Another perspective on the carbon cycle parameters’ posterior distributions can be obtained by examining the change from the prior distributions using the diagnostic likelihood function LF(x), applying the same methodology as was used with the climate parameters (Section 4.3.4). This was done for the first set of distributions obtained above (Section 5.5.1), with the results shown in Figure 5.13. The first and third rows are the probability density histograms for each of the six parameters (i.e., the frequency histograms scaled by the number of observations), with the prior distribution indicated by the grey shaded region with black outline, and the coloured regions the posterior distribution. Then, under each parameter distribution, the likelihood functions are plotted as probability density histograms (the second and fourth rows). The shape of the likelihood functions is a measure of the information gained from the historical observations by the MCMH algorithm. The distribution results were restricted to a 5% to 95% interval to avoid issues caused by the very small numbers at the tails, effectively creating boundaries similar to the limits for a uniform distribution.
Studying the results in this way reveals some of the gains made, but also serves to highlight some issues.
Figure 5.13: Carbon cycle likelihood functions for the 6 parameter prior and posterior distribu-tions from the initial 120,000 iteradistribu-tions, Section 5.5.1 (PD = probability density, LF = likelihood function). The prior distribution is indicated by the grey shaded region with black outline.
120 CHAPTER 5. THE CARBON CYCLE The clearest result is for the single ocean parameter, the ocean carbon cycle impulse response scale factor Or. If the prior had been assumed to be a uniform distribution, the posterior derived from this LF(Or) would be an almost normal distribution. The relatively broad prior distribution, based initially on the range of C4MIP calibrated values, has been substantially reduced. This result can be partly attributed to having only one ocean parameter in the MCMH–MAGICC setup that lines up with the corresponding GCP ocean flux data, although the net fluxes are also constrained by the atmospheric CO2concentration data and the balance with historical emissions.
The results are more mixed for the five terrestrial carbon cycle parameters. The two flux partitions, carbon flux partition, NPP to plant gP, and carbon flux partition, plant to detritus qH, show little change in their distributions. Uniform priors for these would show little change brought about by the MCMH program. This is because the observations used do not relate directly to these two parameters. They are associated with the internal division of carbon between the carbon pools, whereas the observations relate to the flux into the terrestrial carbon cycle as a whole.
The terrestrial carbon cycle parameter that exhibits the most change is the CO2 fertilisation factor βs. It is perhaps the most ‘exposed’ of the five, and hence most affected by the land flux.
It is also the parameter associated with the ‘missing sink’, the term needed to balance the carbon budget. A prior uniform distribution would be transformed into an approximately normal distri-bution with a mean of about 0.7, which is the same value given for the posterior mean in Table 5.5.
The two temperature feedback parameters for respiration σR and NPP σNPPare more prob-lematic. They both have initial prior means of only −0.01. The C4MIP calibrated values span minimum to maximum ranges of −0.20 to 0.19 and −0.06 to 0.04 respectively, so both posi-tive and negaposi-tive values are possible. The MCMH transformations of these two parameters, as indicated by their likelihood functions, have different characteristics.
The LF for the respiration temperature feedback σR has a truncated and skewed profile. The original prior was restricted to an interval of −0.37 to 0.37, a little over twice the standard distribu-tion, in order to limit the spread of accepted priors submitted for testing by MAGICC, effectively increasing the acceptance rate. However, the LF(σR), as compared to a uniform prior, suggests that the lower truncation point should have been extended a little further. The peak of the LF is around σR −0.18. Smaller, more negative, values of this parameter mean less CO2 is produced from increased temperatures.
For the NPP temperature feedback σNPP, the LF(σNPP) is a modified uniform distribution, with some tapering off at the ends, although mainly at the lower or left hand end of the distribution.
There is a slight shift upwards to more positive values for this parameter. This result suggests that σNPPcannot be resolved by the available data.
5.6 Chapter Summary
Calibrating MAGICC’s carbon cycle parameters presents a number of challenges: there are more parameters to deal with than in the climate system, and there is limited data available to help calibrate those parameters, both in terms of the number of observations but also their temporal cover. This problem has been previously dealt with by making use of the results from more
5.6. CHAPTER SUMMARY 121 complex carbon cycle models (Meinshausen et al., 2011a). In this research work, a decision was made to investigate this calibration using observations, aided by the release of data compiled by the Global Carbon Project.
The uncertainty analysis technique introduced in Chapter 4 was first applied to assessing the significance of the carbon cycle parameters to the uncertainty in projected CO2concentrations and temperature changes. A subset of six carbon cycle parameters was selected for calibration based on the outcome of this analysis.
The MCMH method was then successfully applied to obtaining posterior probability distribu-tions for these six carbon cycle parameters. As far as is known, this is the first time MAGICC’s carbon cycle parameters have been constrained against historical observations, rather than against other models. This method is able to take into account uncertainty from the different observations and the response of the carbon cycle to changes in temperature and CO2concentrations. One of the things missing from this analysis is, however, the uncertainty in CO2fossil fuel and land use emis-sions, since these emissions data are processed as part of MAGICC, not as an external observation to constrain the model results. Historical emissions data are estimated to have an uncertainty of
±6% (GCP; http://www.globalcarbonproject.org/carbonbudget/09/hl-full.htm).
The robustness of the results was tested in a number of different ways, including examining the correlations, the number of iterations, amount of observations, and the influence of the prior distribution. These tests showed that the posterior results are somewhat affected by the MCMH set-up, particularly for the respiration feedback factor σR and CO2fertilisation factor βs. Calibration of the two main temperature feedback factors σR and σNPPis particularly difficult, yet they are critical for future projections.
The limited number and time–span of historical observations make it difficult to better estimate MAGICC’s carbon cycle parameters. However, there is potential for improvement, from new observational data, changes to the model design and perhaps using the available data in different ways. For example, observational data may be extended back in time as new analysis of ice core data can potentially provide estimates for land and ocean fluxes extending back over the last century or two. Furthermore, new data will become available as time proceeds, although important decisions concerning mitigation are needed sooner rather than later. It might also be possible to construct independent constraints, such as a land−ocean flux difference index to see if it provides additional information, similar to the land−ocean temperature constraint used with the climate system.
It might be feasible to modify MAGICC, adding the capability for tracking carbon isotopes, particularly if this will provide additional data on the carbon pools and help better estimate the temperature sensitivities. Some care needs to be exercised with this information so that double counting is avoided here. For example, the GCP land flux estimates are already informed by isotopic information. Another option might be to model separate ocean carbon cycles for the biological and chemical pumps, if the relevant observational data exists. Such data might also be divided hemispherically, so that there are Northern and Southern Hemisphere land and ocean fluxes, providing four carbon cycle regions similar to the four climate system regions. Again, this depends on the availability of the requisite data.
122 CHAPTER 5. THE CARBON CYCLE Further testing of the carbon cycle could also be carried out to investigate different parameter choices, including the addition of one or more parameters for the initial carbon pools, and possibly the ocean carbon cycle temperature feedback factor. However, changes to the model and alterna-tive estimates of the carbon cycle parameters that have only a minor influence on projections may not be warranted. The relative importance of the carbon cycle needs to be considered in the context of its contribution to overall system. This is investigated in the next chapter.