Effective Climate Sensitivity Research Articles

Scaling fluctuation analysis and statistical hypothesis testing of anthropogenic warming

Although current global warming may have a large anthropogenic component, its quantification relies primarily on complex General Circulation Models (GCM’s) assumptions and codes; it is desirable to complement this with empirically based methodologies. Previous attempts to use the recent climate record have concentrated on “fingerprinting” or otherwise comparing the record with GCM outputs. By using CO2 radiative forcings as a linear surrogate for all anthropogenic effects we estimate the total anthropogenic warming and (effective) climate sensitivity finding: ΔT anth = 0.87 ± 0.11 K, $$\uplambda_{{2{\text{x}}{\text{CO}}_{2} ,{\text{eff}}}} = 3.08 \pm 0.58\,{\text{K}}$$ . These are close the IPPC AR5 values ΔT anth = 0.85 ± 0.20 K and $$\uplambda_{{2{\text{x}}{\text{CO}}_{2} }} = 1.5\!-\!4.5\,{\text{K}}$$ (equilibrium) climate sensitivity and are independent of GCM models, radiative transfer calculations and emission histories. We statistically formulate the hypothesis of warming through natural variability by using centennial scale probabilities of natural fluctuations estimated using scaling, fluctuation analysis on multiproxy data. We take into account two nonclassical statistical features—long range statistical dependencies and “fat tailed” probability distributions (both of which greatly amplify the probability of extremes). Even in the most unfavourable cases, we may reject the natural variability hypothesis at confidence levels >99 %.

Forcing and feedback in the MPI‐ESM‐LR coupled model under abruptly quadrupled CO2

Radiative feedback mechanisms associated with temperature, water vapor, cloud, and surface albedo change determine climate sensitivity to radiative forcing. Here we use the linearized radiative kernel‐technique in combination with a Gregory analysis to determine the strength and structure of feedbacks, as well as direct and adjusted CO2 forcings in the coupled Max Planck Institute Earth System Model at base resolution (MPI‐ESM‐LR). We show that the combined Kernel‐Gregory approach yields an elegant separation of surface temperature‐dependent feedbacks from contributions to radiative forcing by fast adjustments. MPI‐ESM‐LR exhibits a relatively large cloud adjustment of nearly 2 W m−2 in direct response to quadrupled CO2, with positive cloud adjustment evident throughout the tropics, subtropics and over most landmasses whereas midlatitude storm tracks contribute negatively. The model features a nonlinear regression of radiation imbalance to global mean surface temperature change, resulting in a significantly increasing effective climate sensitivity after about 20 years which is approximately at temperatures 4–5 K above preindustrial. This feature is not uncommon among climate models and is relevant for future climate projections. We analyze the contribution of the individual feedback processes to this behavior and discuss possible origins such as differential ocean warming patterns associated with deep‐ocean heat uptake or state dependencies of the feedback processes.

Quantifying global climate feedbacks, responses and forcing under abrupt and gradual CO2 forcing

Experiments with abrupt CO2 forcing allow the diagnosis of the response of global mean temperature and precipitation in terms of fast temperature independent adjustments and slow, linear temperature-dependent feedbacks. Here we compare responses, feedbacks and forcings in experiments performed as part of version 5 of the coupled model inter-comparison project (CMIP5). The experiments facilitate, for the first time, a comparison of fully coupled atmosphere-ocean general circulation models (GCM’s) under both linearly increasing and abrupt radiative forcing. In the case of a 1 % per year compounded increase in CO2 concentration, we find that the non-linear evolution of surface air temperature in time, when combined with the linear evolution of the radiative balance at the top of the atmosphere, results in a feedback parameter and effective climate sensitivity having an offset compared to values computed from abrupt 4× CO2 forcing experiments. The linear evolution of the radiative balance at the top of the atmosphere also contributes to an offset between the global mean precipitation response predicted in the 1 % experiment using linear theory and that diagnosed from the experiments themselves, and a potential error between the adjusted radiative forcing and that produced using a standard linear formula. The non-linear evolution of temperature and precipitation responses are also evident in the RCP8.5 scenario and have implications for understanding, quantifying and emulating the global response of the CMIP5 climate GCMs.

