Why Are Reconstructions of Global Temperatures Hockey Stick Shaped?

Pages 2K Global Temperature Reconstruction

In 1998 and 1999, Dr. Michael Mann published two studies reconstructing Northern Hemisphere and global temperatures. The studies reconstructed these temperatures using various proxies from around the globe to estimate how temperatures have changed over time. The results for some were shocking. Temperatures had been in a slow but steady decline since about a.d. 1000, and then around the beginning of the 20th Century, temperatures began to rapidly rise, exceeding anything seen in the last millennium. Later reconstructions have improved upon Mann's work, extending the proxy record farther back in history and developing more extensive use of proxies for more coverage of the globe. This later work has largely replicated Mann's work, and the "hockey stick" shape to global temperatures is now well-established in climate science. By one count, Mann's findings have been replicated no less than 50 times in the scientific literature.[1] The question then is, why do all these global temperature reconstructions have this hockey stick shape?

The simplest and shortest answer is because this is what the proxy and instrumental record tells us, but that's also the least interesting. What I want to consider is, what is the physics behind why global temperatures have this "hockey stick" shape? We can describe the physics that explains the hockey stick in four steps.

Step 1 - dF = 5.35*ln(C1/C0) [2] - changes in forcings are proportional to ln (CO2). The relationship between an increase in forcing and a change in CO2 concentrations is logarithmic.

Step 2 - dT = λ*dF - changes in temperature are proportional to changes in forcings.[3] The λ term is called "sensitivity." A special case of sensitivity estimates the amount of warming for doubling CO2. This is called "equilibrium climate sensitivity" or ECS. If ECS = 3 C, then λ = 0.81. Whatever value λ has, though, temperatures rise in proportion to an increase in forcings.

Step 3 - CO2 has been rising exponentially - CO2 concentrations have been rising at exponential rates.

Step 4 - Hockey Stick - the shaft of the hockey stick is “constructed” over the many centuries before the Industrial Revolution (IR) when atmospheric CO2 was roughly constant, and temperature changes were minimal. Variability in global temperatures were largely due to other forcings which are small compared to the increases in GHG concentrations from human activity. The blade is “constructed” over the time period since the IR, where CO2 concentrations have risen exponentially, and temperature rise is linear. Actual temperature rise has accelerated to more than 0.2 C/decade.

The graph above is the results of the Pages 2K project.[8] This project has assembled a large and growing collection of proxies that can be used to estimate global temperatures. There's an extension project called Temperature 12K that has produced a similar reconstruction of the last 12,000 years. One exciting aspect of these projects is that new proxies can be added to the database, and over time, these reconstructions can be improved as more evidence is incorporated. While the hockey stick shape to global temperatures is well-established science, there is still work to be done in constraining these estimated values and in better understanding how regional temperatures changed over time.


References:

[1] “Hockey Stick Papers” https://gist.github.com/priscian/81099e9332c86800d538542fb7027eaf?fbclid=IwAR02HjrebPwdQ7fWCGrG8RndoShrxA9p5RrzzPUmT3v_zAOpDmuYXuI308c

[2] Huang,Yi and Maziar Shahabadi, “Why logarithmic? A note on the dependence of radiative forcing on gas concentration” J. Geophys. Res. Atmos. 119.24 (27 December 2014):13,683-13,689
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2014JD022466

[3] Goodwin, Philip, “On the Time Evolution of Climate Sensitivity and Future Warming” Earth’s Future 6.9 (2018): 1336-1348
https://doi.org/10.1029/2018EF000889
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018EF000889

[4] Lacis, A. A., G. A. Schmidt, D. Rind, and R. A. Ruedy, 2010: Atmospheric CO2: Principal control knob governing Earth’s temperature, 330, 356-359, doi: 10.1126/science.1190653
https://pubs.giss.nasa.gov/docs/2010/2010_Lacis_la09300d.pdf

[5] Lenton, T. M., (2000). Land and ocean cycle feedback effect on global warming in a simple Earth system model, Tellus(2000), 52B, p1169.
https://www.tandfonline.com/doi/abs/10.3402/tellusb.v52i5.17097

[6] Myhre, G., E.J. Highwood, K.P. Shine, and F. Stordal, “New estimates of radiative forcing due to well mixed greenhouse gases.” Geophys. Res. Lett., 25.14 (1998): 2715-2718.
http://go.owu.edu/~chjackso/Climate/papers/Myhre_1998_New%20eatimates%20of%20radiative%20forcing%20due%20to%20well%20mixed%20greenhouse%20gasses.pdf

[7] Etminan, M., G. Myhre, E. J. Highwood, and K. P. Shine (2016), “Radiative forcing of carbon dioxide, methane, and nitrous oxide: A significant revision of the methane radiative forcing,” Geophys. Res. Lett., 43, 12,614–12,623, doi:10.1002/ 2016GL071930.
https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2016GL071930

[8] https://pastglobalchanges.org/science/wg/2k-network/intro