has been observed that ice ages deepen by progressive steps, but the recovery to interglacial conditions occurs in one big step. The graph on

17135-399: The past. Ice sheet dynamics and continental positions (and linked vegetation changes) have been important factors in the long term evolution of the Earth's climate. There is also a close correlation between CO 2 and temperature, where CO 2 has a strong control over global temperatures in Earth's history. Principal components analysis Principal component analysis ( PCA )

17284-515: The points to the line . These directions (i.e., principal components) constitute an orthonormal basis in which different individual dimensions of the data are linearly uncorrelated . Many studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points. Principal component analysis has applications in many fields such as population genetics , microbiome studies, and atmospheric science . When performing PCA,

17433-409: The preindustrial ages have been variations of the Sun, volcanic ashes and exhalations, relative movements of the Earth towards the Sun, and tectonically induced effects as for major sea currents, watersheds, and ocean oscillations. In the early Phanerozoic, increased atmospheric carbon dioxide concentrations have been linked to driving or amplifying increased global temperatures. Royer et al. 2004 found

17582-611: The program used to generate the original MBH98 temperature reconstructions had been made available at the Mann et al. public ftp site. Many scientists protested against Barton's investigation, with 20 prominent climatologists questioning his approach. Alan I. Leshner wrote to him on behalf of the American Association for the Advancement of Science expressing deep concern about the letters, which gave "the impression of

17731-417: The properties of radioactive elements in proxies. In older material, more of the radioactive material will have decayed and the proportion of different elements will be different from newer proxies. One example of radiometric dating is radiocarbon dating . In the air, cosmic rays constantly convert nitrogen into a specific radioactive carbon isotope, C . When plants then use this carbon to grow, this isotope

17880-568: The proxies, the paleoclimate records are used to determine the past states of Earth's atmosphere . The scientific field of paleoclimatology came to maturity in the 20th century. Notable periods studied by paleoclimatologists include the frequent glaciations that Earth has undergone, rapid cooling events like the Younger Dryas , and the rapid warming during the Paleocene–Eocene Thermal Maximum . Studies of past changes in

18029-452: The result. Barton and U.S. Rep. Ed Whitfield requested Edward Wegman to set up a team of statisticians to investigate, and they supported McIntyre and McKitrick's view that there were statistical failings, although they did not quantify whether there was any significant effect. They also produced an extensive network analysis which has been discredited by expert opinion and found to have issues of plagiarism. The increasing politicisation of

18178-430: The right singular vectors W of X are equivalent to the eigenvectors of X X , while the singular values σ ( k ) of X {\displaystyle \mathbf {X} } are equal to the square-root of the eigenvalues λ ( k ) of X X . Using the singular value decomposition the score matrix T can be written so each column of T is given by one of the left singular vectors of X multiplied by

18327-430: The same as that variable, with a small contribution from the other variable, whereas the second component will be almost aligned with the second original variable. This means that whenever the different variables have different units (like temperature and mass), PCA is a somewhat arbitrary method of analysis. (Different results would be obtained if one used Fahrenheit rather than Celsius for example.) Pearson's original paper

18476-565: The same way as the NRC Report, but was sent out to a number of referees before it was released. Wegman lacked the procedures and staff which the NRC had in place to organise peer review. One of the referees, Grace Wahba , later said she was given the report only 3 days in advance, and her criticisms were ignored. The Wegman Report was discussed at hearings of the United States House Energy Subcommittee on Oversight and Investigations under its chairman U.S. Rep. Ed Whitfield . The first hearing

18625-407: The set of points around their mean in order to align with the principal components. This moves as much of the variance as possible (using an orthogonal transformation) into the first few dimensions. The values in the remaining dimensions, therefore, tend to be small and may be dropped with minimal loss of information (see below ). PCA is often used in this manner for dimensionality reduction . PCA has

18774-466: The singular values of X ; U is an n -by- n matrix, the columns of which are orthogonal unit vectors of length n called the left singular vectors of X ; and W is a p -by- p matrix whose columns are orthogonal unit vectors of length p and called the right singular vectors of X . In terms of this factorization, the matrix X X can be written where Σ ^ {\displaystyle \mathbf {\hat {\Sigma }} }

