Samuel Pierpont Langley (1834-1906) was an American astronomer, physicist and inventor. His research on solar and lunar radiation greatly influenced Arrhenius.

Arrhenius used data from Langley's 1890 publication "The Temperature of the Moon" as the basis for his model.

Joseph Fourier (1768-1830) was a French scientist and mathematician who studied heat transfer. He theorized that Earth's atmosphere could act as a thermal insulator by absorbing heat (radiation) emitted by Earth's surface.

The amount of incoming energy from the sun changes drastically between night and day, and varies throughout the year, yet these variations don't affect Earth's surface temperatures as much as would be expected. Tyndall linked the ability of the atmosphere to absorb infrared radiation to this dampening of temperature variation.

The model predicted that atmospheric CO2 levels influence the temperature contrast between the seasons and between night and day. Lower CO2 levels increase the temperature contrast. Higher CO2 levels decrease the contrast.

Based on observations of the geological record, scientists estimated that the temperature in arctic regions during the warm Tertiary Period was 8 to 9 C higher than now.

Using the data generated by his model and summarized in Table VII, Arrhenius concluded that this temperature increase could have been caused by an atmospheric CO2 increase of 2.5 to 3 times current levels.

Arvid Hogbom (1857-1940), a Swedish geologist, was a colleague of Arrhenius, a professor at Stockholm University and a member of the Physical Society.

De Marchi seems to refer to the ability of the atmosphere to let through all wavelengths of radiation. He probably focused on the ability of water vapor in clouds to reflect incoming solar radiation, reducing how much solar energy reaches Earth's surface.

When Arrhenius discusses transparency in relation to his model, he focuses on the ability of water vapor to absorb infrared radiation and re-emit it back toward Earth's surface.

Luigi De Marchi was an Italian meteorologist. The work quoted here is from his prize-winning essay for a competition on the causes of the Ice Age.

A measure of the shape of an ellipse, how far it is flattened from a circular shape. An orbit with low eccentricity is almost circular, whereas an orbit with high eccentricity is highly elliptical.

Items 3, 5 and 9 in De Marchi's list make up the Milankovitch Cycles, which affect how much energy Earth receives from the Sun and how that energy is distributed over the globe.

For more information, see this resource from Climatica: http://climatica.org.uk/climate-science-information/long-term-climate-change-milankovitch-cycles

Also called "precession", this refers to the orientation of Earth's rotational axis relative to its position in its orbit around the Sun.

Items 3, 5 and 9 in De Marchi's list make up the Milankovitch Cycles, which affect how much energy Earth receives from the Sun and how that energy is distributed over the globe.

For more information, see this resource from Climatica: http://climatica.org.uk/climate-science-information/long-term-climate-change-milankovitch-cycles

The tilt of Earth's rotational axis relative to the plane of its orbit around the Sun.

Items 3, 5 and 9 in De Marchi's list make up the Milankovitch Cycles, which affect how much energy Earth receives from the Sun and how that energy is distributed over the globe.

For more information, see this resource from Climatica: http://climatica.org.uk/climate-science-information/long-term-climate-change-milankovitch-cycles

lowering

even more

This is a Latin phrase which translates as "from the stronger". Here, Arrhenius uses it to indicate that the remainder of the sentence presents an even stronger argument than the previous sentence.

unsupportable

namely; in other words

Claude Pouillet (1790-1868) was a French scientist who did research in a variety of areas, including meteorology. Pouillet expanded on Fourier's ideas about Earth's surface temperature and developed an equation for the thermal equilibrium between the atmosphere and the surface.

Because Earth is much colder than the sun, it emits radiation of longer wavelengths, mainly infrared. These are the "dark rays". Gases in the atmosphere can absorb some of these waves and "retain" their energy by re-emitting them back toward the ground.

Solar radiation includes ultraviolet (UV), visible, and infrared waves, with peak intensity in the visible range. The atmosphere absorbs little of the UV and visible waves, allowing them to pass through to reach the surface. These are the "light rays" Arrhenius refers to. Some of the incoming infrared waves are absorbed by the atmosphere.

John Tyndall (1820-1893) was an Irish scientist and professor of physics at the Royal Institution of Great Britain. Tyndall measured the ability of different atmospheric gases, including CO2 and water, to absorb and emit infrared radiation.

For Ice Age temperatures to occur, Arrhenius calculated that atmospheric CO2 levels must decrease to 0.62 to 0.55 times the current levels.

