Methods
Ensemble of MIROC3.2 runs
For these experiments we use the T21L20 slab-ocean version of the state-of-the art GCM MIROC3.2 (Hasumi and Emori, 2004). The atmospheric component is a reduced-resolution version of the standard T42 version used in several modelling studies, including the results analysed by MD06 and Crucifix (2006). The physical and numerical schemes are unchanged, and a “control run” (with the parameter values taken directly from the control T42 model, with the exception of the strongly resolution-dependent gravity wave drag parameter) produced similar results to those of the higher resolution model at both LGM and 2×CO2 states. We used the ensemble Kalman filter (EnKF) to generate three ensembles each of 40 members (Annan et al., 2005). For each experiment, we used the same expert opinion for the prior ranges of 25 parameters which we allowed to vary. The model was tuned to seasonally-averaged (summer and winter only) fields of 15 different climatological variables such as temperature, precipitation, radiation and winds. The only difference between the three experiments was in the judgment as to the model error that we considered reasonable. One ensemble consists of models which actually reproduce the climate fields better (as indicted by a normalised RMS error measure) than the control run, and the other two were less tightly tuned to the data and so covered a wider range of the parameter space. The experiment is described more fully in Annan et al. (2005). Creation of the original ensembles is time consuming and computationally expensive and the study presented in this paper uses the output from these previous experiments. For simplicity and in order to achieve improved statistics we combine the three ensembles and analyse them as one large ensemble. Taken as a whole we have a set of runs which all compare reasonably well with present day climatology but with different values for all the 25 varied parameters. A general understanding of model error (sometimes called “discrepancy”: see Rougier (2006) for more discussion) is at present rather limited, and the model results exhibit a bias towards high sensitivity that we do not consider to be a realistic representation of our overall uncertainties (further investigations and development of the model is ongoing) so we simply combine the three ensembles in our analysis to explore the emergent relationships between different climate states that appear significant in the context of our experiment.
Model runs
After the parameter sets were generated, we then performed 4 experiments with all the model instances: pre-industrial (CTRL) climate, doubled CO2 (2×CO2), LGM (with PMIP2 boundary conditions) and LGMGHG (greenhouse gases and orbital parameters as for PMIP2, but without the ice sheet and insolation changes of the PMIP2 protocol). Table 1 gives an overview of the forcings for the 4 experimental model climates. The experiments were run until the annual average temperatures had converged (at least 24 years for LGM and LGMGHG, 36 years for 2×CO2) and then a further 20 years were averaged for the climatological results discussed below. The 120 member ensemble was run for each of the 4 experiments, but only 119 runs were used in the analysis. One model run, under LGMGHG boundary conditions, exhibited runaway cooling with no sign of equilibrating over a 50 year integration. Strong cooling was centred on the eastern equatorial Pacific. This behaviour appears to be due to the same phenomenon as that noted by Stainforth et al. (2005) (a nonphysical localised cooling instability arising from the limitations of a slab ocean model), and we therefore exclude this member from all of our analyses. Since we are seeking to analyse the relevance of paleo-temperature data for future temperature change prediction, we confine our analysis here to consideration of the modelled surface (2 m) temperatures. We have analysed the 119 member ensemble to look at the correlations between several different components of both model variables, and also the relationship of these with the parameters. The correlations indicate the extent to which our uncertainties about the climate system (as encapsulated by imperfectly known parameter values in the model equations) affect past and future climate simulations in similar ways. Where the historical simulation is weakly related to the future, then increasing our skill in this aspect of the simulation will hardly affect our predictions, even if it does increase our understanding of some physical processes. Conversely, a strong relationship would suggest that simulations which were quantitatively improved in this area could reasonably be expected to give a more accurate and reliable forecast. For 119 independent samples from a distribution, the 99% significant correlation coefficient from the student T test, assuming a independent samples from a normal distribution, is 0.24. Our ensemble is a somewhat ad-hoc mixture of three 40 member ensembles, so, in the rather qualitative discussion in this paper, we use this value as a guide as to the strength of the correlation rather than a definitive threshold. It is also possible that a different experiment with MIROC3.2, varying different parameters and making different prior assumptions could produce an ensemble of equally reasonable model runs with rather different resultant characteristics. Due to the substantial investment in time required to perform this experiment (several months), we have not yet undertaken a repeat experiment of this nature, although one is planned for the future which will also use a revised and updated version of the model. In the following discussion we consider a correlation above 0.5 to be strong and one below 0.3 to be weak. Since our model has a relatively low-resolution T21 grid, we do not expect accurate results at the grid-point level for comparison with in-situ data. Therefore, we focus on zonal averages rather than the location-based estimates. However, for comparison with the MD06 results we have also derived some results for Greenland and Antarctica. It should also be noted that it was recently discovered that this version of the model contained a bug which generated a bias in the air temperatures over land ice. The bias induced in zonal T2 changes at the LGM in the T42 model is close to 1oC north of 80oN and much smaller than that south of this latitude. As shown in Fig. 2 this is a very small fraction of the temperature changes at the LGM. Although due to computational limitations we have not been able to test it, the bias is small enough that we do not expect it to vary greatly across our ensemble. We therefore think it unlikely that this will have significantly affected our analysis which focuses not on the magnitude of temperature changes themselves but on the correlations between the temperature changes for the three experimental climate
states.
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