Posts Tagged ‘statistics’

Is the increase in global average temperature just a ‘random walk’?

March 8, 2010

On the previous thread, a discussion ensued about whether the observed increase in global average temperature is just a ‘random walk’. A rundown (*):

- Anonymous commenter “VS” claims that according to some statistical method, the increase in global average temp is not statistically significant, and that global average temperature behaves like a ‘random walk’. Heiko confirms with a simple excel exercise that under the assumption of stacked cumulative errors a quantity can wander off in any direction in the absence of a forced trend.

- The practical relevance of VS’ claim escapes me in light of the graphs shown in the previous post. E.g. each single year of the past 30 years has been warmer than each single year between 1880 and 1930. Calling this merely coincidence makes me wonder, how lucky do you feel? (**) 

- The applicability of said statistic and of the assumption of stacked cumulative errors is questionable in light of the physical nature of the climate: Temperatures continuing to wander off towards warmer values without a change in radiative forcing as the driving factor would cause a negative energy imbalance, which would force the temperatures back to where they came from: Equilibration. There’s conservation of energy after all. In general, long term changes in global avg temp are the consequence of a non-zero radiative forcing, whereas temp juggle up and down without a clear trend if there is no net radiative forcing acting upon the system.

- The earth’s energy imbalance as measured from space and as deduced from adding up atmospheric and ocean heat content is actually positive: More energy is coming in than radiating back into space (***). This directly contradicts that the increase in global average temperature would be random (since in that case we would expect a negative energy imbalance)

- Radiative forcing of climate is reasonably well known (at least that of the greenhouse gases and of natural forcings such as changes in the output of the sun; much less so for aerosols). The net forcing is positive, so we know that the temperature is being pushed into the warmer direction. I.e. we know that it in this case the warming isn’t random. The question is then: Could such a warming theoretically be observed even in the absence of a forcing? I think not, for the physical reasons stated above (equilibration). But it’s a bit like asking if the bike could have moved downhill all by itself, even if you see that someone is riding the bike downhill. Interesting question for a late night drink at the bar, but not very relevant to the question of how the bike got to the bottom of the hill. Let me add though that understanding the nature of natural variability in global temperatures is definitely important, and the discussion in the previous thread was definitely thought provoking.

- Changes in atmospheric temperatures are not the only sign of a warming climate. There is the increase in ocean heat content, decrease in Arctic sea ice, thinning of Greenland and Antarctic ice sheets, retreat of glaciers, changes in ecology (e.g. growing season, blooming of flowers, etc), sea level rise, etc. Is this all coincidence? How lucky do you feel?

(*): I’ll admit that my knowledge of statistics is not such that I can argue the details of a statistical analysis. Instead, I’ll argue mostly from a physical perspective. I think that’s entirely appropriate –necessary even- in trying to understand a physical system. Conservation of energy is probably a sufficient reason to dismiss the idea of a random walk in temperatures.

(**): If you feel lucky, you may want to arrange a bet about future warming (or lack thereof) with e.g. James Annan or Brian Schmidt.

(***): Satellite measurements of outgoing longwave radiation find an enhanced greenhouse effect (Harries 2001, Griggs 2004, Chen 2007). This result is consistent with measurements from the Earth’s surface observing more infrared radiation returning back to the surface (Wang 2009, Philipona 2004, Evans 2006). Consequently, our planet is experiencing a build-up of heat (Murphy 2009). These findings provide ”direct experimental evidence for a significant increase in the Earth’s greenhouse effect that is consistent with concerns over radiative forcing of climate

Update: Related discussions of the chaotic nature of climate here, here and here. Tamino chimes in as well.


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