3.1 Model Parameters
The most recent MAGICC version 6.3 has a comprehensive set of tuned parameters based on CMIP3 AOGCM results for the climate system and C4MIP (Coupled Carbon Cycle Climate Model Intercomparison Project; Friedlingstein et al., 2006) models for the carbon cycle, as developed by Meinshausen et al.(2011a). However, tuning to the CMIP3 AOGCMs only means that MAGICC has a capacity to emulate these more complex models; it will only produce similar temperature change projections, which may or may not be reliable. For example, there is some evidence that the CMIP3 models do not reproduce the recently observed ocean temperature profile changes all that well, as discussed in Section 3.4. A different set of ocean parameters is required for MAGICC to achieve a better representation of this observed change. This has implications for both the climate sensitivity parameter and simulated future surface temperatures.
The new version of MAGICC has also had many of its climate system parameters reviewed during a historical constraining exercise, as described by Meinshausen et al. (2009). Nevertheless, some issues arise related to these results that concern the cross–correlation of constraints and missing parameters. Although historical surface temperatures for land and ocean, for the Northern and Southern Hemisphere, and trends in ocean heat content, were used to constrain the likely range of possible parameter values, these observations are highly correlated with each other. Some of the important ocean parameters were missed in this analysis, as discussed later in this section, and observations were not used for constraining the carbon cycle.
There were 82 parameters used in the MAGICC parameter space referred to by Meinshausen et al. (2009), which can be divided into three groups: nine parameters that are ‘crucial for the simple energy–balance upwelling–diffusion–entrainment model in MAGICC 6.0’ (Table 3.1); 33 parameters that are connected with the different gas–cycle models and estimates of forcing values in 2005 for different forcing components; and forty scaling factors for apportioning forcing agents across the four regions of the model (ten sets of four).
Note that:
• The carbon cycle parameters are not included in this parameter space;
• The parameter µ is used for asymmetric land ocean heat exchange, but its standard value is one, i.e., it has no effect. It is a new parameter introduced in version 6 for fine tuning MAG-ICC to emulate AOGCMs and does not seem to be ‘crucial’, or even particularly important, to the model;
• Two of the parameters, the feedback sensitivity factor ξ and the ocean warming gradient Γ, are also new in version 6, and are not essential to the model;
• There are no sea–level rise parameters included in the calibration; this is not currently a working feature of MAGICC version 6, although it was in previous versions.
However, some important parameters are missing from the 82 member parameter space: the ratio of surface temperature to mixed–layer temperature α; the mixed–layer depth h; the initial upwelling velocity w0; and the variable upwelling velocity fraction wvar. The significance of these will be made clearer in the following sections of this chapter.
34 CHAPTER 3. CONSTRAINING THE CLIMATE SYSTEM PARAMETERS Table 3.1: MAGICC’s nine ‘crucial’ parameters (adapted from Meinshausen et al., 2009, Table S1).
No. Parameter Description
1 ∆T2x Climate sensitivity
2 K Ocean vertical diffusivity
3 µ Amplification factor for ocean to land heat transport
4 ξ Dependence of feedback factors on forcing
5 κlo Heat exchange coefficient land ocean
6 κns Heat exchange coefficient north south
7 Rlo Ratio land ocean warming
8 Tmoc Upwelling temperature threshold
9 Γ (dKztop/dT ) Dependence of vertical diffusivity on ocean warming gradient
3.1.1 Climate sensitivity
Climate sensitivity is the single most important parameter in MAGICC; results are very sensitive to this setting, as demonstrated in Section 3.2. Its role was introduced in Chapter 2 in the context of the energy–balance equation on which MAGICC is based. However, despite many different studies, the value of this parameter remains uncertain. The IPCC AR4 suggests that the likely range for equilibrium climate sensitivity is 2–4.5◦C, based on investigations using observationally based methods and results from AOGCMs (IPCC, 2007b). It is most unlikely (5% lower confi-dence limit in a normal distribution) to be less than 1.5, but the 95% upper conficonfi-dence limit is not given, since different studies indicate values from 5 to 10◦C; there is no formal way to combine the different probability distributions to obtain this upper value. Part of the uncertainty surround-ing climate sensitivity arises from differences between models, particularly from different cloud feedbacks (Forster and Gregory, 2006). In addition, Roe and Baker (2007) propose that the broad shape of probability distributions for climate sensitivity is a feature of the climate system, and that decreases in uncertainties associated with underlying climate processes is unlikely to reduce the spread of this distribution.
