Turn pre-industrial-to-present CO₂, CH₄ and N₂O concentrations into radiative forcing (W/m²) and combine them with the equilibrium climate sensitivity ECS and SSP scenarios to see the equilibrium temperature rise, 2100 sea level rise and remaining carbon budget — in real time, using IPCC AR6 formulas.
Parameters
Current CO₂ concentration
ppm
2024 observation is about 420 ppm. Doubling (560 ppm) is the ECS reference
Pre-industrial CO₂
ppm
IPCC uses C0 = 278 ppm as standard. Default here is 280 ppm
SSP scenario
Future emissions pathway. Changes the 2100 warming projection
Climate sensitivity ECS
Equilibrium warming for a CO₂ doubling (K)
CH₄ concentration
ppb
Pre-industrial ~722 ppb, 2024 ~1900 ppb
N₂O concentration
ppb
Rising from 270 ppb pre-industrial due to fertilizer and combustion
Cloud cover
%
Visual parameter (cloud density in the animation)
Results
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CO₂ forcing (W/m²)
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CH₄ forcing (W/m²)
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N₂O forcing (W/m²)
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Total RF (W/m²)
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Equilibrium warming (K)
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2100 sea level rise (cm)
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Atmosphere, greenhouse gases and re-radiation
Shortwave solar radiation reaches the surface and the upward longwave radiation is partially absorbed and re-emitted by CO₂, CH₄ and N₂O. Colour intensity tracks the greenhouse effect at the given CO₂ level.
Cumulative CO₂ emissions (GtCO₂) inferred from the concentration gap; subtract from 1,400 GtCO₂ (2 °C reference) for the remaining budget.
Atmospheric CO₂ Radiative Forcing — ECS and IPCC AR6
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I keep hearing "radiative forcing" in climate news, but what exactly does that W/m² number measure?
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Good question. Radiative forcing (RF) is "how much extra energy the planet is gaining or losing at the top of the atmosphere, before the climate system has time to respond", reported in W/m². When you add CO₂ the outgoing longwave radiation gets harder to escape — that "missing" radiation is exactly the RF, and IPCC AR6 uses RF = 5.35·ln(C/C0) for CO₂. Plug in today's 420 ppm and you get ≈ 2.17 W/m². Think of it as turning on two extra 1-watt bulbs over every square meter of Earth.
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When I switch the climate sensitivity ECS from 2 K to 4.5 K, the warming more than doubles for the same CO₂. Why such a big spread?
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ECS is "how much equilibrium warming you get from a CO₂ doubling (≈ 3.71 W/m²)". IPCC AR6 has a best estimate of 3 K, a likely range of 2.5–4 K and a very likely range of 2.0–5.0 K. The spread comes mainly from cloud and water-vapour feedbacks, which are clearly positive but uncertain in strength. Using ΔT_eq = RF_total × ECS / F_2×CO₂ with default inputs, RF_total ≈ 2.99 W/m² and ECS = 3 gives λ ≈ 0.81 and ΔT ≈ 2.42 K. At ECS = 4.5 K, the same RF leads to 3.6 K.
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What do the numbers behind names like SSP2-4.5 and SSP5-8.5 actually mean?
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The trailing number is the 2100 radiative forcing target in W/m². SSP1-2.6 stabilises at about 2.6 W/m² (low emissions), while SSP5-8.5 reaches 8.5 W/m² (fossil-fuel intensive). IPCC AR6 central warming estimates are 1.8 °C for SSP1-2.6, 2.7 °C for SSP2-4.5, 3.6 °C for SSP3-7.0 and 4.4 °C for SSP5-8.5. Only SSP1-1.9 and SSP1-2.6 are compatible with the Paris 1.5 °C target. Sea level scales roughly as 25 cm per 1 °C, so the SSP5-8.5 world means ~110 cm by 2100 — serious coastal defence territory for Tokyo Bay, New York or the Dutch lowlands.
