The Greenhouse Effect - AP Environmental Science

SECTION 1

Historical Context & Motivation

The idea that Earth's atmosphere acts as a thermal blanket is not a recent discovery—it stretches back nearly two centuries to the dawn of quantitative climate science. In the early nineteenth century, natural philosophers began asking a deceptively simple question: why is Earth's surface warmer than a simple radiative equilibrium calculation would predict? The answer, which we now call the greenhouse effect, involves the selective absorption and re-emission of infrared radiation by certain atmospheric gases. Understanding the historical trajectory of this concept is essential for appreciating both its scientific robustness and the policy urgency it now commands.

1824 • Fourier's Heat Hypothesis

Joseph Fourier proposed that Earth's atmosphere traps heat much like the glass of a hothouse, establishing the conceptual foundation for atmospheric energy balance studies.

1859 • Tyndall's Laboratory Proof

John Tyndall experimentally demonstrated that water vapor and CO₂ absorb infrared radiation far more effectively than N₂ or O₂, providing the first empirical evidence of selective absorption.

1896 • Arrhenius Quantifies Climate Sensitivity

Svante Arrhenius calculated that doubling atmospheric CO₂ would raise global mean temperature by approximately 5–6 °C, producing the first quantitative estimate of climate sensitivity.

1958 • Keeling Curve Begins

Charles David Keeling initiated continuous CO₂ monitoring at Mauna Loa Observatory, generating the iconic dataset that documents the relentless rise in atmospheric CO₂ concentration.

1988 • IPCC Established

The Intergovernmental Panel on Climate Change (IPCC) was created to synthesize peer-reviewed research, signaling a global scientific consensus that the enhanced greenhouse effect demands coordinated policy action.

From Fourier's initial qualitative insight to the IPCC's modern assessment reports, the greenhouse effect has evolved from a theoretical curiosity into the central mechanism driving contemporary climate policy. The core question that unites all of these milestones remains: How do trace atmospheric gases regulate the energy balance of an entire planet, and what happens when human activity alters their concentrations?

SECTION 2

Core Principles & Definitions

The greenhouse effect operates through a well-defined chain of radiative interactions between the Sun, Earth's surface, and the atmosphere. To fully grasp this process, you need to internalize several foundational concepts that appear repeatedly on the AP Environmental Science exam, including the distinction between incoming shortwave and outgoing longwave radiation, the role of specific gas molecules, and the difference between the natural and enhanced greenhouse effects.

Insolation & Shortwave Radiation

The Sun emits energy predominantly in the ultraviolet, visible, and near-infrared wavelengths (0.1–4 µm), collectively termed shortwave radiation. Roughly 70% of incoming solar radiation is absorbed by Earth's surface and atmosphere; the remaining 30% is reflected back to space (Earth's albedo).

Terrestrial Longwave Radiation

Earth's warmed surface re-emits energy as longwave infrared radiation (4–100 µm). Unlike shortwave radiation, these wavelengths are strongly absorbed by greenhouse gases, which is the fundamental asymmetry driving the greenhouse effect.

Greenhouse Gases (GHGs)

Molecules with three or more atoms—such as CO₂, CH₄, N₂O, and H₂O—possess vibrational modes that resonate with infrared wavelengths. These greenhouse gases absorb outgoing IR radiation and re-emit it in all directions, including back toward the surface.

Natural vs. Enhanced Effect

The natural greenhouse effect warms Earth from about −18 °C to +15 °C (a 33 °C increase). The enhanced (anthropogenic) greenhouse effect results from fossil fuel combustion, agriculture, and land-use change that elevate GHG concentrations beyond natural levels.

Radiative Forcing

Radiative forcing (measured in W/m²) quantifies the change in net energy flux at the top of the atmosphere caused by an external driver. A positive forcing warms the planet; a negative forcing cools it. Since 1750, cumulative anthropogenic forcing exceeds +2.7 W/m².

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KEY TAKEAWAY

Think of the atmosphere as an insulating layer around a house. Shortwave sunlight enters freely through the windows (the atmosphere is largely transparent to visible light). The interior surfaces absorb this energy and radiate heat (longwave IR). Greenhouse gases function like insulation in the walls—they intercept the outgoing heat and redirect some of it back inside. Adding more GHGs is like adding thicker insulation: the interior temperature rises until a new equilibrium is reached where outgoing energy once again matches incoming energy, but at a higher temperature.