This calculation required him to extrapolate from the data in Table VII because the lowest case he modeled was CO2 at 0.67 times current level.

This is a concise statement of the question Arrhenius sought to answer with his model.

should be 5 - 10 instead of 5 - 0

Current estimates put the last maximum glaciation at 26,500 years ago.

The end of the most recent glaciation is now estimated to have occurred 11,700 years ago.

James Croll was a Scottish scientist who developed a theory linking the ice ages, including glacial and interglacial periods, to variations in Earth's position and orientation relative to the Sun.

To learn more about Croll and his work, see the following article published in the journal History of Meteorology: http://www.meteohistory.org/2006historyofmeteorology3/3fleming_croll.pdf

A geological period of reduced temperatures characterized by the presence of glaciers and polar ice sheets.

Earth is currently in the Quaternary Ice Age which marked the beginning of the Quaternary Period, 2.6 million years ago.

To learn more about ice ages, glacials and interglacials, see the following Wikipedia article: https://en.wikipedia.org/wiki/Ice_age

eliminated

Croll's work made important contributions to the understanding of Earth's climate. However, one problem with his theory was that it led to the conclusion that glacial periods occurred at different times in the Northern and Southern hemispheres.

We now know this is not correct; ice ages are global. But at the time Arrhenius wrote this paper, the geological record of the ice ages was not understood well enough to rule out this possibility of separate glacial periods in the hemispheres.

the area between 40 and 50 degrees of latitude

In the Northern Hemisphere this includes northern China and Japan, Mongolia, southern parts of the former USSR, Italy, the Balkan States, France, northern Spain, the northern United States and southern Canada.

In the Southern Hemisphere this is mainly open ocean. It includes New Zealand, the islands of Tasmania, and the southern part of South America.

An interglacial is a time during an ice age in which temperatures are somewhat warmer, when ice sheets and glaciers may retreat. Interglacials occur between glaciations, which are times when ice sheets and glaciers reach their maximum extent.

Earth is currently in an interglacial, the Holocene Epoch, which began 11,700 years ago.

The cold, dry period of an ice age in which ice sheets and glaciers reach their maximum extent.

Arrhenius uses this term interchangeably with "glacial period" and "glaciation".

pleasant, warm, mild climate

The Tertiary Period is the geological period prior to the current Quaternary Period (Quaternary Ice Age).

cloudiness

carbon dioxide (CO2) gas

Throughout the paper, Arrhenius refers to gaseous carbon dioxide as "carbonic acid", the common name used at that time. Today we distinguish between these two different, though related, chemical species. Carbonic acid (H2CO3) is produced when carbon dioxide (CO2) dissolves in and reacts with water, forming an equilibrium.

Founded in the early 1890's in Stockholm, Sweden, the society was a group of scientists who met regularly to discuss the current questions and latest findings in the physical sciences. Arrhenius was one of the founders and among those who were interested in "cosmic physics", which was similar to what we call "Earth science" today.

This note is from a different publication, an abstract of the paper. The abstract was published in a US journal (Publications of the Astronomical Society of the Pacific), and this note accompanied it. The note should not be included here.

This number may not be correct for the Philosophical Journal publication

"Ground", not "Earth"

Series 5, Volume 41, pp. 237-276

Philosophical Magazine and Journal of Science

Publication date should be April 1896

Introduction: Observations add colon

change 1 to I

This note references information provided by the authors that has been excluded from the main body of the paper to streamline it and save space in the journal. These supporting materials are made available online, instead: Supporting Online Material

The supporting materials include additional data tables, the complete list of references, and the Materials and Methods (MM) section. A MM section is a description of how the study was conducted so that 1) readers can evaluate the quality of the scientific methods, and 2) others can repeat the study to verify that the results are reproducible.

Here the MM section includes descriptions of how the studies were selected for the meta-analysis, the statistical tests that were used, and how the temperature changes and expected range shifts were calculated.

This reference is Chapter 1 of the Assessment Report Climate Change 2007 of the Intergovernmental Panel on Climate Change of the United Nations. Thousands of experts were involved in developing the report, which compiled and evaluated published research related to climate change and was reviewed by the governments of the member countries.

The chapter documents how climate change, especially increasing temperatures, is affecting many systems on Earth, including the physical characteristics and living organisms of land, freshwater, and oceans.