A useful discussion on the history of the climate sensitivity concept is provided by Andronova et al.(2007). Climate sensitivity is defined relative to fast–feedback processes, such as water vapour amount and changes to clouds or sea ice, and based on adjusted forcing estimates within one year in complex models, that is, including stratospheric temperature adjustment, but not slow–
feedback processes, such as a reduction in the area of continental ice sheets, dissolution of car-bonate sediments in the ocean and enhanced chemical weathering on land, processes that involve timescales of hundreds to thousands of years (Harvey et al., 1997). However, some of the cloud response can be considered as a change in forcing and not feedback (Gregory and Webb, 2008).
Hansen et al.(2007) argues that the standard fast–feedback climate sensitivity underestimates the equilibrium climate response, which should be larger on long timescales due to changes in land cover and ice sheets.
With AOGCMs, the climate sensitivity is diagnosed from the state of the model; it is a property of the simulated climate system. In contrast, MAGICC requires a specified climate sensitivity
3.1. MODEL PARAMETERS 35 value for the model to work. Furthermore, this value is notionally for equilibrium, which is a somewhat theoretical construct since it can only be reached many years after greenhouse–gas concentrations have stabilised. Until equilibrium is reached, AOGCM results indicate that climate sensitivity changes. This is a consequence of variations in the strength of different feedbacks, which vary with climate forcing (Colman and McAvaney, 2009).
The issue of a non–constant climate sensitivity was looked at by Senior and Mitchell (2000) using the HadCM2 AOGCM. They found that, for the doubled CO2experiment, the climate sensi-tivity changed from around 2.7◦C after 70 years (doubled CO2) to 3.8◦C after another 830 years.
They concluded that using a fixed climate sensitivity in a simple climate model may lead to error.
If the climate sensitivity chosen is the equilibrium value it will overestimate the warming in the early period, but, if an effective climate sensitivity is selected it will underestimate the long–term equilibrium warming. Raper et al. (2001) noted this problem in tuning MAGICC to the HadCM2 model, and pointed out that the change in effective climate sensitivity resembles that of the global–
mean temperature.
Boer et al.(2005) suggested that, with the NCAR model and their experimental conditions, cli-mate sensitivity increases linearly with temperature, that is, clicli-mate sensitivity is state–dependent (not time–dependent). However, Williams et al. (2008) proposed that the centennial scale variation in climate sensitivity is a product of using forcings that only allow for instantaneous effects and stratospheric adjustment. They argued that, if forcings are adjusted on shorter time scales there is then little long–term change to effective climate sensitivity.
On the other hand, from the calibration of MAGICC against the CMIP3 AOGCMs, Mein-shausen et al.(2011a) stated that many of these models have variable effective climate sensitiv-ities. In order to improve the emulation of models, a state–dependent climate sensitivity was in-vestigated and two new features introduced into MAGICC version 6 to allow the effective climate sensitivity to increase. One modifies the land ocean heat exchange using an additional parameter that varies the standard land ocean heat exchange coefficient to provide for an asymmetric heat exchange. The second feature models a forcing dependency on the sensitivity, so that the land and ocean feedback parameters are scaled in proportion to the change in forcing, using a sensitivity factor as the parameter for this relationship (refer appendices A4.2 and A4.3 in Meinshausen et al., 2011a, for full details).
