Accurate climate models require a thorough understanding of how much light is reflected by clouds and the Earth's surface. These studies shed light on how land cover and clouds impact the global energy balance.

Experimental and theoretical investigations of the effect of aerosols, particularly those released during volcanic eruptions, have allowed for the reliable modeling of cooling periods throughout history.

The development of box diffusion models provided a useful, tunable way to represent the exchange of heat between the atmosphere and ocean in climate models.

Some authors, like Sherwood Idso, argued that scientists were vastly overestimating global warming. These claims were based on simplified atmospheric models, which neglect important features of Earth's energy balance. In 2016, global warming was measured to be 1.00°C above the 20th century average, consistent with the conventional models.

Experimental studies are vital to the construction of accurate climate models. These studies include measurements of the absorption of radiation by gases, aerosols, and the Earth's surface to supply parameters for programs that predict energy flows through the atmosphere.

Hansen, Manabe, and others performed extensive work creating models to represent the atmosphere and predict its response to the emission of greenhouse gases.

Estimates of the available oil and gas reserves have grown with advances in petroleum extraction technologies. While this may stave off fuel scarcity, the abundance of available petroleum magnifies the potential climate impact of the greenhouse gases which would result from its use.

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The emission of chlorofluorocarbons in the 20th century led to substantial loss of the ozone layer before the chemicals were widely banned. Since the passage of the Montreal Protocol which restricts the release of ozone-depleting substances, the ozone layer has healed a great deal of the damage.

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While observations of global warming were less certain at the time of this paper's publication, it is now clear that growing temperatures reflect the expected impact of increasing greenhouse gas emissions.

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Climate simulations even today are subject to a high degree of uncertainty in the range of ecological and geological impacts. While warming is already ongoing and certain to continue for some time, there are likely to be several indirect effects which are difficult to predict before they begin.

The rate of global warming due to the emission of greenhouse gases is greater than any previously known warming period.

The estimate of greater than 2°C of warming by the end of the 21st century is consistent with current expectations.

Global warming results in substantial spatial variation in precipitation. It is predicted that some regions will become much drier and others will become much wetter.

At the time of this paper's publication, there was too much year-to-year variability in temperature measurements to be certain that greenhouse effect warming was already occurring. The model predicts that the overall trend of increased temperatures would be clearer within the decade.

The observed warming since then has risen much further above the noise, and it is now clear that the earth is getting hotter due to the influence of greenhouse gases.

Carbon dioxide has such a great warming potential that increasing its concentration in the atmosphere will result in higher temperatures even if solar output and volcanic eruptions contribute substantially to cooling.

A model that includes only carbon dioxide and volcanic aerosols as inputs produces predictions that agree well with observation. This indicates that these two factors are the primary drivers of the observed climate variation.

The ocean's ability to spread heat into deeper layers has a large impact on the greenhouse effect. By varying this mixing rate and observing how well the model agrees with real observations, the authors find an optimal value to use for further testing.

The authors' atmospheric model is able to produce estimates of temperature change due to the greenhouse effect, which appear to be reliable for a period of several years after a major perturbation.

If the ocean were not able to buffer sudden impacts of atmospheric changes on the climate, volcanic eruptions would cause intense global cooling in the short term.

While the overall warming of the observed period is consistent with predictions, the year-to-year variability cannot be explained by carbon dioxide concentration alone.

At the time of this paper's publication, many mistakenly believed that the earth's climate was cooling. This reconstruction of the global temperature record shows that, while the Northern Hemisphere cooled between 1940 and 1970, this trend did not persist at larger scales. Indeed, by 1981, this localized cooling had been almost entirely reversed.

This model predicts that the atmosphere will warm due to increasing carbon dioxide, but the change in surface temperature also depends strongly on the presence of other gases, suspended particles in air, and variations in solar light output. These factors must also be considered to ensure the accuracy of any predictions.

The predictions of global warming by this model are subject to uncertainty relating to the heat capacity of the ocean. However, even the lower estimate indicates substantial increases in surface temperature over the following decades.

The ocean can only diffuse heat to deeper levels at a finite rate. If the ocean is able to vertically mix at a faster rate, more of the heat in the atmosphere can be absorbed into water rather than contribute to the surface temperature. This reduces the contribution of greenhouse gas concentration to warming in the short term.

Using the best model from the earlier comparisons (Model 4), the authors find that the climate reaches equilibrium in response to doubling carbon dioxide in about six years. This is an indicator of the time it takes for changes in greenhouse gas concentrations to have their full effect on global climate.

Because the authors have developed a model which is simpler than other atmospheric simulations, its reliability must be verified. If it agrees with more complex models, this is a good sign that it captures the important factors.