Sensitivity of distributions of climate system properties to the surface temperature dataset

[1] Surface temperature, upper-air temperature, and ocean heat content data are used to constrain the distributions of the parameters that define three climate system properties in the MIT Integrated Global Systems Model: effective climate sensitivity, the rate of ocean heat uptake into the deep ocean, and net anthropogenic aerosol forcing. Five different surface temperature data records are used to show that the resulting parameter distribution functions are sensitive to the dataset used to estimate the likelihood of model output given the observed climate records. Estimates of effective climate sensitivity mode and mean differ by as much as 1 K between the datasets, with an overall range of 1.2 to 5.3 K. Ocean effective diffusivity distributions are poorly constrained by any dataset. The overall range of net aerosol forcing values, −0.19 to −0.83 Wm−2, is small compared to other uncertainties in climate forcings. Transient climate response (TCR) estimates derived from these distributions range between 0.87 and 2.41 K and the shapes of individual TCR distributions depend on the surface dataset. Understanding the differences in parameter distributions and climate system properties derived from them is critical for understanding the full range of uncertainty involved in climate model calibration and prediction results.

Emulating coupled atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6 – Part 1: Model description and calibration

Abstract. Current scientific knowledge on the future response of the climate system to human-induced perturbations is comprehensively captured by various model intercomparison efforts. In the preparation of the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC), intercomparisons were organized for atmosphere-ocean general circulation models (AOGCMs) and carbon cycle models, named "CMIP3" and "C4MIP", respectively. Despite their tremendous value for the scientific community and policy makers alike, there are some difficulties in interpreting the results. For example, radiative forcings were not standardized across the various AOGCM integrations and carbon cycle runs, and, in some models, key forcings were omitted. Furthermore, the AOGCM analysis of plausible emissions pathways was restricted to only three SRES scenarios. This study attempts to address these issues. We present an updated version of MAGICC, the simple carbon cycle-climate model used in past IPCC Assessment Reports with enhanced representation of time-varying climate sensitivities, carbon cycle feedbacks, aerosol forcings and ocean heat uptake characteristics. This new version, MAGICC6, is successfully calibrated against the higher complexity AOGCMs and carbon cycle models. Parameterizations of MAGICC6 are provided. The mean of the emulations presented here using MAGICC6 deviates from the mean AOGCM responses by only 2.2% on average for the SRES scenarios. This enhanced emulation skill in comparison to previous calibrations is primarily due to: making a "like-with-like comparison" using AOGCM-specific subsets of forcings; employing a new calibration procedure; as well as the fact that the updated simple climate model can now successfully emulate some of the climate-state dependent effective climate sensitivities of AOGCMs. The diagnosed effective climate sensitivity at the time of CO2 doubling for the AOGCMs is on average 2.88 °C, about 0.33 °C cooler than the mean of the reported slab ocean climate sensitivities. In the companion paper (Part 2) of this study, we examine the combined climate system and carbon cycle emulations for the complete range of IPCC SRES emissions scenarios and the new RCP pathways.

