Uncertainty in the 2°C warming threshold related to climate sensitivity and climate feedback

Climate sensitivity is an important index that measures the relationship between the increase in greenhouse gases and the magnitude of global warming. Uncertainties in climate change projection and climate modeling are mostly related to the climate sensitivity. The climate sensitivities of coupled climate models determine the magnitudes of the projected global warming. In this paper, the authors thoroughly review the literature on climate sensitivity, and discuss issues related to climate feedback processes and the methods used in estimating the equilibrium climate sensitivity and transient climate response (TCR), including the TCR to cumulative CO2 emissions. After presenting a summary of the sources that affect the uncertainty of climate sensitivity, the impact of climate sensitivity on climate change projection is discussed by addressing the uncertainties in 2°C warming. Challenges that call for further investigation in the research community, in particular the Chinese community, are discussed.

The ultimate magnitude of the response is not only determined by the forcing, 184 but also strongly influenced by various feedback processes. Stronger the positive 185 feedback leads to higher climate sensitivity, and vice versa. The "forcingresponse -186 feedback" represents a cyclic interaction to a new equilibrium state (Fig. 1). We 187 further present a brief review of the main feedbacks that are recognized up to now. 189 Based on the Stefan-Boltzmann law, the surface heated by the radiative forcing 190 will emit more infrared energy outwards and reduce the net flux at the TOA. This 191 basic negative feedback is called "Black-body radiation feedback" or "Planck 192 feedback". Some studies suggested that this process can be used as a reference 193 system to measure other feedbacks rather than a solo "feedback" because it is the 194 simplest and well-established relation between temperature and radiation (Roe, 2009). 195 When contributions of different processes to the change of T s are focused without  199 Water vapor is the most important GHG that exerts the strongest warming effect.

200
Based on the Clausius-Clapeyron relation, the water vapor in the atmosphere strictly 201 depends on the temperature. Considering the short period of atmospheric 202 hydrological cycle (about 10 d), the water vapor should be treated as "feedback" 203 rather than "forcing". The increased T s induced by external forcing will enhance 204 surface evaporation and hold more water vapor in the air. More water vapor will 205 block more outgoing radiation and increase the forcing at the TOA, which is the 206 well-know "water vapor feedback" (Held et al., 2000).  208 The lapse rate of tropospheric temperature will change when climate system     233 The cloud response is very complex under the background of climate warming.

234
A variety of cloud parameters, such as cloud fraction, height, particle size, phase etc.,   251 If the air-sea CO 2 exchange is considered, more CO 2 will be released into the  The "forcingresponse -feedback" relation describing the physical responses 265 can be linearly expressed as

Other feedbacks
where X is a certain feedback agent, such as water vapor; R is the radiative forcing at 268 the TOA; T is the global mean surface air temperature; K x is called "Feedback  The estimation of climate sensitivity is based on energy conservation,

279
where N is net radiative flux at the TOA; F is radiative forcing exerted by forcing 280 agent; E is the increased outgoing radiation after the atmosphere-earth system When the equilibrium is reached, the net flux N at the TOA is zero (Fig. 2). The

312
ECS is expressed as  Figure 3 shows application of 330 Gregory-style regression to obtain the ECS using the average of 24 CMIP5 models.

331
The response in models shows two stages: a fast response in the first 20 years (green   345 The TCR measures the sensitivity to CO 2 forcing in non-equilibrium state.

346
Besides the feedback, the TCR is affected by the ocean heat uptake (OHU) (Figure 2).

347
For transient response, the energy conservation is also satisfied, so we have The unit of TCRE usually is converted to "K 10 -3 Pg C".

367
The emission-driven Earth System Model is another tool to estimate the TCR.

368
The difference from conventional model is that the value of C e is determined by 369 carbon cycle and related feedbacks which may vary across models. Thus, the TCRE is

453
It should be noted that the uncertainty in the ECS extensively impacts the CO 2 454 concentration under a certain temperature target. If the ECS is 1.5 K, the allowed CO2 455 concentration can be as large as 700 ppm (Fig. 4). However, based on current  We would like to thank two anonymous reviewers for their constructive suggestions 516 and comments, which helped in improving the paper. to 450 ppm CO 2 equivalent in the 21st century. Energ. Econ., 31, S107-S120.