Since the authors' model produces estimates across the globe, it is able to reveal stark regional changes in addition to overall averages.

This model predicts that even large changes in the energy balance that counteract warming due to greenhouse gases will only have a partial effect. These predictions generally agree with observations recorded since the time of publication.

The authors' predictions of warming due to greenhouse gas emissions are generally in line with observed warming since this paper's publication (1981) as well as modern simulations.

The authors use the model to compare energy scenarios in which we use varying amounts of coal, oil, and gas (which emit greenhouse gases) to meet future electricity demand. These scenarios include replacement by either nuclear energy or alternative synthetic fuels. The scenarios also vary in how quickly fossil fuels are removed from the energy mix.

It is difficult to predict future trends in energy consumption, so the authors decide on several scenarios to show the range of possible outcomes in the temperature trend.

Since the authors' model now agrees well with observation, they use it to generate predictions about future temperature trends due to increasing carbon dioxide emissions. To estimate future conditions, they primarily consider emissions due to the energy sector.

Most of the variation in temperature is found to be the result of changes in the energy balance by carbon dioxide concentration and aerosol emissions from volcanic eruptions. This indicates these two factors are the most important in modeling temperature trends.

By varying the unknown parameters and observing when the model best fits the empirical results, the authors find fitted values for those parameters.

By including the best possible values for the parameters in their equation for heat flow, the authors model the temperature trend for the previous century and compare it to the reconstructed global temperature history. The agreement between these results is a good indicator of the reliability of the model.

The authors combine the model results into a single equation which relates the flow of heat into the earth's surface with dependence on solar radiation output, aerosol concentrations and properties, and temperature change.

The ocean takes several years to come into balance with the atmosphere and ground once carbon dioxide concentrations increase. This causes a substantial time delay in the warming of the air due to the greenhouse effect.

When carbon dioxide concentration increases, the model predicts that less radiation is emitted to space. Therefore, after a short increment of time, the stratosphere cools. The troposphere remains roughly the same temperature because the ocean is still absorbing much of the warming.

The authors look at how each component of the energy balance changes when carbon dioxide concentration changes.

The authors observe the impact of regional phenomena on the global energy balance. They observe the model's response to seasonal changes in temperature and solar irradiation of the surface. This test shows agreement between the model and real observations.

The slow response time of the ocean to changes in the energy balance reduces the impact of short-term phenomena, like cooling due to the emission of aerosols from volcanic eruptions.

The authors look at a specific volcanic eruption to verify that the observed effect of the resulting aerosols (suspended solid particles in air, here composed of ash and soot) is consistent with the effect predicted by their model. They confirm that the expected cooling is consistent between measurements and their predictions.

The reconstructed temperature record agrees with the overall expected warming due to carbon dioxide emissions. However, other factors clearly contribute to the year-to-year variations.

The authors verify that their reconstructed temperature record is in agreement with records produced by other methods to show that the chosen formula is reliable.

There is substantial variation in individual weather records as air fronts move and interact with one another. The authors average the data for each subsequent five-year period so that short-term trends interfere less with the visibility of long-term trends.

The authors attempt to reconstruct the global temperature history by taking records from weather stations and applying them to a grid of cells dividing the planet's surface. This helps account for the uneven distribution of weather measurements and provides general trends for the previous century.

The effect of greenhouse gases other than carbon dioxide is significant for warming. Although carbon dioxide is the largest contributor, gases like methane have a much higher effect per amount released.

Increasing albedo (light reflected by the land) reduces warming by causing solar radiation to be reflected back out to space rather than absorbed by the surface.

Stratospheric aerosols can reduce warming by blocking incoming solar radiation.

The authors introduce a number of factors other than carbon dioxide to the model to observe their impact on warming. These components all affect the earth's energy balance in some way: increases in solar output and other greenhouse gases increase warming, whereas stratospheric aerosols and increased surface reflectance reduce warming.

Overall global warming depends on the ability of the ocean to diffuse heat from the surface to deeper water. By varying the ocean's ability to mix, the authors obtain upper and lower bounds for the likely warming as carbon dioxide concentrations increase.

If the ocean has a higher heat capacity (it can store more heat with a lower change in temperature), it can partially buffer overall surface warming due to carbon dioxide.

The feedback mechanisms increase the amount of warming but not the rate of heat flow, so it will take the oceans longer to reach the increased temperature.

Because the models all predict the same flow of heat into the ground (column F in Table 1) if the surface temperature is held constant, this means that the heat flow into the ocean must also not change.

