# Isaac Held's Blog

## 6. Transient response to the well-mixed greenhouse gases

Global mean surface air warming due to well-mixed greenhouse gases in isolation, in 20th century simulations with GFDL’s CM2.1 climate model, smoothed with a 5yr running mean

“It is likely that increases in greenhouse gas concentrations alone would have caused more warming than observed because volcanic and anthropogenic aerosols have offset some warming that would otherwise have taken place.” (AR4 WG1 Summary for Policymakers).

One way of dividing up the factors that are thought to have played some role in forcing climate change over the 20th century is into 1) the well-mixed greenhouse gases (WMGGs: essentially carbon dioxide, methane, nitrous oxide, and the chlorofluorocarbons) and 2) everything else.  The WMGGs are well-mixed in the atmosphere because they are long-lived, so they are often referred to as the long-lived greenhouse gases (LLGGs).  Well-mixed in this context means that we can typically describe their atmospheric concentrations well enough, if we are interested in their effect on climate, with one number for each gas.  These concentrations are not exactly uniform, of course, and studying the departure from uniformity is one of the keys to understanding sources and sinks.

We know the difference in these concentrations from pre-industrial times to the present from ice cores and modern measurements, we know their radiative properties very well, and they affect the troposphere is similar ways.  So it makes sense to lump them together for starters, as one way of cutting through the complexity of multiple forcing agents.

## 5. Time dependent climate sensitivity?

The co-evolution of the global mean surface air temperature (T) and the net energy flux at the top of the atmosphere, in simulations of the response to a doubling of  CO2 with GFDL’s CM2.1 model.
Slightly modified from Winton et al (2010).

Global climate models typically predict transient climate responses that are difficult to reconcile with the simplest energy balance models designed to mimic the GCMs’ climate sensitivity and rate of heat uptake.  This figure helps define the problem.

Take your favorite climate model, instantaneously double the concentration of $CO_2$ in the atmosphere, and watch the model return to equilibrium. I am thinking here of coupled atmosphere-ocean models of the physical climate system in which $CO_2$ is an input, not models in which emissions are prescribed and the evolution of atmospheric $CO_2$ is itself part of the model output.

Now plot the globally-averaged energy imbalance at the top of the atmosphere $\mathcal{N}$ versus the globally-averaged surface temperature $T$.  In the most common simple energy balance models we would have $\mathcal{N} = \mathcal{F} - \beta T$ where both $\mathcal{F}$, the radiative forcing,  and $\beta$, the strength of the radiative restoring, are constants.  The result would be a straight line in the $(T, \mathcal{N})$ plane, connecting $(0, \mathcal{F})$ with $(T_{EQ} \equiv \mathcal{F}/\beta,0)$ as indicated in the figure above.  The particular two-box model discussed in post #4 would also evolve along this linear trajectory; the different way in which the heat uptake is modeled in that case just modifies how fast the model moves along the line.

The figure at the top shows the behavior of GFDL’s CM2.1 model.  The departure from linearity, with the model falling below the expected line, is common if not quite universal among GCMs, and has been discussed by Williams et al (2008) and Winton et al (2010) recently — these papers cite some earlier discussions of this issue as well.  Our CM2.1 model has about as large a departure from linearity as any GCM that we are aware of, which is one reason why we got interested in this issue. Read the rest of this entry »

## 4. Transient vs equilibrium climate responses

Histogram of the ratio of transient climate response (TCR) to equilibrium climate sensitivity in the 18 models for which both values are provided in Ch. 8 of the WG1/AR4/IPCC report

I find the following simple two degree-of-freedom linear model useful when thinking about transient climate responses:

$c \,dT/dt \, = - \beta T - \gamma (T - T_0) + \mathcal{F}(t)$

$c_0 \, dT_0/dt = \gamma (T - T_0)$

$T$ and $T_0$ are meant to represent the perturbations to the global mean surface temperature and deep ocean temperature resulting from the radiative forcing $\mathcal{F}$.  The strength of the radiative restoring is determined by the constant $\beta$, which subsumes all of the radiative feedbacks — water vapor, clouds, snow, sea ice — that attract so much of our attention.  The exchange of energy with the deep ocean is assumed to be proportional to the difference in the temperature perturbations between the surface and the deep layers, with constant of proportionality $\gamma$.  The fast time scale is set by $c$, representing the heat capacity of the well-mixed surface layer, perhaps 50-100m deep on average (the atmosphere’s heat capacity is negligible in comparison), while $c_0$ crudely represents an effective heat capacity of the rest of the ocean. Despite the fact that it seems to ignore everything that we know about oceanic mixing and subduction of surface waters into the deep ocean, I think this model gets you thinking about the right questions. Read the rest of this entry »

## 3. The simplicity of the forced climate response

An estimate of the forced response in global mean surface temperature, from simulations of the 20th century with a global climate model, GFDL’s CM2.1, (red) and the fit to this evolution with the simplest one-box model (black), for two different relaxation times. From Held et al (2010).

When discussing the emergence of the warming due to increasing greenhouse gases from the background noise, we need to clearly distinguish between the forced response and internal variability, and between transient and equilibrium forced responses.   But there is another fundamental, often implicit, assumption that underlies nearly all such discussions: the simplicity of the forced response. Without this simplicity, there is little point in using concepts like “forcing” or “feedback” to help us get our minds around the problem, or in trying to find simple observational constraints on the future climatic response to increasing CO2. The simplicity I am referring to here is “emergent”, roughly analogous to that of a macroscopic equation of state that emerges, in the thermodynamic limit, from exceedingly complex molecular dynamics.