SECTION 3

Visual Explanation — Earth's Energy Budget

The diagram above illustrates Earth's energy budget. Yellow arrows represent incoming shortwave solar radiation; roughly 30% is reflected (cyan) by clouds, aerosols, and bright surfaces. The remaining 70% heats Earth's surface, which re-emits energy as longwave infrared radiation (red arrows). Greenhouse gases in the atmosphere intercept a portion of this outgoing IR and re-emit it in all directions, including back toward the surface (pink arrow), producing the warming known as the greenhouse effect.

Several details in this diagram merit emphasis for exam preparation. First, note that the atmosphere is largely transparent to shortwave visible light but partially opaque to outgoing longwave infrared radiation—this asymmetry is the crux of the greenhouse mechanism. Second, the 33 °C warming (from −18 °C to +15 °C) attributed to the natural greenhouse effect is a figure commonly tested on the AP exam. Third, the balance between absorbed and emitted energy defines the planet's radiative equilibrium; when additional GHGs disturb this equilibrium, the planet must warm until outgoing energy once again matches incoming energy at the top of the atmosphere.

SECTION 4

Mathematical Framework — Radiation & Energy Balance

Although the AP Environmental Science exam does not require deriving climate models from first principles, a quantitative understanding of the Stefan-Boltzmann law and simple energy-balance calculations strengthens conceptual understanding and may appear in calculation-based free-response questions. Two equations are particularly relevant: the Stefan-Boltzmann law for thermal emission and the simplified planetary energy balance used to estimate equilibrium temperature.

STEFAN-BOLTZMANN LAW

E = σ × T⁴

E = radiant energy flux (W/m²), σ = Stefan-Boltzmann constant (5.67 × 10⁻⁸ W·m⁻²·K⁻⁴), T = surface temperature in kelvins (K). This law states that the total energy emitted per unit area by a blackbody is proportional to the fourth power of its absolute temperature.

PLANETARY ENERGY BALANCE (SIMPLIFIED)

S(1 − α) / 4 = σ × Tₑ⁴

S = solar constant (≈ 1361 W/m²), α = planetary albedo (≈ 0.30 for Earth), the factor of 4 accounts for the ratio of Earth's cross-sectional area to its total surface area, Tₑ = effective radiating temperature of the planet. Solving for Tₑ yields approximately 255 K (−18 °C), which is the temperature Earth would have without the greenhouse effect.

GLOBAL WARMING POTENTIAL (GWP)

GWP = (∫₀ᴴ aᵢ × [Cᵢ(t)] dt) / (∫₀ᴴ a_CO₂ × [C_CO₂(t)] dt)

GWP compares the cumulative radiative forcing of 1 kg of a greenhouse gas to 1 kg of CO₂ over a time horizon H (commonly 100 years). aᵢ = radiative efficiency of gas i, Cᵢ(t) = time-dependent atmospheric concentration after a pulse emission. For exam purposes, know the approximate 100-year GWP values: CH₄ ≈ 28, N₂O ≈ 265, CFCs > 1,000.

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EXAM TIP

The AP exam frequently asks you to compare greenhouse gases using GWP. Remember that while CO₂ has the largest total forcing due to its abundance, methane (CH₄) has a much higher per-molecule warming potential over 100 years. When calculating total CO₂ equivalents, multiply the mass of the gas by its GWP: CO₂eq = mass × GWP.

SECTION 5

Major Greenhouse Gases — Sources, Lifetimes & GWP

Not all greenhouse gases contribute equally to the enhanced greenhouse effect. Their relative importance depends on three factors: concentration in the atmosphere, radiative efficiency (how strongly they absorb IR per molecule), and atmospheric lifetime (how long they persist before being removed by chemical reactions or uptake). The table below summarizes the key properties of the most significant anthropogenic greenhouse gases, which is essential reference material for the AP exam.

