cycle MCMH results, as per Table 5.7. The correlations of the parameters before they were condi-tioned by the observations, that is, the prior parameter distributions, are included in Table 5.6. This confirms that they have no prior correlation, which is the expected result since the parameters were generated by a psuedo–random process. The MCMH program conditions these priors by running MAGICC and comparing the model results to the observations, the result of which is a set of ac-cepted parameter sets which are the posterior distributions. The change in the correlation structure therefore provides some information about how successfully the observations have independently constrained the parameters. High correlations indicate that the observations have not been able to separately inform the parameter values, while low correlations suggest the observations have independently informed the parameters.
Table 5.6: Prior correlations between MAGICC carbon cycle parameters (120,000 iterations).
parameter σR βs σNPP Or gP qH
temperature feedback factor, respiration σR 1.00 CO2fertilisation factor βs −0.01 1.00
temperature feedback factor, NPP σNPP 0.02 0.01 1.00
ocean cc impulse response scale factor Or 0.04 0.01 −0.01 1.00
carbon flux partition, NPP to plant gP 0.03 0.02 0.01 −0.03 1.00 carbon flux partition, plant to detritus qH −0.01 0.03 −0.01 0.01 −0.00 1.00
Table 5.7: Posterior correlations between MAGICC carbon cycle parameters for initial 120,000 iteration MCMH run.
parameter σR βs σNPP Or gP qH
temperature feedback factor, respiration σR 1.00
CO2fertilisation factor βs 0.40 1.00
temperature feedback factor, NPP σNPP 0.30 −0.53 1.00
ocean cc impulse response scale factor Or 0.02 0.12 −0.03 1.00 carbon flux partition, NPP to plant gP 0.09 0.08 −0.22 −0.03 1.00 carbon flux partition, plant to detritus qH 0.03 0.11 −0.16 −0.02 0.09 1.00
The strongest correlations are a positive correlation of 0.403 between respiration feedback σRand fertilisation factor βs, and a negative correlation of −0.533 between βs and temperature feedback factor for Net Primary Production σNPP. There are also small correlations between σR and σNPP, σNPPand gP. The remaining correlations are very small.
The three strongest correlation relationships are included here as joint parameter density plots, Figure 5.9(a), (b) and (c).
To help understand these relationships, Figure 5.10 shows the effect that the high, mean and low parameter values for (a) CO2 fertilisation factor βs, (b) CO2respiration feedback factor σR, and (c) temperature feedback factor, NPP σNPP, have on temperature change projections, using the A1FI emission scenario. Note that larger values for βsand σNPPresult in reduced temperature changes, but σR operates in the reverse direction.
114 CHAPTER 5. THE CARBON CYCLE
Figure 5.9: Carbon cycle parameter correlation plot, i.e., joint parameter density plot, for: (a) respiration temperature feedback σR and CO2fertilisation factor βs; (b) σRand NPP temperature feedback σNPP; (c) βsand σNPP.
Anomaly, oC wrt 1765
(a)
Figure 5.10: The influence of three carbon cycle parameter on temperature change: (a) CO2 fer-tilisation factor βs, (b) CO2 respiration feedback factor σR, and (c) temperature feedback factor, NPP σNPP(A1FI emission scenario).
An increase in the CO2 fertilisation factor βs leads to a reduction in the amount of future warming (Figure 5.10(a)). A larger βsmeans more plant production, therefore more CO2 uptake, so that there is a reduction in the atmospheric CO2 concentration and so less warming. However, more plant growth will also increase the amount of material available for respiration as it decays through the rapid turnover, detritus and soil boxes.
The plant decay processes are affected by temperature, parameterised in MAGICC by σR, σH, σS. These create a positive feedback effect, illustrated in Figure 5.10(b) for σR. Increases in these parameter values mean that more CO2is produced from heterotrophic respiration, increasing the atmospheric CO2 concentration, which increases the amount of temperature change. The temperature feedback factor for respiration σR has the largest impact of the three because of a faster decay rate from the rapid turnover part of the living plant box.
At the same time as a bigger σR increases CO2 emissions and hence greater concentrations, increases in atmospheric CO2 encourage increases in living plant material, i.e., more NPP, which is modelled by the CO2fertilisation factor βs, and hence these two parameters will covary. These effects are also coupled in MAGICC because the fertilisation factor is applied to the heterotrophic
5.5. CONSTRAINING THE CARBON CYCLE PARAMETERS 115 respiration flux (Meinshausen et al., 2011a). Hence, it is to be expected that these two parameters are positively correlated, as illustrated in Figure 5.9(a). The observational information supplied to the MCMH program is insufficient to fully separate these two parameters.
