The Long-Term Effects of CO2 on Global Mean Sea Levels

Paleoclimate studies offer some very useful information to help scientists understand where our climate is headed given our current concentrations of greenhouse gases. As I have shared in previous posts, the earth has warmed by 1.2°C above the 1850-1900 mean, with about 2°C total warming built into current CO2 levels, given an energy imbalance exceeding 0.8 W/m^2 and ECS of ~3°C for doubling CO2. However, this only considers rapid feedbacks operating on time scales of decades or so. Long term, over time scales of thousands of years, the Earth's climate system is sensitive enough to these forcings to cause drastic changes to the climate system. Earth System Sensitivity (ESS) is frequently estimated to be about 1.5xECS, so 2°C warming on time scales of decades will be amplified to 3°C warming on time scales of thousands of years.  The difference between the last glacial maximum (LGM) and the Holocene Thermal Maximum (HTM) is only ~4-6°C, but that difference in global average temperature is the difference between a habitable Canada and a Canada covered with thick ice sheets. The 50% increase in CO2 to 420 ppm in the long term suggests anywhere from half to three-quarters of the warming from the LGM to the HTM. So it begs a question, what effect will this have on glacial ice and thermal expansion of the oceans? What will GMSL be after long term feedbacks bring the Earth into full equilibrium with 420 ppm CO2?

Alley and IPCC on GMSL at CO2 Concentrations

Sea Levels at Full Equilibrium with 420 ppm CO2

I found two sources attempting to answer this question. The first comes from a study by RB Alley (who authored the study on the GISP2 ice core). Alley et al 2005[1] plotted four times in the last 35 million years or so with known CO2 and sea levels. He begins with the LGM (21 thousand years ago), then the HTM (preindustrial levels), then the early Oligocene (~32 million years ago) and lastly the most recent time period with permanent globally ice free conditions (>35 million years ago).  These are the values he used (with the error at 1 standard deviation):

Alley estimated, given this data that after long-term feedbacks (taking hundreds to thousands of years), when the Earth's climate system reaches full equilibrium with contemporary CO2 ppm, sea levels will be about 25 m higher than today.  

IPCC-AR6 Chapter 13

The second answer to this question comes from the IPCC's chapter on sea level rise.[11] The IPCC assembled a similar table of paleoclimate data, showing GMST temperature ranges, CO2 ranges, and GMSL ranges at various points of the last 50 million years. On this chart, 420 ppm CO2 corresponds to the highest CO2 levels of the Mid-Pliocene and correlates with perhaps +4°C warming and +25 m of sea level rise. I took the averages of CO2 and GMSL from this table and plotted them with the data from Alley et al 2005. I plotted 420 ppm CO2 at 25 m SLR. Given the uncertainties described in these sources, it's probably safe to say this is 25 ± 5 m (at 1 standard deviation) to be consistent with Alley's CI for 500 ppm. It's likely that we will experience 20 m of sea level rise or more if we maintain 420 ppm CO2 for thousands of years.

Mid-Pliocene Analog to 420 ppm CO2

These two sources seem to generally agree with each other, and the results are consistent with the last time concentrations of CO2 were ~420 ppm during the mid-Pliocene, about 3+ million years ago. This makes the mid-Pliocene the most recent analog to where our climate is headed if CO2 levels stay constant at ~420 ppm. During that time, sea levels were 15-25m higher than today[3] and the Antarctic peninsula was below sea level.[1] Global temperatures were 2-4°C warmer than preindustrial temperatures[2][11], but due to polar amplification, the Arctic was much warmer. Latitudes farther north than 70°N were possibly 10°C warmer or more[1][2], and Greenland supported only an ephemeral ice sheet.[4] Instead, the Arctic supported boreal forests with at least 5 different kinds of pine trees.[5] One study of Lake El’gygytgyn in northeast Arctic Russia had summer temperatures ~8°C warmer than today between 3.6 and 3.4 million years ago and remained warmer than today until about 2.2 million years ago, when NH glaciation began.[4] Meanwhile, in Antarctica 5.3 to 2.6 million years ago, beech trees were growing at Oliver Bluffs, just 300 miles from the South Pole. Summer temperatures were perhaps +5°C, which is about 20°C to 25°C warmer than today. The West Antarctic ice sheet and some of the East Antarctic ice sheet would have been gone.[6][7]. 

Rae et al 2021

Similar results were found by Rae et al 2021,[12] which reconstructed CO2 levels for the last 66 million years, along with surface temperature and GMSL. His reconstruction shows sea levels to be about 20 m higher during the mid-Pliocene. Rae writes of these findings that "CO2 is now higher than any time in the last 3 million years. If the climate system is allowed to catch up to this CO2 level we are headed back to the Pliocene, a time with beech trees on the Antarctic Peninsula and around 20 m higher sea level."[13]

Long-Term Effects of 420 ppm CO2

These findings are also consistent with modeled projections for future warming and sea level rise on time scales of thousands of years.[10] The study estimated the amount of sea level rise to be expected long term under various cumulative emission scenarios. 