Greenhouse Gas	Chemical Formula	Primary Anthropogenic Sources	Atmospheric Lifetime	100-yr GWP
Carbon dioxide	CO₂	Fossil fuel combustion, deforestation, cement production	Variable (centuries to millennia)	1 (reference)
Methane	CH₄	Livestock (enteric fermentation), rice paddies, landfills, natural gas leakage	≈ 12 years	28
Nitrous oxide	N₂O	Agricultural fertilizers, industrial processes, combustion	≈ 114 years	265
Chlorofluorocarbons	CFCs	Refrigerants, aerosol propellants (now regulated by Montreal Protocol)	45–1,700 years	4,660–10,200
Water vapor	H₂O	Evaporation (natural feedback, not directly controlled by emissions)	≈ 9 days	N/A (feedback gas)

Major greenhouse gases and their key properties relevant to the AP Environmental Science exam.

This horizontal bar chart shows the approximate contributions of major anthropogenic greenhouse gases to total radiative forcing since 1750, based on IPCC AR6 data. While CO₂ accounts for roughly 64% of the forcing, methane's 19% share is disproportionately large given its low atmospheric concentration, reflecting its high per-molecule radiative efficiency.

A critical distinction for the AP exam concerns water vapor. Although H₂O is the most abundant greenhouse gas and responsible for the largest fraction of the natural greenhouse effect, it functions primarily as a positive feedback rather than a forcing agent. As temperatures rise due to CO₂-driven warming, evaporation increases, which adds more water vapor to the atmosphere, amplifying the initial warming. Because water vapor's atmospheric residence time is only about 9 days (it precipitates out rapidly), its concentration is controlled by temperature rather than by direct human emissions, which is why it is classified as a feedback gas rather than a driver.

SECTION 6

Worked Example — CO₂ Equivalent Emissions

Many AP Environmental Science free-response questions require you to convert emissions of various greenhouse gases into CO₂ equivalents using Global Warming Potential (GWP). The following worked example walks through a common problem type involving a small dairy farm.

Calculating CO₂ Equivalent Emissions from a Dairy Farm

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Step 1 — Identify Given Values

A dairy farm emits 500 metric tons of CO₂ per year from energy use, 20 metric tons of CH₄ per year from enteric fermentation, and 2 metric tons of N₂O per year from manure management. The 100-year GWP values are: CO₂ = 1, CH₄ = 28, N₂O = 265.
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Step 2 — Apply the CO₂eq Formula

For each gas, multiply the mass emitted by its GWP to convert to CO₂ equivalents: CO₂eq = mass of gas × GWP.
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Step 3 — Calculate Each Gas

CO₂ contribution: 500 metric tons × 1 = 500 metric tons CO₂eq. CH₄ contribution: 20 metric tons × 28 = 560 metric tons CO₂eq. N₂O contribution: 2 metric tons × 265 = 530 metric tons CO₂eq.

CO₂: 500 t CO₂eq | CH₄: 560 t CO₂eq | N₂O: 530 t CO₂eq
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Step 4 — Sum Total CO₂eq Emissions

Total = 500 + 560 + 530 = 1,590 metric tons CO₂eq per year.

Total annual emissions = 1,590 metric tons CO₂eq
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Step 5 — Interpret the Result

Although the farm emits far less CH₄ and N₂O by mass than CO₂, these gases contribute more warming per kilogram. Methane alone accounts for 560/1,590 ≈ 35% of the farm's total CO₂eq footprint despite representing only about 3.8% of the mass emitted. This illustrates why targeting non-CO₂ greenhouse gases can yield significant climate benefits.

CH₄ ≈ 35% of total warming impact despite being < 4% of emissions by mass

SECTION 7

Feedbacks, Limitations & Common Misconceptions

The greenhouse effect does not operate in isolation—it is modulated by a network of climate feedbacks that can either amplify (positive feedback) or dampen (negative feedback) the initial temperature change. Understanding these feedbacks is critical for interpreting model projections and answering AP exam questions about climate sensitivity, tipping points, and uncertainty.

Feedback Mechanism	Type	How It Works
Water vapor feedback	Positive	Warming → more evaporation → more atmospheric H₂O → stronger IR absorption → more warming.
Ice-albedo feedback	Positive	Warming → ice/snow melts → lower albedo → surface absorbs more solar radiation → more warming.
Permafrost thaw	Positive	Warming → permafrost thaws → releases stored CO₂ and CH₄ → increased GHG concentrations → more warming.
Blackbody radiation (Planck response)	Negative	Warming → surface emits more IR (E ∝ T⁴) → increased energy loss to space → opposes further warming.
Cloud feedback	Uncertain	Low clouds reflect sunlight (cooling), high clouds trap IR (warming). Net effect depends on cloud type, altitude, and distribution—the largest source of uncertainty in climate models.

