The Concept of Climate Sensitivity: History and Development

The concept of climate sensitivity: history and development

Natalia Andronova, Michael Schlesinger, Suraje Dessai, Mike Hulme and Bin Li

1.1 Introduction Between the 1960s and 1980s various types of deterministic models were used to estimate climate sensitivity, leading to a The climate sensitivity concept (CSC) has more than a century wide range of results. However, it was a mixture of modeling of history. It is closely related to the concept of “climate results and expert assessment – the Charney report of 1979 forcing” or “radiative forcing,” which was fully presented and (NAS, 1979) – that established the range of 1.5 C to 4.5 C discussed by successive IPCC Assessment Reports (e.g. see that was later reported in all three IPCC Assessment Reports Chapter 6 Houghton et al., 2001). According to CSC, a change (IPCC, 1990, 1996, 2001). in the equilibrium global Currently the primary reason for the substantial range in near-surface air temperature (NST) of the Earth, 1T, due to an model-based estimates of climate sensitivity is widely external disturbance of the Earth’s energy balance (radiative believed to be differences in their treatment of feedbacks forcing), can be linearly related to a change in the net radiation (Schlesinger, 1985, 1988, 1989; Cess et al., 1996; Colman, at some level in the atmosphere, 1F. Thus, 2003) – particularly cloud feedbacks. But systematic comparisons have not been made to conﬁrm that this is true for the 1T ¼ ‚1F; ð1:1Þ current generation of models. Within international climate where ‚ is the climate sensitivity, which characterizes the modeling projects, the development of new models, together ability of the climate system to amplify or reduce the initial with both formal and informal model comparison exercises temperature change initiated by the external forcing. The cli- that are currently being conducted by various groups, suggests mate sensitivity has been estimated using Eq. (1.1) most fre- that a renewed focus on the reasons for different model-based quently from the NST change, 1T2x, resulting from the estimates of climate sensitivity may be particularly useful at radiative forcing due to a doubling of atmospheric carbon this time. dioxide concentration from pre-industrial levels, 1F2x: The probability density and cumulative distribution func- tions for 1T obtained recently using the instrumental tem- 1T 2x ‚ ¼ 2x : ð : Þ peratures and estimated forcing from the mid-nineteenth 1 1 2 F2x century to the present by four groups (Andronova and Schle-

Thus 1T2x has become a surrogate for ‚ and has played a singer, 2001; Forest et al., 2002; Gregory et al., 2002; Knutti central role throughout the history of IPCC in interpreting the et al., 2002), using different methods, indicate that the IPCC 1 output of numerical models, in evaluating future climate range for the climate sensitivity, 1.5 C T2x 4.5 C, is too changes from various scenarios, and in attributing the causes narrow. This is consistent with the observation that experts of observed temperature changes. routinely underestimate uncertainty (Kahneman et al., 1982;

Human-induced Climate Change: An Interdisciplinary Assessment, ed. Michael Schlesinger, Haroon Kheshgi, Joel Smith, Francisco de la Chesnaye, John M. Reilly, Tom Wilson and Charles Kolstad. Published by Cambridge University Press. Ó Cambridge University Press 2007. 6 Andronova et al.

