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It is generally accepted that the Earth's global mean (average) temperature has varied throughout history.

Given the difficulties of accurately measuring and calculating temperatures across the entire planet: does scientific certainty exist that the global mean temperature at sea level has increased since the year 1900, and by what research has that certainty been derived?

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    @Job - notice that you'll find no part in the above question as to why the Earth has warmed. That is by design: it is a completely different question. So why comment? – ropable Apr 27 '11 at 3:37
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    The radioactive decay fluctuations are on the scale of 1/10th of 1%, and oscillate as activity rises, then falls, so the overall decay rates are fundamentally unaltered. Even if that was addressing part of the question, that discovery does not, in any way, refute the existing consensus. FYI. – PoloHoleSet Sep 13 '16 at 18:30
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The following graph shows the global temperature development during the last 130 years (Hansen et al., 2006)

enter image description here

This data is from resarchers of the Goddard Institute for Space Studies (GISS), but there are also groups from the University of East Anglia and the National Climatic Data Center working on similar data. They are based on the same observations in the end, but they use different methods for analysis and thereby provide some cross validation of the methods.

The data this graph is based on comes from meteorological stations on land (Hansen et al., 2001), satellite data and ship-based data on the oceans.

One difficulty in analysis the data from stations is the influence of urban development, cities produce heat which could bias the results. To correct for that, Hansen et al. used satellite light data to adjust stations affected by urban development (Hansen et al., 2001).

There are not many meteorological stations in the arctic, for that region the data is based primarily on satellite measurements (Comiso, 2006).

Independent from the temperature data there are also other indicators for a global warming trend:

The conclusion that global warming is a real climate change, not an artifact due to measurements in urban areas, is confirmed by surface temperature change inferred from borehole temperature profiles at remote locations, the rate of retreat of alpine glaciers around the world, and progressively earlier breakup of ice on rivers and lakes -- Hansen et al., 2006

All the scientific articles I linked are freely available, if you want to dig deeper into the details.

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