I would be the first to admit that I’m a novice when it comes to statistics in climatology, but I can calculate a good linear trend in software. So the next couple of graphs are drawn from monthly combined global land and sea temperatures since 1850 in the CRUTEM data series. All I’ve done is let the computer calculate the trend for each month through the entire series. The first graph shows a plot of how the 30 year linear trend has been behaving. I’ll also say at this point I have not attempted to centre the values I’ve plotted, but have left them right aligned (trailing) if that makes sense.
As you can see (fig 1) the trend has generally been positive since 1919 except for a cooler period from the mid sixties to around 1980, when trends quickly increased to a peak of around +0.2°C (per 30 years) in 2003, before steadying off since then.
The 50 year trend (fig 2) is much smoother, with a peak of around +0.11°C (per 50 years) in 1954, before falling back to almost zero for a time between 1979 and 1987. Since then there has been a steep rise to almost +0.17°C (per 50 years) where it is at moment.
I don’t offer any comment about what the differences indicate about how global temperatures have or will behave in the future, although I will say that the leveling off of the 30 year trend over the last 20 years is a little puzzling (fig 1). I suppose the only conclusion you can draw is that global warming is continuing at around +0.17°C (per 30 year), but the rate of that growth has not been accelerating recently.