Shlyakhter, 1994). The four independent estimates indicate obtained from climate simulations with time-dependent for- that there is no likelihood that 1T2x < 0.6 C (this is a parti- cing, F(t). If the radiative forcing in Eq. (1.3) were made cularly robust finding), but there is a 5% likelihood that time-independent, then dHðtÞ=dt would approach zero 1T2x 9 C. with increasing time as the climate system approaches equi- As we show here, some recent studies suggest that new librium and ‚eff(t) would approach ‚eq. Time series of the insights into the likely range of climate sensitivity may be effective climate sensitivity demonstrate how feedbacks of the possible through comparisons of models and observational climate system evolve with time. data – contemporary, historical and paleoclimatic. Other The transient climate sensitivity (after Murphy and Mitch- recent studies raise issues regarding the applicability of ell, 1995) is given by response/forcing relationships in the climate system – such as 1 ð Þ the degree of predictability of climate and the relevance of T t2x ‚trans ¼ ð1:4Þ climate predictability for estimates of climate sensitivity, and F2x the degree to which forcings such as those due to where 1T(t ) is the change in NST when the CO con- solar variability, well-mixed greenhouse gases, and aerosols 2x 2 centration increases to double the pre-industrial value in a may produce different responses. transient climate simulation, particularly one in which the CO In Section 1.2 we briefly review the history of the climate 2 concentration increases at 1% per year. Because the thermal sensitivity concept. Section 1.3 presents some recent devel- inertia of the ocean 1T(t ) < T , ‚ < ‚ . Calculations of opment of this concept. Section 1.4 discusses some of its 2x 2x trans eq the transient climate sensitivity are primarily used for com- possible future developments. Concluding remarks are given parison among coupled atmosphere/ocean general circulation in Section 1.5. models because these models take thousands of years to equilibrate. However, because the actual climate system is 1.2 History of the climate sensitivity always facing external stresses from multiple simultaneous concept (CSC) forcings, at any particular time the climate system is facing transient sensitivity. Under slowly evolving external forcings, The concept of climate sensitivity and the development of this the transient sensitivity may be approximated by ‚ . concept are directly related to empirical or model estimations eq Model-based estimation of climate sensitivity varies con- that established a linear relationship between radiative forcing siderably from model to model because of different para- and near-surface air temperature. CSC originated from the meterizations of physical processes that are not explicitly concept of the greenhouse effect, introduced by Arrhenius at resolved in the respective models, such as clouds. For exam- the end of the nineteenth century (Arrhenius, 1896). Arrhenius ple, energy balance models (EBMs), typically one- or two- defined the greenhouse effect in terms of 1T . Almost a 2x dimensional, generally predict only the NST and frequently century later, Budyko (1972) and Sellers (1969) repeated only in terms of its globally averaged value. The value of Arrhenius’s calculations using more comprehensive energy 1T obtained by EBMs ranges from 0.24 C (Newell and balance models (North, 1981), and strongly supported the 2x Dopplick, 1979) to 9.6 C (Mo¨ller, 1963). concept of the greenhouse effect. As a result, the climate Radiative-convective models (RCMs) determine the vertical sensitivity concept was promulgated. distribution of atmospheric temperature and the surface tem- Until the third IPCC report (IPCC, 2001), the concept of perature, virtually always in terms of their globally averaged climate sensitivity was based on calculations of the equili- values. As their name indicates, radiative-convective models brium NST change. However, the third IPCC report (Cubasch, include the physical processes of radiative transfer and con- 2001) defined three measures of climate sensitivity, with the vection. The value of 1T obtained by RCMs ranges from differences between the measures arising from the different 2x 0.48 C (Somerville and Remer, 1984) to 4.2 C (Wang and types of simulations performed with the climate model. Stone, 1980). The equilibrium climate sensitivity ‚ is given by Eq. (1.1) eq Atmospheric general circulation models (AGCMs) simulate and is estimated from climate simulations in which the radiative the vertical and geographical distributions of temperature, forcing does not vary with time after an initial change, such as surface pressure, wind velocity, water vapor, vertical velocity, for an instantaneous CO doubling. Most estimations were made 2 geopotential height, ground temperature and moisture, and the for ‚ , which we will review below. eq geographical distribution of snow and ice on the ground. The effective climate sensitivity (after Murphy, 1995) is AGCMs have been coupled with different ocean and sea-ice given by models. These include a swamp ocean which has zero heat 1TðtÞ capacity but infinite water, a mixed-layer ocean which has a ‚ ðtÞ¼ ð1:3Þ eff FðtÞdHðtÞ=dðtÞ prescribed depth, and a full dynamic ocean GCM, which is the oceanic counterpart of the AGCM. Sea-ice models range from where dHðtÞ=dt is the change in heat storage of the climate freezing a swamp ocean (where the temperature would system – essentially the heat taken up or lost by the ocean, otherwise drop below the freezing temperature of seawater) The concept of climate sensitivity 7

