*Nature Climate Change*claims the probability of catastrophic global warming of 6 °C or more is much less than claimed by the IPCC, while the probability of a 2 °C global–mean temperature increase by 2100 is increased. However, the authors admit that the most important factors of "Climate sensitivity, the response of the carbon cycle and aerosol effects remain highly uncertain..." Furthermore, the paper was written in June 2012, prior to recent papers that have found climate sensitivity to be much less than claimed by the IPCC. The authors also assume stratospheric aerosols are man-made, which was disproven by a paper published this week. Thus, the probability of even a 2 °C warming is much less than claimed.

# Uncertainty in temperature projections reduced using carbon cycle and climate observations

- Nature Climate Change
- doi:10.1038/nclimate1903

- Received
- Accepted
- Published online

^{1, 2}. Using a simplified climate model

^{3}, we show that, for a given emission scenario, it is the second most important contributor to this uncertainty after climate sensitivity, followed by aerosol impacts. Historical measurements of carbon dioxide concentrations

^{4}have been used along with global temperature observations

^{5}to help reduce this uncertainty. This results in an increased probability of exceeding a 2 °C global–mean temperature increase by 2100 while reducing the probability of surpassing a 6 °C threshold for non-mitigation scenarios such as the Special Report on Emissions Scenarios A1B and A1FI scenarios

^{6}, as compared with projections from the Fourth Assessment Report

^{7}of the Intergovernmental Panel on Climate Change.

**Climate sensitivity, the response of the carbon cycle and aerosol effects remain highly uncertain**but historical observations of temperature and carbon dioxide imply a trade–off between them so that temperature projections are more certain than they would be considering each factor in isolation. As well as pointing out the promise from the formal use of observational constraints in climate projection, this also highlights the need for an holistic view of uncertainty.

# Main

The past decade has seen a great deal of research into quantifying the uncertainty of climate projections as a guide to sensible adaptation and mitigation activity. The two most common techniques have been multi-model ensembles (such as the Third Coupled Model Intercomparison Project

^{8}(CMIP3) and Coupled Carbon Cycle Climate Model Intercomparison Project^{2}(C4MIP) and perturbed physics experiments^{9}. These experiments have allowed us to isolate those factors responsible for the spread of model ensembles. They have identified factors contributing to the overall climate sensitivity and uncertainty in the radiative response to aerosol changes, as well as the response of the carbon cycle, including some assessment of the feedbacks between climate change and carbon fluxes.
More recently, observations have been used to provide direct constraints on model behaviour

^{10, 11}. Computational complexity has largely precluded the use of full Earth system models and restricted the facets of model behaviour that can be constrained. Full Earth system models generally explore fewer model parameters or use statistical emulation to expand their sample size. Most critically, the carbon cycle behaviour remains largely untreated (with a rare exception^{12}), despite the sensitivity of global-mean temperature change projections to carbon cycle processes^{1}. Instead, typically, simple models have been calibrated against the C4MIP coupled carbon cycle/climate models^{2}, for which only limited formal calibration is possible and which do not address parametric uncertainty.
Here we apply historical observations to address the scientific uncertainty of the climate system. Our general method has been to identify those model parameters most responsible for uncertainty in global-mean temperature changes, and then to constrain them with historical observations. The model used was MAGICC version 6.3 (Model for the Assessment of Greenhouse Gas Induced Climate Change), a reduced complexity Earth system model

^{3}, whose climate system parameters have previously been estimated using historical observations^{11}. More recently, the climate system and carbon cycle parameters have been calibrated against both CMIP3 and C4MIP models^{3}.
MAGICC has been involved in recent studies of temperature change projections using the Special Report on Emissions Scenarios (SRES) and Representative Concentration Pathways scenarios

