J. Meteor. Res.  2015, Vol. 29 Issue (6): 884-895   PDF    
http://dx.doi.org/10.1007/s13351-015-5036-4
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ZHOU Tianjun, CHEN Xiaolong. 2015.
Uncertainty in the 2℃ Warming Threshold Related to Climate Sensitivity and Climate Feedback
J. Meteor. Res., 29(6): 884-895
http://dx.doi.org/10.1007/s13351-015-5036-4

Article History

Received May 19, 2015;
in final form October 15, 2015
Uncertainty in the 2℃ Warming Threshold Related to Climate Sensitivity and Climate Feedback
ZHOU Tianjun1, CHEN Xiaolong1,2     
1 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;
2 University of the Chinese Academy of Sciences, Beijing 100049
ABSTRACT: Climate sensitivity is an important index that measures the relationship between the increase in green-house 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℃ warming. Challenges that call for further investigation in the research community, in particular the Chinese community, are discussed.
Keywords: climate sensitivity     radiative forcing     climate feedback     2℃ threshold     greenhouse gases     clima-te model    
1. Concept of climate sensitivity

The increasing concentration of greenhouse gases(GHGs),represented by CO2,blocks part of the outgo-ing infrared radiation from the atmosphere-earth sys-tem(i.e.,the greenhouse effect). Consequently,unbal-anced downward radiative energy at the top of the at-mosphere(TOA)enters and heats the climate system.In a broad sense,climate sensitivity can be regardedas how fast and strong the climate system respondsto such net heating. Global mean surface air tem-perature(Ts),which is closely related to radiation,isusually used as the climate response index. When theclimate of the earth fully responds under a doubledpre-industrial CO2 concentration and reaches a newequilibrium state,the change in Ts relative to the pre-industrial baseline is defined as equilibrium climatesensitivity(ECS),generally shortened to climate sen-sitivity in practice(Cubasch et al., 2001; Rand all et al., 2007; Wang et al., 2012).

The study of climate sensitivity can be tracedback to the end of the 19th century. Based on sim-ple equilibrium thermal radiation theory,Arrhenius(1896)quantitatively explored the greenhouse effect ofCO2 and obtained a 4.4-K warming of Ts under a dou-bled CO2 concentration when the effects of vapor and snow-ice albedo were considered. The development ofradiation theory and the birth of computing technol-ogy after the 1950s provided more powerful tools forthe climate research community. A one-dimensionalthermal equilibrium model with convective adjustmentwas developed and used to study the sensitivity of Tsto radiative forcing induced by various factors(Manabe and Strickler, 1964). Assuming an unchanged relative humidity,water vapor can double the Ts in-crement caused purely by CO2 forcing(Manabe and Wetherald, 1967). One decade later,a three-dimensional atmospheric general circulation model(AGCM)had been established and showed an approxi-mate 3-K surface warming under doubled CO2 with anidealized l and -sea distribution,fixed cloud cover, and ignored ocean heat transport(Manabe and Wether-ald, 1975). Charney et al.(1979)performed a setof coupled simulations with multiple AGCMs coupledto a mixed-layer ocean(or slab ocean) and provideda possible range of climate sensitivities within 1.5{4.5 K(so-called the Charney sensitivity). After theCharney sensitivity was published,more sophisticatedAGCMs coupled to a slab ocean were developed,in-cluding changeable cloud,prescribed ocean heat trans-port,higher resolution,etc. However,the climate sen-sitivity of these models changed little compared to theCharney sensitivity(IPCC,1990).

The coupled AGCM-slab-ocean system is a pop-ular tool in climate sensitivity research because of itslow computational cost. The equilibrium state can bereached within 20{30 yr after the forcing is imposed.Nevertheless,it may not be appropriate when focusingon long-term climate change,since the change in oceanheat transport is omitted,such as the responses ofthe thermohaline circulation or more specifically,theAtlantic meridional overturning circulation(Zhou et al., 1998,2000). Following improvements in comput-ing capacities in the 1990s,fully coupled atmosphere-ocean models began to be used from the end of thatdecade for long-term climate integrations(Stouffer and Manabe, 1999; Gregory et al., 2004; Danabasoglu and Gent, 2009; Li et al., 2013). However,initially,thesekinds of fully coupled models were too expensive formost modeling groups. Therefore,an analysis basedon the transient response(i.e.,non-equilibrium)wasproposed to estimate the warming magnitude in theequilibrium state(Gregory et al., 2004; Flato et al., 2013). The method was designed to use only a slightlylonger than 100-yr integration with fully coupled mod-els to estimate the ECS. Compared with the resultfrom the equilibrium simulation,the bias in the esti-mation of the transient response was within an accept-able 10%(Li et al., 2013).

The focus of the ECS is the final equilibrium state,regardless of how it is reached. However,both histor-ical and future climate changes in different scenariosare transient responses and cannot be regarded as anequilibrium state. Thus,a new term,the transientclimate response(TCR),was introduced to describethe sensitivity of the climate response in the transientstate. It is defined as the change in Ts relative to thepre-industrial period when the CO2 concentration isdoubled at an increasing rate of 1% per year(Rand all et al., 2007). Recently,it was found that the linearrelation between the Ts change and the accumulatedCO2 concentration in the atmosphere changes littlewith time and scenarios, and reflects the timescale ofwarming from the decadal to in excess of the cen-tury scale(Matthews et al., 2009; Goodwin et al., 2015). A new sensitivity index|TCR to cumulativecarbon emissions(TCRE)|was defined as the changein Ts by one unit of cumulative carbon emissions. TheTCRE can provide the cumulative carbon emissions inthe atmosphere given a certain threshold of Ts change(Collins et al., 2013). It bridges the targets of control-ling temperature and reducing carbon emissions, and is thus an important reference index for formulatingemission reduction policies.