that has only thermodynamics and no transport by wind or Tol and de Vos (1998) (TdV) made one of the first inverse currents, to a fully dynamic-thermodynamic sea-ice model. In estimations of the probability density function (pdf) of climate all cases the atmosphere/ocean model has a finite horizontal sensitivity. They used a simple statistical model and Bayesian and vertical resolution. The value of 1T2x obtained by updating in combination with expert opinion and observational AGCMs ranges from 1.3 C (Washington and Meehl, 1983) to constraints on the initial (prior) pdf of 1T2x. They found that 5.2 C (Wilson and Mitchell, 1987). large values of 1T2x cannot be excluded and that the posterior All of the above ranges of the climate sensitivity estimates pdf is strongly dependent on the prior pdf. are based on a set of individual model runs and should be Starting with the analysis by Andronova and Schlesinger treated in a statistical sense as equally plausible, because each (2001), referred to below as AS01, there have been a handful model has different sets of feedbacks, induced by different of estimates of the pdf and cumulative density function (cdf) model parameterizations, built to be consistent with various for 1T2x using simplified climate models (SCM) to replicate observational data obtained from monitoring of the different the temperature changes observed since the middle of the parts of the climate system. nineteenth century. Andronova and Schlesinger (2001) used an The growing amount of empirical temperature data has SCM consisting of an EBM coupled to an upwelling – diffu- resulted in numerous attempts to use these data to estimate sion model of the ocean to simulate the change in hemi- the climate sensitivity inversely. Budyko (1987) made the spheric-mean temperatures from 1765 to the present for earliest such estimate of the climate sensitivity using paleodata prescribed radiative forcing. Sixteen radiative forcing models of northern hemisphere temperature and atmospheric carbon (RFMs) were examined with all possible combinations of: (1) dioxide concentration for six paleoclimate epochs (a review of anthropogenic radiative forcing consisting of greenhouse-gas these earlier estimates can be found in Schlesinger [1985]). (GHG) forcing due to the increasing concentrations of CO2, The pre-instrumental proxy record consists of quantities that methane, N2O, chlorofluorocarbons and tropospheric ozone, are sensitive to temperature, such as the thickness and isotopic and the direct (clear air) plus indirect (cloudy air) radiative composition of the annual growth rings of trees and corals, and forcing by tropospheric sulfate aerosols (SO4); (2) volcanic the annual layers of glacial ice; the relative abundance and radiative forcing; and (3) solar radiative forcing. The values of isotopic composition of planktonic (living near the sea sur- 1T2x and the unknown sulfate forcing in reference year 1990, face) and benthic (living near the sea floor) foraminifera 1FASA(1990), where ASA is anthropogenic sulfate aerosol, (shell-covered species) that, after dying, fall to the sea floor were estimated for each RFM by optimizing the fit of the where they are covered up by the sedimentary material raining simulated and observed global-mean temperatures (GMT) and down from above; and the relative abundance of pollen in the the interhemispheric temperature differences (ITD), respec- annual growth layers of sediment at the bottom of lakes tively. The difference between the observed and simulated (Ruddiman, 2000). These proxy data are converted into tem- GMT and ITD was bootstrapped to generate 5000 samples of peratures using statistical relations that have been developed the unforced noise to which was added the simulated tem- based on the present climate. The reconstructed temperature perature signal to create 5000 surrogate observational hemi- for any paleoclimate gives the temperature difference from the spheric temperature records. For each ensemble member present, 1Ts. This is used to estimate the climate sensitivity thereof, the values of 1T2x and 1FASA (1990) were estimated from using the same procedure as used for the single real observational record. This method of estimating the climate sensi- 1F2x tivity does not depend on priors for the estimated quantities, 1T2x ¼ 1Ts ð1:5Þ 1F but rather on the combination of the three types of radiative forcing, anthropogenic, solar and volcanic, and the natural where 1F is an estimate of the radiative forcing. The range variability of the observed temperatures. The resulting (AS01) using paleo-based methods is 1.4 C (Hoffert and Covey, cdf for 1T2x has a mean value of 3.40 C, a 90% confidence 1992), for the lowest estimation, to 6.0 C (Barron, 1994), for interval of 1.0 C to 9.3 C, and a 54% likelihood that 1T2x the highest estimation. There are at least three factors that lead lies outside the IPCC range of 1.5 to 4.5 C. to uncertainty in the estimates of 1T2x by the paleo-calibra- Gregory et al. (2002) (GEA02 ) estimated climate sensi- tion method. First, the proxy data for temperature are not tivity from global in extent, hence their global average is uncertain, and 1 0 their conversion to temperature is also uncertain (Mann and T 1T2x ¼ 0 0 ; ð1:6Þ Jones, 2003). Second, estimation of the radiative forcing for Q F paleoclimates relative to the present climate is difficult and 0 where 1T is the change in the observed global-mean near-- thus uncertain. Third, the sensitivity of paleoclimate tem- 0 perature changes from the present climate may be different surface temperature between 1861–1900 and 1957–1994, Q is from the sensitivity of future human-induced temperature the change in the estimated radiative forcing between the two 0 changes from the present because the active feedbacks in each periods, and F is the change in heat uptake between the two period are different. periods – calculated by an SCM for the earlier period and 8 Andronova et al.