^{13,14}. However, calibration with just the C4MIP models neglects structural and methodological uncertainties and is therefore unlikely to represent the range of carbon cycle uncertainties^{14}. Here, for the first time, observations have been used to directly constrain the model’s carbon cycle parameters. We then generate probability distributions for global-mean temperature change that reflect uncertainties for the combined climate system and carbon cycle, taking into account a comprehensive range of model and observational uncertainties.
We see that, before using observations to improve prediction, the climate sensitivity, carbon cycle response and aerosol impacts are the three leading contributors to uncertainty (in that order). This was determined by a linear analysis of the uncertainty contributions to the simulated temperature change in 2100 from the model’s primary parameters. Prior probability distributions for the model’s parameters were estimated based on previous calibration exercises

^{3, 11}and earlier studies^{15}, although larger uncertainties were used for the carbon cycle parameters (see Methods andSupplementary Information for further details).
The uncertainty contributions for the A1FI emission scenario show that about 63% of the uncertainty stems from the climate system parameters, with over 90% of this due to the climate sensitivity parameter (Table 1), while just three further parameters account for much of the remainder (ocean vertical diffusivity, land ocean warming ratio and the land ocean heat exchange coefficient). The carbon cycle accounts for around 30% of the uncertainty in temperature change in 2100, most of which is captured by six parameters: two temperature feedback parameters for respiration and net primary productivity (NPP), plus the CO2 fertilization factor, the fraction of NPP to plant and plant to detritus, plus an ocean carbon cycle impulse response scaling factor.

**A single parameter was used for the aerosol forcing uncertainty, the fossil fuel derived sulphate aerosol forcing in 2005**, with the indirect or cloud albedo effect scaled from the total direct effect. This set of eleven parameters accounts for 96% of the model’s parametric uncertainty.
The Monte Carlo Metropolis–Hastings algorithm (MCMH) was applied to constrain the eleven model parameters identified above using twentieth-century observations. These included global-mean temperature change, land minus ocean and hemispheric temperature differences

^{5}, time series for ocean heat content changes^{16}, and a 1960–2008 ocean vertical temperature change profile^{17}. Observations for the carbon cycle employed atmospheric CO2 concentrations from Mauna Loa^{4}.
Details of the resulting posterior distributions for the parameters are provided in Supplementary Table S1 and Fig. S1. Note that individual distributions are not independent, so that, for example, the distribution for climate sensitivity is not a stand-alone result because the observational constraints introduce sizeable correlations between some of the parameters (parameter correlations are included in Supplementary Table S2). For example, a strong aerosol effect (which reduces temperature changes) requires a higher climate sensitivity to match the observed temperature changes, as found in other studies

^{18}.
We repeated the linear uncertainty analysis with the posterior covariance to determine which parameters and combinations are most responsible for the improved knowledge of projected temperature change (Supplementary Table S4). About 60% of the reduction in temperature standard deviation comes from uncertainty reduction in individual parameters, with the other 40%arising from parameter covariance. The largest single contribution comes from the climate sensitivity. There is also a large contribution from combinations of carbon cycle parameters, even though the individual parameters are not well-constrained. Studies that do not consider these covariances are likely to overestimate uncertainty in temperature change projections.

To assess the benefit of constraining the model’s parameters using the carbon cycle observations, we compared three ensembles of predicted temperature change for 2100 under the SRES A1FI scenario. Ensembles were generated by constraining model parameters with different combinations of constraints. The ‘Combined’ ensemble used both climate and carbon cycle observations, the ‘Without’ case used no carbon cycle observations, and the ‘Hybrid’ case used the prior C4MIP distribution for carbon cycle parameters and the ‘Combined’ ensemble for all others. All cases were constrained by twentieth-century temperature data.

The results (Table 2) show the benefit of including carbon cycle observations in the MCMH algorithm, where the effect is to limit the spread in the right–hand side of the probability distribution, reducing the likelihood of very high CO2 concentration and temperature changes by 2100.