Climate sensitivity has received considerable at-tention because of its importance in describing the re-lation between the increasing GHG concentration and the magnitude of global warming. Estimates of cli-mate sensitivity have a direct influence on the reliabil-ity of projected climate change and are thus useful ref-erences for policymakers in making decisions relevantto the reduction of carbon emissions. As a review,themajor objective of this paper is to summarize recentprogress in studies of climate sensitivity,radiative forc-ing, and feedback processes. In addition,the sources ofuncertainty in estimates of climate sensitivity are dis-cussed,along with their influence on projections underthe 2‰warming threshold. Discussion and recommen-dations regarding future research priorities related toclimate sensitivity are also provided.

2. Climate feedback

By introducing several terminologies in the electronic engineering field,Hansen et al.(1984)proposeda linear feedback analysis that gradually became ast and ard method(Cubasch et al., 2001; Gregory et al., 2002,2004; Roe,2009). Subsequently,more atten-tion was paid to the issue of forcing-response-feedback(Fig. 1). Forcing is the driver of an evolving system,which,in the present context,i.e.,the climate system,is the radiative perturbation at the TOA. This per-turbation is caused by various factors,such as solarradiation change,aerosols emitted by natural processlike volcanos, and GHGs and aerosols emitted by an-thropogenic activities. Besides CO2,anthropogenicGHGs include other tracer gases; some can induce astronger radiative effect than CO2 by one unit changein concentration(Shi,1991; Wang et al., 2000). Forthe convenience of calculation,the concentration ofall GHG species is usually converted to the CO2 con-centration that can induce the same radiative forcing,called the equivalent CO2 concentration.

Fig. 1 Schematic representation of the forcing-response-feedback relation.λX,the feedback parameter for a certain feedback factor,means the induced perturbation of the ra-diative forcing at the TOA by the changes in the feedback factor per global mean surface temperature change.

Idealized radiative forcing is the net flux at theTOA without any response anywhere after the forc-ing agents were imposed. In such a way,the doubledCO2 concentration corresponds to approximately 4.37W m-2(Ramaswamy et al., 2001). As research pro-gressed,climate scientists began to underst and thatthe forcing responsible for the change in Ts is the un-balanced radiation after rapid adjustments. For ex-ample,the stratosphere can adjust to radiative equiliilibrium within one month; whereas,the changes in thetroposphere,which are of greater concern,are slower and caused by the forcing after stratospheric adjust-ment. Taking this into consideration,the Intergovern-mental Panel on Climate Change(IPCC)modified thedefinition of radiative forcing in its third assessmentreport(TAR),with the doubled CO2 forcing revised to3.71 W m-2(Ramaswamy et al., 2001). Although theabove concept of forcing was preserved,other methodsto calculate the forcing were proposed in the fourthIPCC report(Forster et al., 2007),including morerapid processes(but slower than the stratospheric ad-justment),such as aerosol-related cloud changes(Jacob et al., 2005) and temperature adjustment in thetroposphere(Hansen et al., 2005).

Multiple definitions of radiative forcing are sum-marized in the fifth IPCC report(AR5),including theearlier definitions outlined above. A new definition,called effective radiative forcing(ERF)was proposed.The ERF is the doubled CO2 forcing at the TOA,but considers all kinds of rapid adjustments,includ-ing temperature changes in the troposphere and onl and ,aerosol-cloud interaction, and changes in the ver-tical structure of temperature and its effect on cloud(Myhre et al., 2013). The timescale of temperaturechange that we are concerned with is longer than thedecadal scale, and up to the century scale. Hence,theERF can better represent the forcing agents able toimpact the temperature change on longer time scales(Zhang and Huang, 2014). Because current under-st and ing of the rapid adjustments is insu±cient,largeuncertainty is observed in model-based estimations ofthe ERF(2.6{4.3 W m-2; Flato et al., 2013).

The ultimate magnitude of the response is notonly determined by the forcing,but also strongly in-fluenced by various feedback processes. Stronger pos-itive feedback leads to higher climate sensitivity, and vice versa. The forcing-response-feedback paradigmrepresents a cyclic interaction to a new equilibriumstate(Fig. 1). Next,we will review the main feedbackmechanisms recognized to date.

2.1 Planck feedback

Based on the Stefan-Boltzmann law,the surfaceheated by the radiative forcing will emit more infrared energy outwards and reduce the net flux at the TOA.This basic negative feedback is called black-body radi-ation feedback or Planck feedback. Some studies havesuggested that this process can be used as a referencesystem to measure other feedbacks,rather than beinga solo feedback,because it is the simplest and mostwell-established relation between temperature and ra-diation(Roe,2009). When contributions of differentprocesses to the change in Ts are focused upon with-out a reference system,the cooling effect of Planckradiation can be regarded as an important feedback(Gregory and Forster, 2008; Chen et al., 2014; Pithan and Mauritsen, 2014).

2.2 Water vapor feedback

Water vapor is the most important GHG in thatit exerts the strongest warming effect. Based on theClausius-Clapeyron relation,the water vapor in the at-mosphere strictly depends on the temperature. Con-sidering the short period of the atmospheric hydro-logical cycle(about 10 days),the water vapor shouldbe treated as a feedback rather than forcing. The in-creased Ts induced by external forcing will enhancesurface evaporation and hold more water vapor in theair. More water vapor will block more outgoing radia-tion and increase the forcing at the TOA,which is thewell-known water vapor feedback process(Held and Soden, 2000; Han et al., 2015).