estimated from observations for the latter. Normal probability uniform prior distribution of the climate sensitivity and found 0 distributions are assumed for 1T , with 2 between 0.302 C that the surface warming in 2100 exceeded the range projected 0 and 0.368 C; Q , with 2 between 0.3 and þ 1.0 W/m2; and by IPCC for almost half the ensemble members. They noted 0 F , with 2 between 0.00 and 0.32 W/m2. A singularity exists that reduction of the uncertainty in climate sensitivity requires 0 0 0 0 where F approaches Q . When F is larger than Q , a significant reduction in the uncertainties of the observational this implies a negative sensitivity, which was rejected temperatures, as well as better constraints on the reconstructed because it would make the climate system unstable to natural radiative forcing. variations. Figure 1.1a summarizes all estimates of the climate sensi- Forest et al. (2002) used the Massachusetts Institute tivity described in this section. In this figure we sorted the of Technology two-dimensional (latitude–altitude) statistical- estimates into two groups: the deterministic estimates, based dynamical model to simulate climate change from 1860 to on estimation of the single number, and the probabilistic 1995, varying 1T2x, oceanic vertical heat diffusivity, K, and estimates, based on constructing a probability density function anthropogenic aerosol forcing for the 1980s decade relative to (pdf) or cumulative density function (cdf). The left part of pre-1860. They used optimal fingerprint detection in latitude, Figure 1.1a presents ranges of the climate sensitivity based on altitude and time of the simulated climate change in the the deterministic estimates. The right side of this figure pre- observed climate change for surface air temperature, ocean sents ranges of the probabilistic estimates based on the 90% temperature (0 to 3000 m) and tropospheric temperature. Their confidence interval of the probabilistic estimates. Among the optimal fingerprint detection algorithm was based on pattern deterministic estimates we have included the IPCC range. matching for the patterns for surface, upper-air, and deep- Among the probabilistic estimates we have included an esti- ocean temperature changes. The comparison was made for mate given by the Charney report of 1979 (NAS, 1979), four zonal bands (90 S–30 S, 30 S–0,0–30 N, 30 N– namely. “3 C with a probable error of ±1.5 C,” which we 90 N) for decadal-mean temperature for the 1946–95 period have interpreted as the 50% confidence interval, labeled as relative to the 1906–95 climatology using an observational NRC79. The range cited by IPCC originated from NAS data mask. A goodness-of-fit statistic was computed for each (1979). Also, in this figure we have included an expert elici- of the three quantities. In the optimal detection, noise esti- tation of 16 climate “experts” performed by Morgan and Keith mates for each diagnostic were obtained from two atmosphere/ (Morgan and Keith, 1995) of Carnegie-Mellon University ocean GCMs. The surface and upper-air diagnostics reject (CMU95) five years after the IPCC First Assessment Report similar regions, namely low K and high 1T2x, while the ocean was published. For this we combined the 16 experts’ opinions diagnostic rejects high K and high 1T2x. Rejection regions in terms of their mean estimation and variance cited in shift to higher 1T2x for increasing negative aerosol forcing. Morgan and Keith (1995) into a single cdf, under the Bayes’ theorem was used to update the pdfs of parameters assumption that each of the 16 estimations is normally dis- from an assumed starting (prior) pdf. The resulting 1T2x cdfs tributed. It is seen that the CMU95 cdf has a non-zero prob- for a uniform starting pdf is wider than for the expert prior pdf ability that 1T2x < 0. This non-zero probability occurs –the 90% confidence interval for the uniform prior is 1.4 Cto because three of the “experts” had a non-zero probability 7.7 C, and for the expert prior is 1.4 C to 4.1 C. For further that 1T2x < 0. references, we will call the resulting cdfs (FUN02) and The right vertical axis of Figure 1.1a shows the climate (FEX02), respectively. sensitivity estimates in terms of the climate system’s total Knutti et al. (2002) (KEA02) used a climate model of feedback, calculated as defined by Schlesinger (1985, 1988, reduced complexity – a zonally averaged dynamical 1989): ocean model coupled to a zonally and vertically averaged ð4T Þ energy- and moisture-balance model of the atmosphere – to f ¼ 1 2x o : ð1:7Þ make 25 000 Monte Carlo simulations of the changes in 4T2x the surface temperature from 1900 to 2000 and the ocean heat Here ð1T Þ ¼ G 1F is the change in global-mean near- uptake from 1955 to 2000. They used multiple values of 1T , 2x o o 2x 2x surface air temperature without feedback due to a doubling of distributed uniformly over 1 Cto10C, and indirect aerosol the pre-industrial CO concentration with radiative forcing forcing in 2000, uniformly distributed over –2 to 0 W/m2. 2 1F ¼ 3.71 W/m2 (Myhre et al., 1998). They found that the climate sensitivity is only weakly con- 2x strained by the ocean heat uptake, which gave 1T2x ¼ 5.7 T ±3 C (one standard deviation). When they used the surface G ¼ s ¼ 0:30 K=ðW=m2Þð1:8Þ o ð1 fi ÞS temperature as a constraint, it gave 1T2x ¼ 4.6 C, with a p range of 1.8 Cto8.7C. As shown by KEA02, the 95% confidence interval for 1T2x is 2.2 C to 9.1 C. is the gain of the climate system without feedback, with Ts Knutti et al. (2003) used a neural-network-based climate- ¼ 288 K the present global-mean NST, S ¼ 1367 W/m2 the model substitute to produce a large number of ensemble present solar irradiance and fip ¼ 0.3 the present planetary 1 ð1 Þ 1 <ð1 Þ < simulations similar to Knutti et al. (2002). They assumed a albedo. If T2x T2x o, f 0, and if T2x T2x o, f 0. The concept of climate sensitivity 9