The observationally constrained posterior parameter distribution was applied to the SRES A1FI, A1B and A2 emission scenarios. Details for temperature change and CO2 concentrations in 2100 are provided for the prior and posterior distributions, with and without the carbon cycle temperature feedbacks (Table 3), while the global-mean temperature change results are illustrated in Fig. 1.

The median, mode and likely ranges for temperature change in 2090–2099 were compared to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4) best estimate and likely range results for these three scenarios, and illustrated by the uncertainty bars inFig. 1 (numerical details are set out in Supplementary Table S3). The MAGICC mode temperature changes at 2090–2099 are almost the same as the AR4 best estimates for the A1B and A1FI scenarios, whereas the likely ranges are reduced at both extremes. This increases the probability of exceeding a 2 °C global-mean temperature increase by 2100 and reduces the probability of surpassing a 6 °C threshold. The differences arise from the observational constraints imposed by the MCMH calibration process, with the interaction of the individual asymmetric parameter distributions, the interplay of the uncertainties from both the carbon cycle and aerosol radiative forcing, and the amount of sulphur dioxide emissions in the individual scenarios. The central estimate and upper bound for the A2 scenario are noticeably cooler than the AR4 estimates as a result of the higher aerosol cooling.

Projections based on the prior and posterior distributions with and without the carbon cycle temperature feedbacks (Table 3) show how the uncertainty ranges are reduced, although the central estimates reveal little change. The impact of the carbon cycle temperature feedbacks are also evident, with increases in CO2 concentrations demonstrating a net positive feedback effect. The likely ranges are also wider with the temperature feedbacks on, indicating how emissions-driven temperature change projections are affected by both the carbon cycle feedbacks and the uncertainties in those feedbacks. Concentration-driven projections will underestimate the amount of temperature change unless this issue is allowed for.

The posterior parameter distributions also allow an assessment of the probability of exceeding selected temperature targets. For example, for the 2 °C target associated with dangerous climate change

^{19, 20}, Fig. 2 plots the three SRES (ref. 6) scenarios for global-mean temperature change and land-only surface temperature changes, relative to pre-industrial (rather than relative to 1980–1999 as in the previous figures and tables).
The A1B scenario shows a slightly increased probability of exceeding 2 °C as compared to A1FI at the start of the twenty-first century because of higher initial CO2 emissions. The A1FI scenario has a greater than 50% chance of exceeding 2 °C by around 2045, although over the land surface this 50% is exceeded a decade earlier, around 2035. By the end of this century, the probability of exceeding 2 °C global-mean temperature change is more than 95%, whilst the probability over land is close to 100% for all three scenarios.

Limitations in this work stem from inadequacies in the model and our estimation process. MAGICC is a simplified Earth system model which lacks certain processes capable of increasing the uncertainty (for example, water and nutrient cycles and liberation of carbon in permafrost). It also removes the state dependence of other processes such as ocean diffusivity or surface albedo. Finally, a single model cannot explicitly consider structural uncertainty

^{21}, although it can be included in the observational uncertainty^{22}.
The treatment of prior probability density functions in Bayesian calibration always requires care

^{21,23}. The main results of this paper are, however, based on reasonable assumptions or are insensitive to the choice of prior. The extra information available from carbon cycle observations does depend on the prior because, if there is little prior uncertainty, there is little to add. We agree with other work^{14}that the C4MIP ranges underestimate total uncertainty and expanded them accordingly. The impact of uncertainty covariance on temperature projections depends only weakly on the magnitude of the posterior uncertainty itself. The specification of data uncertainty is also beset with difficulty. Here we have used only decadal averaged data consistent with the capabilities of MAGICC and have included observation error correlations to deal with potential persistent errors.
The experiments presented here were based on selected SRES emission scenarios for the purposes of comparison to previous studies. However, emission scenarios need to be reassessed to allow for revised expectations in global economic growth, energy intensity, per capita consumption and demography. Furthermore, it would be useful to provide probabilistic temperature change projections using the Representative Concentration Pathways, perhaps following Rogelj and colleagues

