The Way Back Down: CO₂ Up and Down in Eight Climate Models

CO₂ went up and came back down. Did the climate?

The bold line is a 21-year average, which smooths out each model's weather. The control run is the same model with CO₂ held at the 1850 level the whole time. Every change on this page is measured from it.

The same CO₂, on the way up and on the way down

If the climate kept pace with CO₂, the two lines would lie on top of each other. The gap between them is the climate lagging behind.

Where the way down differs from the way up

Each map is a 21-year average, put onto boxes 3° on a side. The models' own grids differ, so the average of the models is taken box by box.

About this page

What the data show

In this experiment, CO₂ goes up and comes back down along the same path. Each level of CO₂ comes twice: once on the way up and once on the way down. If the climate kept pace with CO₂, it would be the same both times. It isn't. At twice and at three times the starting CO₂, the world is warmer on the way down than it was on the way up, in all eight models: by 0.1 to 2.2 °C at twice the start, and by 1.3 °C in the average of the models. Near today's level of CO₂, one model, NorESM2-LM, is a little cooler on the way down. When CO₂ is back where it started, the world is still 1.0 °C warmer than the control run, in the average of the models over the first 21 years.

The ocean is the main reason. It takes a long time to warm up and a long time to cool down. While CO₂ rises, the ocean soaks up heat, so the surface warms more slowly than it otherwise would. When CO₂ falls, the ocean still holds that heat, and the surface stays warm. So the climate lags behind CO₂, and on a graph against CO₂ the way up and the way down make a loop. Scientists call a loop like this hysteresis: where you are depends on the path that brought you there.

Rain and snow and Arctic sea ice lag too. At twice the starting CO₂, every model that shared its rain and snow has more of it on the way down, and most models have less Arctic sea ice. Sea level keeps rising while CO₂ falls, because the ocean keeps warming and warmer water takes up more room. The IPCC's Sixth Assessment Report shows the same experiment in its Figure 4.37, and finds that changes in key climate variables “substantially lag behind the decline in CO₂” (Lee and others, 2021, section 4.6.3.2).

The runs set the CO₂ in the air. The IPCC calls a fall this fast “unrealistic”: the experiment tests the climate system, and isn't a plan. And it doesn't say how much CO₂ would have to be taken out of the air to make CO₂ fall this way. The land and ocean would give back some of the carbon they took up while CO₂ was rising, so more would have to be removed than the drop in the air. Chapter 9 of the book explains why.

How to use this page

The page has three views of the data, and the tabs at the top move between them. Above them, the menu chooses one model or the average of the models.

"Over time" draws CO₂ in the air at the top and what the model did below, year by year. You choose what to show: surface air temperature, rain and snow, Arctic sea ice in September or sea level from warmer water. The bold line is the average of the 21 years around each year, and its color says what CO₂ was doing. The thin lines are single years, or, for the average of the models, each model's own bold line. The dashed line is the control run. Choose a year with the slider or by clicking the graph. The lines under the graph give its numbers and compare it with the year on the other side of the turn that had the same CO₂.

"Same CO₂, up and down" draws the same numbers against CO₂ instead of time. The way up is orange and the way down is blue. The green bar at the left covers the years after CO₂ was back where it started, from the lowest to the highest of their 21-year averages. Choose a level of CO₂ with the slider or by clicking the graph. The lines under the graph compare the 21 years around it on the way up with the 21 years on the way down that had the same CO₂.

"Map" shows where the changes are, for temperature or for rain and snow. Choose a level of CO₂, then the way up, the way down or the difference between them. Three more choices show the years around the turn and the years after CO₂ was back where it started. Point at the map, or tap it, to read the number for one place.

Under every graph, a few lines say in numbers what it shows.

The address in your browser changes as you move the controls, so you can bookmark a view or send it to someone. Nothing is sent anywhere as you work.

This page is part of the website for Climate Change: Simple, Serious, Solvable, an open textbook by Scott Denning. It goes with Chapter 9, "The One-Way Thermostat".

The experiment

Each model made three runs:

• The control run (piControl in CMIP6). The climate of 1850, held still for centuries, with CO₂ at 284 ppm. Every change on this page is measured from it, over the same years.
• The way up (1pctCO2 in CMIP6). From the control's climate, CO₂ rises 1% a year. After 140 years it is four times where it started, about 1,140 ppm.
• The way down (1pctCO2-cdr in CDRMIP). From four times the start, CO₂ falls 1% a year for 140 years, back to where it started. Then it is held there for at least 60 years.

Only CO₂ changes. The Sun, the volcanoes, the other greenhouse gases, the haze from pollution and the land stay as they were in 1850. The design is Keller and others' (2018), for the Carbon Dioxide Removal Model Intercomparison Project, CDRMIP. Each modeling group ran it on its own Earth system model, so the eight differ in their details.

