Some results on the response of a GCM (GFDL’s CM2.1) to instantaneous doubling or halving of CO2 (left) and to an estimate of the stratospheric aerosols from the Pinatubo eruption. From Merlis et al 2014.
The following is based on the recent paper by Merlis et al 2014 on inferring the Transient Climate Response (TCR) from the cooling due to the aerosols from a volcanic eruption. The TCR is the warming in global mean surface temperature in a model at the time of doubling of CO2 when the CO2 is increasing at 1% per year. You can generally convert the TCR of a model into a good estimate of the model’s warming due to the CO2 increase from the mid-19th century to the present, or due to all of the well-mixed greenhouse gases, by normalizing the TCR by the appropriate radiative forcing. The TCR of GFDL’s CM2.1 model, one of the two models discussed in Merlis et al, is 1.5K. Can you retrieve this value by looking at the model’s response to Pinatubo? This paper was motivated by the feeling that the literature trying to connect volcanic responses to climate sensitivity has focused too much on equilibrium sensitivity rather than directly constraining the TCR.
Another simulation that has become standard for models is to just double (or quadruple) the CO2 instantaneously and watch the system equilibrate. This gives you more information about the various time scales involved in the equilibration. For CM2.1, the upper left panel shows the evolution over the first 20 years (this is an ensemble mean over 10 realizations with different initial conditions taken from different times in a control run). It also shows a fit with a function of the form:
with the radiative forcing due to doubling of CO2 (3.5 W/m2 here — all radiative forcings are computed by holding SSTs fixed, perturbing the system, letting the atmosphere+land equilibrate, and examining the imbalance at the top-of-atmosphere), 1.45K and 2.8 years. In previous posts, I have discussed how one can interpret this short-time scale response in terms of a simple box model for the surface layers of the ocean,
where is the radiative forcing, is the strength of the radiative restoring, taking into account all of the radiative feedbacks, and is the heat uptake into the deeper layers of the ocean. If we set with the heat uptake efficiency, the heat uptake acts as an additional negative feedback. We then have .
The figure also shows the mean of an ensemble of runs with an instantaneous reduction in CO2 by a factor of 2. There is a small difference in the ensemble mean, marginally significant at the 10% level, between these warming and cooling switch-on simulations, with 1.35K fitting the cooling case. (We checked that the radiative forcing is almost exactly logarithmic in the model, so we can use the same forcing for doubling and halving). This qualitative result might be expected from the picture that cooling at the surface reduces the gravitational stability of the water column, increasing the heat uptake efficiency. But the difference between warming and cooling is small on this time scale, which is nice from the perspective of using a cooling perturbation like a volcanic eruption to infer the transient response to warming.
The model is still taking up heat at about 1 W/m2 after 20 years (lower left panel). This model’s equilibrium climate sensitivity is about 3.4K, but it approaches this equilibrium very slowly. Fitting the evolution over longer time scales with a sum of two exponentials,
we get something like and 400-500 years. This large gap in time scales is clearly the best possible situation if you want to infer a response on the time scale of 50-100 years from the response to a much shorter time-scale forcing. See Geoffroy et al 2013 to place the shape of this response function in the context of that found in other GCMs.
As a first approximation to a volcano, we can set to be a spike, a -function, with the result
where is the integral of the volcanic radiative forcing, , which we might call the volcanic radiative impulse. The simple but important point to notice here is the appearance of the factor . If the magnitudes of the temperature responses to a step increase in forcing on the fast and slow time scales are comparable, the response to impulsive forcing will be much smaller on the long time scale, by the ratio . The long weak tail of the volcanic response has been discussed by Wigley et al 2005. Delworth et al 2005 and Gleckler et al 2006 have discussed the closely related long time scale recovery of sea level after a volcano in GCMs. The surface temperature signal on long time scales in the response to a single volcano is effectively unobservable in CM2.1. But given a sequence of volcanoes, the weak long time scale tail would accumulate.