a 10 0.89 TdV AS01 KEA02 9 0.88 8 FUN02 0.86

7 NRC79 0.84 Total feedback, (˚C) x

2 Paleo CMU95

T 6 0.81

D GCM 5 IPCC 0.78 RCM FEX02 4 0.72 f 3 0.63 2 0.44 line of zero Climate sensitivity, Climate sensitivity, 1 –0.11 feedback 0 infinity EBM –1 Deterministic Probabilistic estimates estimates 5 & 95% confidence interval b 1

0.9 FEX02 0.8 KEA02 TdV 0.7 FUN02 0.6 0.5 GEA02 AS01 0.4

0.3 NCR79 0.2 Cumulative distribution function distribution Cumulative CMU95 0.1 0 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 D Climate sensitivity, T2x (˚C) c

8 (˚C) x 2 T

D 6

2 Climate sensitivity, Climate sensitivity,

0 5% confidence median 95% confidence

Figure 1.1 Estimations of the climate sensitivity (see explanations in the text). 10 Andronova et al.

As can be seen from Figure 1.1a, there are only a few 6 estimates for which the net feedback of the climate system is 2xCO2; NST/ NTOA=0.65 5 negative. ) 2% solar; NST/NTOA=0.60 Figure 1.1b presents cdfs of the probabilistic estimates of 2 the climate sensitivity brieﬂy described in this section. As can 4 be seen, the lower end of the climate sensitivity estimates has a much smaller range of uncertainty than the upper end. For 3 illustrative purposes Figure 1.1c summarizes the uncertainty 2 range in terms of box plots for the 5th, 50th and 95th per- 1 centile values of the cdfs for T2x. This ﬁgure is based on six 1 pdfs shown on Figure 1.1b: TdV, AS01, FEX02, FUN02, KEA02 and GEA02. There is disagreement about the median

Change in the net radiation 0 1T2x, from 2.2 C to 5.0 C, and the 95th percentile, from

at the top of atmosphere (W/m 7.5 C to 10.0 C. These empirical studies, based on observa- –1 tions of the present climate, indicate that there is more than a 50% likelihood that 1T2x lies outside the canonical range of –2 1.5 C to 4.5 C, with disquietingly large values not being 0 0.5 1 1.5 2 2.5 3 3.5 precluded. Change in the global near-surface temperature (˚C)

Figure 1.2 Linear regression between near-surface temperature, 1.3 Recent developments NST, and change in the net radiation at the top of the atmosphere, NTOA. The concept of equilibrium climate sensitivity served well for comparison of sophisticated climate models. In addition it The procedure of calculating climate sensitivity from gen- helped to understand some of the models’ feedbacks, which eral circulation models, whether coupled to a non-dynamic might work as well in the real climate system (Cess et al., model of the upper ocean (mixed-layer ocean model) or to a 1996; Colman, 2003). However, researchers were always dynamic model of the full ocean, is complicated (Wetherald dissatisfied with the wide range of uncertainty in the estimates and Manabe, 1988). There are many uncertainties in how to of climate sensitivity. This is mostly because: (1) uncertainties perform the calculation, mostly related to where in the in the observational data do not allow reduction of the atmosphere and when the forcing and temperature changes uncertainties in the magnitude of the models’ parameters; (2) should be sampled. Recently, Gregory et al. (2004) used a the model parameterizations, which reflect the models’ simple method of monitoring the ratio of the change in the inability to explicitly resolve all the physical processes in the global net radiation at the top of the atmosphere to the change climate system, may not represent actual feedbacks; and (3) it in the global near-surface temperature, which approaches the is not a trivial task to apply advanced mathematical methods equilibrium climate sensitivity as the model approaches its to estimate climate sensitivity and, moreover, make an equilibrium climate change. insightful interpretation of the results. This is why recently To illustrate this method we applied it to compare the questions have been asked about the usefulness of the climate sensitivities of our 24-layer troposphere-stratosphere general sensitivity concept, among which are these. (1) Is the climate circulation model (Yang et al., 2000; Yang and Schlesinger, sensitivity a robust characteristic of the climate system that is 2002; Rozanov et al., 2002a, 2002b; Rozanov et al., 2004) useful in climate economics and policy-making? (2) If not, coupled to a mixed-layer ocean model (24-L AGCM-ML) for should we look for another important climate variable, or two disturbances: a CO2 doubling and a 2% increase in the should we live with the uncertainties until they are resolved to amount of incoming solar radiation. Figure 1.2 presents a some degree? (3) Should we look for another concept to scatter diagram of the change in the monthly mean global net characterize the climate system behavior? Some of those radiation at the top of the atmosphere (NTOA, at 1 hPa) questions are nicely highlighted in the previous IPCC reports. against the change in monthly mean global NST for both The second IPCC report (IPCC, 1996, Chapter 2) introduced experiments, together with respective linear regressions. In the concept of radiative forcing, stated how fast and slow this figure, the change in NTOA initially is due to the per- feedbacks in the climate system relate to the climate sensi- turbation and subsequently decreases as the change in NST tivity, and discussed the robustness of the linear relationship increases and the climate system approaches its new equili- between forcing and response for different forcings. The third brium. The intercept of the regression line with the x-axis IPCC report (IPCC, 2001, Chapter 6) paid much more atten- approximates the equilibrium change in NST due to the dis- tion to the assessment of the concept of the radiative forcing as turbance. The slope of the regression line, 1NST/1NTOA, an important part of the concept of the climate sensitivity. approximates the sensitivity of the model to the disturbances. Below we present some new developments. Thus, if the regression lines for different disturbances are The concept of climate sensitivity 11