2.3 Lapse-rate feedback

The lapse rate of tropospheric temperature willchange when the climate system warms. In the trop-ical regions,more water vapor condenses in the mid-upper troposphere and heats the local atmosphere,resulting in the warming in the upper layer beingstronger than in the lower layer. This process is calledmoist adiabatic adjustment,in which the moist adia-batic lapse rate decreases. The warmer upper layer isconducive to the emission of more infrared radiation tospace and a reduction in the forcing at the TOA. Thisis negative lapse-rate feedback. The warmer regionsin the troposphere are usually filled with more watervapor,especially in the tropics. As a result,the posi-tive water vapor feedback and negative lapse-rate feed-back can partly cancel one another out, and the netfeedback is still positive(Cess,1975; Held and Soden, 2000; Soden and Held, 2006). Thus,these two closelyrelated feedbacks are unified under the notion of wa-ter vapor-lapse-rate feedback. However,if we chooserelative humidity instead of specific humidity as thefeedback agent,the compensation will be substantiallyreduced(Held and Shell, 2012; Ingram,2013). In themid-high latitudes,warming is confined to the lowerlayer for a lack of moist adiabatic adjustment. Theconsequent positive lapse-rate feedback mainly con-tributes to the polar amplification phenomenon(Colman,2003; Pithan and Mauritsen, 2014).

2.4 Snow-ice albedo feedback

The snow cover and sea ice in the high latitudescan rapidly respond to surface warming. Melted snow and ice decrease the surface albedo and shortwave ra-diations reflected back to space, and increase the forc-ing at the TOA. This is positive snow-ice albedo feed-back,which is one of the main contributors to polaramplification(Pithan and Mauritsen, 2014),as shownin the earliest study on climate sensitivity(Arrhenius,1896).

2.5 Cloud feedback

The cloud response is very complex against thebackground of climate warming. A variety of cloudparameters,such as cloud fraction,height,particlesize,phase,etc.,can all impact upon the radiativeflux at the TOA. One change in a cloud attribute maybring about both positive and negative feedbacks atthe same time. If the cloud fraction decreases withsurface warming,increased outgoing longwave(inci-dent shortwave)radiation will reduce(amplify)theTOA forcing,acting as a negative(positive)feedback.The sign of the net cloud feedback is then di±cult todetermine. The cloud at different altitudes has dif-ferent radiative effects. High cloud is more opaque tolongwave radiation,whereas low cloud mainly reflectsshortwave radiation. As a result,both an increase inhigh cloud and a decrease in low cloud induced bysurface warming can lead to positive feedback. In thetropics,the cloud top rises with the tropopause as thetropospheric temperature increases,resulting in pos-itive feedback by reducing the emission of longwave radiation. Under global warming,storm tracks shiftpoleward with the expansion of the Hadley circula-tion. As a result,the area covered by frontal cloud isreduced and heated by more solar radiation,acting asa positive feedback. Most of the models used in IPCCAR5 show that the net cloud feedback may be positive(Boucher et al., 2013).

2.6 Other feedbacks

If the air-sea CO2 exchange is considered,moreCO2 will be released into the atmosphere from thewarmer ocean by reducing the solubility,increasing theradiative forcing at the TOA. This is positive solubil-ity feedback. Feedbacks become more complex whenchanges of the biosphere are involved. The responseof vegetation cover to warming could change the l and albedo and produce vegetation-albedo feedback(Zeng and Yoon, 2009). Another example,ocean acidifica-tion due to CO2 uptake may decrease the emission ofdimethylsulphide by marine organisms,which is thelargest natural source of atmospheric sulfur. The de-crease in atmospheric sulfate will affect cloud forma-tion and ultimately the radiative budget(Six et al., 2013). Therefore,in addition to the physical feedbackmentioned above,feedbacks involving biogeochemicalprocesses are also important. Thus,the developmentof earth system models that include biogeochemicalcycles is at the forefront of climate modeling research(Zhou et al., 2014).

The forcing-response-feedback relation describingphysical responses can be linearly expressed as

where X is a certain feedback agent,such as watervapor; R is the radiative forcing at the TOA; T is theglobal mean surface air temperature; KX is called theFeedback Kernel,which describes the contribution ofone unit change in X to R and only depends on theradiative transfer process; dX/dT is the response of Xto surface warming; and λX is the feedback parameterwith respect to X.

For different feedback agents X,how to calculatethe corresponding λX based on Eq.(1)is the cen-tral issue of feedback analysis. Readers are referredto Soden et al.(2008) and Roe(2009)for a more de-tailed description of the feedback analysis method and Radiative Kernel approach to calculating λX.

3. Principle of estimating climate sensitivity

The estimation of climate sensitivity is based onenergy conservation,

where N is the net radiative flux at the TOA; F isthe radiative forcing exerted by the forcing agent; E isthe increased outgoing radiation after the atmosphere-earth system responds; and the positive direction isdownward. To the first-order approximation,E isexpressed as the linear function with respect to thechange in global mean surface air temperature T',where λ is the net feedback parameter,the sum of allfeedback components. Equations(2) and (3)are fun-damental in estimating climate sensitivity based oneither observation or simulation.

3.1 ECS

Under a fixed 2×CO2 concentration,a fully cou-pled ocean-atmosphere model is integrated from thepre-industrial baseline to a new equilibrium. Then,the Ts difference between the two states is the valueof ECS. However,it is not easy to reach the equilib-rium state due to the expensive computational cost.As an alternative,a slab ocean model is usually cou-pled with the AGCM. Though the computing cost ischeap,the simplified climate system cannot introducethe effect of ocean circulation. Technically,coupling aslab ocean model with an AGCM is not easier than thedevelopment of a fully coupled model. Thus,an ap-proximation method was proposed based on the tran-sient state from a fully coupled model to estimate theECS(Gregory et al., 2004). Combining Eqs.(2) and (3),the following can be obtained:

As the CO2 concentration is fixed,F is a constant.Then,N can be regarded as a function with respect to T'. By linear fitting N against T',F at the inter-cept of the y-axis(T'=0)can be obtained, and theequilibrium temperature(i.e.,ECS under 2×CO2)atthe intercept of the x-axis(N = 0). The slope of the fitting line is λ.