The change in temperature as carbon dioxide levels grow is only calculated for changes relative to the early 1980s (when this paper was published). The authors also note that effects occurring over decades or centuries are not considered, as they are assumed to contribute little to the timescale of the projections in this article.

The change in temperature with respect to changes in carbon dioxide concentration in the authors' chosen model is judged to be reliable, partially because it is similar to values generated by more complex calculations.

Model 4 is chosen as the best model for estimating temperature sensitivity to carbon dioxide levels, as the moist adiabatic lapse rate introduced in Model 3 underestimates the temperature response at high latitudes. Furthermore, the overestimation of the effect of cloud temperature is judged to roughly balance the effects of underestimating feedback from snow/ice and vegetation.

In order to estimate how much temperature and reflection of light by plants feed into one another, the authors compare current vegetation levels to models of a previous ice age. During an ice age, one would expect vegetation to be at a minimum, so the difference between climate then and now should be partially due to the difference in plant cover.

The final two models incorporate important feedback mechanisms: as the climate warms, snow and ice melt, reducing the amount of light that is reflected out to space. This causes warming to increase even further since more light is absorbed by the surface and atmosphere. The amount of the surface covered by vegetation also responds to temperature and ice cover.

This model is different from the previous ones, because clouds are now allowed to move between altitudes as their temperature changes instead of remaining at a fixed level. This causes the clouds to always emit the same amount of thermal radiation, limiting the total outgoing radiation from cloudy regions.

This model is distinct from the previous one, in that the decrease in temperature with altitude is not a fixed value. Rather, it depends on temperature more strongly due to the consideration of how water condenses as a parcel of air rises.

From this point forward, the authors fix relative humidity in the models (warmer air holds more water) because it causes the calculations to have better agreement with more complex models.

The second model fixes relative humidity (the amount of water in the air, relative to how much water the air can hold at most) rather than absolute humidity (the amount of water per unit volume of air). This means that warmer air will hold more water than cooler air.

The simplest model shows the effects of only radiation and convection in the atmosphere. The difference between these results and a fuller, more complicated model reveals the total impact of feedback mechanisms, including reflectance off of snow and plants.

Many factors contribute to the energy balance of the atmosphere. The authors evaluate the effect of each by running the model, inserting the various elements one at a time. The difference in the output after each factor is added gives a measure of its importance to the climate predictions in general.

Carbon dioxide absorbs some frequencies more strongly than others. These calculations consider absorption from strong and weak bands of carbon dioxide's absorption spectrum, even though the strongest band is the major contributor to the gas' warming potential.

These calculations account for light that is scattered multiple times as it propagates through air. The model also considers frequencies of light where multiple gases are capable of absorption.

Toon and Pollack designed a model which gave global averages for the size distribution, chemical composition, and optical opaqueness of aerosols in the troposphere and stratosphere.

Large changes in temperature over small vertical distances are unlikely to occur in the real world, so the model is constrained to avoid too steep a slope in the altitude/temperature curve.

The amount of light thatis absorbed, emitted, and scattered by the atmosphere is different for different frequencies of light, so these calculations must be done in parallel for each frequency. The contributions to the energy balance can then be added together.

This model considers the dependence of variables on time by only considering time intervals of fixed duration. This permits the modeling of the atmosphere's response to stimuli without requiring more complicated calculus-based methods.

Observing conditions on other planets allows us to generalize conclusions about Earth, as we cannot conduct a true experiment on the entire atmosphere of Earth to see how different factors are related.

The effective radiating temperature would be the temperature of the surface if only the surface were absorbing and emitting radiation. However, gases in the atmosphere also absorb and emit, so the average altitude from which outgoing radiation originates is somewhere above the surface, and T(e) is the temperature at that altitude.

This model assumes that the Earth emits exactly as much radiation as it absorbs over the long term.

Finding equations that accurately describe historical climate change allows the authors to generate predictions about the future. It is important to look at a variety of approaches to see how the predictions of different models vary.

By constructing mathematical models of climate change, the authors can simulate how different atmospheric effects are related to one another. They can also observe how different models agree and disagree with each other, which allows for the selection of the best model by comparison with measurements.

Satellite measurements have greatly expanded the availability of precision measurements of solar luminosity and other external factors that determine climatic conditions on Earth.

A model of melting sea ice was constructed to account for heat flow in and out of ice, seasonal snow variations, and movement of ice packs. This model was used to predict the effects of a warming atmosphere on the Arctic Ocean.

Climatic conditions thousands of years ago have been studied extensively by combining geological evidence with computational climate models.

