Guest Post by Willis Eschenbach
In my continuing wanderings through the regions cryospherical, I find more side roads than main highways. In my last two posts here and here, I discussed the curious inverse relationship between temperature and ice accumulation rates in Greenland and Antarctica.
Wanting to understand the changes in the polar oceans that occur when the sea ice forms, I got to wondering about the albedo changes between sea ice and water. Obviously, ice reflects more sunshine than water does … but how much more does it reflect? It is important because the more the ice melts, the less solar energy is reflected, the warmer the ocean becomes, and this melts even more ice, and so on. This is a positive feedback called the “ice-albedo” feedback, which will tend to increase a given warming. Naturally, the size of this ice-albedo feedback is of interest.
To start with, I looked at the relationship between the “clear sky” albedo and the ice coverage. The clear sky albedo is the albedo measured by the CERES satellite at the top of the atmosphere when there are no clouds in the sky, so it is an estimate of the albedo of the surface itself. Figure 1 shows the relationship between the two variables, for all 1° latitude by 1° longitude gridcells which have ice during some part of the year.
Figure 1. Ice coverage as a percentage of gridcell area (horizontal axis) versus clear sky albedo (vertical axis). The data is composed of the 12 monthly averages for each gridcell. There are 11,646 gridcells (1°x1°) which contain sea ice at some point during the year, meaning that the total number of data points N is 139,752.
It is clear that as the ice coverage increases, so does the albedo. And there is a fairly steep relationship, going from a polar ocean albedo of about 25% with no ice to an albedo of about 55% with complete ice coverage. This is an albedo change of about 30%.
However, that’s just the surface albedo. Of more interest is the “all sky” albedo, which includes the clouds. In Figure 2, I have added the all sky data in blue to the clear sky data shown in Figure 1.
Figure 2. Ice coverage as a percentage of gridcell (horizontal axis) versus both clear (red) and all sky (blue) albedo (vertical axis). The data is composed of the 12 monthly averages for each gridcell. There are 11,646 gridcells (1°x1°) which contain sea ice at some point during the year, meaning that the total number of data points N is 139,752.
The most obvious change is that the slope of the all-sky data (blue) is much less than that of the clear-sky data (red). Rather than a 30% albedo change from no ice to full ice, in the real world there is only about an 18% albedo change from no ice to full ice.
I was surprised to find that the clouds are brighter (greater albedo) than the ice itself. At all different amounts of ice coverage, including 100%, the albedo with clouds is greater than the surface albedo of just the ice itself. (I haven’t thought through all of the ramifications of this finding, I’m just pointing it out.)
However, this still doesn’t tell us just how much extra energy is reflected by the ice. The problem is that in each hemisphere the ice is at its largest extent when there is the least sunlight and vice versa. So what I did was to actually calculate the amount reflected based on the relationship given by the black line in Figure 2, which shows that the change in the albedo is equal to 0.18 times the change in the ice coverage. I calculated for each gridcell just how much difference that ice-based albedo change makes given the variations in the incoming sunlight. This will not be exactly accurate, but is certainly close enough for a first-cut analysis, and is shown in Figure 3 below.
Here we finally have what I started out to find. This shows that on average, sea ice is only responsible for 1.1% of the total solar reflection. This is the result of what I mentioned above, that when there is a lot of ice there is little sun, and vice versa.
Finally, remember that the blue line is the full effect of the existence of sea ice. Let us assume that we get say a 10% reduction in sea ice. This will have 1/10 the effect of the full change, or about a tenth of a percent of the total reflections.
As a result, I’ve gotta say that on a global level at least, even a 10% change in the amount of sea ice makes very little difference to the total reflections. It only makes the total global reflections vary by a tenth of a percent. Now conveniently, total global reflections are about 100 W/m2, so that means that averaged over the planet, if all the sea ice disappeared it would only make a difference of 1 W/m2 in the global reflections … and this means that a 10% change in sea ice amounts to a globally averaged change of 0.1 W/m2
And this, of course, means that the effect of the ice-albedo feedback is vanishingly small globally. It is certainly possible that it makes some larger difference in the immediate neighborhood of the ice, but in terms of a global effect, it is what I call a third-order variable.
Ranking the variables is my own system for trying to understand what is important in a system. I divide variables in a system into first, second, and third order variables. A first-order variable can change the output measurement by greater than 10%. If for example we’re talking about solar reflections, the clouds are obviously a first-order variable.
A second-order variable can change the output by between 1% and 10%. Regarding solar reflections, an example of a second-order variable is snow cover.
Finally, we have third-order variables, which are those that make a change of less than 1% in the output measurement. That is why I said that variations in sea ice reflections are a third order variable. And typically, third-order variables can be ignored in all but the most accurate analyses … and generally we can’t do analyses anywhere near that accurate in climate science.
Anyhow, that’s what I found out about the size of the ice-albedo feedback … it is a third-order variable, so small that it disappears in the noise.
Jupiter burning in the midnight sky, ah, dear friends, another springtime is upon us here, it is good to still be on the upper side of the grass.
My best wishes to all,
My Usual Request: Misunderstandings destroy communication. If you disagree with me or anyone, please quote the exact words you disagree with, so we can all understand the precise nature of your objection. I can defend my own words. I cannot defend someone else’s interpretation of some unidentified words of mine.
My Other Request: If you think that e.g. I’m using the wrong method or the wrong dataset, please educate me and others by demonstrating the proper use of the right method or the right dataset. Simply claiming I’m wrong doesn’t advance the discussion.