Radiative forcing is a way to measure changes in the balance of energy moving through a planet's atmosphere. This energy balance is affected by several factors, including the amounts of greenhouse gases and aerosols in the air, changes in how much sunlight is reflected by Earth's surface (called surface albedo), and changes in the amount of sunlight reaching Earth (solar irradiance). In scientific terms, radiative forcing is the difference between the energy coming into Earth's atmosphere and the energy leaving it, measured in watts per square meter (W/m²). This difference is caused by changes in external factors that influence Earth's climate, such as human activities. These external factors are different from natural changes and reactions that happen inside the climate system and can affect how much energy is absorbed or released. Scientists study radiative forcing at specific layers of Earth's atmosphere, such as the tropopause and stratopause. It is measured in watts per square meter and often described as an average over Earth's entire surface.

A planet that is in balance with its star and the rest of space has no net radiative forcing and maintains a stable temperature. Radiative forcing is not something that can be directly measured with a single tool. Instead, it is a scientific idea that scientists estimate using basic physics and observations of changes in the atmosphere. Scientists use data about changes in the atmosphere to calculate radiative forcing.

According to the IPCC, human activities have caused a radiative forcing of 2.72 W/m² in 2019 compared to 1750. This increase has warmed Earth's climate system. The warming is mainly due to higher levels of greenhouse gases, but some cooling has occurred because of increased aerosol levels.

Human activities have greatly increased the amount of greenhouse gases in the atmosphere, especially since about 1950. For example, carbon dioxide levels have increased by 50% since 1750 (from 1.0 to 1.5 times the original amount), which corresponds to a radiative forcing change of +2.17 W/m². If current trends continue, doubling carbon dioxide levels (from 1.0 to 2.0 times the original amount) in the coming decades would result in a radiative forcing change of +3.71 W/m².

Radiative forcing helps scientists compare how different human-caused greenhouse gases affect Earth's warming over time. Since the Industrial Revolution, the levels of long-lived and well-mixed greenhouse gases in Earth's atmosphere have increased. Carbon dioxide has the largest effect on total radiative forcing, while methane and chlorofluorocarbons (CFCs) have smaller effects over time. Five major greenhouse gases—water vapor, carbon dioxide, methane, nitrous oxide, and ozone—account for about 96% of the direct radiative forcing caused by long-lived greenhouse gases since 1750. The remaining 4% comes from 15 other less common gases.

Definition and fundamentals

Radiative forcing is described in the IPCC Sixth Assessment Report as the difference between energy entering Earth (from the Sun) and energy leaving Earth (into space), measured in watts per square meter (W/m²). This change happens because of factors that affect Earth's climate, such as changes in carbon dioxide (CO₂) levels, volcanic aerosols, or the Sun's energy output.

Earth's energy balance refers to how much energy the planet absorbs and how much it releases. This balance determines the planet's average temperature. When this balance changes, it is called radiative forcing. These changes can be caused by factors like the strength of sunlight, how much clouds or gases reflect light, how much greenhouse gases or surfaces absorb energy, or how materials emit heat. These changes, along with how the climate reacts, affect Earth's energy balance. This process happens constantly as sunlight reaches Earth, clouds and aerosols form, atmospheric gases change, and seasons alter Earth's surface.

Positive radiative forcing means Earth receives more energy from the Sun than it sends back to space. This extra energy causes global warming. Negative radiative forcing means Earth sends more energy into space than it receives, leading to cooling, or global dimming.

The movement of energy and matter in Earth's atmosphere is explained by principles of thermodynamics. In the early 20th century, scientists developed a detailed understanding of how energy moves through the atmosphere, which they applied to study the Sun and planets. Later, studies of radiative-convective equilibrium (RCE) helped scientists better understand how energy and materials like water move in Earth's atmosphere. These models improved scientists' ability to match observations with predictions.

Equilibrium models are also used to estimate how changes in Earth's system affect its state. RCE research led to a framework that connects changes in energy balance to climate responses, such as changes in Earth's surface temperature. This framework helped scientists calculate how sensitive Earth's climate is to changes, results that match those from General Circulation Models (GCMs). This method suggests that when energy balance is disturbed, the system slowly adjusts to reach a new balance. The term "radiative forcing" was used to describe these disturbances and became widely used in scientific writing by the 1980s.

The concept of radiative forcing has evolved since its first proposal, now called "instantaneous radiative forcing (IRF)." Other methods aim to better connect energy imbalances to global warming, such as changes in Earth's average surface temperature. In 2003, scientists explained how "adjusted troposphere and stratosphere forcing" can be used in models to study climate changes.

Adjusted radiative forcing calculates energy imbalances after adjusting stratospheric temperatures to reach a balance (zero energy gain or loss in the stratosphere). This method does not consider changes in the troposphere (the lower atmosphere) unless another definition, "effective radiative forcing (ERF)," is used. ERF is the main method recommended by CMIP6 studies, though adjusted methods are still used for cases where tropospheric changes are not critical, such as with well-mixed greenhouse gases and ozone. A method called the "radiative kernel approach" estimates climate feedbacks using a simplified calculation based on linear approximations.

Uses

Radiative forcing is a way to measure how different natural and human-caused factors affect Earth's energy balance over time. These factors can cause the planet to warm or cool in various ways. Radiative forcing helps compare the effects of each factor against others.

A related measure called effective radiative forcing (ERF) removes the influence of quick changes in the atmosphere that do not affect long-term temperature changes. ERF allows scientists to compare the effects of different climate change causes more fairly and understand how Earth's surface temperature responds to human activities.

Radiative forcing and climate feedbacks can be used together to estimate how much Earth's surface temperature might change in the long term (called "equilibrium"). This is done using a formula:

A number called λ (lambda) is used in the formula. It is usually measured in K/(W/m²), and ΔF represents the radiative forcing in W/m². An estimated value of λ ≈ 0.8 K/(W/m²) suggests that Earth's temperature would rise about 1.6 K above the 1750 reference level due to increased CO₂ levels (from 278 to 405 ppm, causing a forcing of 2.0 W/m²). It also predicts an additional 1.4 K warming if CO₂ levels doubled from their pre-industrial levels. These calculations assume no other factors are involved.

Historically, radiative forcing has been most useful for predicting changes caused by greenhouse gases. It is less helpful for other human-caused influences, such as soot.

Calculations and measurements

Earth's global radiation balance changes as the planet rotates and orbits the Sun, and as large temperature changes occur in the land, oceans, and atmosphere (e.g., ENSO). Because of these changes, the planet's "instantaneous radiative forcing" (IRF) also changes naturally over time, moving between states of overall warming and cooling. The natural changes caused by repeating and complex processes usually return to balance over periods lasting several years, resulting in an average IRF of zero. These natural changes can hide long-term (over decades) trends caused by human activities, making it harder to directly observe these trends.

Earth's radiation balance has been measured regularly since 1998 by NASA's Clouds and the Earth's Radiant Energy System (CERES) instruments. Each scan of the Earth provides an estimate of the total (all-weather) instantaneous radiation balance. This data shows both natural changes and human effects on IRF, including changes in greenhouse gases, aerosols, and land surfaces. The data also includes delayed responses to radiation imbalances, which occur mainly through Earth system feedbacks, such as changes in temperature, surface reflectivity, atmospheric water vapor, and clouds.

Scientists have used measurements from CERES, AIRS, CloudSat, and other satellite instruments in NASA's Earth Observing System to separate the effects of natural changes and system feedbacks. Removing these effects from the data over several years allows scientists to observe the human-caused trend in top-of-atmosphere (TOA) IRF. The analysis was done in a way that is efficient in calculations and does not rely on most related models. Radiative forcing was directly observed to increase by +0.53 W m (±0.11 W m ) from 2003 to 2018. About 20% of the increase was linked to fewer aerosols in the atmosphere, and most of the remaining 80% was due to more greenhouse gases.

A growing trend in radiative imbalance caused by rising global CO₂ levels has been observed by ground-based instruments. For example, measurements taken under clear-sky conditions at two Atmospheric Radiation Measurement (ARM) sites in Oklahoma and Alaska showed that surface dwellers experienced an increase in infrared heating of +0.2 W m (±0.07 W m ) during the decade ending in 2010. This result focuses only on longwave radiation and the most important forcing gas (CO₂), and it is smaller than the TOA forcing because some heat is absorbed by the atmosphere.

Radiative forcing can be studied based on factors outside the climate system. Basic estimates, summarized in the following sections, are based on the physics of matter and energy. Forcings (ΔF) are expressed as changes across the entire planet's surface over a specific time period. These estimates may be important for understanding global climate changes over decades or longer. Gas forcing estimates in the IPCC's AR6 report include adjustments for "fast" feedbacks (positive or negative) that occur through atmospheric responses (i.e., effective radiative forcing).

Forcing due to changes in atmospheric gases

For a greenhouse gas that is evenly mixed in the atmosphere, scientists use special computer programs to calculate how changes in its concentration affect the Earth's energy balance. These programs analyze how light interacts with the gas in the atmosphere. The calculations can be simplified into a mathematical formula that applies only to that specific gas.

A simple formula for carbon dioxide (CO₂) is:

where C₀ represents a standard concentration level in parts per million (ppm) by volume, and ΔC is the change in concentration in ppm. In some studies, such as those about how sensitive the climate is to changes, C₀ is set to the concentration before major human-caused changes, which was approximately 278 ppm in the year 1750.