Development of a system emulating the global carbon cycle in Earth system models

Abstract. Recent studies have indicated that the uncertainty in the global carbon cycle may have a significant impact on the climate. Since state of the art models are too computationally expensive for it to be possible to explore their parametric uncertainty in anything approaching a comprehensive fashion, we have developed a simplified system for investigating this problem. By combining the strong points of general circulation models (GCMs), which contain detailed and complex processes, and Earth system models of intermediate complexity (EMICs), which are quick and capable of large ensembles, we have developed a loosely coupled model (LCM) which can represent the outputs of a GCM-based Earth system model, using much smaller computational resources. We address the problem of relatively poor representation of precipitation within our EMIC, which prevents us from directly coupling it to a vegetation model, by coupling it to a precomputed transient simulation using a full GCM. The LCM consists of three components: an EMIC (MIROC-lite) which consists of a 2-D energy balance atmosphere coupled to a low resolution 3-D GCM ocean (COCO) including an ocean carbon cycle (an NPZD-type marine ecosystem model); a state of the art vegetation model (Sim-CYCLE); and a database of daily temperature, precipitation, and other necessary climatic fields to drive Sim-CYCLE from a precomputed transient simulation from a state of the art AOGCM. The transient warming of the climate system is calculated from MIROC-lite, with the global temperature anomaly used to select the most appropriate annual climatic field from the pre-computed AOGCM simulation which, in this case, is a 1% pa increasing CO2 concentration scenario. By adjusting the effective climate sensitivity (equivalent to the equilibrium climate sensitivity for an energy balance model) of MIROC-lite, the transient warming of the LCM could be adjusted to closely follow the low sensitivity (with an equilibrium climate sensitivity of 4.0 K) version of MIROC3.2. By tuning of the physical and biogeochemical parameters it was possible to reasonably reproduce the bulk physical and biogeochemical properties of previously published CO2 stabilisation scenarios for that model. As an example of an application of the LCM, the behavior of the high sensitivity version of MIROC3.2 (with a 6.3 K equilibrium climate sensitivity) is also demonstrated. Given the highly adjustable nature of the model, we believe that the LCM should be a very useful tool for studying uncertainty in global climate change, and we have named the model, JUMP-LCM, after the name of our research group (Japan Uncertainty Modelling Project).

Equilibrium Climate Sensitivity: Is It Accurate to Use a Slab Ocean Model?

Abstract The equilibrium climate sensitivity of a climate model is usually defined as the globally averaged equilibrium surface temperature response to a doubling of carbon dioxide. This is virtually always estimated in a version with a slab model for the upper ocean. The question is whether this estimate is accurate for the full climate model version, which includes a full-depth ocean component. This question has been answered for the low-resolution version of the Community Climate System Model, version 3 (CCSM3). The answer is that the equilibrium climate sensitivity using the full-depth ocean model is 0.14°C higher than that using the slab ocean model, which is a small increase. In addition, these sensitivity estimates have a standard deviation of nearly 0.1°C because of interannual variability. These results indicate that the standard practice of using a slab ocean model does give a good estimate of the equilibrium climate sensitivity of the full CCSM3. Another question addressed is whether the effective climate sensitivity is an accurate estimate of the equilibrium climate sensitivity. Again the answer is yes, provided that at least 150 yr of data from the doubled carbon dioxide run are used.

Constraining climate model parameters from observed 20th century changes

We present revised probability density functions for climate model parameters (effective climate sensitivity, the rate of deep-ocean heat uptake, and the strength of the net aerosol forcing) that are based on climate change observations from the 20th century. First, we compare observed changes in surface, upper-air, and deep-ocean temperature changes against simulations of 20th century climate in which the climate model parameters were systematically varied. The estimated 90% range of effective climate sensitivity is 2-5 K but no corresponding upper bound can be placed on the equilibrium climate sensitivity. The net aerosol forcing strength for the 1980s has 90% bounds of -0.70 to -0.27 W m- 2 . The rate of deep-ocean heat uptake corresponds to an effective diffusivity, K v , with a 90% range of 0.04-4.1 cm 2 s- 1 . Second, we estimate the effective climate sensitivity and rate of deep-ocean heat uptake for 11 of the IPCC AR4 AOGCMs. By comparing against the acceptable combinations inferred from the observations, we conclude that the rates of deep-ocean heat uptake for the majority of AOGCMs lie above the observationally based median value. This implies a bias in the predictions inferred from the IPCC models alone.

