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Hockey stick graph (global temperature)

Hockey stick graph (global temperature) is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hockey stick graph (global temperature) rather than just read about it. In short: Hockey stick graphs present global or hemispherical mean global surface temperatures of the distant past, as shown by quantitative climate reconstructions based on climate proxy records, in relation to instrumental temperature records which only go back to around 1850. These reconstructions have consistently shown a slow long term cooling trend changing into relatively rapid warming in the 20th century, with earlier…

Hockey stick graph (global temperature) — main illustration
Hockey stick graph (global temperature) — illustration

Key takeaways

  • Hockey stick graph (global temperature) belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Hockey stick graph (global temperature) to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Hockey stick graph (global temperature) from memory before moving on to harder problems.

Reference excerpt

Hockey stick graphs present global or hemispherical mean global surface temperatures of the distant past, as shown by quantitative climate reconstructions based on climate proxy records, in relation to instrumental temperature records which only go back to around 1850. These reconstructions have consistently shown a slow long term cooling trend changing into relatively rapid warming in the 20th century, with earlier temperatures exceeding the instrumental temperature record by 2000. The term hockey stick graph was popularized by the climatologist Jerry Mahlman, to describe the pattern shown by the Mann, Bradley & Hughes 1999 (MBH99) reconstruction, envisaging a graph that is relatively flat with a downward trend to 1900 as forming an ice hockey stick's "shaft" followed by a sharp, steady increase corresponding to the "blade" portion. The reconstructions have featured in Intergovernmental Panel on Climate Change (IPCC) reports as evidence of global warming. Arguments over the reconstructions have been taken up by fossil fuel industry funded lobbying groups attempting to cast doubt on climate science. Paleoclimatology dates back to the 19th century, and the concept of examining varves in lake beds and tree rings to track local climatic changes was suggested in the 1930s. 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 the Little Ice Age. This was the basis of a "schematic diagram" featured in the IPCC First Assessment Report of 1990 beside cautions that the medieval warming might not have been global. The use of indicators to get quantitative estimates of the temperature record of past centuries was developed, and by the late 1990s a number of competing teams of climatologists found indications that recent warming was exceptional. Bradley & Jones 1993 introduced the "Composite Plus Scaling" (CPS) method which, as of 2009, was still being used by most large-scale reconstructions. Their study was featured in the IPCC Second Assessment Report of 1995. In 1998 Michael E. Mann, Raymond S. Bradley and Malcolm K. Hughes developed new statistical techniques to produce Mann, Bradley & Hughes 1998 (MBH98), the first eigenvector-based climate field reconstruction (CFR). This showed global patterns of annual surface temperature, and included 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. A version of the MBH99 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 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 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, a paper claiming greater medieval warmth was quickly dismissed by scientists in the Soon and Baliunas controversy. Later in 2003, Stephen McIntyre and Ross McKitrick published McIntyre & McKitrick 2003b disputing the data used in MBH98 paper. In 2004 Hans von Storch published criticism of 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 the McIntyre and McKitrick methodology. Political disputes led to the formation of a panel of scientists convened by the United States National Research Council, their North Report in 2006 supported Mann's findings with some qualifications, including agreeing that there were some statistical failings but these had little effect on the result. More than two dozen reconstructions, using various statistical methods and combinations of proxy records, support the broad consensus shown in the original 1998 hockey-stick graph, with variations in how flat the pre-20th century "shaft" appears. The 2007 IPCC Fourth Assessment Report cited 14 reconstructions, 10 of which covered 1,000 years or longer, to support its strengthened conclusion that it was likely that Northern Hemisphere temperatures during the 20th century were the highest in at least the past 1,300 years. Further reconstructions, including Mann et al. 2008 and PAGES 2k Consortium 2013, have supported these general conclusions.