When the equilibrium is reached,the net flux Nat the TOA is zero(Fig. 2). ECS is expressed as

where F is the forcing of 2×CO2,ERF estimatedbased on a specific model,or 3.71 W m-2,as com-monly used before; 1/(-λ)is called the climate sensi-tivity parameter,which describes the warming inducedby 1 W m-2 of forcing at the TOA.

Fig. 2 Schematic representation of the (a) transient re-sponse and (b) equilibrium response.N is net radiative °ux at the TOA;F is radiative forcing induced by forc-ing factors;E is increased outgoing radiative flux of the earth system due to warming;and U denotes ocean heat uptake.For the transient response,N approximates to U,both non-zero.For the equilibrium response,E offsets F,and a new equilibrium state is reached.

To obtain a more evident forced signal,4×CO2forcing is usually used to drive the fully coupled model.Based on the empirical relation between CO2 concen-tration and radiative forcing(Myhre et al., 1998),theforcing of 4×CO2 is exactly twice that of 2×CO2. As-suming λ is unchanged,ECS is half the equilibriumtemperature estimated from the 4×CO2 scenario. Fig-ure 3 shows an application of Gregory-style regressionto obtain ECS using the average of 24 CMIP5 mod-els. The response in the models shows two stages: afast response in the first 20 years(green line) and aslow response later on(blue line),corresponding todifferent λ(Chen et al., 2014). The mean λ estimatedby the ERF and ECS based on the two stages(dashedblack line)is similar to λ calculated by using the wholeperiod(solid black line). ECS estimated only by theslow response stage(the last 130 years)is 0.3 K higherthan that derived from the whole period.

Fig. 3 Relation between surface temperature change ΔT and net radiative flux N at the TOA under the 4×CO2 sce-nario.ΔT and N are the differences between the abrupt 4×CO2 and piControl runs.Gregory-style regression (Gre-gory et al.,2004) is used to estimate ECS.The outputs of the multi-model ensemble of 24 CMIP5 models are shown.The feedback parameter λ is evidently different in two re-sponse stages (roughly before and after the 20th year).

Besides model output,observational data can alsobe used to estimate ECS in nature. However,in thereal world,F evolves with time. Based on Eq.(4),we should know the time series of F contributed fromGHGs,aerosols,l and use,solar perturbation,volcanoactivity, and so on. The unbalanced flux N at theTOA and the surface temperature change T 0 shouldalso be known. Then,we can fit(N - F)against T 0to obtain the value of λ and subsequently use Eq.(5)to estimate ECS(Forster and Gregory, 2006).

3.2 TCR and TCRE

The TCR measures the sensitivity to CO2 forcingin the non-equilibrium state. Besides the feedback,theTCR is affected by the ocean heat uptake(OHU)(Fig. 2). For the transient response,the energy conservation is also satisfied,so we have

where U is the OHU,equal to the net flux at the TOA.Assuming the timescale of OHU is much longer thanthat of the Ts response,U can be approximated as thefirst-order relation with T',where k is the e±ciency of OHU with a positive value.This linear approximation assumes that the ocean hasinfinite heat capacity and the OHU is regarded as onekind of negative feedback,which is applicable to theforcing of a moderate increasing scenario(Gregory and Forster, 2008). Combining Eqs.(6) and (7),we obtainIt is evident that a strong OHU can lead to a smallTCR.

Based on the definition of TCR,in practice,thevalue of TCR is calculated by using the change of Ts,a 20-yr mean state centered on the time of CO2 dou-bling under the 1% yr-1 increasing scenario relativeto the pre-industrial baseline. Using the same experi-ment,we can calculate the cumulative CO2 emissionsin the atmosphere Ce(unit: Pg C)before the CO2concentration is doubled. Then,TCRE is expressedas

The units of TCRE are usually converted to 10-3 K PgC. The emissions-driven earth system model is anothertool that can be used to estimate TCR. The differencefrom the conventional model is that the value of Ce isdetermined by the carbon cycle and related feedbacks,which may vary across models. Thus,TCRE is the re-gression coe±cient by fitting Ts against the cumulativeCO2 emissions(Collins et al., 2013).

4. Uncertainty in climate sensitivity

From IPCC TAR to AR5,extensive studies us-ing paleoclimatic proxy data,historical instrumentalobservations and multi-model simulations,have notreduced the uncertainty of the ECS. The newly sug-gested possible range is 1.5{4.5 K,the same as theCharney sensitivity obtained in 1979(Charney et al., 1979). Besides,a diverse range of results are seenin different studies(Gregory et al., 2002; Forster and Gregory, 2006; Andrews et al., 2012; Olson et al., 2012;Rohling et al., 2012; Masters,2014). It is also believedthat the relation between the feedback and ECS in-trinsically determines the uncertainty(Roe and Baker, 2007).

From Eq.(5),we have

This shows the relation between the uncertainties of λ and ECS under the linearization assumption. If λ issmall,ΔECS will be large following one unit changeof Δλ. This means that the uncertainty of ECS is in-evitably large if ECS itself is not small enough,whichresults in the upper limit of the probability being hardto constrain. It should be noted that these resultsare derived from the assumption of linear feedback.Therefore,it is still controversial in underst and ing therelation between ECS and feedbacks(Roe and Ar-mour, 2011).

