IPCC Fourth Assessment Report: Climate Change 2007
Climate Change 2007: Working Group I: The Physical Science Basis

9.6.2 Estimates of Climate Sensitivity Based on Instrumental Observations Estimates of Climate Sensitivity Based on 20th-Century Warming

A number of recent studies have used instrumental records of surface, ocean and atmospheric temperature changes to estimate climate sensitivity. Most studies use the observed surface temperature changes over the 20th century or the last 150 years (Chapter 3). In addition, some studies also use the estimated ocean heat uptake since 1955 based on Levitus et al. (2000, 2005) (Chapter 5), and temperature changes in the free atmosphere (Chapter 3; see also Table 9.3). For example, Frame et al. (2005) and Andronova and Schlesinger (2000) use surface air temperature alone, while Forest et al. (2002, 2006), Knutti et al. (2002, 2003) and Gregory et al. (2002a) use both surface air temperature and ocean temperature change to constrain climate sensitivity. Forest et al. (2002, 2006) and Lindzen and Giannitsis (2002) use free atmospheric temperature data from radiosondes in addition to surface air temperature. Note that studies using radiosonde data may be affected by recently discovered inhomogeneities (Section, although Forest et al. (2006) illustrate that the impact of the radiosonde atmospheric temperature data on their climate sensitivity estimate is smaller than that of surface and ocean warming data. A further recent study uses Earth Radiation Budget Experiment (ERBE) data (Forster and Gregory, 2006) in addition to surface temperature changes to estimate climate feedbacks (and thus ECS) from observed changes in forcing and climate.

Wigley et al. (1997) pointed out that uncertainties in forcing and response made it impossible to use observed global temperature changes to constrain ECS more tightly than the range explored by climate models at the time (1.5°C to 4.5°C), and particularly the upper end of the range, a conclusion confirmed by subsequent studies. A number of subsequent publications qualitatively describe parameter values that allow models to reproduce features of observed changes, but without directly estimating a climate sensitivity probability density function (PDF). For example, Harvey and Kaufmann (2002) find a best-fit ECS of 2.0°C out of a range of 1°C to 5°C, and constrain fossil fuel and biomass aerosol forcing (Section Lindzen and Giannitsis (2002) pose the hypothesis that the rapid change in tropospheric (850–300 hPa) temperatures around 1976 triggered a delayed response in surface temperature that is best modelled with a climate sensitivity of less than 1°C. However, their estimate does not account for substantial uncertainties in the analysis of such a short time period, most notably those associated with the role of internal climate variability in the rapid tropospheric warming of 1976. The 1976–1977 climate shift occurred along with a phase shift of the PDO, and a concurrent change in the ocean (Section 3.6.3) that appears to contradict the Lindzen and Giannitsis (2002) assumption that the change was initiated by tropospheric forcing. In addition, the authors do not account for uncertainties in the simple model whose sensitivity is fitted. The finding of Lindzen and Giannitsis is in contrast with that of Forest et al. (2002, 2006) who consider the joint evolution of surface and upper air temperatures on much longer time scales.

Several recent studies have derived probability estimates for ECS using a range of models and diagnostics. The diagnostics, which are used to compare model-simulated and observed changes, are often simple temperature indices such as the global mean surface temperature and ocean mean warming (Knutti et al., 2002, 2003) or the differential warming between the SH and NH (together with the global mean; Andronova and Schlesinger, 2001). Results that use more detailed information about the space-time evolution of climate may be able to provide tighter constraints than those that use simpler indices. Forest et al. (2002, 2006) use a so-called ‘optimal’ detection method (Section and Appendix 9.A.1) to diagnose the fit between model-simulated and observed patterns of zonal mean temperature change. Frame et al. (2005) use detection results from an analysis based on several multi-model AOGCM fingerprints (Section that separate the greenhouse gas response from that to other anthropogenic and natural forcings (Stott et al., 2006c). Similarly, Gregory et al. (2002a) apply an inverse estimate of the range of aerosol forcing based on fingerprint detection results. Note that while results from fingerprint detection approaches will be affected by uncertainty in separation between greenhouse gas and aerosol forcing, the resulting uncertainty in estimates of the near-surface temperature response to greenhouse gas forcing is relatively small (Sections 9.2.3 and