This discussion then raises an issue concerning the interpretation of the climate sensitivity parameter in MAGICC; in selecting a value for this parameter, a choice has to be made as to whether it is the long–term equilibrium value or a value for the effective climate sensitivity. In addition, any value derived from fitting to historical observations, as per the later work in this chapter and again in Chapters 4 and 6, is an estimate for an observed climate sensitivity, which may well be less than a future effective climate sensitivity or equilibrium climate sensitivity.
3.1.2 Land ocean warming ratio
The land ocean warming ratio Rlois another important parameter in MAGICC, where it is used to separate the climate sensitivity parameter into land and ocean feedback terms. It is the ratio of annual–mean temperature change averaged over land to that averaged over ocean at equilibrium in response to a change in forcing ∆Q. Since the ocean heat uptake is zero when the Earth’s radiative
36 CHAPTER 3. CONSTRAINING THE CLIMATE SYSTEM PARAMETERS energy balance is zero, the global energy balance equation, Equation 2.2, can be arranged into land and ocean components:
∆Q = λ∆T = flλl∆Tl+ foλo∆To (3.1) where ∆Q, λ and ∆T are the global–mean forcing, climate feedback and global–mean tempera-ture change respectively. The right–hand terms use the land and ocean area fractions, fl and fo, the separate land and ocean feedbacks, λland λo, together with the matching mean temperature changes for the land ∆Tl and for the ocean ∆To. λl and λo are calculated from a set of non-linear equations for a given land ocean warming ratio Rlo(= ∆Tl/∆To) (refer Appendix A.2 and Meinshausen et al., 2011a, for details).
The standard model setting for Rlois 1.3, which was assessed from long–term AOGCM results for equilibrium conditions. The equilibrium Rlo value depends on the difference in evaporation and other surface properties of land and ocean, whereas the transient Rlo also depends on the different heat capacities of land and ocean. Lambert et al. (2011) confirmed that this ratio is a robust feature of both observed and modelled climate change and found that the coupling between land and ocean surface temperature change is largely due to heat transport between the land and ocean surfaces. This value is re-assessed in Section 3.3.2 in the context of applying the land−ocean temperature difference as an observational constraint, and again in the Monte Carlo Metropolis–
Hastings investigations (Sections 4.3 and 6.2).
3.1.3 Surface to ocean temperature ratio
A ratio of ocean near–surface to ocean mixed–layer temperature change α is used within MAG-ICC to calculate the ocean near–surface air temperature changes from the ocean mixed–layer tem-perature changes (i.e., determines the sea–surface temtem-perature anomaly, SST). MAGICC’s only prognostic variables are the hemispheric ocean layer temperature changes: ocean–surface and land–surface temperature changes are then diagnosed from the ocean mixed–layer temperature changes.
This parameter was introduced into version 4.1 as part of a number of changes to improve the model’s performance relative to AOGCM global–mean temperature change results. A value of 1.2 was originally used, based on HadCM2 experiments (Raper et al., 2001), which changed to 1.25 for the IPCC Third Assessment Report experiments. Model results are sensitive to this setting, yet this parameter has received very little discussion in the MAGICC literature. It does not appear as one of the calibrated parameters used in the comprehensive historical calibration exercise by Meinshausen et al.(2009) or in the CMIP3 work by Meinshausen et al. (2011a).
This ratio appears to be a genuine feature of the climate system, and not just a ‘fudge factor’
required to improve the model’s performance. Raper et al. (2001) suggests that there is a physical basis for α: as sea–ice cover is reduced the air temperature will warm more as the cold ice tem-perature felt by the atmosphere is replaced by warmer surface water temtem-peratures. This difference was previously noted in Raper and Cubasch (1996). However, the suggestion that this is a constant ratio for this reason is something of a puzzle. If the rate of warming due to greenhouse–gases was slower or very much faster, the sea–ice melt rate would be different, and hence this ratio would change. Further, if all the sea–ice melted this ratio would presumably no longer apply. It might
3.1. MODEL PARAMETERS 37