No, it hasn't been cooling since 1998. Even if we ignore long term trends and just look at the record-breakers, that wasn't the hottest year ever. Different reports show that, overall, 2005 was hotter than 1998. What's more, globally, the hottest 12-month period ever recorded was from June 2009 to May 2010.
Though humans love record-breakers, they don't, on their own, tell us a much about trends — and it's trends that matter when monitoring Climate Change. Trends only appear by looking at all the data, globally, and taking into account other variables — like the effects of the El Nino ocean current or sunspot activity — not by cherry-picking single points.
There's also a tendency for some people just to concentrate on surface air temperatures when there are other, more useful, indicators that can give us a better idea how rapidly the world is warming. Oceans for instance — due to their immense size and heat storing capability (called 'thermal mass') — tend to give a much more 'steady' indication of the warming that is happening. Records show that the Earth has been warming at a steady rate before and since 1998 and there is no sign of it slowing any time soon (Figure 1). More than 90% of global warming heat goes into warming the oceans, while less than 3% goes into increasing the surface air temperature.
Figure 1: Land, atmosphere, and ice heating (red), 0-700 meter ocean heat content (OHC) increase (light blue), 700-2,000 meter OHC increase (dark blue). From Nuccitelli et al. (2012).
Even if we focus exclusively on global surface temperatures, Cowtan & Way (2013) shows that when we account for temperatures across the entire globe (including the Arctic, which is the part of the planet warming fastest), the global surface warming trend for 1997–2012 is approximatley 0.11 to 0.12°C per decade.
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