^{14}.# Methods

## Sensitivity analysis.

MAGICC was run with a nominally standard set of initial parameter values (10 climate, one combined aerosol and 18 carbon cycle parameters) and A1FI emissions to establish a reference temperature change, then re-run for each parameter in turn, with the parameter value changed by 1% of its standard deviation. The difference in the year 2100 temperature change results then provides an uncertainty measurement of the model outputs for each of the input parameters (the Jacobian of the model

**J**)^{24}. The variance of each parameter provides the content for the covariance matrix**C**(*v*). To first order, the uncertainty of the temperature projection**U**is given by:
where the superscript represents the transpose of the matrix

**J**.
The results, that is, the relative contributions to uncertainty from the primary model parameters for the A1FI emission scenario, are provided in Table 1 (the sensitivity of these results to the emissions pathway, initial parameter values and second-order effects is discussed in the Supplementary Information).

## MCMH algorithm.

Our implementation of the MCMH algorithm compares model results from each iteration to a combined set of historical climate and carbon cycle observations, applying a decision rule to accept or reject each parameter set. The posterior parameter distribution is based on the Bayesian formulation:

where

*L*(**p**)is the likelihood function,*ρ*(**p**) is the prior probability density for the vector of parameters, and*η*is a normalization constant^{25, 26}(refer to the Supplementary Information for further details).
A set of 11 parameters was selected for the MCMH processing on the basis of the uncertainty analysis explained above. Prior parameter distributions were established based on previous studies and existing model calibrations

^{3, 11}. Gaussian uncertainties were assumed for both prior parameters and the observations. Our method included boundary values that result in truncated normal distributions for the model parameters, with boundaries selected to restrict the parameter space to physically realistic settings. All of the data, except the ocean temperature change profile, were organized into decadal averages to smooth out natural variability, as MAGICC does not simulate this feature of the climate system. Measurement uncertainties were obtained from the respective data sets, in addition to a component for the natural variability, to derive an overall observational standard deviation; these formed the diagonal elements of the error covariance matrix.
We analysed the error residuals from an initial run and found that they were well represented by a correlation timescale of 30 years. The MCMH algorithm was then re-run, using these correlations. It was executed 50,000 times to obtain 37,926 accepted parameter sets, where the relatively high acceptance rate reflects the quality of the estimated priors. The resulting posterior distribution can then be used in conjunction with a given emission scenario to produce probabilistic global-mean temperature change projections.

It only requires the input of just one measured independent variable in a conservation of energy equation to accurately calculate average global temperatures since before 1900.

ReplyDeleteTwo papers on line provide some eye-opening insight on possible cause of change to average global temperature.

The first one is 'Global warming made simple' at http://lowaltitudeclouds.blogspot.com/. It shows, with simple calculations, how a tiny change in low altitude clouds could account for half of the average global temperature change in the 20th century, and what could have caused that tiny change. (The other half of the temperature change is from natural ocean oscillation which is dominated by the PDO)

The second paper is 'Natural Climate change has been hiding in plain sight' at http://climatechange90.blogspot.com/2013/05/natural-climate-change-has-been.html . This paper presents a simple equation that calculates average global temperatures since they have been accurately measured world wide with an accuracy of 90%, irrespective of whether the influence of CO2 is included or not. The equation uses a proxy of the time-integral of sunspot numbers. A graph is included which shows the calculated trajectory overlaid on measurements.

A third paper, ‘The End of Global Warming’ at http://endofgw.blogspot.com/ expands recent measurements and includes a graph showing the growing separation between the rising CO2 and not-rising average global temperature.

http://www.nipccreport.org/articles/2014/may/27may2014a3.html

ReplyDeletehttp://www.earth-syst-sci-data.net/6/235/2014/essd-6-235-2014.pdf

ReplyDelete