Comparison of equilibrium and transient responses to CO2 increase in eight state-of-the-art climate models

We compared the climate response of doubled CO 2 equilibrium experiments (2 x CO 2 ) by atmosphere-slab ocean coupled general circulation models (ASGCMs) and that of 1% per year CO 2 increase experiments (1%CO 2 by atmosphere-ocean coupled general circulation models (AOGCMs) using eight state-of-the-art climate models. Climate feedback processes in 2 x CO 2 are different from those in 1 %CO 2 , and the equilibrium climate sensitivity (T 2x ) in 2 x CO 2 is different from the effective climate sensitivity (T 2x.cff ) in 1%CO 2 . The difference between T 2x and T 2x.cff is from - 1.3 to 1.6 K, a large part of which can be explained by the difference in the ice-albedo and cloud feedback. The largest contribution is cloud SW feedback, and the difference in cloud SW feedback for 2 x CO 2 and 1%CO 2 could be determined by the distribution of the SAT anomaly which causes differences in the atmospheric thermal structure. An important factor which determines the difference in ice-albedo feedback is the initial sea ice distribution at the Southern Ocean, which is generally overestimated in 2 x CO 2 as compared to 1%CO 2 and observation. Through the comparison of climate feedback processes in 2 x CO 2 and 1%CO 2 , the possible behaviour of the time evolution of T 2x.cff is discussed.

Time Variation of Effective Climate Sensitivity in GCMs

Abstract Effective climate sensitivity is often assumed to be constant (if uncertain), but some previous studies of general circulation model (GCM) simulations have found it varying as the simulation progresses. This complicates the fitting of simple models to such simulations, as well as having implications for the estimation of climate sensitivity from observations. This study examines the evolution of the feedbacks determining the climate sensitivity in GCMs submitted to the Coupled Model Intercomparison Project. Apparent centennial-time-scale variations of effective climate sensitivity during stabilization to a forcing can be considered an artifact of using conventional forcings, which only allow for instantaneous effects and stratospheric adjustment. If the forcing is adjusted for processes occurring on time scales that are short compared to the climate stabilization time scale, then there is little centennial-time-scale evolution of effective climate sensitivity in any of the GCMs. Here it is suggested that much of the apparent variation in effective climate sensitivity identified in previous studies is actually due to the comparatively fast forcing adjustment. Persistent differences are found in the strength of the feedbacks between the coupled atmosphere–ocean (AO) versions and their atmosphere–mixed layer ocean (AML) counterparts (the latter are often assumed to give the equilibrium climate sensitivity of the AOGCM). The AML model can typically only estimate the equilibrium climate sensitivity of the parallel AO version to within about 0.5 K. The adjustment to the forcing to account for comparatively fast processes varies in magnitude and sign between GCMs, as well as differing between AO and AML versions of the same model. There is evidence from one AOGCM that the forcing adjustment may take a couple of decades, with implications for observationally based estimates of equilibrium climate sensitivity. It is suggested that at least some of the spread in twenty-first-century global temperature predictions between GCMs is due to differing adjustment processes, hence work to understand these differences should be a priority.

Constraining climate model parameters from observed 20th century changes

We present revised probability density functions for climate model parameters (effective climate sensitivity, the rate of deep-ocean heat uptake, and the strength of the net aerosol forcing) that are based on climate change observations from the 20th century. First, we compare observed changes in surface, upper-air, and deep-ocean temperature changes against simulations of 20th century climate in which the climate model parameters were systematically varied. The estimated 90% range of effective climate sensitivity is 2–5 K but no corresponding upper bound can be placed on the equilibrium climate sensitivity. The net aerosol forcing strength for the 1980s has 90% bounds of −0.70 to −0.27 Wm−2. The rate of deep-ocean heat uptake corresponds to an effective diffusivity, Kv , with a 90% range of 0.04–4.1 cm2 s−1. Second, we estimate the effective climate sensitivity and rate of deep-ocean heat uptake for 11 of the IPCC AR4 AOGCMs. By comparing against the acceptable combinations inferred from the observations, we conclude that the rates of deep-ocean heat uptake for the majority of AOGCMs lie above the observationally based median value. This implies a bias in the predictions inferred from the IPCC models alone.