The authors examined the ranges of a wide variety of taxonomic groups in the United Kingdom between 1960 and 2000, a period during which the regional climate warmed. They studied many groups, including many invertebrate species, fish, mammals, birds, and herptiles.

Most of the taxonomic groups expanded their ranges to higher latitudes and/or elevations during the period. These range shifts were comparable to those identified in other studies for more well-documented species.

This study was an important source of data for the current meta-analysis.

This reference is Chapter 4 of the Assessment Report Climate Change 2007 of the Intergovernmental Panel on Climate Change of the United Nations. Thousands of experts were involved in developing the report, which compiled and evaluated published research related to climate change and was reviewed by the governments of the member countries.

The chapter summarized what was known at the time about the impact of climate change on the Earth's ecosystems. Among other effects, the authors estimated that 20 to 30% of animals and plants that were assessed face an increasing risk of extinction as global temperatures rise.

Predictions.

Here, prognoses is used to mean predictions of how a particular species will respond to a change in the climate of the area where it lives.

Here, novel refers to an ecosystem that is humanmade and doesn't occur naturally.

Loarie et al. found that spatial temperature gradients (degrees per distance) are larger for mountainous areas compared to flat areas. This means that, for the same change in temperature, a species that lives in a flat area must move much farther than one that lives in a mountainous area.

Therefore, the authors conclude that it should be easier for a species to keep up with climate change by changing elevation than by changing latitude, if distance is the only factor.

A measurement of the strength of a linear correlation (relationship) between two variables.

A coefficient value close to +1 indicates a strong positive linear correlation: When one variable increases, the other also increases. A value of 0 indicates no linear correlation.

As the climate warms, plants and animals may need to shift their ranges to keep living in a suitable climate. Because temperature gradients vary in different types of ecosystems, we expect the size of range shifts to be variable, too.

For example, two regions experience the same increase in temperature over a period of 20 years. The temperature gradients are 1.3° per 100 km in the first region and 0.9° per 100 km in the second. Species in the first region will have to move farther to maintain their climate than those in the second region.

The balance of some ecosystems may be upset by changes in temperature.

Extreme temperatures may limit survival of some species, such as plants which cannot tolerate freezing temperatures or animals which experience heat stress at high temperatures.

Changes in the timing of seasonal temperature may affect life cycles; for example, early springlike temperatures can change the timing of reproduction or migration.

A complex, interacting community of living organisms (plants, animals, microorganisms) and nonliving matter and energy.

Ecosystems can be very different in complexity and size. Some are small, like a decaying log or a home aquarium. Examples of large ecosystems are deserts, lakes, and rainforests.

One of the Prince Edward Islands in the southwestern Indian Ocean, between Africa and Antarctica.

These studies show that increases in temperature are linked to changes in the life cycles of plants and animals. The dates of seasonal events, such as blooming, migrating, and egg laying, have changed for many species as their habitat has warmed.

The studies have demonstrated a statistical relationship between temperature and the timing of life cycle events: Larger changes in event timing occur in areas with greater temperature changes.

References 1-8 link biodiversity declines to climate change by showing that extinctions occur or are predicted to occur in areas where the climate has warmed.

This risk of biodiversity loss is a reason that the current meta-analysis is important: Quantifying how species ranges respond to climate change will help scientists and policymakers predict and hopefully prevent biodiversity loss in the future.

A measure of how far north or south a point on Earth is, recorded in degrees. The latitude of the Equator is 0°.

Compared to lower latitudes, higher latitudes are farther from the Equator and tend to experience lower average temperatures and more seasonal climate variability.

This is a review article, which explains the current understanding of a topic based on a review and summary of the published literature. The authors summarized what was known at the time (2000) about the occurrence of extreme weather and climate events and their effects on human societies and natural systems.

This study combined analyses at both large and small scales to examine the role of climate warming in the extinction of amphibians in tropical regions of the Americas. The extinctions were previously attributed to an epidemic of a fungal disease.

The authors show that climate warming was a key factor in the extinctions. They propose that a warmer climate encourages growth of the fungus and thereby increases disease outbreaks.

This article examines evidence that effects of climate change may be underestimated. The authors show that population declines and range retractions may not be detected if a study does not evaluate the populations at a sufficiently small scale. More detailed studies can also help determine how much climate and other factors have contributed to the effects.

Most studies of the effects of climate on living organisms examine areas of a kilometer-scale size. However, organisms actually experience climate extremes on a much smaller scale.