Human activities have caused greenhouse gas levels in the atmosphere to rise quickly, especially since about the year 1950. For carbon dioxide, the increase in concentration from 1750 to 2020 (a 50% rise, where C/C₀ = 1.5) resulted in a total change in radiative forcing (ΔF) of +2.17 W/m². If current trends continue, a doubling of concentrations (C/C₀ = 2) in the coming decades would lead to a total change in radiative forcing (ΔF) of +3.71 W/m².

The relationship between CO₂ and radiative forcing follows a logarithmic pattern up to about eight times the current concentration level. This means that as CO₂ increases, the warming effect becomes smaller with each additional increase. However, this simple formula does not accurately describe the relationship at very high concentrations. CO₂ does not fully absorb infrared radiation, and the logarithmic pattern is influenced by the way CO₂'s molecular structure spreads out its absorption in the 15-μm wavelength range, a phenomenon linked to a property called Fermi resonance.

Other greenhouse gases, such as methane and N₂O, have different formulas for calculating their radiative forcing. Methane follows a square-root pattern, while CFCs follow a linear pattern. Specific values for these formulas can be found in reports from the Intergovernmental Panel on Climate Change (IPCC). A 2016 study suggested that the formula for methane in IPCC reports may need to be updated. Information about the radiative forcing caused by the most important greenhouse gases is included in sections discussing recent trends and the IPCC list of greenhouse gases.

Water vapor is currently the most important greenhouse gas in the atmosphere and is responsible for about half of all greenhouse gas forcing. Its concentration depends mostly on the Earth's average temperature. For every degree Celsius increase in temperature, water vapor levels could rise by up to 7% (see also: Clausius–Clapeyron relation). Over long time periods, water vapor acts as a feedback mechanism, increasing the warming effect caused by rising concentrations of carbon dioxide and other gases.

Forcing due to changes in solar irradiance

The total amount of solar energy reaching Earth, including all light wavelengths, is called Total Solar Irradiance (TSI). On average, this value is known as the solar constant and is about 1361 watts per square meter (W/m²) at Earth's average distance from the Sun, measured at the top of Earth's atmosphere. Earth's TSI changes based on solar activity, such as sunspots, and Earth's position in its orbit around the Sun. Since 1978, several satellite instruments, including ERB, ACRIM 1-3, VIRGO, and TIM, have measured TSI with increasing accuracy.

If Earth is considered a sphere, the area facing the Sun (πr²) is one-fourth of Earth's total surface area (4πr²). The average solar energy received per square meter of Earth's surface (I₀) is one-fourth of TSI, which is about 340 W/m².

Earth travels in an oval-shaped orbit around the Sun, so TSI varies throughout the year. At its farthest point (aphelion) in early July, TSI is about 1321 W/m², and at its closest point (perihelion) in early January, it is about 1412 W/m². This yearly variation of about ±3.4% has minor effects on weather and climate, which are mostly influenced by Earth's tilt. These yearly changes do not add or remove energy over long periods.

Over an 11-year cycle of sunspot activity, average TSI ranges between 1360 W/m² and 1362 W/m² (±0.05%). Sunspot activity has been studied since around 1600 and shows longer patterns, such as the Gleissberg and DeVries/Seuss cycles, which affect the 11-year cycle. Despite these patterns, the 11-year cycle remains the most noticeable variation.

Changes in TSI linked to sunspots contribute a small but measurable effect on climate over decades. Some studies suggest sunspots may have influenced climate changes during the Little Ice Age, along with volcanic activity and deforestation. Since the late 20th century, average TSI has slightly decreased as sunspot activity has declined.

Long-term changes in solar energy, such as those during Milankovitch cycles, affect Earth's climate over tens of thousands to hundreds of thousands of years. These cycles include changes in Earth's orbit shape, tilt, and the direction of its tilt. The 100,000-year cycle in orbit shape causes TSI to vary by about ±0.2%. Currently, Earth's orbit is becoming more circular, causing TSI to slowly decrease. These orbital changes are expected to remain stable for at least the next 10 million years.

Since forming about 4.5 billion years ago, the Sun has used about half of its hydrogen fuel. As the Sun ages, TSI will gradually increase by about 1% every 100 million years. This change is too slow to be noticed in human timescales.

The maximum changes in Earth's solar energy over the last decade are shown in the accompanying table. Each variation contributes a forcing calculated using Earth's reflectivity (R=0.30). Changes in solar energy are expected to have minor effects on climate, even if new solar physics is discovered.