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The default settings give a "remaining carbon budget" of 309 GtCO₂. How fast does humanity burn through that?
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Global fossil CO₂ emissions are about 37 GtCO₂/yr (2023), or ~40 GtCO₂/yr including land-use change. The 1,400 GtCO₂ in the tool is the 2 °C (50% probability) budget; subtract the inferred cumulative 1,091 GtCO₂ and you get 309 GtCO₂ left. At 40 GtCO₂/yr that is 7–8 years. For 1.5 °C (about 500 GtCO₂), we are already roughly 591 GtCO₂ over budget — already used up. That is why IPCC asks for emissions to halve by 2030 relative to 2019.
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I tried doubling CO₂ (560 ppm) and got ΔT ≈ 3.7 K. Does that mean game over?
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No — the ΔT here is the equilibrium value if you hold the concentration forever. The ocean has a time constant of decades to centuries, so the actual warming lags. "If we stay at 560 ppm forever, we eventually reach 3.7 K" is the right reading. Large-scale CO₂ removal (direct air capture, reforestation, ocean alkalinity enhancement) could pull the value back. But tipping points (Amazon dieback, Greenland ice sheet, permafrost methane) make parts of that warming irreversible, so "you have less time than you think" is the safer attitude.
Frequently Asked Questions
Radiative forcing (RF) is the change in the net top-of-atmosphere radiation budget (W/m²) caused by a perturbation such as a change in greenhouse gas concentration, before the climate system responds. For CO₂, IPCC AR5/AR6 use RF = 5.35·ln(C/C0), with the pre-industrial reference C0 = 280 ppm. At today's ~420 ppm, RF_CO₂ ≈ 2.17 W/m²; adding CH₄, N₂O and other forcers gives a total of roughly 2.7–3.0 W/m². Positive RF warms the planet.
Equilibrium climate sensitivity (ECS) is the equilibrium warming for a doubling of CO₂ (about 3.71 W/m²). IPCC AR6 gives a best estimate of 3 °C and a very likely range of 2.0–5.0 °C. For the same total RF = 3 W/m², ECS = 2 K gives ≈ 1.6 °C, ECS = 3 K gives ≈ 2.4 °C and ECS = 4.5 K gives ≈ 3.6 °C. The uncertainty in ECS is one of the largest contributors to the spread of future projections.
SSPs (Shared Socioeconomic Pathways) combine socioeconomic assumptions with climate policy. Central 2100 warming estimates are about 1.8 °C for SSP1-2.6, 2.7 °C for SSP2-4.5, 3.6 °C for SSP3-7.0 and 4.4 °C for SSP5-8.5. Only SSP1-1.9 (not included here) and SSP1-2.6 are consistent with the Paris 1.5 °C target; SSP2-4.5 and above clearly overshoot it.
The remaining carbon budget is the additional cumulative CO₂ (GtCO₂) humanity can still emit before reaching a given temperature target. IPCC AR6 gives roughly 500 GtCO₂ for 1.5 °C (50% probability) and 1,400 GtCO₂ for 2.0 °C. Global emissions are about 40 GtCO₂/yr, so the 1.5 °C budget would be exhausted in 10–12 years. This tool subtracts cumulative emissions inferred from the concentration gap from the 1,400 GtCO₂ (2 °C) reference.
Real-world applications
Climate policy and NDC evaluation: The Paris Agreement requires each country to submit Nationally Determined Contributions (NDCs). Mapping them onto radiative forcing and warming formulas — much like the Climate Action Tracker does — answers the question "if every country meets its NDC, what is the 2100 warming?". Switching SSP scenarios in this tool gives an intuitive feel for the link between policy ambition and warming.
Carbon pricing and credit design: Distributing the remaining carbon budget over future years yields an estimate of the Social Cost of Carbon (SCC). The US EPA raised SCC to 190 USD/tCO₂ in 2023. A tighter remaining budget pushes SCC upward, which in turn shapes carbon taxes and cap-and-trade programmes.