The models that didn't share a number for both halves of the run are left out of that number. CAS-ESM2-0 ran the way down too, but it shared rain and snow and not temperature, and no rain and snow for the way up, so the two halves can't be compared. NorESM2-LM shared its rain and snow on the way down only day by day, and MIROC-ES2L shared no sea ice for the way down. The rain and snow, sea ice and sea level of CNRM-ESM2-1's way down, the sea level of GFDL-ESM4 and the sea ice of UKESM1-0-LL's way down couldn't be downloaded when this page was made, in November 2026. UKESM1-0-LL ran the way down for centuries; this page uses its first 340 years, the length the experiment asks for.

How the numbers are worked out

1. How much CO₂ is in the air?

C is CO₂ in parts per million (ppm), and C₀ is 284.317 ppm, the level CMIP6 uses for 1850. t is the time since the run started, in years. Each year multiplies CO₂ by 1.01: that's 1% a year. A year of the run is numbered e, from 1, and its middle comes at t = e − 0.5. CO₂ has doubled after about 70 years, and it is four times the start after about 139 years.

2. Which year on the way down matches a year on the way up?

B is the number of years CO₂ rose before the model turned it around. It's 140 for most of the models (see the table above). Year e on the way up and year d on the way down are the same distance from the turn, so CO₂ is the same in both. After year 2B, CO₂ is held at C₀.

3. How much did it change?

A model's climate drifts a little, even in its control run. So the control run's yearly values, over the same years as the experiment, get a straight line: c is the control's level in year e, and a and b make the line fit as closely as it can (by least squares). The change ΔX in a year is the value X that year minus the line. Temperature changes are in °C, and sea level changes in centimetres. Rain and snow are given as a percentage of the line:

Arctic sea ice is shown as it is, in millions of square kilometres, with the control's line drawn dashed.

4. What do the averages average?

• A year is the average of its 12 months, each counted by its number of days.
• The globe: each box of the model's grid counts by its area, so a box near the pole, which is small, counts for less than one at the equator.
• Arctic sea ice is September's: the area of ocean north of the equator covered by ice, adding up each box's share of ice times its area.
• Sea level from warmer water is the model's own global number for how much the ocean has expanded as it warmed (zostoga in CMIP6). It leaves out melting ice.
• The bold lines and every comparison use 21-year averages: a year and the 10 years each side of it. On the way down, the 21 years mirror those on the way up, so the two have the same CO₂ year for year.
• The maps are 21-year averages too, put onto boxes 3° on a side by averaging nine points a degree apart in each box.
• The average of the models lines them up by the turn. CanESM5 turned a year later than the others and MIROC-ES2L a year earlier, so their years are shifted by one to match. In the same year, their CO₂ is then 1% higher or lower than the others'. The average stops where the shortest run stops.

A worked example

1. GFDL-ESM4 turned CO₂ around after B = 140 years. Take year e = 70 on the way up. Its match on the way down is d = 2 × 140 + 1 − 70 = 211.
2. The middle of year 70 is at t = 70 − 0.5 = 69.5, so C = 284.317 × 1.01^69.5 = 567.7 ppm, about twice the start.
3. Year 211 mirrors it: t = 2 × 140 − 211 + 0.5 = 69.5, the same, so CO₂ is the same.
4. In GFDL-ESM4, on the way up, years 60 to 80 averaged +1.58 °C above the control run. On the way down, years 201 to 221 averaged +2.40 °C.
5. So the way down is 2.40 − 1.58 = 0.82 °C warmer. The page shows it as 0.8 °C, under "Same CO₂, up and down", with GFDL-ESM4 chosen and CO₂ at 568 ppm.

Things to try

1. In "Over time", with the average of the models and surface air temperature, find the top of the bold line. It's highest in year 150, 10 years after CO₂ started to fall. The surface kept warming for a while after CO₂ began to come down.
2. Choose NorESM2-LM and sea level from warmer water. Sea level was 27 cm at the turn, when CO₂ was highest, and 35 cm when CO₂ is back where it started. It kept rising for decades while CO₂ fell.
3. In "Same CO₂, up and down", choose GFDL-ESM4 and Arctic sea ice in September. At twice the starting CO₂, there was 2.3 million km² on the way up and 0.7 million km² on the way down. Try the other models: in which is the gap biggest?
4. In "Map", choose CO₂ twice the start and "The way down minus the way up". Where is the way down much warmer? Is anywhere cooler?
5. Then choose "Back at the start: 40 to 60 years on". Where is it still warmer than the control run?