18923-565: The solar nebula dissipated, the gases would have escaped, partly driven off by the solar wind . The next atmosphere, consisting largely of nitrogen , carbon dioxide , and inert gases, was produced by outgassing from volcanism , supplemented by gases produced during the late heavy bombardment of Earth by huge asteroids . A major part of carbon dioxide emissions were soon dissolved in water and built up carbonate sediments. Water-related sediments have been found dating from as early as 3.8 billion years ago. About 3.4 billion years ago, nitrogen

19072-415: The square roots of the eigenvalues of the matrix X X . Each eigenvalue is proportional to the portion of the "variance" (more correctly of the sum of the squared distances of the points from their multidimensional mean) that is associated with each eigenvector. The sum of all the eigenvalues is equal to the sum of the squared distances of the points from their multidimensional mean. PCA essentially rotates

19221-445: The statistical techniques as tending to underplay variations in earlier parts of the graph, though this was disputed and he later accepted that the effect was very small. In 2005 McIntyre and McKitrick published criticisms of the principal components analysis methodology as used in MBH98 and MBH99. Their analysis was subsequently disputed by published papers including Huybers 2005 and Wahl & Ammann 2007 which pointed to errors in

19370-408: The sum of these processes from Earth's spheres is what affects the climate. Greenhouse gasses act as the internal forcing of the climate system. Particular interests in climate science and paleoclimatology focus on the study of Earth climate sensitivity , in response to the sum of forcings. Analyzing the sum of these forcings contributes to the ability of scientists to make broad conclusive estimates on

19519-428: The three scientists Mann , Bradley and Hughes . The letters told the scientist to provide not just data and methods, but also personal information about their finances and careers, information about grants provided to the institutions they had worked for, and the exact computer codes used to generate their results. Sherwood Boehlert , chairman of the House Science Committee , told his fellow Republican Joe Barton it

19668-466: The time of the dinosaur extinction, "Hothouse", endured from 56 Mya to 47 Mya and was ~14 °C warmer than average modern temperatures. The Precambrian took place between the time when Earth first formed 4.6 billion years ( Ga ) ago, and 542 million years ago. The Precambrian can be split into two eons, the Archean and the Proterozoic, which can be further subdivided into eras. The reconstruction of

19817-464: The use of lake sediment cores and speleothems. These utilize an analysis of sediment layers and rock growth formations respectively, amongst element-dating methods utilizing oxygen, carbon and uranium. The Direct Quantitative Measurements method is the most direct approach to understand the change in a climate. Comparisons between recent data to older data allows a researcher to gain a basic understanding of weather and climate changes within an area. There

19966-428: The variables in a dataset are noisy. If each column of the dataset contains independent identically distributed Gaussian noise, then the columns of T will also contain similarly identically distributed Gaussian noise (such a distribution is invariant under the effects of the matrix W , which can be thought of as a high-dimensional rotation of the co-ordinate axes). However, with more of the total variance concentrated in

20115-422: The variance is explained. PCA is most commonly used when many of the variables are highly correlated with each other and it is desirable to reduce their number to an independent set. The first principal component can equivalently be defined as a direction that maximizes the variance of the projected data. The i {\displaystyle i} -th principal component can be taken as a direction orthogonal to

20264-602: The variation of the amount of oxygen in the atmosphere is not known. Periods with much oxygen in the atmosphere are associated with rapid development of animals. Today's atmosphere contains 21% oxygen, which is high enough for rapid development of animals. In 2020 scientists published a continuous, high-fidelity record of variations in Earth's climate during the past 66 million years and identified four climate states , separated by transitions that include changing greenhouse gas levels and polar ice sheets volumes. They integrated data of various sources. The warmest climate state since

20413-421: The vectors happen to share an equal repeated value). The product in the final line is therefore zero; there is no sample covariance between different principal components over the dataset. Another way to characterise the principal components transformation is therefore as the transformation to coordinates which diagonalise the empirical sample covariance matrix. In matrix form, the empirical covariance matrix for

20562-436: The warmest year, in at least a millennium' because the uncertainties inherent in temperature reconstructions for individual years and decades are larger than those for longer time periods and because not all of the available proxies record temperature information on such short timescales." It noted that "Surface temperature reconstructions for periods prior to the industrial era are only one of multiple lines of evidence supporting