This study demonstrates the extent of microclimate effects on temperature extremes. Variations in topography and vegetation type generated large local temperature differences in an area.

The authors state that these microclimate effects must be quantified and included in analyses to understand and predict the impacts of climate change on biodiversity.

The authors predicted the velocity of temperature change, a measurement of how annual average temperatures move over time, throughout the world. They found that predicted velocity varies widely depending on the type of topography; values ranged from 0.08 km per year to 1.26 km per year.

Plants and animals may need to shift their ranges along with the average temperature to keep living in a suitable climate. The authors determined that, in some cases, species will not be able to move their ranges fast enough to keep up with climate change.

This article addresses the difficulties the Intergovernmental Panel on Climate Change had reaching an agreement (in 2001) on the extent to which climate change is causing changes in biological systems. The authors suggest that differences in approach, particularly between biologists and economists, were a source of disagreement.

To bridge the gap between the disciplines, they used several analyses, combinations of biological and economic approaches, to analyze a large set of global biological data. They concluded that there is sufficient evidence to say with very high confidence that climate change is already affecting living systems.

The authors examined how changes in climate have influenced the timing of periodic life cycle events, such as leaves unfolding and fruit ripening. They analyzed a large set of data for European plants and a few animals, over the years 1971 to 2000.

They found that spring and summer life cycle events were happening earlier in the year and that these changes matched the patterns of climate warming.

This paragraph is the authors' summary of the results and conclusions of the paper.

Climate is only one of many factors that determine the range of a species. These other factors may alter the way a species responds to climate change.

In the following sentence, the authors give examples of this.

Climate change can produce changes in extreme temperatures in addition to, or instead of, changes in average temperatures. A species that is sensitive to extreme high or extreme low temperatures may respond to these extremes rather than to the average.

Because extremes may change at a different rate from averages, these species may not appear to track climate change when it is measured by average temperatures (as in the current analysis).

Different species have different traits that may affect how quickly they can shift their range boundaries in response to changing temperatures. These traits include reproduction rates, ability to move, and ability to thrive in different habitats.

Species that can thrive only in very specific environments which contain resources such as certain types of food or shelter.

This is in contrast to habitat generalists, species which can thrive in a variety of environments, making use of a variety of different resources.

Organisms that cannot move on their own, including most plants and some animals.

Although external forces can move these organisms, as when wind disperses seeds, it will be difficult for them to shift their range if new suitable habitat is too far away.

Relating to physiology, which is the study of how living systems work and the processes that keep a living organism alive.

Among individual species, there is much variation in range shift response to climate change. Therefore, the average range shift rates do not provide enough information to predict how an individual species will react to climate change.

On average, 22% to 25% of the species in each taxonomic group moved in a direction opposite to that expected based on the temperature change.

The latitudinal range shift variation among species within four typical taxonomic groups was evaluated in Figure 2. This was compared to the overall variation among all the latitude taxonomic groups in the meta-analysis.

The authors also calculated the percentage of species in each taxonomic group which moved in a direction opposite to that expected based on temperature change.

Related to a microclimate, which is the distinctive climate of a small area.

For example, a large boulder could create two microclimates: one on the side that gets more sun and is exposed to the wind, and the other on the side of the boulder that is mostly sheltered from the sun and wind. The two microclimates may contain different living organisms which prefer one or the other.

Related to topography, which describes the physical surface features of an area, such as the steepness of a slope.

Living organisms may prefer certain types of topography.

The observed elevation shifts are mostly smaller than the expected shifts. Elevation responses appear to lag behind climate change.

The authors express surprise at this result, and discuss possible reasons for it in the rest of the paragraph.

The observed latitudinal shifts match the expected shifts. The authors conclude that the average latitude responses are sufficient to track climate change.

The symbol is the Greek letter chi (pronounced "ki", as in kite).

Chi-squared is part of the chi-square goodness-of-fit test. Its purpose here is to measure how well a model describes a set of data.

If species are tracking climate change, then the observed range shifts should equal the expected range shifts. The authors did a chi-square (goodness-of-fit) statistical test to measure how well this 1:1 relationship describes the data.

Responding less than would be expected if climate change were the only factor.

In this context, lagging means having a range shift that is less than expected based on the temperature change.

Observed latitudinal range shifts had a positive, significant correlation with expected range shifts. The correlation of elevational range shifts was also positive, though less significant.

With these results, the authors demonstrated the direct statistical link between range shifts and levels of climate warming that was not demonstrated by previous studies.

This correlation test examined the relationship between observed range shifts and expected range shifts (based on temperature change patterns).

For an explanation of how the expected range shifts were calculated, please see the notes for Table S1.

The authors conducted a statistical correlation test to determine if there is a linear correlation (relationship) between range shifts and temperature changes.

A temperature gradient quantifies how temperature changes through space (spatial) or time (temporal).

Here the authors refer to a spatial gradient: how the annual average temperature changes with position (latitude or elevation). The gradient is measured in degrees Celsius per distance (kilometers or meters).

Taxonomic groups in locations with larger temperature increases made larger range shifts.

Researchers have documented that many species' ranges have shifted to higher latitudes and/or higher elevations during the same time period that the climate has warmed. However, they have not shown that the range shifts are statistically linked to the temperature change.

If species range shifts are directly linked to climate warming, we should find a positive trend between the two: the larger the temperature increase, the larger the range shift.

The balance of some ecosystems may be upset by changes in water balance.

Some organisms may not survive if rainfall or humidity is either too high or too low. Examples of moisture-limited ecosystems include deserts and rainforests.

The temperate and tropical zones are two of the three major climate zones on Earth.

See a map of the major climate zones here: climate zone map

The observed rates of range shift are significantly higher than those reported in Reference 14.

This analysis is an important update using the results of studies that were not yet available when the previous meta-analysis was done.

The authors did a one-sample t test to compare their range shift rates to those in Reference 14.

A meta-analysis, published in 2003, found range shifts in a large number of species, in directions consistent with climate change.

The p-value (P) is a measure of statistical significance, or how unlikely it is that the data are a result of random chance.

When a statistical test compares two situations, a small p-value indicates a very small probability that the situations are the same. We can then conclude that the situations are significantly different.

A one-sample t test is a statistical test that compares the mean of a sample set to a particular value. Its purpose is to determine if the sample set could have come from a larger group of data (a population) with that particular mean value.

In statistics, N is the number of data points in a group.

Standard error (SE) is a measure of variability within a set of data. The SE value is used in the calculation of statistical tests, such as the one-sample t test.

For each group in Table S1, the authors calculated a rate of range shift by dividing the observed range shift by the duration.

They found statistically significant rates of range shift both in latitude (median 16.9 kilometers poleward per decade) and elevation (median 11.0 meters uphill per decade).

For each group in Table S1, the authors calculated a rate of range shift by dividing the observed range shift by the duration.

The authors conducted the current study to determine if there is a positive trend between observed range shifts and climate warming. They performed a meta-analysis of a very large set of data for diverse species and geographic regions.

The data used in the meta-analysis are summarized in Tables S1a and S1b. Rates of range shift and statistical analyses were calculated as described in the notes for Table S1.

Living organisms grouped together because they share certain characteristics.

Taxonomic groups can range from very general, such as all plants, to very specific, such as a particular species of wasp.

One goal of this meta-analysis was to demonstrate this direct link between temperature change and range shifts.

Large studies have shown that land-based populations of many living organisms have shifted to higher latitudes and/or elevations as the climate has warmed during the 20th century. These studies include plants and animals in many different locations around the world.

A change in either the average climate of an area or the amount of climate variability, measured over a period of time.

In this paper, the authors use the change in annual average temperature as a measure of climate change.

A measure of the variety of individuals, species, and ecosystems in an environment.

Maintaining biodiversity is important because Earth's natural systems are highly interconnected. Losing species or altering ecosystems can have widespread consequences.

A change in location of the boundaries of a species' range.

In this paper, the ranges are defined by upper and lower boundaries of either latitude or elevation. A range shift can occur at either boundary or both.

In statistics, the median is the middle value in a group of data points. Half of the data points are less than the median, and half are greater than the median.

A statistical analysis of data combined from multiple scientific studies.

Combining data from many different studies can increase the statistical power of the results, reveal new patterns in the data, and help to minimize effects of error or bias in individual studies.

A measure of the height of a point on Earth above sea level.

Higher elevations, like mountains, tend to experience lower average temperatures than lower elevations.

Plants and animals that live most or all of their lives on land.

The area where a species is found.

The authors use the terms range, distribution, and geographic distribution interchangeably in this paper.