Larger, more positive values for σNPPmean an increase in NPP as temperature increases, so more CO2is taken up by living plants, reducing the atmospheric CO2concentration and reducing temperature changes, as shown in Figure 5.10(c). That plants are happier when warmer and tend to put on biomass is a gross global–scale generalisation that assumes no water or nutrient limitations.
del Grosso et al.(2008) shows that temperature is less well correlated with NPP than precipitation, and that for non-tree dominated systems using NPP as a function of temperature increased model error in their case. These complexities can not be allowed for with MAGICC since it does not model precipitation or vegetation types. Instead, the temperature feedback parameters allow for the general uncertainty in how NPP will change in response to temperature changes at the global–
scale.
The two temperature feedbacks σNPPand σR show a small positive correlation of 0.3 (illus-trated by Figure 5.9(b)). They are connected to the amount of NPP or new plant material produced each year. If NPP is increased by a larger temperature feedback factor σNPPthen the amount of CO2 from decaying material will have to be increased to maintain the carbon budget (since more NPP means a reduction in atmospheric CO2). A bigger value for σR will help to achieve this balance, and hence the correlation between these two.
The negative correlation of βswith σNPP(Figure 5.9(c)) is also a consequence of maintaining the carbon budget. If βs is larger, with more plant production, reducing atmospheric CO2, then the temperature feedback σNPPchange needed to offset this requires a smaller value.
The ocean carbon cycle impulse response scale factor Or is largely isolated from the other parameters by the observations. The correlations are all very small, except for a small correlation with the CO2 fertilisation factor βs. This small interaction is unsurprising since βsis associated with balancing the carbon budget, which is the balance of emissions with the land flux and ocean flux to achieve the atmospheric CO2concentrations.
Excluding the temperature sensitivity of the ocean to carbon uptake (the ocean carbon cycle temperature feedback αT parameter) from the set of carbon cycle parameter has helped to reduce the complexity of these MCMH results. This was justified on the basis of the earlier uncertainty analysis, although it is known that the ocean temperature has an important influence on the solu-bility of CO2.
5.5.2 Further carbon cycle MCMH testing
Some alternative strategies were investigated to further test the initial MCMH carbon cycle only results, looking at the affect of the time period for the observed CO2 concentrations and CO2
fluxes.
(i) Adding CO2observations from 1900. In this case, the carbon cycle was switched to using historical emissions in 1910 (rather than 1960), using both observed decadal global–mean temper-atures and CO2concentrations as observational constraints, but without flux data until the 1960–69 decade.
116 CHAPTER 5. THE CARBON CYCLE This outcome reveals some differences as compared to the previous results, mainly in the means of the first two parameters, with surprisingly little change in the standard distributions, changes which may also be affected by the smaller number of iterations performed (12k rather than 120k). The changes in the two feedback terms, σRand σNPPare small, but significant for longer–
term projections. The additional pre-1960 CO2 concentrations and global–mean temperatures,1 in the absence of additional flux data, are perhaps also influencing the results, despite the smaller changes in atmospheric concentrations and temperatures that occurred in the first half of the 20th–
century.
Table 5.8: Prior and posterior distributions for key MAGICC carbon cycle parameters, with addi-tional CO2concentration observations and using historical emissions from 1910 onwards (12,000 iterations).
parameter prior mean post mean prior σ post σ
temperature feedback factor, respiration σR −0.01 0.00 0.15 0.13
CO2 fertilisation factor βs 0.50 1.16 0.50 0.26
temperature feedback factor, NPP σNPP −0.01 −0.04 0.05 0.04 ocean cc impulse response scale factor Or 1.50 0.76 1.00 0.21 carbon flux partition, NPP to plant gP 0.50 0.54 0.25 0.19 carbon flux partition, plant to detritus qH 0.80 0.75 0.20 0.14
(ii) The impact of dropping the last decade of observations (2000–2009), as compared to the initial results, was also tested, i.e., using four decades of observed fluxes and CO2concentrations, rather than five decades. These results (Table 5.9) also display noticeable changes in the posterior means for σR, βs, σNPPand Or, and in the standard deviations for σRand βs.
These differences point to the value that additional observational information provides. In-deed, it is really only the relatively recent emergence of the Global Carbon Project data that has made it possible to use historical observations to constrain MAGICC’s carbon cycle parameters.
MAGICC does not have the capability of tracking carbon isotopes which would otherwise be another source of observations for helping to calibrate the carbon cycle parameters.
The carbon cycle parameters will be better constrained as more observations are accumulated.
The value of additional observations could be further tested with a synthetic data experiment, whereby a forward model run is used to generate ‘observations’, which are then treated as a set of randomly distributed results and used as observational constraint to see how the posterior distri-butions change in response to the extra data.
An issue that has not been explored here is the role of the initial carbon pools. The uncertainty analysis indicated that the temperature change results are hardly affected by these values. How-ever, this may be because the method used has the effect of dissipating the influence of the pool size by the time the carbon cycle is activated in 2005. This is a topic that perhaps warrants further investigation.
1CO2 concentrations from NASA GISS 2002 GCM runs, as given on
http://www.giss.nasa.gov/data/simodel/ghgases/GCM.html and included in MAGICC’s history files; temperature data is HadCRUT3.
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