Comparison of equilibrium and transient responses to CO2 increase in eight state-of-the-art climate models

We compared the climate response of doubled CO2 equilibrium experiments (2 × CO2) by atmosphere—slab ocean coupled general circulation models (ASGCMs) and that of 1% per year CO2 increase experiments (1%CO2 by atmosphere—ocean coupled general circulation models (AOGCMs) using eight state-of-the-art climate models. Climate feedback processes in 2 × CO2 are different from those in 1%CO2, and the equilibrium climate sensitivity (T2×) in 2 × CO2 is different from the effective climate sensitivity (T2×, eff) in 1%CO2. The difference between T2× and T2×, eff is from −1.3 to 1.6 K, a large part of which can be explained by the difference in the ice-albedo and cloud feedback. The largest contribution is cloud SW feedback, and the difference in cloud SW feedback for 2 ×CO2 and 1%CO2 could be determined by the distribution of the SAT anomaly which causes differences in the atmospheric thermal structure. An important factor which determines the difference in ice-albedo feedback is the initial sea ice distribution at the Southern Ocean, which is generally overestimated in 2 ×CO2 as compared to 1%CO2 and observation. Through the comparison of climate feedback processes in 2 ×CO2 and 1%CO2, the possible behaviour of the time evolution of T2×, eff is discussed.

The Relationship Between Radiative Forcing and Temperature: What Do Statistical Analyses of the Instrumental Temperature Record Measure?

Comparing statistical estimates for the long-run temperature effect of doubled CO2 with those generated by climate models begs the question, is the long-run temperature effect of doubled CO2 that is estimated from the instrumental temperature record using statistical techniques consistent with the transient climate response, the equilibrium climate sensitivity, or the effective climate sensitivity. Here, we attempt to answer the question, what do statistical analyses of the observational record measure, by using these same statistical techniques to estimate the temperature effect of a doubling in the atmospheric concentration of carbon dioxide from seventeen simulations run for the Coupled Model Intercomparison Project 2 (CMIP2). The results indicate that the temperature effect estimated by the statistical methodology is consistent with the transient climate response and that this consistency is relatively unaffected by sample size or the increase in radiative forcing in the sample.

The New Hadley Centre Climate Model (HadGEM1): Evaluation of Coupled Simulations

Abstract A new coupled general circulation climate model developed at the Met Office's Hadley Centre is presented, and aspects of its performance in climate simulations run for the Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4) documented with reference to previous models. The Hadley Centre Global Environmental Model version 1 (HadGEM1) is built around a new atmospheric dynamical core; uses higher resolution than the previous Hadley Centre model, HadCM3; and contains several improvements in its formulation including interactive atmospheric aerosols (sulphate, black carbon, biomass burning, and sea salt) plus their direct and indirect effects. The ocean component also has higher resolution and incorporates a sea ice component more advanced than HadCM3 in terms of both dynamics and thermodynamics. HadGEM1 thus permits experiments including some interactive processes not feasible with HadCM3. The simulation of present-day mean climate in HadGEM1 is significantly better overall in comparison to HadCM3, although some deficiencies exist in the simulation of tropical climate and El Niño variability. We quantify the overall improvement using a quasi-objective climate index encompassing a range of atmospheric, oceanic, and sea ice variables. It arises partly from higher resolution but also from greater fidelity in modeling dynamical and physical processes, for example, in the representation of clouds and sea ice. HadGEM1 has a similar effective climate sensitivity (2.8 K) to a CO2 doubling as HadCM3 (3.1 K), although there are significant regional differences in their response patterns, especially in the Tropics. HadGEM1 is anticipated to be used as the basis both for higher-resolution and higher-complexity Earth System studies in the near future.

