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Thursday, November 7, 2019

Attribution of recent climate change

From Wikipedia, the free encyclopedia
 
Accumulation in the atmosphere of greenhouse gases, especially those resulting from humans burning fossil fuels, has been found to be the predominant cause of global warming and climate change.
 
Attribution of recent climate change is the effort to scientifically ascertain mechanisms responsible for recent global warming and related climate changes on Earth. The effort has focused on changes observed during the period of instrumental temperature record, particularly in the last 50 years. This is the period when human activity has grown fastest and observations of the atmosphere above the surface have become available. According to the Intergovernmental Panel on Climate Change (IPCC), it is "extremely likely" that human influence was the dominant cause of global warming between 1951 and 2010. The best estimate is that observed warming since 1951 has been entirely human caused. 

Some of the main human activities that contribute to global warming are:
In addition to human activities, some natural mechanisms can also cause climate change, including for example, climate oscillations, changes in solar activity, and volcanic activity. 

Multiple lines of evidence support attribution of recent climate change to human activities:
  • A physical understanding of the climate system: greenhouse gas concentrations have increased and their warming properties are well-established.
  • Historical estimates of past climate changes suggest that the recent changes in global surface temperature are unusual.
  • Computer-based climate models are unable to replicate the observed warming unless human greenhouse gas emissions are included.
  • Natural forces alone (such as solar and volcanic activity) cannot explain the observed warming.
The IPCC's attribution of recent global warming to human activities is a view shared by the scientific community, and is also supported by 196 other scientific organizations worldwide.

Background

The Keeling Curve shows the long-term increase of atmospheric carbon dioxide (CO
2
) concentrations from 1958–2018. Monthly CO
2
measurements display seasonal oscillations in an upward trend. Each year's maximum occurs during the Northern Hemisphere's late spring.

Factors affecting Earth's climate can be broken down into feedbacks and forcings. A forcing is something that is imposed externally on the climate system. External forcings include natural phenomena such as volcanic eruptions and variations in the sun's output. Human activities can also impose forcings, for example, through changing the composition of the atmosphere.

Radiative forcing is a measure of how various factors alter the energy balance of the Earth's atmosphere. A positive radiative forcing will tend to increase the energy of the Earth-atmosphere system, leading to a warming of the system. Between the start of the Industrial Revolution in 1750, and the year 2005, the increase in the atmospheric concentration of carbon dioxide (chemical formula: CO
2
) led to a positive radiative forcing, averaged over the Earth's surface area, of about 1.66 watts per square metre (abbreviated W m−2).

Climate feedbacks can either amplify or dampen the response of the climate to a given forcing. There are many feedback mechanisms in the climate system that can either amplify (a positive feedback) or diminish (a negative feedback) the effects of a change in climate forcing.

The climate system will vary in response to changes in forcings. The climate system will show internal variability both in the presence and absence of forcings imposed on it, (see images opposite). This internal variability is a result of complex interactions between components of the climate system, such as the coupling between the atmosphere and ocean (see also the later section on Internal climate variability and global warming). An example of internal variability is the El Niño–Southern Oscillation.

Detection vs. attribution

Probability density function (PDF) of fraction of surface temperature trends since 1950 attributable to human activity, based on IPCC AR5 10.5
 
Refer to caption and adjacent text
In detection and attribution, the natural factors considered usually include changes in the Sun's output and volcanic eruptions, as well as natural modes of variability such as El Niño and La Niña. Human factors include the emissions of heat-trapping "greenhouse" gases and particulates as well as clearing of forests and other land-use changes. Figure source: NOAA NCDC.
 
Detection and attribution of climate signals, as well as its common-sense meaning, has a more precise definition within the climate change literature, as expressed by the IPCC. Detection of a climate signal does not always imply significant attribution. The IPCC's Fourth Assessment Report says "it is extremely likely that human activities have exerted a substantial net warming influence on climate since 1750," where "extremely likely" indicates a probability greater than 95%. Detection of a signal requires demonstrating that an observed change is statistically significantly different from that which can be explained by natural internal variability
.
Attribution requires demonstrating that a signal is:
  • unlikely to be due entirely to internal variability;
  • consistent with the estimated responses to the given combination of anthropogenic and natural forcing
  • not consistent with alternative, physically plausible explanations of recent climate change that exclude important elements of the given combination of forcings.

Key attributions

Greenhouse gases

Carbon dioxide is the primary greenhouse gas that is contributing to recent climate change. CO
2
is absorbed and emitted naturally as part of the carbon cycle, through animal and plant respiration, volcanic eruptions, and ocean-atmosphere exchange. Human activities, such as the burning of fossil fuels and changes in land use (see below), release large amounts of carbon to the atmosphere, causing CO
2
concentrations in the atmosphere to rise.

The high-accuracy measurements of atmospheric CO
2
concentration, initiated by Charles David Keeling in 1958, constitute the master time series documenting the changing composition of the atmosphere. These data have iconic status in climate change science as evidence of the effect of human activities on the chemical composition of the global atmosphere.

In May 2019 the concentration of CO2 in the atmosphere reached 415 PPM. The last time when it reached this level was 2.6 - 5.3 million years ago. Without human intervention, it would be 280 PPM
.
Along with CO
2
, methane and to a lesser extent nitrous oxide are also major forcing contributors to the greenhouse effect. The Kyoto Protocol lists these together with hydrofluorocarbon (HFCs), perfluorocarbons (PFCs), and sulfur hexafluoride (SF6), which are entirely artificial gases, as contributors to radiative forcing. The chart at right attributes anthropogenic greenhouse gas emissions to eight main economic sectors, of which the largest contributors are power stations (many of which burn coal or other fossil fuels), industrial processes, transportation fuels (generally fossil fuels), and agricultural by-products (mainly methane from enteric fermentation and nitrous oxide from fertilizer use).

Water vapor

Refer to adjacent text
Emission Database for Global Atmospheric Research version 4.2, fast track 2010 project
 
Water vapor is the most abundant greenhouse gas and is the largest contributor to the natural greenhouse effect, despite having a short atmospheric lifetime (about 10 days). Some human activities can influence local water vapor levels. However, on a global scale, the concentration of water vapor is controlled by temperature, which influences overall rates of evaporation and precipitation. Therefore, the global concentration of water vapor is not substantially affected by direct human emissions.

