Negative feedback

Each day we hear more and more bad news about global warming. Just in the past week alone, we find that old growth forests are thinning leading to perhaps more C02 in the atmosphere (van Mantgem et al. Widespread Increase of Tree Mortality Rates in the Western United States, Science 23 January 2009:Vol. 323. no. 5913, pp. 521 – 524) and that the damage currently done by CO2 emissions is largely irreversible for at least 1000 years (Solomon et al., Irreversible climate change due to carbon dioxide emissions, PNAS).  Now, I certainly do believe that the effects of added greenhouse gases are real and we are seeing evidence of global warming, but all the high profile reports always seem to show positive feedback (i.e. warming leads to more warming).  It makes me wonder about the negative feedback.

If we really are in a situation with only positive feedback then that means either 1) We are already past the point of no return and we’re headed to some new fixed point so we may as well just forget about it and live it up while we can or 2) there never was a stable fixed point to begin with so that we’ve been lucky to have been around at all.  I doubt either of these two possibilities are true.  Given that C02 levels and temperatures were confined to a fairly narrow band for most of the geological record implies to me that climate was near a stable fixed point or at least regulated to some degree.  Sure there have been warmer periods in the past and periodic ice ages but for the most part temperatures have been remarkably stable. After all, we could be like Venus and have an atmosphere of 97% CO2 with a temperature of 500^\circ C or be like Mars and have a very thin atmosphere and be cold with large fluctuations in temperature.  We do benefit from a magnetic field that shields us from the solar wind and keeps our atmosphere from getting blown away (losing our magnetic field is what really keeps me up at night) but I think our biosphere is in some sort of homeostasis.

However, if we are (were) at a stable fixed point then the first response to warming should be negative feedback opposing an increase in temperature.  Let’s consider a naive toy model of temperature variation around  the mean that behaves like \dot{T}\simeq -a T + bT^2\cdots.  So as long as T<a/b then the temperature will be stabilized by negative feedback that is proportional to the deviation from the fixed point.  Beyond this temperature, we enter an unstable regime where there is only positive nonlinear feedback.  There can also be neutral or marginal stability where a and b are both zero, in which case we would see neither negative nor positive feedback.

Now, obviously this model is wrong and the climate is much more complex where negative and positive feedback can coexist.   However if we are in a regime of just positive feedback then there probably is nothing we can do about climate change save drastic geo-engineering methods like spreading sulfur in the atmosphere to block sunlight or using giant pumps to suck CO2 out of the air.  If this is true then we should know about it.  However, it could also be that the instances of negative feedback are simply not reported or investigated.  I don’t think there is a conspiracy but it probably does a scientist no good to find good news right now where careers are made by finding the worst possible news – glaciers in Greenland and the Anatarctic are melting,  rivers are drying up, the oceans are rising.  This is what gets published in the high profile journals and written about in the New York Times.

If this is even partially true that means we really don’t know what will happen. Unless we have a full accounting of all the forces we can’t know if the climate is stable, unstable or marginal.   I do recall a time where the reporting in the popular press was more balanced and peopled talked about possibilities such as increasing albedo due to clouds as a negative feedback mechanism. Nowadays it’s just doom and gloom.  This is  probably due to overcompensating for the fact that climate change had not been taken seriously over this past decade and so there was the concern that any good news would  diminish the urgency to do something.  However, given that almost everyone believes in global warming now, it might be time to devote some attention to possible mitigating responses to increasing CO2 and temperatures.

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