A further consideration in assessing these results is the extent to which realistic forcing estimates were used, and whether forcing uncertainty was included. Most studies consider a range of anthropogenic forcing factors, including greenhouse gases and sulphate aerosol forcing, sometimes directly including the indirect forcing effect, such as Knutti et al. (2002, 2003), and sometimes indirectly accounting for the indirect effect by using a wide range of direct forcing (e.g., Andronova and Schlesinger, 2001; Forest et al., 2002, 2006). Many studies also consider tropospheric ozone (e.g., Andronova and Schlesinger, 2001; Knutti et al., 2002, 2003). Forest et al. (2006) demonstrate that the inclusion of natural forcing affects the estimated PDF of climate sensitivity since net negative natural forcing in the second half of the 20th century favours higher sensitivities than earlier results that disregarded natural forcing (Forest et al., 2002; see Figure 9.20), particularly if the same ocean warming estimates were used. Note that some of the changes due to inclusion of natural forcing are offset by using recently revised ocean warming data (Levitus et al., 2005), which favour somewhat smaller ocean heat uptakes than earlier data (Levitus et al., 2001; Forest et al., 2006). Only a few estimates account for uncertainty in forcings other than from aerosols (e.g., Gregory et al., 2002a; Knutti et al., 2002, 2003); some other studies perform some sensitivity testing to assess the effect of forcing uncertainty not accounted for, for example, in natural forcing (e.g., Forest et al., 2006; see Table 9.1 for an overview).

The treatment of uncertainty in the ocean’s uptake of heat varies, from assuming a fixed value for a model’s ocean diffusivity (Andronova and Schlesinger, 2001) to trying to allow for a wide range of ocean mixing parameters (Knutti et al., 2002, 2003) or systematically varying the ocean’s effective diffusivity (e.g., Forest et al., 2002, 2006; Frame et al., 2005). Furthermore, all approaches that use the climate’s time evolution attempt to account for uncertainty due to internal climate variability, either by bootstrapping (Andronova and Schlesinger, 2001), by using a noise model in fingerprint studies whose results are used (Frame et al., 2005) or directly (Forest et al., 2002, 2006).

Figure 9.20

Figure 9.20. Comparison between different estimates of the PDF (or relative likelihood) for ECS (°C). All PDFs/likelihoods have been scaled to integrate to unity between 0°C and 10°C ECS. The bars show the respective 5 to 95% ranges, dots the median estimate. The PDFs/likelihoods based on instrumental data are from Andronova and Schlesinger (2001), Forest et al. (2002; dashed line, considering anthropogenic forcings only), Forest et al. (2006; solid, anthropogenic and natural forcings), Gregory et al. (2002a), Knutti et al. (2002), Frame et al. (2005), and Forster and Gregory (2006), transformed to a uniform prior distribution in ECS using the method after Frame et al. (2005). Hegerl et al. (2006a) is based on multiple palaeoclimatic reconstructions of NH mean temperatures over the last 700 years. Also shown are the 5 to 95% approximate ranges for two estimates from the LGM (dashed, Annan et al., 2005; solid, Schneider von Deimling et al., 2006) which are based on models with different structural properties. Note that ranges extending beyond the published range in Annan et al. (2005), and beyond that sampled by the climate model used there, are indicated by dots and an arrow, since Annan et al. only provide an upper limit. For details of the likelihood estimates, see Table 9.3. After Hegerl et al. (2006a).

