Ponderous Pachyderms Prevent Permafrost

Guest Post by Willis Eschenbach

Anthony Watts has pointed to a curious new paper in his article “Climate Craziness of the Week: The AGU peddles a mammoth climate change theory”  I thought I’d use it as an example of how I take a first cut at whether a theory is reasonable or not. The new paper claims that the extinctualization of the mammoths warmed the world.

The original article is reviewed on ScienceNow, and is accompanied by this image:

Figure 1. Mammoths, the animals that can blow both hot and cold.

Gotta love these folks, no matter what happens it changes the climate. I discussed in my post “Anthropogenic Decline in Natural Gas” the previous study that claimed that the loss of mammoth flatulence when the mammoths were extinctified was the cause of radical global cooling. Now the same mammoth extinctivication is claimed to have caused global warming. Here is the new claim:

Earth system scientist Chris Doughty of the Carnegie Institution for Science in Stanford, California, and colleagues decided to find out whether the change in Betula [birch tree] proliferation was connected to the disappearance of the mammoths. They started by studying Betula pollen records compiled from soil cores taken in Siberia and Beringia. Next, the team examined mammoth fossil records to establish the timeline for their disappearance from the region. They also used studies of elephant-feeding habits to estimate the impact of the loss of the mammoths on the grasslands, and they applied climate models to compute the effect of the vegetation change on global temperatures.

The results, the researchers report in a paper to be published in an upcoming issue of Geophysical Research Letters, suggest that when the mammoths disappeared, the Betula trees expanded across Beringia, forming forests that replaced as much as one-quarter of the grassland. The trees’ leaves, which are darker than grasses, absorbed more solar radiation, and their trunks and branches, which jutted above the snowpack, continued the effect even in winter. The researchers calculated that the mammoths’ disappearance contributed at least 0.1˚C to the average warming of the world around 15,000 years ago. Within Beringia, the warming due to the loss of the mammoths was probably closer to 0.2˚C, the team concluded.

To figure out if something like this makes sense, I generally do a back-of-the-envelope type of calculation. My cut on this particular one is as follows:

1. Figure out the surface area that we are talking about.

2. Figure out the change in albedo.

3. Figure out the change in forcing and thus the change in temperature.

First, the area. At the time in question, the mammoths were centered in an area called “Beringia”, which stretched from 60° to 75°N, and from 150°W to 170°E. This area comprises 0.6% of the surface area of the planet. Let’s triple that to make sure we have a conservative estimate, so we have 2% of the surface area.

Next, the change in albedo. “Albedo over the boreal forest”  gives the following figures:

Representative daily average albedo values in summer are 0.2 over grass, 0.15 for aspen, and 0.083 for the conifer sites. In winter the corresponding mean albedo for snow-covered grass, aspen, and conifer sites with snow under the canopy are 0.75, 0.21, and 0.13. … . Forest albedo increases at all sites in winter (with snow on the ground under the canopy) as the ratio of diffuse to total solar flux increases.

From this we can see that the difference is small in the summer. It is theoretically larger in the winter, but in the winter there is very little heating from the sun because it is so low on the horizon. In addition, this increases the albedo of all surfaces, because of the increased reflectance due to the low angle of incidence. Finally, the low birch trees described in the source article would have greater winter albedo than the aspen, because more of the snow would show through underneath.

So lets use .2 and .8 for the summer and winter albedo for grass, and .15 and .55 for the summer and winter albedo for dwarf birch. These average out to .5 for grass and 0.35 for dwarf birch. This means birch growth increases the absorbed sunlight by about 50%. However, not all of the land surface will be changed. Let’s be real generous and say that half the land surface in the mammoth area is actually where they graze, although it is likely much less than that. There’s a lot of barren land that far north, mountains and bogs and such. So the increase in absorbed sunlight might be 25%. Then the authors (above) say that the extinguination of the mammoths would change a quarter of the grazing area. So we’re down to about a 6% change in albedo. (In fact it will be less, because the higher winter albedo affects less incoming sun, but we’ll leave it at that to make sure the figures are conservative).

Now, how much will that change the absorbed sunlight? Well, Anne Wilber et al. put the annual surface sunlight absorbed by the surface at 60°-75°N (the mammoth range) at 100 W/m2. They also give an average albedo for the area of 0.34.

But the most interesting thing about the Wilber et al. study is this: in the far northern regions, the average net short wave (the amount of sunlight absorbed by the surface) has almost nothing to do with the surface conditions. Figure 2 shows the map of the downwelling short wave (DSW, the amount of sunlight striking the surface) and the net short wave (NSW, the amount of sunlight absorbed by the surface) averaged over the year.

Figure 2. Solar flux. (a) Solar radiation striking the surface (downwelling shortwave, DSW). (b) Absorbed solar radiation (net shortwave, NSW) at the surface.

In Fig. 2(b) we see that while in the tropical regions there are clear differences between things like deserts, rainforests, and the ocean, this is not true in the far North. Up there in Mammothville, you can see very little difference between energy absorbed by the ocean and the land. In addition there is very little variation within the land itself, with the exception of the perpetual ice cover of Greenland.

This is for two reasons. First, the surface radiation in the far north is dominated by clouds, not the surface. Second, the composition of the surface makes little difference. The surface albedo is high because of the low angle of the sun, not because of the exact composition of the surface.

In any case, we can see that any changes in the surface albedo of the far north, such as the change due to mammoth extinctualations, do not affect the overall albedo very much. The Wilber et al. study puts the change in ground cover as explaining only about 2% of the absorbed sunlight. That’s the maximum that changing the surface albedo will do.

So the maximum change from mammoth extinguishment is 2% of the absorbed sunlight due to surface albedo, times 100 W/m2 insolation in the mammoth area, times 2% of the surface covered by mammoths, times a 6% increase in absorbed sunlight from the surface change due to birch growth. This gives us a change of about 0.0025 watts per square metre … which using the Stefan-Boltzmann law gives us a temperature change of .00045°. This would be increased by the greenhouse effect by about 35%. That would give us a temperature change of 0.0006° …

Now my estimate could be low by an order of magnitude (a factor of 10). Seems doubtful, because I’ve used fairly conservative numbers. But it’s certainly possible. Mammoths might have covered a larger area, my other estimates could have been low, this kind of calculation is usually only good to within an order of magnitude.

And it’s possible that it is out by two orders of magnitude. But I’d say that was very doubtful. And that’s how far wrong it would have to be to match their estimate of a .1°C change from mammoths.

My conclusion? Nothing firm, because this is a back-of-the-envelope calculation. However, the calculation says that it’s very doubtful that mammoth exstrangulation caused the planet to warm … I’d have to see a whole lot of very solid data before I’d believe that one.