To the extent that one is able to focus on the fast response in isolation we can average over time, returning to the single box interpretation if you like,
where is a time long compared to the fast decay and short compared to the slow decay. The setup for computing TCR involves linearly increasing radiative forcing (since this forcing is logarithmic in CO2) for 70 years. For a two-box model mimicking CM2.1, this results in a TCR very accurately given by . So the estimate of TCR provided by the volcano is
This integral method does not involve an estimate of the time scale of the fast response.
Merlis et al piggyback on the ensemble of simulations of the response in CM2.1 to the Pinatubo eruption described in Stenchikov et al 2009 which used an ensemble of 20 runs, 10 initialized during an El Nino event in the model’s control simulation and 10 initialized in La Nina events. (Pinatubo occurred during an El Nino, so it is of interest if this modifies the forced response to the volcano. The response is nominally a bit larger in the La Nina ensemble mean, but larger ensembles would be needed to quantify this difference.) The Pinatubo forcing in this model is shown as the light blue line in panel d above. It’s not a -function, but its duration is less than the model’s dominant fast response time. The volcanic radiative impulse is -6.5 Wm-2-yrs.
The temperature response is shown in panel c. The ensemble mean integrated response up to year 20 is 2.35K-yrs. This gives an estimate of TCR of 1.3K. This is close to the models TCR of 1.5K but a little low. The figure also shows the fit that you get with this one-timescale model, constraining it to fit the integral of the response and using the time scale from the instantaneous doubling simulation. You can also fit the volcanic response varying the two paramaters and simultaneously. This two-parameter fit gives an estimate of TCR that is smaller still — about 1.1K. The single time scale model is not a perfect fit to the GCM response.. One can understand the sensitivity to fitting procedure qualitatively if you assume, for example, that the fast response in the GCM actually occurs on two time scales — let’s say 1 year and 4 years, conserving the sum of these two responses and playing with their ratio.
Since the model’s TCR is 1.5K, the underestimate 1.1K is not trivial. It is the sum of little things in this model — the slight difference between warming and cooling perturbations, a small effect in this model of time scales longer than the dominant fast response time, plus a distortion due to the fitting procedure when the fast response itself is not well fit with a single time scale.
We do not need to estimate the separate effects of radiative feedbacks and heat uptake, or and , to estimate TCR in this way, and there is no need to refer to equilibrium climate sensitivity.
We have used 20 realizations of the response to Pinatubo to get these results. How is this relevant to the problem of determining TCR from a single realization (and without a no-volcano control)? Merlis et al describes what you get if you take one realization of CM2.1, remove the average of the 10 years before the eruption and also remove an estimate of the ENSO contribution based on the relationship between global mean temperature and NINO3.4 SSTs in this GCM. You have to do something like this to get any meaningful results from a single realization, and we don’t claim that this is optimal . We also find it difficult to use the integral method with single realizations, so use the two parameter fitting procedure that results in 1.1K using the ensemble mean response. We get the following:
The whiskers span the entire range of values obtained from the 20 realizations, the box represents the middle half (25-75%) and the red line the median (with the red and blue dots corresponding to the La Nina and El Nino ensembles). The median is close to the “correct” value of 1.1K for the two-parameter fit. The blue dotted line indicates the value inferred from fitting to the fast response in the 0.5X instantaneous cooling simulation. My suspicion is that this spread is too large, partly because the interanual variability of global mean surface temperature in this model is too big, mostly due to too large an ENSO amplitude — and partly because you can probably do better than this with a better algorithm, possibly multivariate, for isolating the volcanic signal in a single realization. Even with this much uncertainty, this would be useful as one piece of information among others, if coupled to some theoretical guidance for the bias involved.
There’s the rub, I think — because this underestimate could be much larger in reality than in CM2.1 if intermediate time scales play a larger role than they do in this particular model. I’ll return to this issue in Part II.
[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.]