Key climate feedback mechanisms and their effect on greenhouse warming.

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COMMON MISCONCEPTION

The greenhouse effect is often conflated with ozone depletion—these are distinct phenomena. The greenhouse effect involves IR absorption by GHGs in the troposphere, while ozone depletion involves the destruction of stratospheric O₃ by halogenated compounds, which increases UV radiation reaching the surface. Although some ozone-depleting substances (like CFCs) are also potent greenhouse gases, the mechanisms and atmospheric layers involved are fundamentally different. The AP exam frequently presents answer choices that test whether you can distinguish between these two processes.

An atmospheric illustration shows incoming ultraviolet absorbed at stratospheric ozone. Surface-emitted infrared is absorbed by a greenhouse gas and re-emitted in two directions. Gas markers are distributed in the troposphere. Ozone shielding mainly concerns absorption of incoming ultraviolet radiation in the stratosphere. Greenhouse warming concerns infrared absorption and emission by gases distributed through the atmosphere, including the troposphere. Lines and markers are schematic, not solid atmospheric layers.

SECTION 8

Connections to Climate Change & Policy

The greenhouse effect is the physical mechanism underlying anthropogenic climate change, but the full picture involves additional layers of complexity studied in advanced atmospheric science and Earth system modeling. On the AP Environmental Science exam, you should be prepared to connect the greenhouse effect to broader topics such as ocean acidification, sea-level rise, shifting biome boundaries, and international policy frameworks. This section maps the foundational concepts from this lesson onto those advanced and applied topics.

Foundational Concept (This Lesson)	Advanced / Applied Topic	Exam Relevance
Radiative forcing from CO₂	Climate sensitivity (°C per doubling of CO₂)	FRQ may ask you to interpret graphs of projected warming under different emission scenarios (RCPs or SSPs).
CO₂ absorption by oceans	Ocean acidification (CO₂ + H₂O → H₂CO₃)	Tested as a secondary impact of elevated atmospheric CO₂; connects to coral reef decline and marine food webs.
Enhanced greenhouse effect → warming	Thermal expansion & ice sheet melt → sea-level rise	Multiple-choice and FRQ questions about coastal impacts and environmental justice.
GWP and CO₂ equivalents	Carbon footprint analysis & emissions trading (cap-and-trade)	Calculation FRQs may involve converting CH₄ or N₂O emissions to CO₂eq and proposing mitigation strategies.
Positive feedbacks (ice-albedo, water vapor)	Tipping points and climate thresholds	Critical thinking questions about non-linear system behavior and irreversible changes.

Mapping foundational greenhouse effect concepts to advanced topics and exam contexts.

International policy frameworks represent a direct application of greenhouse science to governance. The Paris Agreement (2015) aims to limit warming to well below 2 °C above preindustrial levels, with a stretch target of 1.5 °C, by requiring nationally determined contributions (NDCs) to reduce GHG emissions. The Kyoto Protocol (1997) was the first treaty to set binding emission targets for industrialized nations using CO₂ equivalents calculated from the same GWP framework covered in this lesson. When the AP exam asks about proposed solutions or policy evaluations, linking your answer back to the underlying physics of radiative forcing demonstrates the interdisciplinary thinking that earns full credit.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

Which of the following best explains why Earth's actual average surface temperature (approximately +15 °C) is significantly higher than the calculated effective radiating temperature (approximately −18 °C)?

A. The ozone layer absorbs ultraviolet radiation and converts it to heat in the troposphere.
B. Greenhouse gases absorb outgoing longwave infrared radiation and re-emit some of it back toward Earth's surface.
C. Earth's magnetic field traps solar wind particles that contribute additional thermal energy to the lower atmosphere.
D. Volcanic activity continuously adds heat from Earth's interior, raising the mean surface temperature by 33 °C.