parallel to each other, then for these disturbances the model’s Oregon State University (Hall, 1986) to a CO2 doubling. The sensitivities are the same. In the case presented in Figure 1.2, AM allowed the calculation of all linear sensitivities of each the 24-L AGCM-ML has approximately the same sensitivity model parameter to the perturbation and to the initial condi- to the CO2 doubling and 2% increase in solar irradiance. tions, all in one model simulation. However, at that time the Obviously, there are some shortcomings in this approach, application of the AM to larger models did not look feasible, which are discussed in Gregory et al. (2004). The simplicity because of the technical burden of re-writing the model code of the presentation and interpretation, however, makes this to include the model’s adjoint equations and the mathematical method well suited for estimating the equilibrium climate problem of inverting large matrices. Thus, AM was not widely sensitivity, without any additional calculations of the forcing. accepted by the “climate sensitivity community.” But AM has Murphy et al. (2004) presented the Perturbed Physics been extensively applied by the “data assimilation commu- Ensemble Method (PPEM) to estimate the pdf of climate nity,” who developed the Tangent and Adjoint Model Com- sensitivity for an atmospheric general circulation model cou- piler (TAMC) to automatically generate adjoint model code. pled to a mixed-layer ocean model. PPEM consists of running TAMC has been used to monitor and predict the linear ten- multiple realizations of the model with subjectively selected dencies of model variables. Further information is available at model parameters chosen randomly, one by one, from their www.autodiff.com/tamc/. subjectively prescribed range. In terms of computing costs, Large numerical models calculate the climate sensitivity this method has become possible owing to the appearance of directly, but a similar value of the climate sensitivity may be faster computers and massive parallelization of a model’s obtained by different models even if they have different code. One of the limitations of PPEM is that the set of the representations of the models’ physical processes. Learning perturbed parameters is chosen by expert opinion and this may about new parameterizations for the subgrid-scale processes, omit key model parameters. Another important limitation is inventing and applying new techniques for tuning model that parameters are tested one by one and their synergetic parameters, and systematic comparison of the models and their effect on the climate sensitivity is not considered. And com- modules will definitely improve the models, if and only if the puter power still remains a major limiting factor for this kind observational data have satisfactory temporal and spatial of “massive” experiment. However, if it is possible to elim- resolution and low observational errors. Thus most likely we inate most of the shortcomings and use it for many GCMs, will not be able to learn the “true” climate sensitivity from the PPEM should give some very useful insights on GCMs and large models soon, at least not from the IPCC Fourth their climate sensitivities. Assessment Report (AR4) planned for 2007. Figure 1.3 presents a comparison of the climate sensitivity Inverse estimations of climate sensitivity depend heavily values from Murphy et al. (2004) with other estimations. on the uncertainties in the observations. As an example, Figure Figure 1.3a and 1.3b compares two cases from Murphy et al. 1.4 compares the observed historical hemispheric temperature (2004) with some of the estimates presented in Figure 1.1, departures of Jones et al. (2003), J2003, and Folland et al. namely the deterministic climate sensitivity range for existing (2001), F2001, and Figure 1.5 shows the influence of their GCMs, the expert elicitation CMU95, and FEX02 and AS01 differences on the estimate of climate sensitivity. Figures 1.4a which have the smallest and largest 90% confidence interval and 1.4b present a comparison of these data for northern and for climate sensitivity, respectively. The estimates of Murphy southern hemispheres, respectively. It can be seen that the et al. (2004) have a 90% confidence interval for climate sen- northern hemisphere data are very close to each ther, while for sitivity of 1.8 C to 5.2 C for M1, where all model versions the southern hemisphere the F2001 record is warmer in gen- are assumed equally likely, and 2.4 C to 5.2 C for M2, which eral than the J2003 SH record. Figure 1.4c and 1.4d shows the accounts for a reliability-based weighting of model versions temporal behavior of the first two principal components of the according to the climate Prediction Index described in Murphy temperature departure time evolution extracted using Singular et al. (2004). It can be seen that both M1 and M2 are closest to Spectrum Analysis for the northern and southern hemispheres, FEX02, which uses an expert prior, and they are similar to the respectively. Again, it can be recognized that in the southern deterministic range for GCMs with a slightly higher minimum hemisphere there are considerable differences in the temporal estimation. Recently, Stainforth et al. (2005), using the PPME behavior of the two data sets. These differences make a major method, obtained the range of the climate sensitivity 1.5 Cto input into representation of the natural and forced variability 11.5 C by varying combinations of perturbations in six model of the observed temperature departure. Figure 1.5 shows the parameters. This large range of uncertainties for a GCM brings estimation of climate sensitivity using the inverse technique up an old question of the validity of some GCM para- presented in Andronova and Schlesinger (2001), briefly meterizations, especially of cloud microphysics. described in the previous section. This technique is based on We note that the idea of computing the sensitivities of a bootstrapping the residuals – the difference between the model to its parameters is not new. Hall et al. (1982) applied observed and simulated temperatures. Figure 1.5 shows the the adjoint method (AM), formulated by Cacuci (1981) for use climate sensitivity estimated for four radiative forcing models in numerical models, to calculate the sensitivities of a simple used by Andronova and Schlesinger (2001): G – greenhouse radiative-convective model and later the two-layer AGCM of gases only, GA – greenhouse gases and anthropogenic sulfate 12 Andronova et al.

