The more substantive discussion is on the accompanying 1988 prediction paper. This was a remarkable achievement, which used runs of an early GISS GCM to forecast temperatures for the next thirty years. These forecasts are now often checked against observations. I wrote about them here, here and here. Each post had an active plotter which allowed you to superimpose various observation data on Hansen's original model results. It's annual data, to match Hansen's prediction. Since sientists can't know how much carbon society will choose to burn, Hansen analysed three scenarios (A, B and C) which covered the range between no restraint and successful limiting. Arguments then ensue as to which scenario actually happened. At least, that is what people should argue about, although they have a tendency to drift off into "Hansen said..." or even orse "we were told...".
Anyway, I'll leave discussion of that for the moment, and show the interactive plotter. The diagram in the background is Hansen's original plot, which is of anomalies relative to base years 1951-80, and uses GISS Ts as the observed data set (this had recently been published (Hansen and Lebedeff)). I have used that base where possible, else I match the dataset to GISS Ts over 1981-2010 (satellite data). Data is annual to end 2017. Sources are linked here.
To operate, just choose datasets to plot using the radio buttons, and Clear All if you want to start again. You can't erase curves without restart.
In interpreting these, I think weight should be given to GISS Ts, since it is what Hansen had available and used. Later indices incorporating SST rise more slowly. And I have reluctantly included troposphere data, which is definitely not what Hansen was predicting. Properly interpreted, I think the predictions are excellent. But that comes back to deciding which scenario is appropriate. I discussed this extensively here. We have detailed versions of the sequences of gas concentrations that quantified the scenarios, and while CO2 followed scenario B, others were much lower. CH4 and CFCs were below scenario C, so overall a result between B and C is to be expected. And that is what is mostly observed, though GISS Ts is higher.
Update. I have a zipfile online here which has numerical data for both scenario gases and temperature prediction; details here. I used it to calculate trends, in °C/Century, for the 30 years 1988-2017: (Further update - I fixed an error in scenario rates - now trend for B is larger)
In that analysis of scenarios, I showed some old plots. Gavin Schmidt, at Real Climate, has shown some updated values, and I'll show his plots. I mentioned that there are two sets of scenario data. One is IMO the original, as I discuss there, but Gavin uses a slightly different set, which I think was digitised from graphs. Anyway, here is the RC plot:
For the CFC plots; scenario C assumed that the Montreal agreements on curbing them, still being negotiated, would be approved and would work. A and B were more sceptical, but C was right. For methane, the concentration not only rose rather slowly, but was revised downward even before 1988.
Overall, in placing the outcome between scenarios B and C, Gavin gives this plot of combined forcings:
What the showing of combined temperature records shows is that Hansen's 1988 prediction is about as good as it could be, because it sits within the scatter of modern records. The difference between GISS Ts and GISS land/ocean is comparable to the difference between GISSlo and scenario B.
As a check on my active plot above, here is RealClimate's rendition of the case for GISS land/ocean with the same scenarios: