Suppose that most of the global mean surface warming in the past half century was due to internal variability rather than external forcing, contrary to one of the central conclusions in the IPCC/AR4/WG1 Summary for Policymakers. Let’s think about the implications for ocean heat uptake. Considering the past half century in this context is convenient because we have direct, albeit imprecise, estimates of ocean heat uptake over this period.
Set the temperature change in question, , equal to the sum of a forced part and an internal variability part: , with , so is the fraction of the temperature change that is forced. The assumption is that this is a linear superposition of two independent pieces, so I’ll write the heat uptake as .
When the surface of the Earth warms due to external forcing, we expect the Earth to take up heat. But what do we expect when the surface warms due to internal variability? Can we use observations of heat uptake to constrain ?
The strength of the radiative heat loss to space per unit warming of global mean surface temperature is a key quantity of interest, as usual. In post #5 I tried to emphasize that this parameter, which I denote by , should depend, among other things, on the horizontal structure of the surface warming. This issue is of vital importance when discussing observational constraints on climate sensitivity, since the natural changes we observe – due to ENSO, AMO, volcanoes – do not all share the same horizontal structure as the forced response to CO2.
But consider the two limiting cases: either the forced response dominates the half-century trend or internal variability is dominant. If both of these limiting cases are going to be viable, then they both have to have the same spatial structure, that of the observed warming. (In actuality, I am very skeptical that internal variability can create this spatial structure, but I am suspending this skepticism for the moment.) So, within the confines of this argument, with the intent of focusing on the limiting cases, it is interesting to assume that the strength of the radiative restoring is the same for the forced and the internal components.
For the forced response, I’ll use the framework for discussing the transient climate response in post #4 in which the forcing is balanced by the radiation to space and heat uptake, both of which are assumed to be proportional to : . So , and the heat uptake associated with the forced response is . A fraction of the radiative forcing is taken up by the Earth, the rest is radiated away due to the increase in temperature. This fraction can be quite modest. For example, using the numbers that mimic the behavior of GFDL’s CM2.1, a GCM discussed in post #4, this ratio is 0.7/(1.6+0.7) 0.3 . In this sense the forced response is rather inefficient at storing heat.
I am going to assume that and are given and that the value of is the point of contention. The fraction of the response that is forced depends on the value of the radiative restoring according to
or, expressing as a function of ,
Meanwhile suppose there exists internal variability with the spatial structure of the warming trend. As discussed above, I assume that it radiates energy to space at about the same rate as the forced response of the same magnitude. So the contribution of this internal component to the heat uptake is , and the total heat uptake is
Substituting for , the heat uptake as a function of is
or, in a non-dimensional form,
The first term is the uptake per unit forcing computed as if the entire temperature change were forced – the second term is the correction needed if internal variability contributes. It is important that this second term is more or less inversely proportional to ; a bigger (smaller climate sensitivity) is required to make room for the internal contribution, resulting in stronger radiative restoring of this internal component and greater heat loss.
A typical value for the first term, , might be 0.3 as already discussed above. Using this estimate, the value of needed to produce near zero heat uptake by the oceans is , so internal variability need only contribute about 25% of the total warming to fully compensate for the heat uptake due to the forced response. If internal variability contributes 50% of the warming, then the heat lost by the oceans would be more than twice as larger as the heat gain computed by the alternative model in which the internal variability contribution is small. This heat loss increases more and more rapidly as is reduced further.
While the specifics of the calculations of heat uptake over the past half century continue to be refined, the sign of the heat uptake, averaged over this period, seems secure – I am not aware of any published estimates that show the oceanic heat content decreasing, on average, over these 50 years. Accepting that the the sign of the heat uptake is positive, one could eliminate the possibility of — if one could justify using the same strength radiative restoring for the forced and internal components.
But this little derivation cannot be taken at face value when is large. If one accepts that the forced response dominates, one can consistently free up the horizontal structure of the internal component, potentially producing a dramatically different, and possibly much weaker, radiative restoring for the internal component– and allowing to be reduced more than indicated by this calculation before the heat uptake changes sign.
I have recently looked at 1,000 years of a control run of CM2.1 (with no time-varying forcing agents) and located the 50 year period with the largest global mean warming trend at the surface, which turns out to be roughly 0.5K/50 years. This warming is strongly centered on the subpolar Northern oceans, diffusing over the continents, but with little resemblance to the observed long-term warming pattern. (We don’t have a lot of confidence in the model’s simulation of these low frequency variations, but you can argue on very general grounds that these low frequency structures should emanate from the subpolar oceans. I’ll try to return to this issue of the spatial structure of low frequency internal variability in another post.) Heat is being lost from the oceans to space in this period, but at a much slower rate than in the forced response to CO2, due in large part to positive feedback from polar ice and snow (and low clouds over the oceans) in the model. As discussed in post #5, it seems that the more polar concentrated the response the weaker the radiative restoring.
I am not aware of any study summarizing the strength of the global mean radiative restoring of low frequency variations in control simulations in the CMIP3/AR4 archive. It would be interesting to look at these if someone has not already done so. Supposing that we accept the model results for this radiative restoring of low frequency internal variability,what does this yield for the value of at which the heat uptake changes sign?
Like many others, I am watching with great interest and, I hope, an open mind, as the heat storage estimates from ARGO and the constraints imposed on steric sea level rise by the combination of altimeter and gravity measurements slowly emerge. And I would like to understand the effects of internal variability on heat uptake a lot better. But I see no plausible way of arguing for a small- picture. With a dominant internal component having the structure of the observed warming, and with radiative restoring strong enough to keep the forced component small, how can one keep the very strong radiative restoring from producing heat loss from the oceans totally inconsistent with any measures of changes in oceanic heat content?
[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]