Parameter Sensitivity

Table 3.4: MAGICC’s ocean parameters.

Abbreviation Description Units

K ocean vertical diffusivity cm²s⁻¹

κ_lo heat exchange coefficient land ocean W m^{−2 ◦}C⁻¹

κ_ns heat exchange coefficient north south W m^{−2 ◦}C⁻¹

Tmoc variable upwelling temperature threshold ^◦C

h mixed–layer depth m

w upwelling velocity m yr⁻¹

w0 initial upwelling velocity m yr⁻¹

w_var variable upwelling velocity fraction

β ratio of polar sink water to mixed–layer temperature

in a span of K values from 0.43 to 2.6 cm²s⁻¹, with an average value of 1.30 cm²s⁻¹, while the value for the aggregate CMIP3 temperature response is 1.1 cm²s⁻¹.

However, it is important to keep in mind that the ocean circulation in MAGICC is only a rep-resentation of the real processes. In MAGICC, the ocean is modelled by narrow sinking polewards cool limbs balanced by broadscale uniform upwelling in the rest of the ocean. The upper–ocean vertical temperature gradient is maintained by uniform vertical mixing, scaled by the effective ocean diffusivity parameter K. In the real ocean, the vertical temperature gradient in the upper 1000m is largely maintained by wind–driven ocean subduction of the meridional temperature gra-dient (Luyten et al., 1983) and interior ocean mixing actually plays little role in setting the vertical scale of this gradient. Consequently, the upwelling–diffusion balance in MAGICC should only be regarded as a proxy for the ocean subduction process.

The temperature dependence of w has been addressed in different ways, based on an initial upwelling velocity w0 and a variable component. The parameter Tmoc is closely tied into this relationship, which complicates their calibration. This is discussed further in Section 3.4.1.

Three new parameters were introduced into MAGICC version 6.3, as noted previously: an am-plification factor to allow for asymmetric ocean to land heat transport µ; a parameter that allows for a dependence of feedback factors on forcing ξ, which provides for a variable climate sensitiv-ity; and a dependence of the ocean vertical diffusivity on the ocean warming gradient Γ. These have been added as refinements that enable additional tuning options to better emulate AOGCMs.

However, the first two are not important in setting MAGICC’s ocean temperature profile. The third parameter is discussed further in Section 3.4, which investigates the ocean parameters in the context of improving the fit between the observed and modelled ocean temperature change profile.

Note that there is no direct relationship between the ocean parameters and the carbon uptake, since the latter is modeled by an impulse response function that is not connected to ocean param-eters such as K and w. There is some linkage from the temperature change effects that can alter K and w, and the temperature feedback term in the ocean carbon cycle. This is a limitation of this type of model (this was also pointed out by Urban and Keller, 2010).

3.2 Parameter Sensitivity

MAGICC’s climate system parameters are examined in this section to assess and quantify the rela-tive sensitivity of MAGICC’s temperature projections to changes in parameter values as a basis for

40 CHAPTER 3. CONSTRAINING THE CLIMATE SYSTEM PARAMETERS subsequent research using historical observations to constrain the model’s parameters. Included in this investigation are sub–sections that look at parameter sensitivity for global–mean temperatures, land−ocean and Northern−Southern Hemisphere temperature differences. The relative sensitivity of the parameters helps in prioritising efforts to constrain the parameter values to best estimate the climate system response.

Pulse response testing was used for the sensitivity study in this chapter. A specified radiative forcing pulse was applied to the model and its response determined for different parameter set-tings. The difference in the peak temperature response and the overall change over time provide a measure of the individual parameter sensitivity. Previous studies have reported on the importance of climate sensitivity, ocean heat uptake parameters, and the land ocean equilibrium–warming ratio (e.g., Wigley and Raper, 2001; 2002). The latter is important for obtaining the correct land ocean temperature contrasts, as well as having significant implications for climate change impacts.

This study confirms these findings, but also demonstrates the relative sensitivity of the model to some of the other parameters.

3.2.1 Global–mean temperature case

The parameter sensitivity in relation to global–mean temperatures is considered here (parameter sensitivity in relation to the ocean temperature profile is examined in Section 3.4). A ‘Standard Run’ was established using historical concentrations and radiative forcings up to 1999 followed by constant concentrations and radiative forcing for the period 2000–2100, with standard parameter settings. A ‘Perturbed Run’ used the ‘Standard Run’ but with an added radiative forcing pulse of 1.0 W m⁻² for five years, 2010–2014. Sets of model results were created for each climate model parameter, varying one parameter at a time over a range of values, with all the others left at the standard settings.

The difference between the peak temperature response and the corresponding standard tem-perature is an indication of the parameter sensitivity. These differences are recorded in Table 3.5 for the lowest and highest parameter settings, sorted by the peak temperature difference, where the peak difference refers to the maximum difference between the ‘Perturbed Run’ and the ‘Standard Run’ for each parameter. In addition, the area–under–the–curve for the time integral temperature response for the period 2000 to 2100 was determined (Table 3.6), which provides an alternate sensitivity measure that takes into account the model’s adjustment time to the perturbation. The tabled ‘Area diff’ is the difference between the areas for the lowest and highest parameter settings.

It is evident that MAGICC is more responsive to some parameter changes than others, with rapid rises and falls in temperature, while others have longer–term effects. These response differences essentially depend on how each parameter relates to the ocean’s thermal inertia.

Selected results for some of the parameters are illustrated in Figures 3.1 to 3.3 for climate sensitivity ∆T2x, ocean vertical diffusivity K, and the land ocean warming ratio R_lo. Table 3.5 and Table 3.6 present the climate parameters in descending order of sensitivity, sorted by the peak temperature difference in Table 3.5, and by the area–under–the–curve in Table 3.6.

It is clear that climate sensitivity ∆T2x, followed by ocean diffusivity K, are the two most important parameters for MAGICC’s global–mean temperature change projections. This is con-sistent with previous studies and, accordingly, these two are going to take priority when seeking to

3.2. PARAMETER SENSITIVITY 41 constrain MAGICC’s parameters using historical observations. However, the next two parameters in Table 3.5, R_lo and α, are an unexpected result, in that these parameters are relatively signif-icant but have received little attention in the MAGICC related literature. Over the longer–term, T_moc, β, and w0become more significant than Rloand α to a short–term perturbation. The ocean mixed–layer depth, h, has only a limited influence on the global–mean temperature change results.

Changes in both κloand κnshave little effect on the results.

20000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 0.2

0.4 0.6 0.8 1 1.2 1.4 1.6

Year Temperature anomaly, o C, wrt 1990

Variable dT2x Temperature Anomaly

standard perturbed dT2x 1.0 dT2x 1.5 dT2x 2.0 dT2x 2.5 dT2x 3.0 dT2x 3.5 dT2x 4.0 dT2x 4.5 dT2x 5.0 dT2x 5.5 dT2x 6.0 dT2x 6.5 dT2x 7.0 dT2x 7.5 dT2x 8.0 dT2x 8.5 dT2x 9.0 dT2x 9.5 dT2x 10.0

Figure 3.1: Varying the climate sensitivity parameter, ∆T2x.

42 CHAPTER 3. CONSTRAINING THE CLIMATE SYSTEM PARAMETERS

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 0.1 Temperature anomaly, o C, wrt 1990

Variable K Temperature Anomaly

Figure 3.2: Varying the ocean diffusivity parameter, K.

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 0.1 Temperature anomaly, o C, wrt 1990

Variable RLO Temperature Anomaly

Figure 3.3: Varying the land/ocean warming ratio parameter, R_lo.