Simulated climate change during the last 1,000 years: comparing the ECHO-G general circulation model with the MAGICC simple climate model

An intercomparison of eight climate simulations, each driven with estimated natural and anthropogenic forcings for the last millennium, indicates that the so-called “Erik” simulation of the ECHO-G coupled ocean-atmosphere climate model exhibits atypical behaviour. The ECHO-G simulation has a much stronger cooling trend from 1000 to 1700 and a higher rate of warming since 1800 than the other simulations, with the result that the overall amplitude of millennial-scale temperature variations in the ECHO-G simulation is much greater than in the other models. The MAGICC (Model for the Assessment of Greenhouse-gas-Induced Climate Change) simple climate model is used to investigate possible causes of this atypical behaviour. It is shown that disequilibrium in the initial conditions probably contributes spuriously to the cooling trend in the early centuries of the simulation, and that the omission of tropospheric sulphate aerosol forcing is the likely explanation for the anomalously large recent warming. The simple climate model results are used to adjust the ECHO-G Erik simulation to mitigate these effects, which brings the simulation into better agreement with the other seven models considered here and greatly reduces the overall range of temperature variations during the last millennium simulated by ECHO-G. Smaller inter-model differences remain which can probably be explained by a combination of the particular forcing histories and model sensitivities of each experiment. These have not been investigated here, though we have diagnosed the effective climate sensitivity of ECHO-G to be 2.39±0.11 K for a doubling of CO2.

Present-Day Climate and Climate Sensitivity in the Meteorological Research Institute Coupled GCM Version 2.3 (MRI-CGCM2.3)

A new version of the Meteorological Research Institute (MRI) coupled general circulation model MRICGCM2 (MRI2.3) is developed and compared with the previous version (MRI2.0). The cloud scheme includes diagnostic function for cloud amount separately specified for convective and layer clouds, which is one of the major modifications contributing to the improved model performance. MRI2.3 exhibits better agreement with the observations in many aspects of present-day climate simulations, including the global energy budget, meridional distributions of shortwave and longwave radiation at the top of the atmosphere, and geographical distributions of surface air temperature and precipitation. The effective climate sensitivity of each version is evaluated based on an experiment with a transient (1%/year) increase of carbon dioxide concentration. The effective climate sensitivity of MRI2.3 (2.9 K) is about twice that of MRI2.0 (1.4 K). The change in the cloud-forcing response, particularly for shortwave cloud forcing, is essential for increasing climate sensitivity. A difference in tropical low-level clouds over the subsidence regions contributes significantly to the difference in cloud-forcing changes in response to a climate change. Analyses based on circulation regimes, defined by the vertical velocity at the mid-troposphere, suggest that the cloud-forcing response in the tropics is controlled more by thermodynamic characteristics, such as changes of the stability in the lower troposphere, rather than by large-scale circulation changes, such as a change in the subsidence strength.

Climate sensitivity and climate change under strong forcing

A version of the National Centre for Atmospheric Research (NCAR) coupled climate model is integrated under current climate conditions and in a series of experiments with climate forcings ranging from modest to very strong. The purpose of the experiments is to investigate the nature and behaviour of the climate feedback/sensitivity of the model, its evolution with time and climate state, the robustness of model parameterizations as forcing levels increase, and the possibility of a “runaway” warming under strong forcing. The model is integrated for 50 years, or to failure, after increasing the solar constant by 2.5, 10, 15, 25, 35, and 45% of its control value. The model successfully completes 50 years of integration for the 2.5, 10, 15, and 25% solar constant increases but fails for increases of 35% and 45%. The effective global climate sensitivity evolves with time and analysis indicates that a new equilibrium will be obtained for the 2.5, 10, and 15% cases but that runaway warming is underway for the 25% increase in solar constant. Feedback processes are analysed both locally and globally in terms of longwave and shortwave, clear-sky/surface, and cloud forcing components. Feedbacks in the system must be negative overall and of sufficient strength to balance the positive forcing if the system is to attain a new equilibrium. Longwave negative feedback processes strengthen in a reasonably linear fashion as temperature increases but shortwave feedback processes do not. In particular, solar cloud feedback becomes less negative and, for the 25% forcing case, eventually becomes positive, resulting in temperatures that “run away”. The conditions under which a runaway climate warming might occur have previously been investigated using simpler models. For sufficiently strong forcing, the greenhouse effect of increasing water vapour in a warmer atmosphere is expected to overwhelm the negative feedback of the longwave cooling to space as temperature increases. This is not, however, the reason for the climate instability experienced in the GCM. Instead, the model experiences a “cloud feedback” warming whereby the decrease in cloudiness that occurs when temperature increases beyond a critical value results in an increased absorption of solar radiation by the system, leading to the runaway warming.