Forcing due to changes in albedo and aerosols

A portion of sunlight that reaches Earth is reflected by clouds, aerosols, oceans, land, snow, ice, plants, and other natural or human-made surfaces. This reflected portion is called Earth's bond albedo (R). It is measured at the top of Earth's atmosphere and averages about 30% globally each year. The remaining 70% of sunlight is absorbed by Earth.

Clouds and water vapor in the atmosphere are the main contributors to Earth's albedo, with clouds alone accounting for about half. This is because most of Earth's surface is covered by liquid water. Clouds and water vapor form and move in complex patterns, influenced by ocean heat and wind systems like jet streams. Studies show that Earth's northern and southern hemispheres have nearly equal albedos, within 0.2%. This is notable because more than two-thirds of Earth's land and 85% of its human population are in the northern hemisphere.

Since 1998, satellite tools such as MODIS, VIIRS, and CERES have measured Earth's albedo. Landsat satellite images, available since 1972, have also been used in some research. Over time, measurements have become more accurate, allowing scientists to better understand recent changes in Earth's albedo. However, the data collected so far is not long enough to predict long-term trends or answer all related questions.

Earth's albedo changes seasonally due to natural cycles, such as Earth's tilt, which affects sunlight distribution. These changes are linked to shifts in vegetation, snow, and sea ice. Each year, Earth's albedo varies by about ±7% around its average value, with the highest values occurring near the two solar equinoxes. This cycle does not contribute to long-term climate changes because it balances out over time.

Albedo also changes yearly in different regions due to natural events, human activities, and feedbacks between systems. For example, cutting down forests usually increases Earth's reflectivity, while adding water storage or irrigation in dry areas can decrease it. In polar regions, melting ice lowers albedo, while desert expansion in lower latitudes raises it.

Between 2000 and 2012, no clear long-term trend in Earth's albedo was found in data from CERES. Some scientists believe the small yearly changes suggest that complex natural feedbacks may be keeping Earth's albedo stable. However, major events like large volcanic eruptions can temporarily and significantly change Earth's albedo for years.

Satellite data from the early 2000s show small yearly changes in Earth's albedo. These changes affect the amount of solar energy Earth absorbs. Despite recent changes caused by humans and nature, satellite observations suggest that natural feedbacks have kept Earth's albedo relatively stable. However, it is unclear whether these feedbacks will continue to balance changes over longer time periods.

Recent growth trends

The IPCC explained that scientists agree human activities have caused a radiative forcing of 2.72 [1.96 to 3.48] W/m² in 2019 compared to 1750. This has warmed the climate system, mainly because of higher greenhouse gas (GHG) levels, which are partly offset by cooling from more aerosols in the air.

Radiative forcing helps compare how different human-caused greenhouse gases contribute to warming over time.

Since the industrial revolution, radiative forcing from long-lived and well-mixed greenhouse gases has increased in Earth's atmosphere. The table lists direct effects from carbon dioxide (CO₂), methane (CH₄), nitrous oxide (N₂O), chlorofluorocarbons (CFCs) 12 and 11, and 15 other halogenated gases. These data do not include effects from shorter-lived gases, aerosols, or indirect influences like methane decay and some halogen changes. They also do not account for land use changes or solar activity.

These data show that CO₂ is the main contributor to total forcing, while methane and CFCs have become smaller contributors over time. Five major greenhouse gases account for about 96% of the direct radiative forcing from long-lived gases since 1750. The remaining 4% comes from the 15 minor halogenated gases.

In 2016, the total forcing was 3.027 W/m². Using a commonly accepted climate sensitivity value of 0.8 K/(W/m²), this would predict a global temperature increase of 2.4 K, which is much higher than the observed increase of about 1.2 K. Some of this difference is because the Earth has not yet fully warmed to match the forcing. The rest may be due to cooling from aerosols, lower climate sensitivity, or a mix of these factors.

The table also includes the "Annual Greenhouse Gas Index" (AGGI), which compares the total direct radiative forcing from long-lived greenhouse gases in any given year to the level in 1990. This year was chosen because it is the baseline for the Kyoto Protocol. The AGGI measures yearly changes in conditions affecting CO₂ emissions and absorption, methane and nitrous oxide sources and sinks, the decline in ozone-depleting chemicals linked to the Montreal Protocol, and the rise in their substitutes (hydrogenated CFCs (HCFCs) and hydrofluorocarbons (HFCs)). Most of the increase in AGGI is due to CO₂. In 2013, the AGGI was 1.34, meaning total direct radiative forcing had increased by 34% since 1990. CO₂ alone contributed a 46% increase in forcing since 1990. The decline in CFCs reduced the overall increase in radiative forcing.

Another table, used for comparing climate models, includes all types of forcing, not just greenhouse gases.