The global temperature series is one of the clearest pieces of evidence that the planet is heating up. Over the past century, it’s easy to see from, say, NASA’s data that surface temperatures have risen dramatically. But there’s also a fair bit of short-term natural fluctuation from year to year, which can sometimes obscure what, exactly, is going on.

For instance, according to the World Meterological Association, 2011 looks to be the 10th-warmest year on record. But this year was also a La Niña year, part of a natural weather cycle in which oceans run a little cold and temperatures tend to drop (as it happens, 2011 will likely prove to be the warmest La Niña year on record). So how do we tease out the human influence on climate from these short-term natural variations? A number of climate researchers have tried to do just that, but a new paper from statistician Grant Foster and climatologist Stefan Rahmstorf provides two graphs that show rather clearly how we’re warming the planet.

First, Foster and Rahmstorf took the raw data from five different global temperature series since 1978, including surface data and lower-atmosphere data from satellites:

So, in their paper, Foster and Rahmstorf tried to separate the signal from the noise. Using statistical techniques (detailed further by Foster here), they factored out the influence of the three biggest known natural mechanisms that can influence global temperatures in the short term — the El Niño oscillation, solar variability and volcanic eruptions. When those are removed, here’s what the graph looks like:

Stuart Saniford tries to take this analysis a step further and extrapolate how much warming we could expect by the end of the century, based on the linear trend over the past 30 years. This isn’t necessarily a good way to predict the future — after all, the climate can change in non-linear ways, which is why climate models that take into account the physics of the system are so important for predictions — but it gives a rough sense of what to expect if we keep emitting carbon pollution at our current rate. All told, though, Foster and Rahmstorf’s work suggests that there’s no basis for claiming that global warming is slowing or stopping.