Global temperature trends are affected by a large number of factors on short time scales. This variation from year to year can obscure long-term trends until they grow sufficiently large to rise above the noise. Statistical methods like these can be used to predict such trends and estimate when they will be clearly visible.

The structure of sunspots was correlated with temperature variations on Earth. This correlation was argued to be due to sunspots reducing the amount of radiation emitted by the Sun.

Sunspots are darker, cooler areas of the sun's surface. The umbra is the darkest part of a sunspot, at its center. It is surrounded by the lighter penumbra.

The Mount Agung eruption provided an opportunity for researchers to collect data on stratospheric aerosols and compare the resulting climate effects with theoretical models. This work provided evidence for the viability of climate models for predicting atmospheric responses to large perturbations.

Early estimates of global cooling underrepresented climate trends in the Southern Hemisphere. Better data collection and analysis of data from stations south of the equator helped to correct these calculations.

Chlorofluorocarbons (CFCs), previously used as refrigerants, were predicted to deplete stratospheric ozone by a series of rapid chain reactions. This effect was shown to be the primary cause of widespread ozone depletion, resulting in the adoption of the Montreal Protocol, which banned the use of CFCs globally in 1987.

Even chlorofluorocarbons, which are relatively low in abundance, have been estimated to have significant climate forcing effects.

Global temperature changes due to human modification of the land were estimated. These modifications include the clearing of forests, construction of settlements, and expansion of deserts.

Simple models based only on variation of solar radiation and volcanic eruptions agree well with other estimates of preindustrial temperatures, indicating that these factors contribute strongly to overall climate variation in the absence of forcing by greenhouse gases.

Historical global fuel consumption was used to estimate the amount of carbon dioxide in the atmosphere before reliable measurements were taken. This model estimates a concentration of 293 ppm in 1880.

Box diffusion models assume a well-mixed atmosphere and divide the ocean into surface and deep ocean boxes. Diffusion into the shallow ocean occurs much faster than diffusion into the deep ocean. These models outperform box models that only consider the ocean as a single reservoir.

Careful measurements of the radiation absorbed by different atmospheric gases have greatly improved the accuracy of climate models.

Radiative-convective models assume that the atmosphere maintains a balance between heating (by the surface and by condensation of water) and cooling (by radiation into space).

A complex computational model was constructed that considers geography, seasonal variation, and the circulation of heat and water across the entire globe. When the carbon dioxide concentration is increased quickly, the model predicts substantial heating of the Earth's surface.

Modeling of the effect of various manmade gases in the atmosphere showed that many pollutants absorb radiation that would otherwise be emitted to space. This causes energy to build up in the lower atmosphere, causing warming at the surface.

The interactions between the atmosphere, ocean, and land were modeled. These calculations showed that increased fossil fuel consumption was a much larger contributor to carbon dioxide levels than deforestation.

The altithermal, also known as the Holocene climatic optimum, was a warm period which occurred from around 9,000 to 5,000 years ago.

The mean radiating level is the average altitude at which radiation is emitted from Earth out to space.

In 1980, the United States experienced an intense heat wave that remains among the most destructive natural disasters in American history.

Paleoclimatology is the study of climate before direct measurements were taken. Analysis of samples from rock, ice, and trees can allow scientists to reconstruct climate patterns from hundreds to thousands of years ago.

Here, σ refers to standard deviation, a measure of the amount of variation in a dataset.

Smoothed datasets use approximations that combine points with their surrounding values in order to capture the largest patterns without small variations.

A posteriori means based on empirical evidence, rather than by theoretical deduction.

The correlation coefficient is a measure of how closely the variation in one quantity is related to the variation in another quantity. This value ranges from 0 to 1, with 0 indicating no correlation and 1 indicating perfect correlation.

A radiative forcing is a change in the energy flows in the atmosphere.

Solar insolation refers to the power per unit area received from the sun.

Mount Agung is an active volcano in Bali, Indonesia. Its eruption in 1963 sent debris 10 km into the air and killed over 1,000 people. The volcano experienced several smaller eruptions between 2017 and 2019.

Heterogeneous distributions are unevely spread out.

The stratosphere is the layer of the atmosphere above the troposphere. The stratosphere extends to around 50 km above sea level.

Optical thickness, or optical depth, is a measure of how much light can be transmitted through a material. The higher the optical thickness, the less light will make it through the substance.

The thermocline is the horizontal layer in a body of water where the change in temperature with depth is greater than the layers above or below. Most sunlight is absorbed by the ocean above the thermocline, and this is also where most of the turbulent mixing by waves occurs.

e-Folding time is the time interval in which a quantity increases by a factor of e, or about 2.72.