The uncertainties of ECS estimated by modelsmainly come from feedback processes,especially cloudfeedback,which contributes about 70% of inter-modelvariance of ECS. The shortwave feedback of low cloudin the tropical and subtropical regions(including shal-low convective cloud and stratocumulus)is highly un-certain(Rand all et al., 2007; Klocke et al., 2011; Vial et al., 2013). The uncertainty of observation-based es-timations of ECS comes from the observational datathemselves,such as the net flux at the TOA,the forc-ing exerted by a variety of agents, and the OHU. Al-though ECS is the sensitivity to the CO2 concentra-tion,the observed change in Ts is the result of multipleforcing agents(Ma et al., 2005). Hence,to accuratelyestimate the climate feedback,the forcing from all theagents should be known. Besides the GHG forcing,aerosol is another important forcing agent that canexert forcing directly(the direct effect) and also im-pact the radiative budget via interactions with cloud(the indirect effect). The di±culty in estimating theaerosol forcing adds more uncertainty to the accurateestimation of the ECS/TCR.

The OHU plays an important role in theTCR/TCRE. A strong OHU delays the warming(Zhao and Shi, 1995; Stouffer et al., 2006). The simu-lation of eddy mixing intensity in ocean models cansignificantly affect the OHU in the vertical profile.Strong mixing in the Southern Ocean favors more heattaken up by the ocean,which is further transportedinto the deep ocean through the meridional overturn-ing circulation(Zhang and Vallis, 2013). Large diver-gence in the spatial distribution of the OHU acrossmodels has been observed. Two typical distributionsare prominent in the zonally mean pattern: high-latitude OHU and low-latitude OHU, and these havedifferent influences on the global warming. Followinga more effective high-latitude OHU,weaker warmingis witnessed(Winton et al., 2010; Rose et al., 2014).If the carbon cycle is considered,the increasing rateof the cumulative CO2 emissions is closely relatedto the carbon sources and sinks on l and and in theocean. The uncertainties in the ecological processes and the interactions with temperature,precipitation, and ocean circulation,can further impact the magni-tude of the TCRE(Gillett et al., 2013).

5. Relationship between the 2‰ threshold and climate sensitivity

The 2℃‰ threshold issue is of wide concern amongthe public and research community. The 2℃‰ warm-ing of Ts above the pre-industrial level is consideredas a threshold that indicates dangerous anthropogenicinterference(Mann,2009). Given the same radiativeforcing and OHU,a larger ECS will shorten the timethat it takes to reach a 2℃‰ warming. If ECS is rela-tively large,the aim of an ultimate warming below 2℃‰requires a small forcing(CO2 concentration),whichputs greater stress on emission reduction for humansociety. The issue can be understood based on theforcing-response relation.

Based on Eq.(4),the ultimate equilibrium tem-perature ΔT is proportional to the forcing F. Assum-ing constant feedback λ,we obtain

where C(ppm)is the current concentration of CO2,which is assumed to remain unchanged; 278 ppm isthe pre-industrial reference CO2 concentration. TheCO2 concentration C can be expressed as a functionof equilibrium warming ΔT and ECS,

The relationship between C and ECS given at ΔT= 1.5‰(blue line),2‰(black line), and 3‰(magentaline)is shown in Fig. 4. The range of ECS is fromthe IPCC estimation,i.e.,1.5{4.5 K. When ΔT = 2‰ and the value of ECS is near the median of the range(about 3 K,50% probability higher or lower),the cor-responding CO2 concentration is about 450 ppm. Thisforms the basis of the statement that the atmosphericCO2 concentration should not exceed 450 ppm if thewarming is intended to be below the 2‰ threshold(Schneider et al., 2007; Calvin et al., 2009; Wang et al., 2013; Oppenheimer et al., 2014).

It should be noted that the uncertainty in ECShas a substantial impact on the CO2 concentrationunder a certain temperature target. If ECS is 1.5 K,the CO2 concentration can be as large as 700 ppm(Fig. 4). However,based on current knowledge,theprobability of an ECS below 1.5 K is very small(lessthan 0.05; Stocker et al., 2013). That is why Mann(2014)emphasized the importance and urgency of re-ducing GHG emissions,although we have experienced a flat warming period referred to as the global warm-ing hiatus during the last decade.

Fig. 4 Relationship between the equivalent CO2 concen-tration and ECS constrained by a certain warming thresh-old.The range of ECS is from the new estimation in IPCC AR5.The curves under the 1.5℃‰(blue),2‰℃(black),and 3‰(magenta) threshold are shown.For the 2℃‰ threshold,the corresponding equivalent CO2 concentration is about 450 ppm when ECS is the median estimated value.
6. Research prospects

The history of research on climate sensitivity canbe traced back 100 years. Following the increase inobservational data,the development of fully coupledclimate system or even earth system models, and theimprovement of approaches to feedback analysis,ourunderst and ings on the issue have greatly improved.Nevertheless,there remain a great number of chal-lenges. For example,high-quality observational datahave too short history to detect the climate change sig-nal,especially in the Southern Ocean where the OHUis substantially large. In addition,the parameteriza-tion processes in current state-of-the-art climate mod-els are far from perfect. This further reduces the relia-bility and limits the application of model output. Thedi±culty in reducing the uncertainty of climate sensi-tivity can be either due to the intrinsic climate systemor the deficiency of our current knowledge. Based onour review of recent progress in this field,the follow-ing research priorities are recommended to the climatesensitivity research community,in particular the Chi-nese community where the contribution of climate sen-sitivity studies remains weak.

6.1 Nonlinear interaction of feedbacks

Linear feedback analysis is a mature method. TheRadiative Kernel approach based on linear feedbackanalysis can provide spatial distribution informationon different feedback processes. However,large gapsbetween the sum of individual feedbacks and totalfeedback are found in many models,indicating thatstrong nonlinear interactions are non-negligible(Via et al., 2013). The climate sensitivity is determinedby feedback. Therefore,the interactions among differ-ent feedback processes should be highlighted in futureresearch.