Show answer (B)

B is correct. The 33 °C difference between the effective radiating temperature and Earth's actual surface temperature is due to the natural greenhouse effect: greenhouse gases (CO₂, H₂O, CH₄, N₂O, O₃) absorb outgoing longwave infrared radiation emitted by Earth's surface and re-emit a portion of it back downward, effectively trapping thermal energy in the lower atmosphere. A is incorrect because while ozone absorbs UV in the stratosphere, this process warms the stratosphere, not the troposphere, and does not account for the 33 °C discrepancy. C is incorrect because the magnetosphere deflects charged particles but does not contribute measurable thermal energy to the surface. D is incorrect because geothermal heat flux (≈ 0.09 W/m²) is negligible compared to the ~240 W/m² of absorbed solar energy.

Question 2: BASIC CALCULATION

A landfill releases 15 metric tons of methane (CH₄) per year. Using a 100-year GWP of 28 for CH₄, what is the annual emission in metric tons of CO₂ equivalents?

A. 43 metric tons CO₂eq
B. 280 metric tons CO₂eq
C. 420 metric tons CO₂eq
D. 4,200 metric tons CO₂eq

Show answer (C)

C is correct. CO₂eq = mass × GWP = 15 metric tons × 28 = 420 metric tons CO₂eq. A (43) appears to result from dividing 15 by 28 rather than multiplying—an arithmetic error in the wrong direction. B (280) would result from mistakenly multiplying only 10 metric tons by 28, perhaps misreading the given value. D (4,200) is off by a factor of 10, likely from misplacing a decimal. Remember: the GWP is a multiplicative conversion factor that expresses how many tons of CO₂ would produce the same warming as one ton of the gas in question.

Question 3: INTERMEDIATE

A positive feedback loop involving the ice-albedo effect operates as follows: warming temperatures cause ice to melt, exposing darker surfaces beneath, which absorb more solar radiation and cause further warming. Which of the following would represent a negative feedback that could partially counteract this positive feedback?

A. Increased ocean temperatures lead to greater evaporation, adding more water vapor (a greenhouse gas) to the atmosphere.
B. Warmer temperatures cause permafrost to thaw, releasing stored methane and carbon dioxide into the atmosphere.
C. Higher atmospheric CO₂ concentrations stimulate increased plant growth, which removes more CO₂ from the atmosphere through photosynthesis.
D. Melting of sea ice allows more heat absorption by dark ocean water, further accelerating ice loss in adjacent regions.

Show answer (C)

C is correct. CO₂ fertilization of plant growth is a negative feedback: higher CO₂ → increased photosynthesis → more CO₂ removed from the atmosphere → reduced greenhouse forcing → partially counteracts warming. A is incorrect because the water vapor feedback is a positive feedback—it amplifies warming rather than counteracting it. B is incorrect because permafrost thaw releases additional GHGs, constituting another positive feedback that amplifies warming. D is incorrect because it simply restates the ice-albedo positive feedback described in the question. On the AP exam, distinguishing positive from negative feedbacks requires identifying whether the response opposes (negative) or reinforces (positive) the initial perturbation.

Question 4: APPLIED

4 pts

A group of AP Environmental Science students hypothesizes that increasing CO₂ concentration in a sealed chamber will cause a measurable increase in air temperature when exposed to a heat lamp simulating solar radiation. (a) Identify the independent variable, dependent variable, and one controlled variable for this experiment. (1 point) (b) Describe a procedure the students should follow to test their hypothesis, including how they will vary the independent variable and measure the dependent variable. (2 points) (c) Explain how the students should establish a proper control group and why it is necessary. (1 point)

Show answer

RUBRIC (4 points total): (a) Variables — 1 point: • Independent variable: CO₂ concentration in the sealed chamber. • Dependent variable: Air temperature inside the chamber (measured with a thermometer or temperature probe). • Controlled variable: Any ONE of the following — distance from heat lamp, wattage of heat lamp, volume of chamber, initial temperature, duration of exposure, or type of chamber material. (Award 1 point for correctly identifying all three.) (b) Procedure — 2 points: • Point 1: The students should set up multiple sealed transparent chambers (or repeat trials with the same chamber). They introduce different known concentrations of CO₂ (e.g., ambient ~420 ppm, 600 ppm, 800 ppm, 1000 ppm) using a CO₂ source such as dry ice sublimation, baking soda and vinegar, or a compressed CO₂ tank, measured with a CO₂ sensor. • Point 2: They expose each chamber to the same heat lamp at the same distance for the same duration (e.g., 15 minutes), recording temperature at regular intervals (e.g., every minute) using a digital temperature probe. Multiple trials (at least 3) should be conducted at each CO₂ concentration, and results should be averaged. (c) Control group — 1 point: • The control group is a chamber filled with ambient air (approximately 420 ppm CO₂) exposed to the same heat lamp under identical conditions. This control is necessary to establish a baseline temperature increase against which the experimental chambers (with elevated CO₂) can be compared, ensuring that any observed temperature differences are attributable to the increased CO₂ concentration rather than to the heat lamp alone or other confounding variables.