Figure 9.20 compares results from many of these studies. All PDFs shown are based on a uniform prior distribution of ECS and have been rescaled to integrate to unity for all positive sensitivities up to 10°C to enable comparisons of results using different ranges of uniform prior distributions (this affects both median and upper 95th percentiles if original estimates were based on a wider uniform range). Thus, zero prior probability is assumed for sensitivities exceeding 10°C, since many results do not consider those, and for negative sensitivities. Negative climate sensitivity would lead to cooling in response to a positive forcing and is inconsistent with understanding of the energy balance of the system (Stouffer et al., 2000; Gregory et al., 2002a; Lindzen and Giannitsis, 2002). This figure shows that best estimates of the ECS (mode of the estimated PDFs) typically range between 1.2°C and 4°C when inferred from constraints provided by historical instrumental data, in agreement with estimates derived from more comprehensive climate models. Most studies suggest a 5th percentile for climate sensitivity of 1°C or above. The upper 95th percentile is not well constrained, particularly in studies that account conservatively for uncertainty in, for example, 20th-century radiative forcing and ocean heat uptake. The upper tail is particularly long in studies using diagnostics based on large-scale mean data because separation of the greenhouse gas response from that to aerosols or climate variability is more difficult with such diagnostics (Andronova and Schlesinger, 2001; Gregory et al., 2002a; Knutti et al., 2002, 2003). Forest et al. (2006) find a 5 to 95% range of 2.1°C to 8.9°C for climate sensitivity (Table 9.3), which is a wider range than their earlier result based on anthropogenic forcing only (Forest et al., 2002). Frame et al. (2005) infer a 5 to 95% uncertainty range for the ECS of 1.2°C to 11.8°C, using a uniform prior distribution that extends well beyond 10°C sensitivity. Studies generally do not find meaningful constraints on the rate at which the climate system mixes heat into the deep ocean (e.g., Forest et al., 2002, 2006). However, Forest et al. (2006) find that many coupled AOGCMs mix heat too rapidly into the deep ocean, which is broadly consistent with comparisons based on heat uptake (Section,). However the relevance of this finding is unclear because most MMD AOGCMs were not included in the Forest et al. comparison, and because they used a relatively simple ocean model. Knutti et al. (2002) also determine that strongly negative aerosol forcing, as has been suggested by several observational studies (Anderson et al., 2003), is incompatible with the observed warming trend over the last century (Section and Table 9.1).

Table 9.3. Results from key studies on observational estimates of ECS (in °C) from instrumental data, individual volcanic eruptions, data for the last millennium, and simulations of the LGM . The final three rows list some studies using non-uniform prior distributions, while the other studies use uniform prior distributions of ECS. Errata

Study Observational Data Used to Constrain Studya Modelb External Forcings Includedc Treatment of uncertaintiesd Estimated ECS Range 5 to 95% (°C) 
From Instrumental Data 
Forest et al. (2006) Upper air, surface and deep ocean space-time 20th-century temperatures Prior 0°C to 10°C 2-D EMIC (~E6)  G, Sul, Sol, Vol, OzS, land surface changes (2002: G, Sul, OzS) εobs, noise, k, εaer, sensitivity tests for solar/volcanic. forcing uncertainty 2.1 to 8.9 (1.4 to 7.7 without natural forcings) 
Andronova and Schlesinger (2001) Global mean and hemispheric difference in surface air temperature 1856 to 1997 EBM G, OzT, Sul, Sol, Vol Noise (bootstrap residual), choice of radiative forcing factors 1.0 to 9.3 prob ~ 54% that ECS outside 1.5 to 4.5 
Knutti et al. (2002; 2003) Global mean ocean heat uptake 1955 to 1995, mean surface air temperature 1860 to 2000 Prior 0°C to 10°C EMIC (~E1) plus neural net G, OzT, OzS, fossil fuel and biomass burning BC+OM, stratospheric water vapour, Vol, Sol, Sul, Suli εobs, εforc for multiple forcings from IPCC (2001), k, different ocean mixing schemes 2.2 to 9.2 prob ~ 50% that ECS outside 1.5 to 4.5  
Gregory et al. (2002a) Global mean change in surface air temperature and ocean heat change between 1861 to 1900 and 1957 to 1994 1-Box G, Sul and Suli (top down via Stott et al., 2001), Sol, Vol εobs, εforc 1.1 to ∞  
Frame et al. (2005) Global change in surface temperature  EBM G, accounted for other anthropogenic and natural forcing by fingerprints, Sul, Nat Noise, uncertainty in amplitude but not pattern of natural and anthropogenic. forcings and response (scaling factors), k (range consistent with ocean warming) 1.2 to 11.8  
Study Observational Data Used to Constrain Studya Modelb External Forcings Includedc Treatment of uncertaintiesd Estimated ECS Range 5 to 95% (°C) 
Forster and Gregory (2006) 1985 to 1996 ERBE data 60°N to 60°S, global surface temperature Prior 0°C to 18.5°C, transformed after Frame et al. (2005) 1-Box G, Vol, Sol, Sul εobs, εforc 1.2 to 14.2  
From individual volcanic eruptions 
Wigley et al. (2005a) Global mean surface temperature EBM From volcanic forcing only El Niño Agung: 1.3 to 6.3; El Chichon: 0.3 to 7.7; Mt. Pinatubo: 1.8 to 5.2 
From last millenium 
Hegerl et al. (2006a) NH mean surface air temperature pre-industrial (1270/1505 to 1850) from multiple reconstructions Prior 0°C to 10°C 2D EBM G, Sul, Sol, Vol Noise (from residual), k, uncertainty in magnitude of reconstructions and solar and volcanic forcing 1.2 to 8.6 
From LGM 
Schneider von Deimling et al. (2006) LGM tropical SSTs and other LGM data EMIC (~E3) LGM forcing: greenhouse gases, dust, ice sheets, vegetation, insolation uncertainty of proxy-based ice age SSTs (one type of data); attempt to account for structural uncertainty, estimate of forcing uncertainty 1.2 to 4.3 (based on encompassing several ranges given)  
Annan et al. (2005) LGM tropical SSTs, present-day seasonal cycle of a number of variables for sampling prior distribution of model parameters AGCM with mixed-layer ocean PMIP2 LGM forcing Observational uncertainty in tropical SST estimates (one type of data) <7% chance of sensitivity >6 
Using non-uniform prior distributions 
Forest et al. (2002, 2006) Expert prior, 20th-century temperature change (see above) See Forest et al. see above See individual estimates 1.9 to 4.7  
Annan et al. (2006) Estimates from LGM, 20th-century change, volcanism combined See Annan et al. see above See individual estimates > 1.7 to 4.5 
Hegerl et al. (2006a) 1950 to 2000 surface temperature change (Frame et al., 2005), NH mean pre-industrial surface air temperature from last millennium See Hegerl et al. and Frame et al. (2005) see above See individual estimates 1.5 to 6.2 