a 10 0.89 AS01 9 0.88

8 0.86

7 0.84 (˚C) Total feedback, x CMU95 2 6 0.81 T M1 M2 GCM 5 IPCC 0.78 FEX02 4 0.72

3 0.63 f

2 0.44 Climate sensitivity, Climate sensitivity, line of zero feedback 1 –0.11

0 infinity –1 Deterministic Probabilistic estimates estimates 5 & 95% confidence interval b

0.9 FEX02 AS01 0.8

0.7

0.6 M2 0.5

0.4

0.3

Cumulative distribution function distribution Cumulative M1 0.2 CMU95 0.1

0 –3–2 –1 0 1 2 3 4 5 6 7 8 9 10 Climate sensitivity, T2x (˚C)

Figure 1.3 Comparison of estimation from Murphy et al. (2004) with estimations in Figure 1.1.

aerosol, GAS – GA plus the solar irradiance variability con- data differences are reconciled, the uncertainty in climate structed by Lean and colleagues (Frohlich and Lean, 1998; sensitivity will remain large. Lean et al., 1995), and GTA – GA plus radiative forcing by Retrospectively, we can look at how the range of the cli- tropospheric ozone. For 100 Monte Carlo estimates of the mate sensitivity evolves with time as new information on climate sensitivity, all three cases show a smaller median and instrumental temperature departures (from the 1961–1990 range for the F2001 data than for the J2003 data. It is neces- average) is added. For this we estimate the climate sensitivity sary to note that the difference between the two instrumental for different record lengths of the J2003 temperature depar- data sets arises from two different methods used to compile tures starting in 1860 and ending in 1940 and then them: the optimal averaging and the area-weighted averaging adding each 10 years of data thereto until the data reach 2000. (Rayner, personal communication) which coincide with Figure 1.6 illustrates the resulting evolution of the climate increasing spatial coverage in both hemispheres. Until these sensitivity for greenhouse gas, tropospheric ozone and aerosol The concept of climate sensitivity 13

a c 0.8 0.3 Northern Hemisphere Northern Hemisphere 0.6 0.2 0.4 0.1 0.2 2d PCs 0 0 –0.1 –0.2 1st PCs –0.2 –0.4

J2003 amplitude (˚C) Component’s –0.6 –0.3 F2001 J2003 Temperature departure (J2003) (˚C) Temperature F2001 –0.8 –0.4 1860 1880 1900 1920 1940 1960 1980 2000 0 50 100 150 Year bdYear 0.6 0.3 Southern Hemisphere Southern Hemisphere 0.2 0.4 0.1 2d PCs 0.2 0

0 –0.1

–0.2 –0.2 1st PCs –0.3 –0.4 amplitude (˚C) Component’s J2003 –0.4

Temperature departure (J2003) (˚C) Temperature F2001 J2003 F2001 –0.6 –0.5 1860 1880 1900 1920 1940 1960 1980 2000 0 50 100 150 Year Year

Figure 1.4 Comparison of the observed near-surface temperature data F2001 and J2003 for northern and southern hemispheres (A and B) and their two ﬁrst principal components calculated using singular spectrum analysis (c and d).