20711-625: Was "speculation and conspiracy theory" in John Mashey's analysis, and said that "[t]hese attacks are unprecedented in my 42 years as an academic and scholar." He stated that the Wegman Report never "intended to take intellectual credit for any aspect of paleoclimate reconstruction science or for any original research aspect of social network analysis." As an extension of the part of the Wegman Report which used social network analysis to suggest that there had been inappropriate close collaboration between some climate scientists, Wegman and Said published

20860-553: Was a "misguided and illegitimate investigation" into something that should properly be under the jurisdiction of the Science Committee, and wrote "My primary concern about your investigation is that its purpose seems to be to intimidate scientists rather than to learn from them, and to substitute congressional political review for scientific review." Barton's committee spokesman sent a sarcastic response to this and to Democrat Henry A. Waxman 's letter asking Barton to withdraw

21009-448: Was a "personnel matter". The manuscript of the paper had been submitted on 8 July 2007 and accepted for publication on 14 July 2007. Network analysis expert Kathleen Carley described it as an opinion piece which speculated that collaboration between scientists "leads to peer review abuse. No data is provided to support this argument". Wegman's student had attended a one-week course taught by Carley, thus becoming what Wegman described as

21158-470: Was entitled "On Lines and Planes of Closest Fit to Systems of Points in Space" – "in space" implies physical Euclidean space where such concerns do not arise. One way of making the PCA less arbitrary is to use variables scaled so as to have unit variance, by standardizing the data and hence use the autocorrelation matrix instead of the autocovariance matrix as a basis for PCA. However, this compresses (or expands)

21307-453: Was held on 19 July 2006, five days after the report was announced and released. Michael E. Mann was given only three days notice of the hearing and advised the committee that he was unable to attend on that date due to a commitment to look after his baby daughter, but the hearing went ahead with testimony from paleoclimatologist Tom Crowley who Mann recommended in his absence. The other scientists giving testimony were Gerald North , chairman of

21456-461: Was inadequate sharing of methods and data. Wegman's institution, George Mason University , confirmed in October 2010 that they were investigating misconduct charges, following a March 2010 formal complaint by Raymond S. Bradley alleging plagiarism and fabrications in the Wegman Report. A 250-page study by computer scientist John Mashey , posted on the "Deep Climate" website, claims that 35 of

21605-473: Was reasonable. In November 2005, Science Committee chair Sherwood Boehlert requested the National Academy of Science to arrange a review of the matter, and its National Research Council set up a special committee to investigate and report . At the request of the U.S. Congress, initiated by Representative Sherwood Boehlert as chairman of the U.S. House of Representatives Committee on Science ,

21754-449: Was that the late 20th century warmth in the Northern Hemisphere was unprecedented during at least the last 1,000 years. This conclusion has subsequently been supported by an array of evidence that includes both additional large-scale surface temperature reconstructions and pronounced changes in a variety of local proxy indicators". It said "Based on the analyses presented in the original papers by Mann et al. and this newer supporting evidence,

21903-457: Was the major part of the then stable "second atmosphere". An influence of life has to be taken into account rather soon in the history of the atmosphere because hints of early life forms have been dated to as early as 3.5 to 4.3 billion years ago. The fact that it is not perfectly in line with the 30% lower solar radiance (compared to today) of the early Sun has been described as the " faint young Sun paradox ". The geological record, however, shows

22052-416: Was used by the climatologist Jerry Mahlman to describe the pattern this showed, envisaging a graph that is relatively flat to 1900 as forming an ice hockey stick 's "shaft", followed by a sharp increase corresponding to the "blade". A version of this graph was featured prominently in the 2001 IPCC Third Assessment Report (TAR), which also drew on Jones et al. 1998 and three other reconstructions to support

22201-442: Was very much in line with what is found today, suggesting that the fundamental features of the carbon cycle were established as early as 4 billion years ago. The constant rearrangement of continents by plate tectonics influences the long-term evolution of the atmosphere by transferring carbon dioxide to and from large continental carbonate stores. Free oxygen did not exist in the atmosphere until about 2.4 billion years ago, during

#171828