There’s a new post on Watts Up With That (WUWT) called New study – climate system is only about half as sensitive to increasing CO2 as previously believed. It refers to a new paper by Roy Spencer and William Braswell called The role of ENSO in global ocean temperature changes during 1955–2011 simulated with a 1D climate model. The main conclusion of the paper (and why WUWT is so excited) is that they conclude that climate sensitivity is likely 1.3oC, significantly lower than the 3oC predicted via other methods.
I worked through the paper a little last night (yes, my life is boring) and I have some issues with what they present. Admittedly, I’m no expert at this so others are welcome to correct my misunderstandings through the comments. What the Spencer and Braswell study does is to consider three situations, illustrated in the figure below. Case I is when there is anthropogenic and volcanic forcings plus diffusion in the oceans. Case 2 is anthropogenic plus volcanic forcings, diffusion in the oceans, and mixing in the upper layers through El Nino/La Nina. Case 3 is one in which there is anthropogenic and volcanic forcings, diffusion in the oceans, mixing in the upper layers through El Nino/La Nina, and an assumed forcing associated with El Nino/La Nina events.
The basic model equations are below. As far as I can tell, the model only considers the ocean temperatures and divides the ocean into 40, 50m thick layers. Hence, the model has 40 equations that determine how the temperature in each layer changes with time. The N(t) term is the anthropogenic and volcanic forcings taken from RCP6. The λΔT1 is the feedback term (i.e., the term in brackets in the first equation is essentially the radiative imbalance). The S terms are the terms used to model the El Nino/La Nina mixing, and the final term in each equation is the diffusion term that allows for vertical mixing. The ΔTs in each equation are also relative to some assumed average oceanic temperature profile, including a thermocline, which the ocean relaxes to when there are temperature perturbations away from that profile. In each case considered, the model was required to match the 0-50 m observed temperature trend for 1955-2011 to within 0.002 deg. C per decade. So, as far as I can tell, parameters in the model were tuned so as to match the observed (from Levitus 2012) temperature trend for the 0-50m region of the ocean.
So, where is my issue with the model? If we consider Case 1, all the S terms in the equations above are zero and the model is evolved using only the anthropogenic and volcanic forcings and the diffusion terms. However, the diffusion coefficients in the top 6 layers are all different and, unless I’m mistaken, are tuned so as to best match the observed 0-50m temperature trend. So, unless I’m missing something, the diffusion terms don’t conserve energy. Normally you’d expect diffusion to transfer energy between the different layers. Here, they seem to simply act to try and drive the temperature in each layer back to the assumed average. So, it seems that the diffusion terms are simply acting to, essentially independently, add or subtract energy from each layer and are tuned to as to produce a result that matches the observed trend for the 0-50m layer. The other problem is that the climate sensitivity factor, λ, appears to be defined relative to the change in temperature in the upper layer of the ocean, rather than relative to the surface which would normally also include the land. I don’t know if this is a major factor or not in such a simple model though.
The next issue I have is that in their Case 2 they add El Nino/La Nina mixing terms, S, to the top four layers. The equations for parametrising these terms are below, where MEI is the Multivariate ENSO index. When they include this they find that the climate sensitivity drops to 2oC, from the 2.2oC they get from their Case 1. Well this seems to be because they’re tuning their parameters to only match the temperatures trends in the 0-50m layer. If this mixing term adds energy to this layer, then that immediately implies that the radiative imbalance term will need to be smaller (so as to keep the energy going into this layer constant) and the only way to do this is for λ to be bigger, and hence for climate sensitivity to be smaller. Fine, but that does imply that the radiative imbalance in Case 1 and Case 2 are different and hence the change in total Ocean Heat Content will be different for these two different cases. Everything seems to hinge on the 0-50m layer.
Maybe the biggest issue I have relates to their Case 3. Here they assume that the forcing term N(t) is modified to include a forcing due to ENSO events. The equation they use is below, where MEI is again the multivariate ENSO index and α is a coefficient of proportionality. Essentially, they seem to simply assume that ENSO produce some kind of internal forcing which they say could involve some combination of cloud shortwave albedo, cloud longwave, or water vapor changes. When they include this forcing, the climate sensitivity drops to 1.3oC. Sure, but that’s because you’ve assumed an extra forcing term (that is not really physically justified) and the only way to then match the 0-50m temperature trend is to increase the value of λ and hence reduce climate sensitivity.
So, as you might imagine, I’m rather unconvinced by this work. It seems to be a simple 1D model with diffusion terms that can simply be tuned so as to match a temperature trend in the 0-50m layer. Not obvious to me how this is conserving energy as it seems as though the amount of energy that one layer gains or loses is not related to the energy gained or lost in the adjacent layers. Everything seems to be tuned so as to match the temperature trend in the 0-50m layer only, and so there is no sense of whether or not they are matching the overall change in ocean heat content (I would guess not since some of the cases have different radiative imbalances). Finally they seem to simply add an internal forcing term that is largely physically unmotivated and then suggest that, because of this term, climate sensitivity is much smaller (1.3oC) than other estimates suggest (3oC). Well, if such an internal forcing does indeed exist one could have shown that the climate sensitivity would indeed be lower without needing to do any kind of modelling (1D or otherwise). The main problem, though, is that – as far as I’m aware – there is no evidence for the existence of such an internal forcing.