Land use

Climate change is attributed to land use for two main reasons. Between 1750 and 2007, about two-thirds of anthropogenic CO
2
emissions were produced from burning fossil fuels, and about one-third of emissions from changes in land use, primarily deforestation. Deforestation both reduces the amount of carbon dioxide absorbed by deforested regions and releases greenhouse gases directly, together with aerosols, through biomass burning that frequently accompanies it.

Some of the causes of climate change are, generally, not connected with it directly in the media coverage. For example, the harm done by humans to the populations of Elephants and Monkeys contributes to deforestation therefore to climate change.

A second reason that climate change has been attributed to land use is that the terrestrial albedo is often altered by use, which leads to radiative forcing. This effect is more significant locally than globally.

Livestock and land use

Worldwide, livestock production occupies 70% of all land used for agriculture, or 30% of the ice-free land surface of the Earth. More than 18% of anthropogenic greenhouse gas emissions are attributed to livestock and livestock-related activities such as deforestation and increasingly fuel-intensive farming practices. Specific attributions to the livestock sector include:

Aerosols

With virtual certainty, scientific consensus has attributed various forms of climate change, chiefly cooling effects, to aerosols, which are small particles or droplets suspended in the atmosphere. Key sources to which anthropogenic aerosols are attributed include:

Attribution of 20th century climate change

Refer to caption
One global climate model's reconstruction of temperature change during the 20th century as the result of five studied forcing factors and the amount of temperature change attributed to each.
 
Over the past 150 years human activities have released increasing quantities of greenhouse gases into the atmosphere. This has led to increases in mean global temperature, or global warming. Other human effects are relevant—for example, sulphate aerosols are believed to have a cooling effect. Natural factors also contribute. According to the historical temperature record of the last century, the Earth's near-surface air temperature has risen around 0.74 ± 0.18 °Celsius (1.3 ± 0.32 °Fahrenheit).

A historically important question in climate change research has regarded the relative importance of human activity and non-anthropogenic causes during the period of instrumental record. In the 1995 Second Assessment Report (SAR), the IPCC made the widely quoted statement that "The balance of evidence suggests a discernible human influence on global climate". The phrase "balance of evidence" suggested the (English) common-law standard of proof required in civil as opposed to criminal courts: not as high as "beyond reasonable doubt". In 2001 the Third Assessment Report (TAR) refined this, saying "There is new and stronger evidence that most of the warming observed over the last 50 years is attributable to human activities". The 2007 Fourth Assessment Report (AR4) strengthened this finding:
  • "Anthropogenic warming of the climate system is widespread and can be detected in temperature observations taken at the surface, in the free atmosphere and in the oceans. Evidence of the effect of external influences, both anthropogenic and natural, on the climate system has continued to accumulate since the TAR."
Other findings of the IPCC Fourth Assessment Report include:
  • "It is extremely unlikely (<5 and="" be="" being="" can="" century="" during="" explained="" external="" forcing="" global="" half="" i.e.="" i="" inconsistent="" internal="" is="" it="" of="" past="" pattern="" result="" that="" the="" variability="" warming="" with="" without="">very unlikely
that it is due to known natural external causes alone. The warming occurred in both the ocean and the atmosphere and took place at a time when natural external forcing factors would likely have produced cooling."
  • "From new estimates of the combined anthropogenic forcing due to greenhouse gases, aerosols, and land surface changes, it is extremely likely (>95%) that human activities have exerted a substantial net warming influence on climate since 1750."
  • "It is virtually certain that anthropogenic aerosols produce a net negative radiative forcing (cooling influence) with a greater magnitude in the Northern Hemisphere than in the Southern Hemisphere."
  • Over the past five decades there has been a global warming of approximately 0.65 °C (1.17 °F) at the Earth's surface (see historical temperature record). Among the possible factors that could produce changes in global mean temperature are internal variability of the climate system, external forcing, an increase in concentration of greenhouse gases, or any combination of these. Current studies indicate that the increase in greenhouse gases, most notably CO
    2
    , is mostly responsible for the observed warming. Evidence for this conclusion includes:
    • Estimates of internal variability from climate models, and reconstructions of past temperatures, indicate that the warming is unlikely to be entirely natural.
    • Climate models forced by natural factors and increased greenhouse gases and aerosols reproduce the observed global temperature changes; those forced by natural factors alone do not.
    • "Fingerprint" methods (see below) indicate that the pattern of change is closer to that expected from greenhouse gas-forced change than from natural change.
    • The plateau in warming from the 1940s to 1960s can be attributed largely to sulphate aerosol cooling.

    Details on attribution

    Refer to caption
    For Northern Hemisphere temperature, recent decades appear to be the warmest since at least about 1000AD, and the warming since the late 19th century is unprecedented over the last 1000 years. Older data are insufficient to provide reliable hemispheric temperature estimates.
     
    Recent scientific assessments find that most of the warming of the Earth's surface over the past 50 years has been caused by human activities. This conclusion rests on multiple lines of evidence. Like the warming "signal" that has gradually emerged from the "noise" of natural climate variability, the scientific evidence for a human influence on global climate has accumulated over the past several decades, from many hundreds of studies. No single study is a "smoking gun." Nor has any single study or combination of studies undermined the large body of evidence supporting the conclusion that human activity is the primary driver of recent warming.

    The first line of evidence is based on a physical understanding of how greenhouse gases trap heat, how the climate system responds to increases in greenhouse gases, and how other human and natural factors influence climate. The second line of evidence is from indirect estimates of climate changes over the last 1,000 to 2,000 years. These records are obtained from living things and their remains (like tree rings and corals) and from physical quantities (like the ratio between lighter and heavier isotopes of oxygen in ice cores), which change in measurable ways as climate changes. The lesson from these data is that global surface temperatures over the last several decades are clearly unusual, in that they were higher than at any time during at least the past 400 years. For the Northern Hemisphere, the recent temperature rise is clearly unusual in at least the last 1,000 years (see graph opposite).

    The third line of evidence is based on the broad, qualitative consistency between observed changes in climate and the computer model simulations of how climate would be expected to change in response to human activities. For example, when climate models are run with historical increases in greenhouse gases, they show gradual warming of the Earth and ocean surface, increases in ocean heat content and the temperature of the lower atmosphere, a rise in global sea level, retreat of sea ice and snow cover, cooling of the stratosphere, an increase in the amount of atmospheric water vapor, and changes in large-scale precipitation and pressure patterns. These and other aspects of modelled climate change are in agreement with observations.

    "Fingerprint" studies

    Refer to caption
    Reconstructions of global temperature that include greenhouse gas increases and other human influences (red line, based on many models) closely match measured temperatures (dashed line). Those that only include natural influences (blue line, based on many models) show a slight cooling, which has not occurred. The ability of models to generate reasonable histories of global temperature is verified by their response to four 20th-century volcanic eruptions: each eruption caused brief cooling that appeared in observed as well as modeled records.
     
    Finally, there is extensive statistical evidence from so-called "fingerprint" studies. Each factor that affects climate produces a unique pattern of climate response, much as each person has a unique fingerprint. Fingerprint studies exploit these unique signatures, and allow detailed comparisons of modelled and observed climate change patterns. Scientists rely on such studies to attribute observed changes in climate to a particular cause or set of causes. In the real world, the climate changes that have occurred since the start of the Industrial Revolution are due to a complex mixture of human and natural causes. The importance of each individual influence in this mixture changes over time. Of course, there are not multiple Earths, which would allow an experimenter to change one factor at a time on each Earth, thus helping to isolate different fingerprints. Therefore, climate models are used to study how individual factors affect climate. For example, a single factor (like greenhouse gases) or a set of factors can be varied, and the response of the modelled climate system to these individual or combined changes can thus be studied.

    refer to caption
    key to above map of temperature changes
    Two fingerprints of human activities on the climate are that land areas will warm more than the oceans, and that high latitudes will warm more than low latitudes. These projections have been confirmed by observations (shown above).
     
    For example, when climate model simulations of the last century include all of the major influences on climate, both human-induced and natural, they can reproduce many important features of observed climate change patterns. When human influences are removed from the model experiments, results suggest that the surface of the Earth would actually have cooled slightly over the last 50 years (see graph, opposite). The clear message from fingerprint studies is that the observed warming over the last half-century cannot be explained by natural factors, and is instead caused primarily by human factors.

    Another fingerprint of human effects on climate has been identified by looking at a slice through the layers of the atmosphere, and studying the pattern of temperature changes from the surface up through the stratosphere (see the section on solar activity). The earliest fingerprint work focused on changes in surface and atmospheric temperature. Scientists then applied fingerprint methods to a whole range of climate variables, identifying human-caused climate signals in the heat content of the oceans, the height of the tropopause (the boundary between the troposphere and stratosphere, which has shifted upward by hundreds of feet in recent decades), the geographical patterns of precipitation, drought, surface pressure, and the runoff from major river basins.

    Studies published after the appearance of the IPCC Fourth Assessment Report in 2007 have also found human fingerprints in the increased levels of atmospheric moisture (both close to the surface and over the full extent of the atmosphere), in the decline of Arctic sea ice extent, and in the patterns of changes in Arctic and Antarctic surface temperatures.

    The message from this entire body of work is that the climate system is telling a consistent story of increasingly dominant human influence – the changes in temperature, ice extent, moisture, and circulation patterns fit together in a physically consistent way, like pieces in a complex puzzle.

    Increasingly, this type of fingerprint work is shifting its emphasis. As noted, clear and compelling scientific evidence supports the case for a pronounced human influence on global climate. Much of the recent attention is now on climate changes at continental and regional scales, and on variables that can have large impacts on societies. For example, scientists have established causal links between human activities and the changes in snowpack, maximum and minimum (diurnal) temperature, and the seasonal timing of runoff over mountainous regions of the western United States. Human activity is likely to have made a substantial contribution to ocean surface temperature changes in hurricane formation regions. Researchers are also looking beyond the physical climate system, and are beginning to tie changes in the distribution and seasonal behaviour of plant and animal species to human-caused changes in temperature and precipitation.

    For over a decade, one aspect of the climate change story seemed to show a significant difference between models and observations. In the tropics, all models predicted that with a rise in greenhouse gases, the troposphere would be expected to warm more rapidly than the surface. Observations from weather balloons, satellites, and surface thermometers seemed to show the opposite behaviour (more rapid warming of the surface than the troposphere). This issue was a stumbling block in understanding the causes of climate change. It is now largely resolved. Research showed that there were large uncertainties in the satellite and weather balloon data. When uncertainties in models and observations are properly accounted for, newer observational data sets (with better treatment of known problems) are in agreement with climate model results.

    This set of graphs shows the estimated contribution of various natural and human factors to changes in global mean temperature between 1889–2006. Estimated contributions are based on multivariate analysis rather than model simulations. The graphs show that human influence on climate has eclipsed the magnitude of natural temperature changes over the past 120 years. Natural influences on temperature—El Niño, solar variability, and volcanic aerosols—have varied approximately plus and minus 0.2 °C (0.4 °F), (averaging to about zero), while human influences have contributed roughly 0.8 °C (1 °F) of warming since 1889.
     
    Top chart: Observed global average temperature change (1870— ). Bottom chart: Data more recent than that plotted at left, and merged for display on the same axis to emphasize relative strengths of forces affecting temperature change. Human-caused forces have increasingly dominated.
     
    This does not mean, however, that all remaining differences between models and observations have been resolved. The observed changes in some climate variables, such as Arctic sea ice, some aspects of precipitation, and patterns of surface pressure, appear to be proceeding much more rapidly than models have projected. The reasons for these differences are not well understood. Nevertheless, the bottom-line conclusion from climate fingerprinting is that most of the observed changes studied to date are consistent with each other, and are also consistent with our scientific understanding of how the climate system would be expected to respond to the increase in heat-trapping gases resulting from human activities.

    Extreme weather events

    refer to caption
    Frequency of occurrence (vertical axis) of local June–July–August temperature anomalies (relative to 1951–1980 mean) for Northern Hemisphere land in units of local standard deviation (horizontal axis). According to Hansen et al. (2012), the distribution of anomalies has shifted to the right as a consequence of global warming, meaning that unusually hot summers have become more common. This is analogous to the rolling of a dice: cool summers now cover only half of one side of a six-sided die, white covers one side, red covers four sides, and an extremely hot (red-brown) anomaly covers half of one side.
     
    One of the subjects discussed in the literature is whether or not extreme weather events can be attributed to human activities. Seneviratne et al. (2012) stated that attributing individual extreme weather events to human activities was challenging. They were, however, more confident over attributing changes in long-term trends of extreme weather. For example, Seneviratne et al. (2012) concluded that human activities had likely led to a warming of extreme daily minimum and maximum temperatures at the global scale. 

    Another way of viewing the problem is to consider the effects of human-induced climate change on the probability of future extreme weather events. Stott et al. (2003), for example, considered whether or not human activities had increased the risk of severe heat waves in Europe, like the one experienced in 2003. Their conclusion was that human activities had very likely more than doubled the risk of heat waves of this magnitude.

    An analogy can be made between an athlete on steroids and human-induced climate change. In the same way that an athlete's performance may increase from using steroids, human-induced climate change increases the risk of some extreme weather events. 

    Hansen et al. (2012) suggested that human activities have greatly increased the risk of summertime heat waves. According to their analysis, the land area of the Earth affected by very hot summer temperature anomalies has greatly increased over time. In the base period 1951-1980, these anomalies covered a few tenths of 1% of the global land area. In recent years, this has increased to around 10% of the global land area. With high confidence, Hansen et al. (2012) attributed the 2010 Moscow and 2011 Texas heat waves to human-induced global warming.

    An earlier study by Dole et al. (2011) concluded that the 2010 Moscow heatwave was mostly due to natural weather variability. While not directly citing Dole et al. (2011), Hansen et al. (2012) rejected this type of explanation. Hansen et al. (2012) stated that a combination of natural weather variability and human-induced global warming was responsible for the Moscow and Texas heat waves.

    Scientific literature and opinion

    There are a number of examples of published and informal support for the consensus view. As mentioned earlier, the IPCC has concluded that most of the observed increase in globally averaged temperatures since the mid-20th century is "very likely" due to human activities. The IPCC's conclusions are consistent with those of several reports produced by the US National Research Council. A report published in 2009 by the U.S. Global Change Research Program concluded that "[global] warming is unequivocal and primarily human-induced." A number of scientific organizations have issued statements that support the consensus view. Two examples include:

    Detection and attribution studies

    Refer to caption
    This image shows three examples of internal climate variability measured between 1950 and 2012: the El Niño–Southern oscillation, the Arctic oscillation, and the North Atlantic oscillation.
     
    The IPCC Fourth Assessment Report (2007), concluded that attribution was possible for a number of observed changes in the climate. However, attribution was found to be more difficult when assessing changes over smaller regions (less than continental scale) and over short time periods (less than 50 years). Over larger regions, averaging reduces natural variability of the climate, making detection and attribution easier.
    • In 1996, in a paper in Nature titled "A search for human influences on the thermal structure of the atmosphere", Benjamin D. Santer et al. wrote: "The observed spatial patterns of temperature change in the free atmosphere from 1963 to 1987 are similar to those predicted by state-of-the-art climate models incorporating various combinations of changes in carbon dioxide, anthropogenic sulphate aerosol and stratospheric ozone concentrations. The degree of pattern similarity between models and observations increases through this period. It is likely that this trend is partially due to human activities, although many uncertainties remain, particularly relating to estimates of natural variability."
    • A 2002 paper in the Journal of Geophysical Research says "Our analysis suggests that the early twentieth century warming can best be explained by a combination of warming due to increases in greenhouse gases and natural forcing, some cooling due to other anthropogenic forcings, and a substantial, but not implausible, contribution from internal variability. In the second half of the century we find that the warming is largely caused by changes in greenhouse gases, with changes in sulphates and, perhaps, volcanic aerosol offsetting approximately one third of the warming."
    • A 2005 review of detection and attribution studies by the International Ad Hoc Detection and Attribution Group found that "natural drivers such as solar variability and volcanic activity are at most partially responsible for the large-scale temperature changes observed over the past century, and that a large fraction of the warming over the last 50 yr can be attributed to greenhouse gas increases. Thus, the recent research supports and strengthens the IPCC Third Assessment Report conclusion that 'most of the global warming over the past 50 years is likely due to the increase in greenhouse gases.'"
    • Barnett and colleagues (2005) say that the observed warming of the oceans "cannot be explained by natural internal climate variability or solar and volcanic forcing, but is well simulated by two anthropogenically forced climate models," concluding that "it is of human origin, a conclusion robust to observational sampling and model differences".
    • Two papers in the journal Science in August 2005 resolve the problem, evident at the time of the TAR, of tropospheric temperature trends (see also the section on "fingerprint" studies) . The UAH version of the record contained errors, and there is evidence of spurious cooling trends in the radiosonde record, particularly in the tropics. See satellite temperature measurements for details; and the 2006 US CCSP report.
    • Multiple independent reconstructions of the temperature record of the past 1000 years confirm that the late 20th century is probably the warmest period in that time (see the preceding section -details on attribution).

    Reviews of scientific opinion

    • An essay in Science surveyed 928 abstracts related to climate change, and concluded that most journal reports accepted the consensus. This is discussed further in scientific consensus on climate change.
    • A 2010 paper in the Proceedings of the National Academy of Sciences found that among a pool of roughly 1,000 researchers who work directly on climate issues and publish the most frequently on the subject, 97% agree that anthropogenic climate change is happening.
    • A 2011 paper from George Mason University published in the International Journal of Public Opinion Research, "The Structure of Scientific Opinion on Climate Change," collected the opinions of scientists in the earth, space, atmospheric, oceanic or hydrological sciences. The 489 survey respondents—representing nearly half of all those eligible according to the survey's specific standards – work in academia, government, and industry, and are members of prominent professional organizations. The study found that 97% of the 489 scientists surveyed agreed that global temperatures have risen over the past century. Moreover, 84% agreed that "human-induced greenhouse warming" is now occurring." Only 5% disagreed with the idea that human activity is a significant cause of global warming.
    As described above, a small minority of scientists do disagree with the consensus: see list of scientists opposing global warming consensus. For example, Willie Soon and Richard Lindzen say that there is insufficient proof for anthropogenic attribution. Generally this position requires new physical mechanisms to explain the observed warming.

    Solar activity

    The graph shows the solar irradiance without a long-term trend. The 11 year solar cycle is also visible. The temperature, in contrast, shows an upward trend.
    Solar irradiance (yellow) plotted together with temperature (red) over 1880 to 2018.
     
    Modelled simulation of the effect of various factors (including GHGs, Solar irradiance) singly and in combination, showing in particular that solar activity produces a small and nearly uniform warming, unlike what is observed.
     
    Solar sunspot maximum occurs when the magnetic field of the sun collapses and reverse as part of its average 11 year solar cycle (22 years for complete North to North restoration). 

    The role of the sun in recent climate change has been looked at by climate scientists. Since 1978, output from the Sun has been measured by satellites significantly more accurately than was previously possible from the surface. These measurements indicate that the Sun's total solar irradiance has not increased since 1978, so the warming during the past 30 years cannot be directly attributed to an increase in total solar energy reaching the Earth (see graph above, left). In the three decades since 1978, the combination of solar and volcanic activity probably had a slight cooling influence on the climate.

    Climate models have been used to examine the role of the sun in recent climate change. Models are unable to reproduce the rapid warming observed in recent decades when they only take into account variations in total solar irradiance and volcanic activity. Models are, however, able to simulate the observed 20th century changes in temperature when they include all of the most important external forcings, including human influences and natural forcings. As has already been stated, Hegerl et al. (2007) concluded that greenhouse gas forcing had "very likely" caused most of the observed global warming since the mid-20th century. In making this conclusion, Hegerl et al. (2007) allowed for the possibility that climate models had been underestimated the effect of solar forcing.

    The role of solar activity in climate change has also been calculated over longer time periods using "proxy" datasets, such as tree rings. Models indicate that solar and volcanic forcings can explain periods of relative warmth and cold between A.D. 1000 and 1900, but human-induced forcings are needed to reproduce the late-20th century warming.

    Another line of evidence against the sun having caused recent climate change comes from looking at how temperatures at different levels in the Earth's atmosphere have changed. Models and observations (see figure above, middle) show that greenhouse gas results in warming of the lower atmosphere at the surface (called the troposphere) but cooling of the upper atmosphere (called the stratosphere). Depletion of the ozone layer by chemical refrigerants has also resulted in a cooling effect in the stratosphere. If the sun was responsible for observed warming, warming of the troposphere at the surface and warming at the top of the stratosphere would be expected as increase solar activity would replenish ozone and oxides of nitrogen. The stratosphere has a reverse temperature gradient than the troposphere so as the temperature of the troposphere cools with altitude, the stratosphere rises with altitude. Hadley cells are the mechanism by which equatorial generated ozone in the tropics (highest area of UV irradiance in the stratosphere) is moved poleward. Global climate models suggest that climate change may widen the Hadley cells and push the jetstream northward thereby expanding the tropics region and resulting in warmer, dryer conditions in those areas overall.

    Non-consensus views

    Refer to caption
    Contribution of natural factors and human activities to radiative forcing of climate change. Radiative forcing values are for the year 2005, relative to the pre-industrial era (1750). The contribution of solar irradiance to radiative forcing is 5% the value of the combined radiative forcing due to increases in the atmospheric concentrations of carbon dioxide, methane and nitrous oxide.

    Habibullo Abdussamatov (2004), head of space research at St. Petersburg's Pulkovo Astronomical Observatory in Russia, has argued that the sun is responsible for recently observed climate change. Journalists for news sources canada.com (Solomon, 2007b), National Geographic News (Ravillious, 2007), and LiveScience (Than, 2007) reported on the story of warming on Mars. In these articles, Abdussamatov was quoted. He stated that warming on Mars was evidence that global warming on Earth was being caused by changes in the sun.

    Ravillious (2007) quoted two scientists who disagreed with Abdussamatov: Amato Evan, a climate scientist at the University of Wisconsin–Madison, in the US, and Colin Wilson, a planetary physicist at Oxford University in the UK. According to Wilson, "Wobbles in the orbit of Mars are the main cause of its climate change in the current era" (see also orbital forcing). Than (2007) quoted Charles Long, a climate physicist at Pacific Northwest National Laboratories in the US, who disagreed with Abdussamatov.

    Than (2007) pointed to the view of Benny Peiser, a social anthropologist at Liverpool John Moores University in the UK. In his newsletter, Peiser had cited a blog that had commented on warming observed on several planetary bodies in the Solar system. These included Neptune's moon Triton, Jupiter, Pluto and Mars. In an e-mail interview with Than (2007), Peiser stated that:
    "I think it is an intriguing coincidence that warming trends have been observed on a number of very diverse planetary bodies in our solar system, (...) Perhaps this is just a fluke."
    Than (2007) provided alternative explanations of why warming had occurred on Triton, Pluto, Jupiter and Mars. 

    The US Environmental Protection Agency (US EPA, 2009) responded to public comments on climate change attribution. A number of commenters had argued that recent climate change could be attributed to changes in solar irradiance. According to the US EPA (2009), this attribution was not supported by the bulk of the scientific literature. Citing the work of the IPCC (2007), the US EPA pointed to the low contribution of solar irradiance to radiative forcing since the start of the Industrial Revolution in 1750. Over this time period (1750 to 2005), the estimated contribution of solar irradiance to radiative forcing was 5% the value of the combined radiative forcing due to increases in the atmospheric concentrations of carbon dioxide, methane and nitrous oxide (see graph opposite).

    Effect of cosmic rays

    Henrik Svensmark has suggested that the magnetic activity of the sun deflects cosmic rays, and that this may influence the generation of cloud condensation nuclei, and thereby have an effect on the climate. The website ScienceDaily reported on a 2009 study that looked at how past changes in climate have been affected by the Earth's magnetic field. Geophysicist Mads Faurschou Knudsen, who co-authored the study, stated that the study's results supported Svensmark's theory. The authors of the study also acknowledged that CO
    2
    plays an important role in climate change.

    Consensus view on cosmic rays

    The view that cosmic rays could provide the mechanism by which changes in solar activity affect climate is not supported by the literature. Solomon et al. (2007) state:
    [..] the cosmic ray time series does not appear to correspond to global total cloud cover after 1991 or to global low-level cloud cover after 1994. Together with the lack of a proven physical mechanism and the plausibility of other causal factors affecting changes in cloud cover, this makes the association between galactic cosmic ray-induced changes in aerosol and cloud formation controversial
    Studies by Lockwood and Fröhlich (2007) and Sloan and Wolfendale (2008) found no relation between warming in recent decades and cosmic rays. Pierce and Adams (2009) used a model to simulate the effect of cosmic rays on cloud properties. They concluded that the hypothesized effect of cosmic rays was too small to explain recent climate change. Pierce and Adams (2009) noted that their findings did not rule out a possible connection between cosmic rays and climate change, and recommended further research. 

    Erlykin et al. (2009) found that the evidence showed that connections between solar variation and climate were more likely to be mediated by direct variation of insolation rather than cosmic rays, and concluded: "Hence within our assumptions, the effect of varying solar activity, either by direct solar irradiance or by varying cosmic ray rates, must be less than 0.07 °C since 1956, i.e. less than 14% of the observed global warming." Carslaw (2009) and Pittock (2009) review the recent and historical literature in this field and continue to find that the link between cosmic rays and climate is tenuous, though they encourage continued research. US EPA (2009) commented on research by Duplissy et al. (2009):
    The CLOUD experiments at CERN are interesting research but do not provide conclusive evidence that cosmic rays can serve as a major source of cloud seeding. Preliminary results from the experiment (Duplissy et al., 2009) suggest that though there was some evidence of ion mediated nucleation, for most of the nucleation events observed the contribution of ion processes appeared to be minor. These experiments also showed the difficulty in maintaining sufficiently clean conditions and stable temperatures to prevent spurious aerosol bursts. There is no indication that the earlier Svensmark experiments could even have matched the controlled conditions of the CERN experiment. We find that the Svensmark results on cloud seeding have not yet been shown to be robust or sufficient to materially alter the conclusions of the assessment literature, especially given the abundance of recent literature that is skeptical of the cosmic ray-climate linkage

    Loop quantum gravity (partial)

    From Wikipedia, the free encyclopedia

    Loop quantum gravity (LQG) is a theory of quantum gravity attempting to merge quantum mechanics and general relativity, including the incorporation of the matter of the standard model into the framework established for the pure quantum gravity case. LQG competes with string theory as a candidate for quantum gravity, but unlike string theory is not a candidate for a theory of everything.

    According to Einstein, gravity is not a force – it is a property of spacetime itself. So far, all attempts to treat gravity as another quantum force equal in importance to electromagnetism and the nuclear forces have failed, and loop quantum gravity is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force. To do this, in LQG theory space and time are quantized analogously to the way quantities like energy and momentum are quantized in quantum mechanics. The theory gives a physical picture of spacetime where space and time are granular and discrete directly because of quantization just like photons in the quantum theory of electromagnetism and the discrete energy levels of atoms. An implication of a quantized space is that a minimum distance exists.

    The structure of space prefers an extremely fine fabric or network woven of finite loops. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale on the order of a Planck length, approximately 10−35 metres, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure.

    The vast areas of research involve about 30 research groups worldwide. They all share the basic physical assumptions and the mathematical description of quantum space. Research has evolved in two directions: the more traditional canonical loop quantum gravity, and the newer covariant loop quantum gravity, called spin foam theory. 

    The most well-developed consequences of the theory apply to cosmology, called loop quantum cosmology (LQC), the study of the early universe and the physics of the Big Bang. Its greatest consequence sees the evolution of the universe continuing beyond the Big Bang called the Big Bounce.

    History

    In 1986, Abhay Ashtekar reformulated Einstein's general relativity in a language closer to that of the rest of fundamental physics. Shortly after, Ted Jacobson and Lee Smolin realized that the formal equation of quantum gravity, called the Wheeler–DeWitt equation, admitted solutions labelled by loops when rewritten in the new Ashtekar variables. Carlo Rovelli and Lee Smolin defined a nonperturbative and background-independent quantum theory of gravity in terms of these loop solutions. Jorge Pullin and Jerzy Lewandowski understood that the intersections of the loops are essential for the consistency of the theory, and the theory should be formulated in terms of intersecting loops, or graphs.

    In 1994, Rovelli and Smolin showed that the quantum operators of the theory associated to area and volume have a discrete spectrum. That is, geometry is quantized. This result defines an explicit basis of states of quantum geometry, which turned out to be labelled by Roger Penrose's spin networks, which are graphs labelled by spins.

    The canonical version of the dynamics was put on firm ground by Thomas Thiemann, who defined an anomaly-free Hamiltonian operator, showing the existence of a mathematically consistent background-independent theory. The covariant or spin foam version of the dynamics developed during several decades, and crystallized in 2008, from the joint work of research groups in France, Canada, UK, Poland, and Germany, leading to the definition of a family of transition amplitudes, which in the classical limit can be shown to be related to a family of truncations of general relativity. The finiteness of these amplitudes was proven in 2011. It requires the existence of a positive cosmological constant, and this is consistent with observed acceleration in the expansion of the Universe.

    General covariance and background independence

    In theoretical physics, general covariance is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws. A more significant requirement is the principle of general relativity that states that the laws of physics take the same form in all reference systems. This is a generalization of the principle of special relativity which states that the laws of physics take the same form in all inertial frames.

    In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth. These are the defining symmetry transformations of General Relativity since the theory is formulated only in terms of a differentiable manifold.

    In general relativity, general covariance is intimately related to "diffeomorphism invariance". This symmetry is one of the defining features of the theory. However, it is a common misunderstanding that "diffeomorphism invariance" refers to the invariance of the physical predictions of a theory under arbitrary coordinate transformations; this is untrue and in fact every physical theory is invariant under coordinate transformations this way. Diffeomorphisms, as mathematicians define them, correspond to something much more radical; intuitively a way they can be envisaged is as simultaneously dragging all the physical fields (including the gravitational field) over the bare differentiable manifold while staying in the same coordinate system. Diffeomorphisms are the true symmetry transformations of general relativity, and come about from the assertion that the formulation of the theory is based on a bare differentiable manifold, but not on any prior geometry — the theory is background-independent (this is a profound shift, as all physical theories before general relativity had as part of their formulation a prior geometry). What is preserved under such transformations are the coincidences between the values the gravitational field takes at such and such a "place" and the values the matter fields take there. From these relationships one can form a notion of matter being located with respect to the gravitational field, or vice versa. This is what Einstein discovered: that physical entities are located with respect to one another only and not with respect to the spacetime manifold. As Carlo Rovelli puts it: "No more fields on spacetime: just fields on fields". This is the true meaning of the saying "The stage disappears and becomes one of the actors"; space-time as a "container" over which physics takes place has no objective physical meaning and instead the gravitational interaction is represented as just one of the fields forming the world. This is known as the relationalist interpretation of space-time. The realization by Einstein that general relativity should be interpreted this way is the origin of his remark "Beyond my wildest expectations". 

    In LQG this aspect of general relativity is taken seriously and this symmetry is preserved by requiring that the physical states remain invariant under the generators of diffeomorphisms. The interpretation of this condition is well understood for purely spatial diffeomorphisms. However, the understanding of diffeomorphisms involving time (the Hamiltonian constraint) is more subtle because it is related to dynamics and the so-called "problem of time" in general relativity. A generally accepted calculational framework to account for this constraint has yet to be found. A plausible candidate for the quantum hamiltonian constraint is the operator introduced by Thiemann.

    LQG is formally background independent. The equations of LQG are not embedded in, or dependent on, space and time (except for its invariant topology). Instead, they are expected to give rise to space and time at distances which are large compared to the Planck length. The issue of background independence in LQG still has some unresolved subtleties. For example, some derivations require a fixed choice of the topology, while any consistent quantum theory of gravity should include topology change as a dynamical process.

    Wednesday, November 6, 2019

    Last Glacial Maximum

    From Wikipedia, the free encyclopedia
     
    A map of sea surface temperature changes and glacial extent during the last glacial maximum
     
    The Last Glacial Maximum (LGM) was the most recent time during the Last Glacial Period that ice sheets were at their greatest extent. Vast ice sheets covered much of North America, Northern Europe, and Asia and profoundly affected Earth's climate by causing drought, desertification, and a large drop in sea levels. According to Clark et al, growth of ice sheets commenced 33,000 years ago and maximum coverage was between 26,500 years and 19-20,000 years ago, when deglaciation commenced in the Northern Hemisphere, causing an abrupt rise in sea level. Decline of the West Antarctica ice sheet occurred between 14,000 and 15,000 years ago, consistent with evidence for another abrupt rise in the sea level about 14,500 ka ago.

    The LGM is referred to in Britain as the Dimlington Stadial, dated by Nick Ashton to between 31,000 and 16,000 years. In the archaeology of Paleolithic Europe, the LGM spans the Aurignacian, Gravettian, Solutrean, Magdalenian and Périgordian cultures. 

    The LGM was followed by the Late Glacial Interstadial.

    Glacial climate

    Evolution of temperatures in the Post-Glacial period according to Greenland ice cores.
     
    Temperature proxies for the last 40,000 years.
     
    According to Blue Marble 3000 (a video by the Zurich University of Applied Sciences), the average global temperature around 19,000 BC (about 21,000 years ago) was 9.0 °C (48.2 °F). This is about 6.0 °C (10.8°F) colder than the 2013-2017 average. 

    According to the United States Geological Survey (USGS), permanent summer ice covered about 8% of Earth's surface and 25% of the land area during the last glacial maximum. The USGS also states that sea level was about 125 meters (410 feet) lower than in present times (2012).

    When comparing to the present, the average global temperature was 15.0 °C (58.9 °F) for the 2013-2017 period. Currently (as of 2012), about 3.1% of Earth's surface and 10.7% of the land area is covered in year-round ice.

    The formation of an ice sheet or ice cap requires both prolonged cold and precipitation (snow). Hence, despite having temperatures similar to those of glaciated areas in North America and Europe, East Asia remained unglaciated except at higher elevations. This difference was because the ice sheets in Europe produced extensive anticyclones above them.

    These anticyclones generated air masses that were so dry on reaching Siberia and Manchuria that precipitation sufficient for the formation of glaciers could never occur (except in Kamchatka where these westerly winds lifted moisture from the Sea of Japan). The relative warmth of the Pacific Ocean due to the shutting down of the Oyashio Current and the presence of large 'east-west' mountain ranges were secondary factors preventing continental glaciation in Asia.

    All over the world, climates at the Last Glacial Maximum were cooler and almost everywhere drier. In extreme cases, such as South Australia and the Sahel, rainfall could be diminished by up to 90% from present, with florae diminished to almost the same degree as in glaciated areas of Europe and North America. Even in less affected regions, rainforest cover was greatly diminished, especially in West Africa where a few refugia were surrounded by tropical grasslands.

    The Amazon rainforest was split into two large blocks by extensive savanna, and the tropical rainforests of Southeast Asia probably were similarly affected, with deciduous forests expanding in their place except on the east and west extremities of the Sundaland shelf. Only in Central America and the Chocó region of Colombia did tropical rainforests remain substantially intact – probably due to the extraordinarily heavy rainfall of these regions. 

    A map of vegetation patterns during the last glacial maximum.
     
    Most of the world's deserts expanded. Exceptions were in what is now the western United States, where changes in the jet stream brought heavy rain to areas that are now desert and large pluvial lakes formed, the best known being Lake Bonneville in Utah. This also occurred in Afghanistan and Iran, where a major lake formed in the Dasht-e Kavir

    In Australia, shifting sand dunes covered half the continent, whilst the Chaco and Pampas in South America became similarly dry. Present-day subtropical regions also lost most of their forest cover, notably in eastern Australia, the Atlantic Forest of Brazil, and southern China, where open woodland became dominant due to drier conditions. In northern China – unglaciated despite its cold climate – a mixture of grassland and tundra prevailed, and even here, the northern limit of tree growth was at least 20° farther south than today.

    In the period before the Last Glacial Maximum, many areas that became completely barren desert were wetter than they are today, notably in southern Australia, where Aboriginal occupation is believed to coincide with a wet period between 40,000 and 60,000 years Before Present (BP, a formal measurement of uncalibrated radiocarbon years, counted from 1950 CE).

    World impact

    During the Last Glacial Maximum, much of the world was cold, dry, and inhospitable, with frequent storms and a dust-laden atmosphere. The dustiness of the atmosphere is a prominent feature in ice cores; dust levels were as much as 20 to 25 times greater than now. This was probably due to a number of factors: reduced vegetation, stronger global winds, and less precipitation to clear dust from the atmosphere. The massive sheets of ice locked away water, lowering the sea level, exposing continental shelves, joining land masses together, and creating extensive coastal plains. During the last glacial maximum, 21,000 years ago, the sea level was about 125 meters (about 410 feet) lower than it is today.

    Europe

    Northern Europe was largely covered by ice, the southern boundary of the ice sheets passing through Germany and Poland. This ice extended northward to cover Svalbard and Franz Josef Land and northeastward to occupy the Barents Sea, the Kara Sea and Novaya Zemlya, ending at the Taymyr Peninsula.