Where the data come from

The runs are part of CMIP6, the sixth phase of the Coupled Model Intercomparison Project (Eyring and others, 2016). The modeling groups share them through the Earth System Grid Federation, under the Creative Commons Attribution 4.0 licence (CC BY 4.0). Each run has its own DOI:

• ACCESS-ESM1-5, CSIRO. The way up: Ziehn and others (2019), doi:10.22033/ESGF/CMIP6.4231; the way down: Ziehn and others (2019), doi:10.22033/ESGF/CMIP6.4233; the control run: Ziehn and others (2019), doi:10.22033/ESGF/CMIP6.4312.
• CanESM5, Canadian Centre for Climate Modelling and Analysis. The way up: Swart and others (2019), doi:10.22033/ESGF/CMIP6.3151; the way down: Swart and others (2019), doi:10.22033/ESGF/CMIP6.10223; the control run: Swart and others (2019), doi:10.22033/ESGF/CMIP6.3673.
• CESM2, National Center for Atmospheric Research. The way up: Danabasoglu (2019), doi:10.22033/ESGF/CMIP6.7497; the way down: Danabasoglu (2019), doi:10.22033/ESGF/CMIP6.7500; the control run: Danabasoglu and others (2019), doi:10.22033/ESGF/CMIP6.7733.
• CNRM-ESM2-1, CNRM-CERFACS. The way up: Seferian (2018), doi:10.22033/ESGF/CMIP6.3714; the way down: Seferian (2021), doi:10.22033/ESGF/CMIP6.9581; the control run: Seferian (2018), doi:10.22033/ESGF/CMIP6.4165.
• GFDL-ESM4, NOAA Geophysical Fluid Dynamics Laboratory. The way up: Krasting and others (2018), doi:10.22033/ESGF/CMIP6.8473; the way down: John and others (2018), doi:10.22033/ESGF/CMIP6.8476; the control run: Krasting and others (2018), doi:10.22033/ESGF/CMIP6.8669.
• MIROC-ES2L, JAMSTEC, AORI and NIES. The way up: Hajima and others (2019), doi:10.22033/ESGF/CMIP6.5370; the way down: Hajima and others (2020), doi:10.22033/ESGF/CMIP6.5377; the control run: Hajima and others (2019), doi:10.22033/ESGF/CMIP6.5710.
• NorESM2-LM, NorESM Climate modeling Consortium. The way up: Seland and others (2019), doi:10.22033/ESGF/CMIP6.7802; the way down: Tjiputra and others (2019), doi:10.22033/ESGF/CMIP6.13725; the control run: Seland and others (2019), doi:10.22033/ESGF/CMIP6.8217.
• UKESM1-0-LL, Met Office Hadley Centre and NERC. The way up: Tang and others (2019), doi:10.22033/ESGF/CMIP6.5792; the way down: Jones and others (2020), doi:10.22033/ESGF/CMIP6.12183; the control run: Tang and others (2019), doi:10.22033/ESGF/CMIP6.6298.

Eyring, V., Bony, S., Meehl, G. A., Senior, C. A., Stevens, B., Stouffer, R. J. and Taylor, K. E. (2016). Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geoscientific Model Development, 9, 1937–1958. doi:10.5194/gmd-9-1937-2016

Keller, D. P., Lenton, A., Scott, V., Vaughan, N. E. and others (2018). The Carbon Dioxide Removal Model Intercomparison Project (CDRMIP): rationale and experimental protocol for CMIP6. Geoscientific Model Development, 11, 1133–1160. doi:10.5194/gmd-11-1133-2018

Lee, J.-Y., Marotzke, J., Bala, G. and others (2021). Future global climate: scenario-based projections and near-term information. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, pages 553–672. Cambridge University Press. doi:10.1017/9781009157896.006

Meehl, G. A., Senior, C. A., Eyring, V., Flato, G. and others (2020). Context for interpreting equilibrium climate sensitivity and transient climate response from the CMIP6 Earth system models. Science Advances, 6, eaba1981. doi:10.1126/sciadv.aba1981

How they were checked

• Every file matched the SHA-256 checksum that ESGF lists for it: 389 files, about 18 GB.
• The runs line up as their files say. Each way down starts where its file says it left the way up, and each way up where it left the control run.
• The way up's average over years 60 to 79 is each model's transient climate response, the warming at the time CO₂ has doubled. For all eight models it is within 0.13 °C of the values Meehl and others (2020) give, which are rounded to 0.1 °C.
• The maps agree with the global numbers. Averaged over the globe, each map of the way down minus the way up is within 0.1 °C of the difference between the two global averages.
• numbers.js gives the same numbers as a second copy of its arithmetic, written in Python. The tests also check every number on this tab against the data.

The code

Two files run this page, and they use no outside software. The comments in numbers.js use the same step numbers and letters as above.

To keep a copy, save numbers.js or app.js. The page's data are in data/series.json, which has every model's yearly numbers as changes from its control run.

Credits

By Scott Denning, for Climate Change: Simple, Serious, Solvable.

The runs are the work of the eight modeling groups in the table above, for CMIP6 and CDRMIP. Claude, from Anthropic, chose the runs from an entry in Scott Denning's list of open climate data, worked out the numbers on this page from them and built the page. The coastlines are from Natural Earth, which is in the public domain.