I have checked the results from the ‘apples to apples’ paper (see discussion here) by downloading the Python software and most of the CMIP5 model results thanks to Kevin Cowtan. The main conclusion of the paper is that there is a small bias whereby models slightly overestimate the surface warming when comparing to Hadcrut4.4. The reason for this is a small difference between sea surface temperatures (as measured by HADSST3) and surface (2m) air temperatures over oceans. Surface temperatures tend to be slightly cooler than air temperatures. Possible reasons for this are latent heat loss from the surface and heat flow to the abyss from the mixed layer. I have checked the calculations and my conclusion is that the code is good and the published result is sound. However it remains a rather small effect of just -0.05C ‘bias’ when comparing Hadcrut4.4 in 2015. This is still within measurement errors.
The bias grows to around -0.2C if, as predicted by models, temperatures rise by ~4C by 2100, which then becomes significant. It turns out that the net bias is simply proportional to the net warming relative to 1961-1990, and therefore remains at a constant 7% of the temperature anomaly. This also explains why the bias is positive before 1970.
Note that this bias is a model only effect which does not change the measured Hadcrut4.4 surface temperature measurements. It also includes a modelled sea ice melt change which only really makes sense if future HadSST measurements extend into such areas.
Thanks to Kevin Cowtan for providing the data. I was able to download the majority of the CMIP5 results while travelling around Australia. I have about 31 model runs which will be helpful for future comparisons.