Port and coastal infrastructure design: Sea level rise competes directly with the 50–100 year design life of major structures. The "2100 sea level rise" figure produced here (about 68 cm for SSP2-4.5) feeds into sea wall heights, storm surge barriers and underground flood protection. Tokyo Bay reclamation areas, the New York subway and Dutch dikes are already being redesigned around these numbers.
Agriculture and water resources: Warming beyond 2 °C reduces tropical and sub-tropical yields of staple crops (wheat, maize) by 10–25% according to IPCC AR6. Toggling ECS and SSP here is a starting point to discuss how to bake climate uncertainty into the migration of crop zones (e.g. rice moving north in Hokkaido), irrigation water demand and heat stress on livestock.
Common misconceptions and pitfalls
The first misconception is that "the RF formula is logarithmic, so adding more CO₂ saturates and stops mattering". The formula RF = 5.35·ln(C/C0) is indeed logarithmic, so the marginal RF per added ppm decreases. But it does not go to zero — at today's level dRF/dC = 5.35/C ≈ 0.013 W/m²/ppm. With CO₂ rising at 2.4 ppm/yr that is 0.031 W/m²/yr, or 0.31 W/m² per decade, which by itself produces ~0.25 K of committed warming. "It is logarithmic, so we can ignore it" is an order-of-magnitude mistake.
The second misconception is that "if ΔT_eq comes out as 2.4 K, we must already be 2.4 K warmer". The ΔT_eq reported here is the equilibrium value if the current concentration were held forever. In reality the ocean has a 40–200 year heat-transport time constant, so observed warming (about 1.2 °C in 2023) is only somewhat more than half of the eventual equilibrium. Stopping emissions today would still leave about 1 °C of committed warming on the way.
The third misconception is that "only CO₂ matters". The tool already shows non-trivial contributions from CH₄ (≈ 0.60 W/m²) and N₂O (≈ 0.22 W/m²). CH₄ has a short atmospheric lifetime (~12 years), making its cuts a fast lever — hence the Global Methane Pledge to cut 30% by 2030. Meanwhile sulphate and organic aerosols currently cool the planet by ~0.9 W/m²; cleaning up air pollution removes that mask and accelerates warming. A serious climate strategy must manage CO₂, short-lived climate pollutants and aerosols together.
How to Use
Enter current atmospheric CO₂ concentration (ppm) in the CO₂ field; typical current value is 420 ppm versus pre-industrial baseline of 280 ppm
Input CH₄ (methane) in ppb and N₂O (nitrous oxide) in ppb; current levels are approximately 1900 ppb and 335 ppb respectively
The simulator calculates radiative forcing (W/m²) for each gas using IPCC radiative transfer equations, then sums total RF and derives equilibrium warming (K) and 2100 sea level rise (cm)
Worked Example
Set CO₂ at 420 ppm (pre-industrial 280 ppm): forcing = 2.0 W/m². Add CH₄ at 1900 ppb (baseline 722 ppb): forcing = 0.48 W/m². Add N₂O at 335 ppb (baseline 270 ppb): forcing = 0.17 W/m². Total RF = 2.65 W/m², producing equilibrium warming of approximately 1.9 K and 2100 sea level rise of 38 cm using Myhre et al. (1998) parameterization with TCRE factor 0.55 K/(W/m²).
Practical Notes
IPCC AR6 uses non-linearity corrections for CO₂ forcing at high concentrations (>560 ppm); this simulator applies standard Myhre correction factor 5.35 ln(C/C₀)
Methane and N₂O forcing equations include overlap effects since atmospheric windows overlap; do not sum gas forcings naively
Sea level rise projections assume thermal expansion at 2 mm/year per W/m² of sustained forcing plus ice sheet dynamics; pre-2020 observations show 3.4 mm/year actual rise
Range sliders allow sensitivity analysis: CO₂ uncertainty typically ±10 ppm, CH₄ ±100 ppb reflects measurement variability across global networks