Origins: the first paleoclimate reconstructions

Paleoclimatology influenced the 19th century physicists John Tyndall and Svante Arrhenius who found the greenhouse gas effect of carbon dioxide (CO2) in the atmosphere to explain how past ice ages had ended. From 1919 to 1923, Alfred Wegener did pioneering work on reconstructing the climate of past eras in collaboration with Milutin Milanković, publishing Die Klimate der geologischen Vorzeit ("The Climates of the Geological Past") together with Wladimir Köppen, in 1924. In the 1930s Guy Stewart Callendar compiled temperature records to look for changes. Wilmot H. Bradley showed that annual varves in lake beds showed climate cycles, and A. E. Douglass found that tree rings could track past climatic changes but these were thought to only show random variations in the local region. It was only in the 1960s that accurate use of tree rings as climate proxies for reconstructions was pioneered by Harold C. Fritts.

… excerpt ends here. Continue reading the full article.

Illustrations

Hockey stick graph (global temperature): The original Northern Hemisphere hockey stick graph of Mann, Bradley & Hughes 1999, smoothed curve shown in blue with its uncertainty range in light blue, overlaid with green dots showing the 30-year global average of the PAGES 2k Consortium 2013 reconstruction. The red curve shows measured global mean temperature, according to HadCRUT4 data from 1850 to 2013.
The original Northern Hemisphere hockey stick graph of Mann, Bradley & Hughes 1999, smoothed curve shown in blue with its uncertainty range in light blue, overlaid with green dots showing the 30-year global average of the PAGES 2k Consortium 2013 reconstruction. The red curve shows measured global mean temperature, according to HadCRUT4 data from 1850 to 2013.
Hockey stick graph (global temperature): By 2020, numerous studies supported the MBH99 conclusions, and extended the graph to more than 2,000 years.
By 2020, numerous studies supported the MBH99 conclusions, and extended the graph to more than 2,000 years.
Hockey stick graph (global temperature): Red line: the IPCC 1990 Figure 7.1(c) schematic diagram (based on Lamb 1965) closely follows central England temperatures; green dashed line shows central England temperatures to 2007.[17] The blue line is the Mann, Bradley & Hughes 1998 40 year average from the IPCC TAR 2001 "hockey stick", the black line is the Moberg et al. 2005 low frequency signal.
Red line: the IPCC 1990 Figure 7.1(c) schematic diagram (based on Lamb 1965) closely follows central England temperatures; green dashed line shows central England temperatures to 2007.[17] The blue line is the Mann, Bradley & Hughes 1998 40 year average from the IPCC TAR 2001 "hockey stick", the black line is the Moberg et al. 2005 low frequency signal.
Hockey stick graph (global temperature): IPCC WG1 Co-chair Sir John T. Houghton showing the IPCC fig. 2.20 hockey stick graph at a climate conference in 2005
IPCC WG1 Co-chair Sir John T. Houghton showing the IPCC fig. 2.20 hockey stick graph at a climate conference in 2005
Hockey stick graph (global temperature): Ten of the hemispheric temperature reconstructions published by December 2005. Four were omitted because they had been superseded by later reconstructions or due to data plotting issues.
Ten of the hemispheric temperature reconstructions published by December 2005. Four were omitted because they had been superseded by later reconstructions or due to data plotting issues.

Worked examples

Example 1 — a first encounter with Hockey stick graph (global temperature)

Start with the simplest possible case. Write down what Hockey stick graph (global temperature) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hockey stick graph (global temperature) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hockey stick graph (global temperature) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hockey stick graph (global temperature)

In research
Hockey stick graph (global temperature) appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Hockey stick graph (global temperature) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Hockey stick graph (global temperature) is common in secondary-school and first-year university syllabi. It links to neighbouring topics Historical climatology, History of climate variability and change, Statistical charts and diagrams, so understanding it makes those chapters shorter.
In everyday life
Look for Hockey stick graph (global temperature) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Hockey stick graph (global temperature) in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Hockey stick graph (global temperature) means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Hockey stick graph (global temperature) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hockey stick graph (global temperature) in simple terms?

Hockey stick graphs present global or hemispherical mean global surface temperatures of the distant past, as shown by quantitative climate reconstructions based on climate proxy records, in relation to instrumental temperature records which only go back to around 1850. These reconstructions have co…

Why does Hockey stick graph (global temperature) matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hockey stick graph (global temperature)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hockey stick graph (global temperature).

Tags

  • Historical climatology
  • History of climate variability and change
  • Statistical charts and diagrams

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