a Range covered by uniform prior distribution if narrower than 0°C to 20°C.

b Energy Balance Model (EBM), often with upwelling-diffusive ocean; 1-box energy balance models; EMIC (numbers refer to related EMICs described in Table 8.3).

c G: greenhouse gases; Sul: direct sulphate aerosol effect; Suli: (first) indirect sulphate effect; OzT: tropospheric ozone; OzS: stratospheric ozone; Vol: volcanism; Sol: solar; BC+OM: black carbon and organic matter.).

d Uncertainties taken into account (e.g., uncertainty in ocean diffusivity K, or total aerosol forcing εforc). Ideally, studies account for model uncertainty, forcing uncertainty (for example, in aerosol forcing εaer or natural forcing εnat), uncertainty in observations, εobs, and internal climate variability (‘noise’).

Some studies have further attempted to use non-uniform prior distributions. Forest et al. (2002, 2006) obtained narrower uncertainty ranges when using expert prior distributions (Table 9.3). While they reflect credible prior ranges of ECS, expert priors may also be influenced by knowledge about observed climate change, and thus may yield overly confident estimates when combined with the same data (Supplementary Material, Appendix 9.B). Frame et al. (2005) find that sampling uniformly in TCR results in an estimated ECS of 1.2°C to 5.2°C with a median value of 2.3°C. In addition, several approaches have been based on a uniform prior distribution of climate feedback. Translating these results into ECS estimates is equivalent to using a prior distribution that favours smaller sensitivities, and hence tends to result in narrower ECS ranges (Frame et al., 2005). Forster and Gregory (2006) estimate ECS based on radiation budget data from the ERBE combined with surface temperature observations based on a regression approach, using the observation that there was little change in aerosol forcing over that time. They find a climate feedback parameter of 2.3 ± 1.4 W m–2 °C–1, which corresponds to a 5 to 95% ECS range of 1.0°C to 4.1°C if using a prior distribution that puts more emphasis on lower sensitivities as discussed above, and a wider range if the prior distribution is reformulated so that it is uniform in sensitivity (Table 9.3). The climate feedback parameter estimated from the MMD AOGCMs ranges from about 0.7 to 2.0 W m–2 °C–1 (Supplementary Material, Table S8.1).