Equilibrium climate sensitivity (ECS) is usually defined as the global mean equilibrium temperature response to a doubling CO2 concentration of its preindustrial level in the atmosphere [ Hegerl et al ., 2007 ; Meehl et al ., 2007 ]. The pre-industrial concentration of CO2 is generally accepted to be 280×10−6 and the doubled concentration was considered to be 560×10−6 accordingly in early studies. New studies tend to use 600×10−6 instead to stand for the doubled concentration of CO2 around 1900 AD. The initial values of ECS estimated by professionals [ Charney et al., 1979 ], including those reported in IPCC FAR [ Mitchell et al., 1990 ], SAR [ Kattenberg et al., 1996 ] and TAR [ Cubasch et al., 2001 ], were in the range of (3±1.5)°C or 1.5–4.5°C. Since IPCC TAR, great many efforts have been made to re-examine the ranges of ECS. As a result, IPCC AR4 [ Meehl et al., 2007 ] offered a comprehensive discussions on this issue and proposed the range of ECS to be 2.0–4.5°C, which was slightly narrower than previous estimations. Figure 1 , derived from IPCC AR4, shows the probability density function of ECS from 10 studies, among which the first 7 results [ Forster and Gregory, 2006 ; Frame et al ., 2005 ; Knutti et al ., 2002 ; Andronova and Schlesinger, 2001 ; Forest et al ., 2002 ; Forest et al ., 2006 ; Gregory et al ., 2002 ] were from observation-constrained simulations and the other 3 results [ Hegerl et al ., 2006 ; von Schneider et al ., 2006 ; Annan et al ., 2005 ] came from Last Glacial Maximum(LGM) and millennia-scale proxy data constrained simulations. It is evident in Figure 1 that the spread of the probability density functions differs widely with the peaks of the curves ranging from around 0.2 to above 0.6 and the broadness of the curves also varies greatly while the mean values of ECS are at 2.0–3.5°C, which are often greater than the most likely values of ECS (corresponding to the peaks of the probability curves).
Comparison between different estimates of the probability density function for equilibrium climate sensitivity (ECS) (the bars show the respective 5% to 95% ranges, dots show the median estimate) [ Hegerl et al., 2007 ]
If should be noted that the uncertainty in estimated ECS mainly comes from the different sources of data that used to constrain the models. The observations with centennial length and LGM proxys were already used to constrain models to improve the results. Although the use of more data and the improvement of the models can potentially narrow the range for ECS estimation [ Schmittner et al., 2011 ], the uncertainty in estimating the upper limit of ECS still remains controversial according to the comments made by Hegerl and Russon  in the same issue of Science. Another review paper [ Knutti and Hegerl , 2008 ], published after IPCC AR4, also confirmed and emphasized this point.
Another big challenge for ECS came from the paleoclimate field. In July 2011, the journal of Nature Geoscience published three review articles [ Valdes, 2011 ; Zeebe, 2011 ; Beerling and Royer, 2011 ] accompanied with editorial comments [ Editorial, 2011 ], which indicated that the challenges for ECS came from two key directions: paleoclimate and model. For the first problem, Zeebe  indicated that the ECS should intrinsically include not only those sensitivities of rapid feedbacks but also those slow and entire earth system sensitivities. The behind key idea is that the discussion about ECS should always depend on the various time-scales. For example, the response of continental ice sheet to radiative forcing is extremely slow, which is negligible on the centennial timescale but apparently important on longer-than-millennial timescale. Thus, the comparison between current models’ ECS with paleoclimatic proxy data is nearly an apple-to-orange comparison. The ECS reported in IPCC AR4 is in the range of 2.0–4.5°C, which corresponds to the timescale of those processes already involved in current models such as non-CO2 greenhouse gases, dynamical vegetation, dust/aerosol, ice sheet, oceanic circulation, oceanic productivity, chemical weathering, and other feedback processes. However, the ECS in Pliocene epoch (5.3–2.6 MaBP) reached 7–10°C [ Pagani et al., 2010 ]. In March 2011, a workshop held in Amsterdam particularly discussed this problem in detail, and a report to be released soon will introduce new perspectives on ECS [ Zeebe, 2011 ].
For the second problem, Valdes  indicated that all the current IPCC models, which are quite stable due to fitting modern Earth’s climate, cannot successfully reproduce abrupt climate change that occurred in paleoclimatic conditions. Generally speaking, we need to input ten times the real forcing into the models to trigger an abrupt change, which is defined as the climatic process with much faster responses than the external forcing. Valdes  demonstrated four examples of past abrupt climate changes as follows to show the importance of understanding these abrupt climate changes for the 21st century climate projections.
The Palaeocene-Eocene thermal maximum (PETM) A rapid warming event occurred about 55.8 million years ago. The tropical temperature increased 5°C, whereas the high-latitudes increased 20°C within nearly 1,000 years. Thus, the equator-pole gradient of temperatures was much lower than the present, which however cannot be captured by current climate models. In addition, there were two other warm intervals (less than the PETM), mid-Miocene (18–15 MaBP) and mid-Pliocene (3.6–2.6 MaBP), worth to be investigated in depth, since the CO2 concentration is estimated to reach 500×10−6 , which is close to the doubled CO2 level as what we expected for future [ Beerling and Royer, 2011 ].
The desertification of North Africa Between about 9,000 and 5,500 years ago, the region that is now the Sahara was much wetter and more humid than present climate, and therefore was named as Green Sahara. The vegetation changed very quickly into desert within only a couple of decades to centennials. However, current climate models cannot reproduce the quick transition of vegetation from Green Sahara in early-Holocene to desert after mid-Holocene, especially the rapid desertification near 5,500 years ago.
Collapse of the Atlantic meridional overturning circulation (AMOC) In the last glacial period there were six Heinrich events occurred when AMOC collapsed. They were possibly the responses to hosing fresh water in the North Atlantic. The current climate models can only reproduce this type of event by hosing 1 Sv (= 106 m3 s−1 ) fresh water fluxes, whereas the estimated water flux should be just 0.1–0.2 Sv. If the observed water flux value were used to force the model, the resulted reduction of the strength of AMOC would be around 30%, which is far from the shutdown mode in observations; and the cooling in Greenland’s temperature would be at 2–3°C, which is far below the derived values in the proxy data (up to 10°C).
Dansgaard-Oeschger (D/O) rapid warming events Between two Heinrich events, there were at least 25 incidences of rapid warming with 8°C change happened within a couple of decades, as recorded in Greenland ice cores. Some methane evidence further confirmed that this kind of rapid warming also happened in other places. We do not understand the underlying mechanism yet. Current climate models almost certainly cannot reproduce these rapid warming events unless abundant fresh water can be injected into the model for more than thousand years, which is apparently unrealistic length of time compared to proxy evidence.
From the above four examples, it is concluded that current climate models still cannot reproduce those abrupt climate events. On one hand, we need to more accurately understand the paleo-climatic forcing and the physical and dynamical conditions for the occurrence of abrupt climate changes. On the other hand, we also need to develop better climate models so that our successful modeling of abrupt climate changes can provide a solid foundation for more reliable climate projection of the future. Unfortunately, it is reported in 2011 [ MB, 2011 ] that although the models have already been significantly improved in the last 5 years, the spread of modeled ECS remains large. Apparently, we still have a long way to go in reducing the uncertainties of ECS.
This work is supported by the National Natural Science Foundation of China (No. 41005035), and the Strategic Priority Research Program of Chinese Academy of Sciences (No. XDA05080801 and XDA05090104).
Received: 11 November 2012