6.2 Constraining climate sensitivity by combining new observations and model development

One precondition for reliable climate sensitivityin a model is that the historical climate change shouldbe reasonably reproduced by the model,such as thewarming trend in the 20th century. Many modelsstill show limitations in this regard(Zhou and Yu, 2006; Zhou et al., 2013). The uncertainty of a climatemodel's sensitivity could be reduced if the model hasbeen su±ciently constrained by observations(Jackson et al., 2008). Cloud-related convection is one impor-tant source of uncertainty in climate sensitivity(Sherwood et al., 2014). It is necessary to improve the spa-tiotemporal resolution of cloud and convection moni-toring on the global scale,to promote underst and ing ofthe interactions between cloud,convection and large-scale circulation, and properly parameterize these pro-cesses in climate models(Stevens and Bony, 2013). Inaddition,it remains a great challenge for climate mod-els to simulate the abrupt change recorded in paleo-climatic record,which is a strict criterion to test theperformance of climate models(Wang et al., 2013).

6.3 Estimating earth system sensitivity

Under the concept of traditional physical climate,the focus of climate sensitivity research is the forcing-response-feedback process following an increase of at-mospheric CO2. However,the responses of l and and ocean carbon repositories are not taken into account.In nature,the carbon cycle,including biological ef-fects,can further feed back to the increasing atmo-spheric CO2 concentration and surface warming. Thiskind of process can influence the change in Ts from thedecadal to the millennial timescales, and impact theestimation of ECS. The carbon cycle and related feed-backs determine the increasing rate of cumulative CO2emissions,adding further uncertainty to the TCRE.Thus,more effort is needed in terms of estimating theearth system sensitivity, and developing an optimalemission path using the concept of TCRE.

Acknowledgments: We would like to thankthe two anonymous reviewers for their constructivesuggestions and comments,which helped in improv-ing the paper.