Question 5: CRITICAL THINKING

4 pts

A country reports the following annual greenhouse gas emissions from its agricultural sector: • 800,000 metric tons of CO₂ from machinery and transportation • 50,000 metric tons of CH₄ from rice cultivation and livestock • 5,000 metric tons of N₂O from synthetic fertilizer application Use the following 100-year GWP values: CO₂ = 1, CH₄ = 28, N₂O = 265. (a) Calculate the total agricultural greenhouse gas emissions in metric tons of CO₂ equivalents. Show your work. (2 points) (b) The government proposes reducing CH₄ emissions from agriculture by 40% through improved livestock management practices. Calculate the reduction in CO₂ equivalents that this policy would achieve. (1 point) (c) A critic argues that the government should instead focus on reducing CO₂ emissions from agricultural machinery because CO₂ is the most abundant emission by mass. Evaluate this argument using your calculations from parts (a) and (b), and explain whether focusing on CH₄ reduction is a more effective climate strategy for this sector. (1 point)

Show answer

RUBRIC (4 points total): (a) Total CO₂eq calculation — 2 points: • Point 1 (individual conversions): CO₂: 800,000 × 1 = 800,000 metric tons CO₂eq CH₄: 50,000 × 28 = 1,400,000 metric tons CO₂eq N₂O: 5,000 × 265 = 1,325,000 metric tons CO₂eq • Point 2 (correct total): Total = 800,000 + 1,400,000 + 1,325,000 = 3,525,000 metric tons CO₂eq (b) CH₄ reduction — 1 point: 40% of CH₄ CO₂eq = 0.40 × 1,400,000 = 560,000 metric tons CO₂eq reduction. (Award 1 point for the correct calculation.) (c) Evaluation — 1 point: The critic's argument is flawed. Although CO₂ is the largest emission by mass (800,000 metric tons), its CO₂eq contribution (800,000 metric tons CO₂eq) is actually the smallest of the three gases in terms of climate impact. Methane contributes 1,400,000 metric tons CO₂eq—nearly 40% of the sector's total warming impact—despite constituting only about 5.8% of emissions by mass. A 40% reduction in CH₄ would eliminate 560,000 metric tons CO₂eq, which is 70% of the entire CO₂ contribution from machinery. This demonstrates that targeting high-GWP gases like methane can deliver larger climate benefits per unit of emission reduced, making it a more effective near-term strategy. Additionally, CH₄'s short atmospheric lifetime (~12 years) means reductions would yield faster temperature benefits compared to CO₂ reductions. (Award 1 point for a well-reasoned evaluation that references the calculated values and correctly explains why the mass-based argument is misleading.)

SUMMARY

Lesson Summary

Summary

The greenhouse effect is the process by which certain atmospheric gases—principally CO₂, CH₄, N₂O, H₂O, and O₃—absorb outgoing longwave infrared radiation emitted by Earth's surface and re-emit a portion of it back downward, raising the equilibrium surface temperature by approximately 33 °C (from −18 °C to +15 °C). This natural mechanism makes Earth habitable, but the enhanced (anthropogenic) greenhouse effect—driven by fossil fuel combustion, deforestation, agriculture, and industrial processes—is increasing GHG concentrations beyond natural levels, producing a positive radiative forcing that warms the global climate.

Key quantitative tools include the Stefan-Boltzmann law (E = σT⁴), the planetary energy balance equation, and Global Warming Potential (GWP) for converting emissions of different gases to CO₂ equivalents. Critical positive feedbacks—including the water vapor, ice-albedo, and permafrost thaw feedbacks—amplify initial warming, while the Planck (blackbody) response provides a stabilizing negative feedback. For the AP exam, remember to distinguish the greenhouse effect from ozone depletion, apply GWP calculations accurately, and connect the physics of radiative forcing to real-world policy solutions such as the Paris Agreement and cap-and-trade systems.