Climate sensitivity (˚C) 4

0 G GA GAS GTA G GA GAS GTA Jones et al. (2003) Folland et al. (2001)

Figure 1.5 Estimation of the climate sensitivity for different radiative forcing models using two data sets. Each box encloses 50% of the data with the median value of the variable displayed as a line. The top (UQ) and bottom (LQ) of the box mark the limits of ±25% of the variable population. The lines extending from the top and bottom of each box mark the minimum and maximum values within the data set that fall within an acceptable range. Any value outside this range, that is greater than UQ þ1.5(UQ LQ) or less than LQ 1.5(UQ LQ), called an outlier, is displayed as an individual point. 14 Andronova et al.

a 0.8 1.4 Future perspectives

0.6 The new IPCC process, started in preparation for the fourth scientiﬁc assessment (AR4) in 2007, began a new discussion 0.4 about the concept of climate sensitivity. Most likely, in the 0.2 new report the climate sensitivity concept will not be dis- missed – it has proven to be useful. Thus, the answer to the 0 question “Has any progress been made in the application and development of the concept of climate sensitivity for under- –0.2 standing climate change?” is “yes”. The estimation of climate sensitivity has progressed from a single value estimate to a –0.4 probability distribution to characterize uncertainty. In addi-

Temperature departure (J2003) (˚C) Temperature –0.6 NH tion, many new methods for estimating climate sensitivity SH have been developed and understanding of climatic processes –0.8 has deﬁnitely improved. However, because of the large 1860 1880 1900 1920 1940 1960 1980 2000 uncertainty in the published estimates of climate sensitivity, Year which is difﬁcult to apply in policy-relevant problems (see b 30 Dessai and Hulme (2004) for a review of the use of climate GTA probabilities in decision-making), the climate sensitivity 25 concept has been questioned in a few aspects, some of which were discussed in the previous section. Also, reduction of the uncertainty in the estimates of climate sensitivity will prob- 20 ably not be possible in the time frame of the AR4, hence policy-makers will need to learn how to deal with this

(˚C) 15

x (Lempert and Schlesinger, 2000; Yohe et al., 2004). The range 2

T of uncertainty in the climate sensitivity, in comparison with 10 just having a single value, requires policy-makers to create new approaches in mitigation and abatement policy, particularly in rigorously counting all the possible outcomes for 5 adaptation to, and coping with, climate change. The larger the change that would occur, the more difﬁcult it would be for 0 humans and natural systems to adapt. 1940 1950 1960 1970 1980 1990 2000 From another viewpoint, because of regional heterogeneity of Decades the temperature response to different forcings, there are some Figure 1.6 Observed temperature departure (Jones and Moberg, difﬁculties in “translating” the “global” climate sensitivity into 2003) for northern and southern hemispheres (a) and evolution of the regional climate changes. Regional climate sensitivities may be climate sensitivity uncertainties (b). different from the global sensitivity because different feedbacks may be regionally but not globally important (Boer and Yu, 2003). Thus, further enrichment of the climate sensitivity con- radiative forcing (GTA). Figure 1.6a presents the J2003 cept requires the search for a set of climate variables that temperature departures for the northern and southern hemi- characterizes climate change in full on both regional and spheres for the entire period. Figure 1.6b presents the evolu- global scales. Understandably, the search for this set of tion of the climate sensitivity, in box-plot form, obtained by variables will be limited to existing databases of observations marching 10 years forward. It shows that starting in 1950 the and/or reconstructions, and will include all corresponding cooling in the temperature record dramatically increases the uncertainties. uncertainty in the estimated climate sensitivity, which is Development of the methodological aspects of the based on the record from 1860 to 1950, because it becomes climate sensitivity concept will mostly likely be related to inconsistent with the increasing tendency in the greenhouse understanding the climate feedbacks on the different spatial forcing. However, later on with the additional observational and temporal scales. Already there are a few intercomparison data, the uncertainty decreases because of the persistence of projects in progress (e.g., Working Group on Coupled Models; the GA signal and averaging out the natural climate varia- Global Analysis Interpretation and Modeling; Coupled Model bility. The main point of this illustration is that it takes a long Intercomparison Project) whose goals are to improve large time to reduce uncertainties in the estimation of climate numerical models (a brief description of some of them can be sensitivity. found at www.clivar.org/science/mips.htm). Furthermore, The concept of climate sensitivity 15

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