Posts Tagged ‘OLS’

The relevance of rooting for a unit root

March 18, 2010

So what if the global average temperature series contained a unit root? It would mean that ordinary least squares regression may lead to spurious results in terms of inflated trend significance. It would *not* mean that phsyics-based climate models are suddenly invalid or that AGW is suddenly falsified (just as gravity is not falsified by observing a bird in the sky).

On a previous post, ‘VS’ commented that

“(…) global temperature contains a stochastic rather than deterministic trend, and is statistically speaking, a random walk.”

He later clarified (updated):

I agree with you that temperatures are not ‘in essence’ a random walk, just like many (if not all) economic variables observed as random walks are in fact not random walks.

And later still:

“I’m not ‘disproving’ AGWH here.
I’m not claiming that temperatures are a random walk.
I’m not ‘denying’ the laws of physics.”

However, many commenters started chiming in with a sense of “Yeah, somebody is taking on climate science and seems to have refuted it all!” Uhm, no.

Basically, a random walk towards warmer air temperatures would cause either a negative radiative imbalance at the top of the atmosphere, or the energy would have to come from other parts of the earth’s system. Neither is the case. It’s actually opposite: There is a positive radiation imbalance and other reservoirs (e.g. oceans, cryosphere) are also gaining more energy. Which makes sense, in the face of a radiative forcing.

Explaining the increase in global average temperatures by a mere ‘random walk’ would violate conservation of energy.

Ramanathan and Feng describe the earth’s radiation balance as follows:

So the process of the net incoming (downward solar energy minus the reflected) solar energy warming the system and the outgoing heat radiation from the warmer planet escaping to space goes on, until the two components of the energy are in balance. On an average sense, it is this radiation energy balance that provides a powerful constraint for the global average temperature of the planet.

I.e. The global average temperature only changes over climatic timescales (multiple decades or longer) if there is an imbalance in the radiation budget. As is now indeed the case. Climate is to a certain extent deterministic, irrespective of unit roots.

The presence/absence of a unit root (dependent on the nature of the assumed trend amongst other choices) does not disprove/prove that the extra greenhouse gases we put in the atmosphere are warming the planet.

Update: This discussion has focussed on global average air temperatures, but changes have been observed in many other parts of the earth system that point to a changing (warming) climate: Sea level rise, ocean heat content, ice sheets , sea ice, glaciers, ecosystems, radiation budget. A statement along the lines of ‘nothing anomalous is happening’ should take all these changes into account.


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