The Wisconsin ice age, also known as the Wisconsin glaciation, was a period of colder temperatures and glacier advance in North America. This glaciation occurred between 75,000 and 11,000 years ago.

The moist adiabatic lapse rate is the rate at which the temperature of a moist air parcel changes as it rises adiabatically (zero heat transfer).

Unlike the dry adiabatic lapse rate, the moist rate depends strongly on temperature. This is because cold air can hold less water than warm air, so as the parcel rises, water begins to condense and release heat to the air around it. This means that the moist rate is generally lower than the dry rate.

Absolute humidity is the ratio of the mass of water in a parcel of air to the volume of that parcel.

Relative humidity is the ratio of how much water is in the air to how much water the air can hold at the temperature of measurement.

The model sensitivity refers to how much the output changes for a given change in input. Here, we are interested in the amount of warming predicted for a doubling in carbon dioxide concentration.

Mie scattering theory is a model of light scattering that assumes that the particles scattering the light are spherical. This theory applies best when the particles have similar diameter to the wavelength of the incident light. Scattering in the lower 4,500 m of the atmosphere is well described by these equations.

The absorption coefficient of a substance is how efficiently it absorbs radiation at a given frequency.

The radiative transfer equation mathematically describes how a beam of radiation responds to absorption, emission, and scattering processes.

The divergence of a flux is a measure of how much some process flows in or out through a surface. If something is a source of the flow, its divergence will be positive, and if it is a sink, its divergence will be negative.

Heat capacity is the energy it takes to raise the temperature of a substance by a given amount (e.g., 1 degree). It usually has units of joules per mole per kelvin.

Convective stability is the ability of a mass of air to resist vertical motion (convection). When an atmosphere is unstable, air masses have larger vertical movements. In the extreme, this can create turbulence and sometimes severe weather.

Latent heat is heat transfer that is not accompanied by a change in temperature. This occurs when water condenses (releasing heat) or evaporates (absorbing heat).

This is the mechanism by which sweat cools our bodies, even though the temperature of the water remains the same before and immediately after evaporation.

An adiabatic process is one that occurs with no heat transfer between a system and its surroundings.

As an air mass rises or falls adiabatically, its temperature changes with altitude due to the change in pressure. The rate of this change for a dry air mass is the dry adiabatic lapse rate.

The troposphere is the lowest layer of Earth's atmosphere, extending from the surface to 13 km above ground on average. This layer contains most of the mass of the atmosphere and is where most weather phenomena take place.

The lapse rate is the rate at which temperature changes with altitude in the atmosphere.

Radiant flux refers to light emitted through a surface and has units of watts per square meter. A spherical object emitting radiation will have a radiant flux that gets smaller as one gets further from the source's center.

The Stefan-Boltzmann constant is a number used in the Stefan-Boltzmann law. This equation relates an object's temperature to the wavelengths of light it emits.

The constant's value is about 5.67 W / (m^2 K^4).

Albedo is the proportion of incoming light that is reflected back into space. This reflected light is in the visible and ultraviolet range, rather than the light emitted by Earth itself which is in the infrared.

Clouds and snow are responsible for much of the planet's albedo.

The greenhouse effect is the warming of Earth's surface due to the behavior of certain atmospheric gases, called greenhouse gases.

Greenhouse gases absorb and emit the same wavelengths of light (infrared) that are emitted by the planet's surface. This slows down the loss of heat energy to space.

An order of magnitude generally refers to a factor of ten. If two results disagree by an order magnitude or more, they are quite different from each other.

Radiative perturbations are changes to the balance of light energy exchanged between Earth and space.

The atmospheric window refers to the range of wavelengths of light that are emitted from Earth to space with little absorption by atmospheric gases.

Radiation in this range allows the Earth to get rid of excess heat energy from the Sun and maintain a constant temperature.

Anthropogenic pollutants are harmful substances released into the environment from human activities.

Carbon dioxide is one such pollutant, and is released from the burning of fossil fuels, such as coal and gasoline.

If a gas has a concentration in a mixture of one part per million (ppm), there is one particle of that gas for every million particles in the mixture.

The Northwest Passage is the sea route that connects the Atlantic and Pacific Oceans along the northern coast of North America.

Early European explorers believed the Northwest Passage could allow easy access to Asia, but the waters were too shallow and icy to be navigable.

The noise level in a dataset refers to the amount of natural variation that is present.

Solar luminosity is a measure of how much energy the Sun emits as light every second.

Aerosols are small particles of solid and liquid that are suspended in air.

When volcanoes erupt, they release a large quantity of aerosols. These aerosols can reflect sunlight back into space, cooling the ground below.