A new method for diagnosing radiative forcing and climate sensitivity

We describe a new method for evaluating the radiative forcing, the climate feedback parameter (W m−2 K−1) and hence the effective climate sensitivity from any GCM experiment in which the climate is responding to a constant forcing. The method is simply to regress the top of atmosphere radiative flux against the global average surface air temperature change. This method does not require special integrations or off‐line estimates, such as for stratospheric adjustment, to obtain the forcing, and eliminates the need for double radiation calculations and tropopause radiative fluxes. We show that for CO2 and solar forcing in a slab model and an AOGCM the method gives results consistent with those obtained by conventional methods. For a single integration it is less precise but since it does not require a steady state to be reached its precision could be improved by running an ensemble of short integrations.

An Observationally Based Estimate of the Climate Sensitivity

A probability distribution for values of the effective climate sensitivity, with a lower bound of 1.6 K (5th percentile), is obtained on the basis of the increase in ocean heat content in recent decades from analyses of observed interior-ocean temperature changes, surface temperature changes measured since 1860, and estimates of anthropogenic and natural radiative forcing of the climate system. Radiative forcing is the greatest source of uncertainty in the calculation; the result also depends somewhat on the rate of ocean heat uptake in the late nineteenth century, for which an assumption is needed as there is no observational estimate. Because the method does not use the climate sensitivity simulated by a general circulation model, it provides an independent observationally based constraint on this important parameter of the climate system.

Use of an upwelling-diffusion energy balance climate model to simulate and diagnose A/OGCM results

We demonstrate that a hemispherically averaged upwelling-diffusion energy-balance climate model (UD/EBM) can emulate the surface air temperature change and sea-level rise due to thermal expansion, predicted by the HadCM2 coupled atmosphere-ocean general circulation model, for various scenarios of anthropogenic radiative forcing over 1860–2100. A climate sensitivity of 2.6 °C is assumed, and a representation of the effect of sea-ice retreat on surface air temperature is required. In an extended experiment, with CO2 concentration held constant at twice the control run value, the HadCM2 effective climate sensitivity is found to increase from about 2.0 °C at the beginning of the integration to 3.85 °C after 900 years. The sea-level rise by this time is almost 1.0 m and the rate of rise fairly steady, implying that the final equilibrium value (the `commitment') is large. The base UD/EBM can fit the 900-year simulation of surface temperature change and thermal expansion provided that the time-dependent climate sensitivity is specified, but the vertical profile of warming in the ocean is not well reproduced. The main discrepancy is the relatively large mid-depth warming in the HadCM2 ocean, that can be emulated by (1) diagnosing depth-dependent diffusivities that increase through time; (2) diagnosing depth-dependent diffusivities for a pure-diffusion (zero upwelling) model; or (3) diagnosing higher depth-dependent diffusivities that are applied to temperature perturbations only. The latter two models can be run to equilibrium, and with a climate sensitivity of 3.85 °C, they give sea-level rise commitments of 1.7 m and 1.3 m, respectively.