References
Andrews, T., J. M. Gregory, M. J. Webb, et al., 2012: Forcing, feedbacks and climate sensitivity in CMIP5 coupled atmosphere-ocean climate models. Geophys. Res. Lett., 39, L09712.
Arrhenius, S., 1896: On the influence of carbonic acid in the air upon the temperature of the ground. Philos. Mag., 41, 237-276.
Boucher, O., D. Randall, P. Artaxo, et al., 2013: Clouds and aerosols. Climate Change 2013:The Physical Science Basis. Stocker, T. F., D. H. Qin, G.-K. Plattner, et al., Eds., Cambridge University Press, Cambridge, United Kingdom and New York, USA, 1535 pp.
Calvin, K. V., J. A. Edmonds, B. Bond-Lamberty, et al., 2009: 2. 6:Limiting climate change to 450 ppm CO2 equivalent in the 21st century. Energ. Econ., 31, S107-S120.
Cess, R. D., 1975: Global climate change:An investiga-tion of atmospheric feedback mechanisms. Tellus, 27, 193-198.
Charney, J., A. Arakawa, D. J. Baker, et al., 1979: Car-bon dioxide and climate:A scientific assessment. Report of an Ad Hoc Study Group on Carbon Diox-ide and Climate. National Academy of Sciences Press, Washington D. C., 22 pp.
Chen Xiaolong, Zhou Tianjun, and Guo Zhun, 2014: Cli-mate sensitivities of two versions of FGOALS model to idealized radiative forcing. Sci. China (Earth Sci.), 57, 1363-1373.
Collins, M., R. Knutti, J. Arblaster, et al., 2013: Long-term climate change:Projections, commitments and irreversibility. Climate Change 2013:The Physical Science Basis. Stocker, T. F., D. H. Qin, G.-K. Plattner, et al., Eds., Cambridge University Press, Cambridge, United Kingdom and New York, USA, 1535 pp.
Colman, R., 2003: Seasonal contributions to climate feed-backs. Climate Dyn., 20, 825-841.
Cubasch, U., G. Meehl, G. J. Boer, et al., 2001: Pro-jections of future climate change. Climate Change 2001:The Scientific Basis. Houghton, J. T., Y. H. Ding, D. J. Griggs, et al., Eds., Cambridge Univer-sity Press, Cambridge, United Kingdom and New York, USA, 881 pp.
Danabasoglu, G., and P. R. Gent, 2009: Equilibrium cli-mate sensitivity:Is it accurate to use a slab ocean model? J. Climate, 22, 2494-2499.
Flato, G., J. Marotzke, B. Abiodun, et al., 2013: Evalu-ation of climate models. Climate Change 2013:The Physical Science Basis. Stocker, T. F., D. H. Qin, G.-K. Plattner, et al., Eds., Cambridge University Press, Cambridge, United Kingdom and New York, USA, 1535 pp.
Forster, P. M. F., and J. M. Gregory, 2006: The climate sensitivity and its components diagnosed from earth radiation budget data. J. Climate, 19, 39-52.
Forster, P., V. Ramaswamy, P. Artaxo, et al., 2007: Changes in atmospheric constituents and in radia-tive forcing. Climate Change 2007:The Physical Science Basis. Solomon, S., D. H. Qin, M. Manning, et al., Eds., Cambridge University Press, Cambridge, United Kingdom and New York, USA, 996 pp.
Gillett, N. P., V. K. Arora, D. Matthews, et al., 2013: Constraining the ratio of global warming to cumu-lative CO2 emissions using CMIP5 simulations. J. Climate, 26, 6844-6858.
Goodwin, P., R. G. Williams, and A. Ridgwell, 2015: Sensitivity of climate to cumulative carbon emis-sions due to compensation of ocean heat and carbon uptake. Nat. Geosci., 8, 29-34.
Gregory, J. M., R. J. Stouffer, S. C. B. Raper, et al., 2002: An observationally based estimate of the cli-mate sensitivity. J. Climate, 15, 3117-3121.
Gregory, J. M., W. J. Ingram, M. A. Palmer, et al., 2004: A new method for diagnosing radiative forc-ing and climate sensitivity. Geophys. Res. Lett., 31, L03205.
Gregory, J. M., and P. Forster, 2008: Transient climate response estimated from radiative forcing and ob-served temperature change. J. Geophys. Res., 113, D23105.
Han Bo, Lü Shihua, et al., 2015: Connection between atmospheric latent energy and energy fluxes simu-lated by nine CMIP5 models. J. Meteor. Res., 29, 412-431.
Hansen, J., A. Lacis, D. Rind, et al., 1984: Climate sensitivity:Analysis of feedback mechanisms. Cli-mate Processes and Climate Sensitivity. Hansen, J. E., and T. Takahashi, Eds., American Geophysical Union, Washington D. C., 130-163.
Hansen, J., M. Sato, R. Ruedy, et al., 2005: Efficacy of climate forcings. J. Geophys. Res., 110, D18104.
Held, I. M., and B. J. Soden, 2000: Water vapor feedback and global warming. Annu. Rev. Energy Environ., 25, 441-475.
Held, I. M., and K. M. Shell, 2012: Using relative humid-ity as a state variable in climate feedback analysis. J. Climate, 25, 2578-2582.
Ingram, W., 2013: A new way of quantifying GCM water vapour feedback. Climate Dyn., 40, 913-924.
IPCC, 1990: Climate Change:The IPCC Scientific As-sessment. Houghton, J. T., G. J. Jenkins, J. J.
Ephraums, Eds., Cambridge University Press, Cam-bridge, United Kingdom and New York, USA, 365 pp.
Jacob, D. J., R. Avissar, G. C. Bond, et al., 2005: Ra-diative Forcing of Climate Change:Expanding the Concept and Addressing Uncertainties. The Na-tional Academies Press, Washington D. C., 207 pp. Klocke, D., R. Pincus, and J. Quaas, 2011:On constrain-ing estimates of climate sensitivity with present-day observations through model weighting. J. Climate, 24, 6092-6099.
Li, C., J.-S. Von Storch, and J. Marotzke, 2013: Deep-ocean heat uptake and equilibrium climate response. Climate Dyn., 40, 1071-1086.
Ma Xiaoyan, Shi Guangyu, Guo Yufu, et al., 2005: Radia-tive forcing by greenhouse gases and sulfate aerosol. Acta Meteor. Sinica, 63, 41-48. (in Chinese)
Manabe, S., and R. F. Strickler, 1964: Thermal equilib-rium of the atmosphere with a convective adjust-ment. J. Atoms. Sci., 21, 361-385.
Manabe, S., and R. T. Wetherald, 1967: Thermal equi-librium of the atmosphere with a given distribution of relative humidity. J. Atoms. Sci., 24, 241-259.
Manabe, S., and R. T. Wetherald, 1975: The effects of doubling the CO2 concentration on the climate of a general circulation model. J. Atoms. Sci., 32, 3-15. Mann, M. E., 2009:Defining dangerous anthropogenic interference. Proc. Nat. Acad. Sci. USA, 106, 4065-4066.
Mann, M. E., 2014: False hope. Sci. Am., 310, 78-81. Masters, T., 2014:Observational estimate of climate sensitivity from changes in the rate of ocean heat uptake and comparison to CMIP5 models. Climate Dyn., 42, 2173-2181.
Matthews, H. D., N. P. Gillet, P. A. Stott, et al., 2009: The proportionality of global warming to cumulative carbon emissions. Nature, 459, 829-832.
Myhre, G., E. J. Highwood, K. P. Shine, et al., 1998: New estimates of radiative forcing due to well mixed greenhouse gases. Geophys. Res. Lett., 25, 2715-2718.
