Annual mean surface air temperature response to a doubling of CO2. Upper left: equilibrated atmosphere/land response (GFDL AM2.1/LM2.1) with fixed seasonally varying sea surface temperatures (SSTs) and sea ice. Other plots are coupled model (CM2.1) responses in a single realization with CO2 increasing at 1%/year till doubling (year 70) then held fixed. Upper right — average over years 60-80, around the time of doubling; lower left — years 160-180; lower right — years 580-600. Contour interval is 0.5C in upper left and 1C elsewhere. Colors same in all plots.
Returning to our discussion of the time scales of the climatic response, it might be useful to take a closer look at the evolution of the warming in a GCM for the standard idealized scenario in which, starting from an equilibrated state, CO2 is increased at 1% per year until it doubles and is then held fixed. This plot shows the results from our CM2.1 model.
I want to focus especially on the upper left panel; the other panels are mainly included here to provide context. The upper left panel is not generated from the fully coupled model, but from the atmosphere/land components of this model in isolation, holding the sea surface temperature (SST) and sea ice distribution fixed at their unperturbed climatological seasonal cycles, while doubling the CO2. This model equilibrates to a change in CO2 in a couple of months (there is no interactive vegetation or even permafrost in this model, both of which would create the potential for longer time scales regionally). The response depends on the season, so one has to integrate for at least a year before this annual mean pattern emerges. We might call this the ultra-fast response, distinguishing it from fast (oceanic mixed layer), slow (oceanic interior), and ultra-slow (anything slower than the thermal adjustment time of the interior ocean, such as aspects of glacier dynamics). One can visualize this as the first step in the response, but one that is evidently dramatically modified over time by the ocean warming and sea ice retreat.
(To think about this atmospheric relaxation time scale: the heat capacity at constant pressure of air is 103 J/(Kg C), and multiplying by the mass of a tropospheric column of about 8 x 103 Kg/m2 gives a heat capacity for the column of 8 x 106 J/(m2 C); with a radiative restoring strength of 2 W/(m2 C) we get a relaxation time of 4 x 106 s or roughly a month and a half).
This ultra-fast response is weak, far smaller than the transient climate response (defined as the global mean of the upper right panel). Averaged over all of the continents, the surface air warming with fixed SSTs and sea ice is about 0.35C in this model, rising above 1C only in the interiors of the Eurasia and North America. So, in this model, most of the warming over land results from warming of the oceans (and, especially in high latitudes, the retreat of sea ice). This qualitative result is robust across all of the models that I have ever looked at. A rough feeling for this coupling can be obtained from a simple diffusive model. If one tries to mimic atmospheric horizontal energy transports in the midlatitude atmosphere with a turbulent diffusivity , the number one comes up with is about 1-2 x 106 m2/s. To get something of this magnitude, setting VL, one needs, say, V, an rms velocity, of 10m/s and L, an eddy mixing length, of 1-2 x 106 m. (I have spent a signifcant part of my career trying to understand the characteristics of this tropospheric “macroturbulence”.) With a relaxation time scale as estimated above, the diffusivity penetrates a distance of about 2-3 x 106 m. This is pretty crude and a little low, especially in the zonal direction, for which mean winds contribute to the transport . (Jerry North and others have looked extensively at diffusive atmospheric models in which the land-ocean geometry enters only through a spatially-varying heat capacity — for example, here). So this GCM’s response with fixed SSTs is more or less as expected – the atmosphere’s radiative relaxation time scale and the time it takes to mix from the oceans to the continental interiors are of comparable magnitude, so the warming over much of the land surface is tightly coupled to the oceanic warming.
Using a GCM, can we regenerate the land temperature record from the ocean record using observed SSTs and sea ice distribution as a boundary condition? This is not simply a question of “turbulent diffusion” by the atmosphere but also of wave-like “teleconnections” propagating away from regions of tropical convection that are altered by the pattern of tropical warming. Compo and Sardeshmukh, 2009 provide a recent discussion, strongly supporting the strength of the oceanic constraint on land temperature trends. So there does seem to be considerable redundancy between the observed land and ocean records of temperature trends. This does not make the land record any less important. Redundancy is critical when data sets and models are imperfect.
One final point. There is something else that one can do with the atmosphere/land only computation with fixed SSTs and sea ice: one can compute the globally averaged net energy flowing in at the top of the atmosphere (TOA), or, what is essentially equivalent, the energy flux into the ocean. This is how we compute the “forcing” for use in the simple energy balance model described in post #3. There are things that happen on this ultra-fast time scale in response to the increase in CO2 other than the modest warming in the continental interiors, one of the most important being that the stratosphere cools. If one tries to compute radiative forcing without taking into account the stratosphere cooling, one has to deal with a big difference between the energy imbalance between the TOA and the tropopause — this imbalance being precisely what causes the cooling. But focusing on the flux imbalance at the tropopause is a bit awkward, partly because the definition of the tropopause can be fuzzy. It can be simpler to just let the model adjust the stratosphere as it sees fit, then see how much energy is flowing into the system. This is an essential feature of the classical 1-D radiative convective model. In a GCM, fixing the SSTs and sea ice is a simple approximate way to do the same thing. It seems to have the drawback that one is allowing the land to adjust a bit — and other things happen to the hydrological cycle as well — introducing some model-dependence into the definition of forcing. But why allow some of the ultra-fast adjustment to occur (the stratospheric part) and not others? Defining a “forcing” before the TOA, tropopause, and surface ocean fluxes come into agreement can be confusing — for many purposes it is simpler to wait for the ultra-fast adjustment to occur to bring these three in line.
[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.]