    In northwestern Russia the Fennoscandian Ice Sheet reached its LGM extent 17 ka BP, five thousand years later than in Denmark, Germany and Western Poland. Outside the Baltic Shield, and in Russia in particular, the LGM ice margin of the Fennoscandian Ice Sheet was highly lobate. The main LGM lobes of Russia followed the Dvina, Vologda and Rybinsk basins respectively. Lobes originated as result of ice following shallow topographic depressions filled with a soft sediment substrate.

    Permafrost covered Europe south of the ice sheet down to present-day Szeged in Southern Hungary. Ice covered the whole of Iceland and almost all of the British Isles with the exception of southern England. Britain was no more than a peninsula of Europe, its north capped in ice, and its south a polar desert.

    Asia

    There were ice sheets in modern Tibet (although scientists continue to debate the extent to which the Tibetan Plateau was covered with ice) as well as in Baltistan and Ladakh. In Southeast Asia, many smaller mountain glaciers formed, and permafrost covered Asia as far south as Beijing. Because of lowered sea levels, many of today's islands were joined to the continents: the Indonesian islands as far east as Borneo and Bali were connected to the Asian continent in a landmass called Sundaland. Palawan was also part of Sundaland, while the rest of the Philippine Islands formed one large island separated from the continent only by the Sibutu Passage and the Mindoro Strait.

    Africa and the Middle East

    In Africa and the Middle East, many smaller mountain glaciers formed, and the Sahara and other sandy deserts were greatly expanded in extent.

    The Persian Gulf averages about 35 metres in depth and the seabed between Abu Dhabi and Qatar is even shallower, being mostly less than 15 metres deep. For thousands of years the Ur-Shatt (a confluence of the Tigris-Euphrates Rivers) provided fresh water to the Gulf, as it flowed through the Strait of Hormuz into the Gulf of Oman.

    Bathymetric data suggests there were two palaeo-basins in the Persian Gulf. The central basin may have approached an area of 20,000 km2, comparable at its fullest extent to lakes such as Lake Malawi in Africa. Between 12,000 and 9000 years ago much of the Gulf floor would have remained exposed, only being flooded by the sea after 8,000 years ago.

    It is estimated that annual average temperatures in Southern Africa were 6 °C lower than at present during the Last Glacial Maximum. This alone would however not have been enough to create a widespread glaciation or permafrost in the Drakensberg Mountains or the Lesotho Highlands. Seasonal freezing of the ground in the Lesotho Highlands might have reached depths of 2 meter or more below the surface. A few small glaciers did however develop during the Last Glacial Maximum, in particular in south-facing slopes. In the Hex River Mountains, in the Western Cape, block streams and terraces found near the summit of Matroosberg evidences past periglacial activity which likely occurred during the Last Glacial Maximum.

    Australasia

    The Australian mainland, New Guinea, Tasmania and many smaller islands comprised a single land mass. This continent is now referred to sometimes as Sahul.

    Between Sahul and Sundaland – a peninsula of South East Asia that comprised present-day Malaysia and western and northern Indonesia – there remained an archipelago of islands known as Wallacea. The water gaps between these islands, Sahul and Sundaland were considerably narrower and fewer in number.

    The two main islands of New Zealand, along with associated smaller islands, were joined as one landmass. Virtually all of the Southern Alps were under permanent ice, with glaciers extending into much of the surrounding high country.

    North America

    In North America, the ice covered essentially all of Canada and extended roughly to the Missouri and Ohio Rivers, and eastward to Manhattan. In addition to the large Cordilleran Ice Sheet in Canada and Montana, alpine glaciers advanced and (in some locations) ice caps covered much of the Rocky Mountains further south. Latitudinal gradients were so sharp that permafrost did not reach far south of the ice sheets except at high elevations. Glaciers forced the early human populations who had originally migrated from northeast Siberia into refugia, reshaping their genetic variation by mutation and drift. This phenomenon established the older haplogroups found among Native Americans, and later migrations are responsible for northern North American haplogroups.

    On the Island of Hawaii, geologists have long recognized deposits formed by glaciers on Mauna Kea during recent ice ages. The latest work indicates that deposits of three glacial episodes since 150,000 to 200,000 years ago are preserved on the volcano. Glacial moraines on the volcano formed about 70,000 years ago and from about 40,000 to 13,000 years ago. If glacial deposits were formed on Mauna Loa, they have long since been buried by younger lava flows.

    South America

    During the Last Glacial Maximum valley glaciers in the southern Andes (38–43° S) merged and descended from the Andes occupying lacustrine and marine basins where they spread out forming large piedmont glacier lobes. Glaciers extended about 7 km west of the modern Llanquihue Lake but not more than 2 to 3 km south of it. Nahuel Huapi Lake in Argentina was also glaciated by the same time. Over most Chiloé glacier advance peaked in 26,000 yrs BP forming a long north-south moraine system along the eastern coast of Chiloé Island (41.5–43° S). By that time the glaciation at the latitude of Chiloé was of ice sheet type contrasting to the valley glaciation found further north in Chile.

    Despite glacier advances much of the area west of Llanquihue Lake was still ice-free during the Last Glacial Maximum. During the coldest period of the Last Glacial Maximum vegetation at this location was dominated by Alpine herbs in wide open surfaces. The global warming that followed caused a slow change in vegetation towards a sparsely distributed vegetation dominated by Nothofagus species. Within this parkland vegetation Magellanic moorland alternated with Nothofagus forest, and as warming progressed even warm-climate trees begun to grow in the area. It is estimated that the tree line was depressed about 1000 m relative to present day elevations during the coldest period, but it rose gradually until 19,300 yr BP. At that time a cold reversal caused a replacement of much of the arboreal vegetation with Magellanic moorland and Alpine species.

    Little is known about the extent of glaciers during Last Glacial Maximum north of the Chilean Lake District. To the north, in the dry Andes of Central and the Last Glacial Maximum is associated with increased humidity and the verified advance of at least some mountain glaciers.

    In the Southern Hemisphere, the Patagonian Ice Sheet covered the whole southern third of Chile and adjacent areas of Argentina. On the western side of the Andes the ice sheet reached sea level as far north as in the 41 degrees south at Chacao Channel. The western coast of Patagonia was largely glaciated, but some authors have pointed out the possible existence of ice-free refugia for some plant species. On the eastern side of the Andes, glacier lobes occupied the depressions of Seno Skyring, Seno Otway, Inútil Bay, and Beagle Channel. On the Straits of Magellan, ice reached as far as Segunda Angostura.

    Inequality (mathematics)

    From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Inequality...