Myhre, G., D. Shindell, F.-M. Bréon, et al., 2013: An-thropogenic and natural radiative forcing. Climate Change 2013:The Physical Science Basis. Stocker, T. F., Qin Dahe, G.-K. Plattner, et al., Eds., Cam-bridge University Press, Cambridge, United King-dom and New York, USA, 1535 pp.
Olson, R., R. Sriver, M. Geos, et al., 2012: A climate sensitivity estimate using Bayesian fusion of instru-mental observations and an Earth System model. J. Geophys. Res., 117, D04103.
Oppenheimer, M., M. Campos, R. Warren, et al., 2014: Emergent risks and key vulnerabilities. Climate Change 2014:Impacts, Adaptation, and Vulnera-bility. Part A:Global and Sectoral Aspects. Field, C. B., V. R. Barros, D. J. Dokken, et al., Eds., Cambridge University Press, Cambridge, United Kingdom and New York, USA, 1820 pp.
Pithan, F., and T. Mauritsen, 2014: Arctic amplification dominated by temperature feedbacks in contempo-rary climate models. Nat. Geosci., 7, 181-184.
Ramaswamy, V., O. Boucher, J. Haigh, et al., 2001: Ra-diative forcing of climate change. Climate Change 2001:The Scientific Basis. Houghton, J. T., Y. H. Ding, D. J. Griggs, et al., Eds., Cambridge Univer-sity Press, Cambridge, United Kingdom and New York, USA, 881 pp.
Randall, D. A., R. A. Wood, S. Bony, et al., 2007: Cli-mate models and their evaluation. Climate Change 2007:The Physical Science Basis. Solomon, S., D. H. Qin, M. Manning, et al., Eds., Cambridge Uni-versity Press, Cambridge, United Kingdom and New York, USA, 996 pp.
Roe, G., 2009: Feedbacks, timescales, and seeing red. Annu. Rev. Earth Planet Sci., 37, 93-115.
Roe, G. H., and M. B. Baker, 2007: Why is climate sen-sitivity so unpredictable? Science, 318, 629-632.
Roe, G. H., and K. C. Armour, 2011: How sensitive is cli-mate sensitivity? Geophys. Res. Lett., 38, L14708.
Rohling, E. J., A. Sluijs, H. A. Dijkstra, et al., 2012: Making sense of palaeoclimate sensitivity. Nature, 491, 683-691.
Rose, B. E. J., K. C. Armour, D. S. Battisti, et al., 2014: The dependence of transient climate sensitivity and radiative feedbacks on the spatial pattern of ocean heat uptake. Geophys. Res. Lett., 41, 1071-1078.
Schneider, S. H., S. Semenov, A. Patwardhan, et al., 2007: Assessing key vulnerabilities and the risk from climate change. Climate Change 2007:Im-pacts, Adaptation and Vulnerability. Solomon, S., D. H. Qin, M. Manning, et al., Eds., Cambridge University Press, Cambridge, United Kingdom and New York, USA, 976 pp.
Sherwood, S. C., S. Bony, and J.-L. Dufresne, 2014: Spread in model climate sensitivity traced to atmo-spheric convective mixing. Nature, 505, 37-42.
Shi Guangyu, 1991: Radiative forcing and greenhouse ef-fect due to the atmospheric trace gases. Sci. China (Ser. B), 35, 217-229.
Six, K. D., S. Kloster, T. Ilyina, et al., 2013: Global warming amplified by reduced sulphur fluxes as a result of ocean acidification. Nat. Climate Change, 3, 975-978.
Soden, B. J., and I. M. Held, 2006: An assessment of cli-mate feedbacks in coupled ocean-atmosphere mod-els. J. Climate, 19, 3354-3360.
Soden, B. J., I. M. Held, R. Colman, et al., 2008: Quan-tifying climate feedbacks using radiative kernels. J. Climate, 21, 3504-3520.
Stevens, B., and S. Bony, 2013: What are climate models missing? Science, 340, 1053-1054.
Stocker, T. F., D. H. Qin, G.-K. Plattner, et al., 2013: Technical summary. Climate Change 2013:The Physical Science Basis. Stocker, T. F., D. H. Qin, G.-K. Plattner, et al., Eds., Cambridge University Press, Cambridge, United Kingdom and New York, USA, 1535 pp.
Stouffer, R. J., and S. Manabe, 1999: Response of a coupled ocean-atmosphere model to increasing at-mospheric carbon dioxide:Sensitivity to the rate of increase. J. Climate, 12, 2224-2237.
Stouffer, R. J., J. Russell, and M. J. Spelman, 2006: Im-portance of oceanic heat uptake in transient climate change. Geophys. Res. Lett., 33, L17704.
Vial, J., J.-L. Dufresne, and S. Bony, 2013: On the inter-pretation of inter-model spread in CMIP5 climate sensitivity estimates. Climate Dyn., 41, 3339-3362.
Wang Mingxing, Zhang Renjian, and Zheng Xunhua, 2000: Sources and sinks of greenhouse gases. Cli-matic Environ. Res., 5, 75-79. (in Chinese)
Wang Shaowu, Luo Yong, Zhao Zongci, et al., 2012: Equi-librium climate sensitivity. Adv. Climate Change Res., 8, 232-234. (in Chinese)
Wang Shaowu, Luo Yong, Zhao Zongci, et al., 2013: The Sciences of Global Warming. China Meteorological Press, Beijing, 205 pp. (in Chinese)
Winton, M., K. Takahashi, and I. M. Held, 2010: Im-portance of ocean heat uptake efficacy to transient climate change. J. Climate, 23, 2333-2344.
Zeng, N., and J. Yoon, 2009: Expansion of the world's deserts due to vegetation-albedo feedback under global warming. Geophys. Res. Lett., 36, L17401.
Zhang Hua and Huang Jianping, 2014: Interpretation of the IPCC Fifth Assessment Report on anthro-pogenic and natural radiative forcing. Adv. Climate Change Res., 10, 40-44. (in Chinese)
Zhang, Y., and G. K. Vallis, 2013: Ocean heat uptake in eddying and non-eddying ocean circulation mod-els in a warming climate. J. Phys. Oceanogr., 43, 2211-2229.
Zhao Fengsheng and Shi Guangyu, 1995: A study of the transient and time-dependent greenhouse gas-induced climate change. Acta Geogra. Sinica, 50, 430-438. (in Chinese)
Zhou Tianjun, Song Fengfei, and Chen Xiaolong, 2013: Historical evolution of global and regional sur-face air temperature simulated by FGOALS-s2 and FGOALS-g2:How reliable are the model results? Adv. Atmos. Sci., 30, 638-657.
Zhou Tianjun, Wang Shaowu, and Zhang Xuehong, 1998: Proceeding of modelling studies on the stability and variability of the thermohaline circulation. Adv. Earth Sci., 13, 334-343. (in Chinese)
Zhou Tianjun, Wang Shaowu, and Zhang Xuehong, 2000: Comments on the role of thermohaline circulation in global climate system. Adv. Earth Sci., 15, 654-660. (in Chinese)
Zhou, T. J., and R. C. Yu, 2006: Twentieth-century surface air temperature over China and the globe simulated by coupled climate models. J. Climate, 19, 5843-5858.
Zhou Tianjun, Zou Liwei, Wu Bo, et al., 2014: Devel-opment of earth/climate system models in China:A review from the coupled model intercomparison project perspective. J. Meteor. Res., 28, 762-779.
Jackson, C. S., M. K. Sen, G. Huerta, et al., 2008: Error reduction and convergence in climate prediction. J. Climate, 21, 6698-6709.