4 Present-day climate from historical simulations

4.1 Performance indices

In order to objectively characterize the performance of the historical simulations compared to observations, we use modified performance indices by Reichler and Kim (2008) as described in Sidorenko et al. (2015) for the atmosphere and in Rackow et al. (2019) for the ocean. The referenced reanalysis and observation data the model is compared to and a description of the computation of the index are given in the Appendix section A2.
The index measures model error compared to observations relative to the average model error of CMIP5 models. A performance index of 0.5 would indicate an excellent performance as the mean absolute error is halved compared to the CMIP5 models while a performance index of 2 would indicate a doubling of the mean absolute error compared to the CMIP5 models.
Table 2 shows the atmosphere performance indices of the first ensemble member of the historical simulations. For the other four ensemble members of the historical simulations, the results are very similar (not shown). While the performance indices are first computed for each season individually, here, for brevity, we show the annual average. Globally, AWI-CM shows a good performance in all considered variables and is better than the CMIP5 multi-model mean. Especially Antarctic large-scale circulation and sea ice concentration are very well represented compared to the average of the CMIP5 models. However, there are a few variables such as precipitation, 500 hPa geopotential, and Arctic sea ice which are not in all regions represented better than by the CMIP5 models (only global mean, Arctic and Antarctic shown for brevity). As pointed out in section 5.2.2, the Arctic sea ice extent is very well represented both in terms of the mean value and in terms of the trend over the past 3 decades. The sea ice concentration is underestimated in boreal summer and autumn in the interior Arctic - see section 4.5 - but the sea ice extent is not affected by this since values are generally between 50 and 90% and therefore still well above the threshold of 15%.
Table 2: Atmosphere and sea ice performance indices for years 1985-2014 of the first ensemble member of AWI-CM historical simulations averaged over the four seasons. The set of CMIP5 models consists of CCSM4, MPI-ESM-LR, GFDL-CM3, HadGEM2-ES, and MIROC-ESM.