Clark et al 2016

Since our emissions stay in the atmosphere for thousands of years, all our emissions now commit us to long term changes in the earth's climate, including sea level rise. Cumulative emissions of ~1000 PgC or more likely commit us to 20 m of sea level rise. This would be roughly the equivalent of continuing our current emission rates of 10 PgC/yr for 100 years.

Clark et al 2016

Obviously, these amounts of SLR will not materialize over the next 100 years. These papers are very clear that this is SLR that various emission scenarios commit us to these outcomes on time scales of thousands of years. The IPCC's long-term projections for SLR are based on the amount of peak warming, not CO2 concentrations, but they estimate that if we experience peak warming of 5°C we can expect about 19-22 m of SLR over the next 2000 years at medium agreement due to limited evidence.[11] But at time scales longer than 2000 years, it's still possible that global climate will achieve ~25 m of SLR eventually even if warming peaks at mid-Pliocene temperatures (+2.5 - 4°C).

And it should also be acknowledged that on those time scales, our ability to develop technologies to mitigate climate change and remove excess CO2 from the atmosphere is likely to grow to address the cause of rising sea levels. But the clear message of paleo evidence is that on longer time scales, our emissions have long-term large consequences. After all, the Antarctic Ice Sheet began to form about 34 million  years ago when CO2 levels were ~760 ppm (with likely range of 450 ppm to 1500 ppm).[8][9] So it stands to reason that if we allow CO2 levels to increase to and remain at 750 ppm, we may well lose the entire Antarctic Ice Sheet and experience ~70 m of sea level rise. I hope that's unlikely. But even at ~420 ppm now, we are pushing the Earth's climate system out of anything seen in the Quaternary and into a global climate where glaciers and ice sheets are greatly diminished and sea levels are multiple meters higher than today. 

References:

[1] Alley RB, Clark PU, Huybrechts P, Joughin I. Ice-sheet and sea-level changes. Science. 2005 Oct 21;310(5747):456-60. doi: 10.1126/science.1114613. PMID: 16239468.

https://pubmed.ncbi.nlm.nih.gov/16239468/

[2] M. Robinson, “Pliocene Role in Assessing Future Climate Impacts” Eos 89, No. 49 (2008). https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2008EO490001

[3] IPCC AR4, 6.3.2 “What Does the Record of the Mid-Pliocene Show?” https://www.ipcc.ch/site/assets/uploads/2018/02/ar4-wg1-chapter6-1.pdf

[4] Julie Brigham-Grette, “Pliocene Warmth, Polar Amplification, and Stepped Pleistocene Cooling Recorded in NE Arctic Russia” Science 340 (June 21, 2013).
http://science.sciencemag.org/content/340/6139/1421

[5] Stephanie Paige Ogburn etal. “Ice-Free Arctic in Pliocene, Last Time CO2 Levels above 400 PPM: Sediment cores from an undisturbed Siberian lake reveal a warmer, wetter Arctic.” SA
https://www.scientificamerican.com/article/ice-free-arctic-in-pliocene-last-time-co2-levels-above-400ppm/

[6] Rhian L.Rees-Owen. “The last forests on Antarctica: Reconstructing flora and temperature from the Neogene Sirius Group, Transantarctic Mountains” Organic Geochemistry Volume 118, April 2018, Pages 4-14
https://www.sciencedirect.com/science/article/pii/S014663801730219X

[7] Damian Carrington, “Last time CO2 levels were this high, there were trees at the South Pole.” The Guardian
https://www.theguardian.com/science/2019/apr/03/south-pole-tree-fossils-indicate-impact-of-climate-change

[8] Pearson, P., Foster, G. & Wade, B. Atmospheric carbon dioxide through the Eocene–Oligocene climate transition. Nature 461, 1110–1113 (2009). https://doi.org/10.1038/nature08447

[9] "New CO2 data helps unlock the secrets of Antarctic formation."
https://phys.org/news/2009-09-co2-secrets-antarctic-formation.htm

[10] Clark, P. U., Shakun, J. D., Marcott, S. A., Mix, A. C., Eby, M., Kulp, S., … Plattner, G.-K. (2016). Consequences of twenty-first-century policy for multi-millennial climate and sea-level change. Nature Climate Change, 6(4), 360–369. doi:10.1038/nclimate2923 

[11] IPCC. "Ocean, Cryosphere and Sea Level Change." AR6, WG1, chapter 9.
https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Chapter09.pdf

[12] James W.B. Rae, Yi Ge Zhang, Xiaoqing Liu, Gavin L. Foster, Heather M. Stoll, Ross D.M. Whiteford. "Atmospheric CO2 over the Past 66 Million Years from Marine Archives." Annual Review of Earth and Planetary Sciences 2021 49:1, 609-641.

https://www.annualreviews.org/doi/full/10.1146/annurev-earth-082420-063026

[13] https://twitter.com/mudwaterclimate/status/1399727424775114761