Albedic Meanderings

Guest Post by Willis Eschenbach

I’ve been considering the nature of the relationship between the albedo and temperature. I have hypothesized elsewhere that variations in tropical cloud albedo are one of the main mechanisms that maintain the global surface temperature within a fairly narrow range (e.g. within ± 0.3°C during the entire 20th Century). To provide observational support for the hypothesis, I’ve been looking at the relationship between temperature and albedo, both globally and more particularly in the tropics.

To start with, the “albedo” of an object is a number from 0.0 to 1.0 that measures the fraction of solar radiation that is reflected from the surface of the object. It’s often given as a fraction, although I prefer it as a percentage. The albedo of the earth is about 0.29, meaning 29% of the sunlight is reflected back to space. Figure 1 shows the average albedo around the planet.

Figure 1. Average total albedo, including surface and cloud albedo. Calculations in the heading are for the northern and southern hemispheres (NH, SH) the tropics (Trop), the Arctic (Arc), the Antarctic (Ant), and the land and ocean.

Figure 1 shows some salient features. One is the inter-tropical convergence zone (ITCZ), which is the light green area just north of the Equator. It marks (as the name suggests) the average boundary between the northern and southern hemispheric air masses. The ITCZ is the area of deep tropical convection, the area increased clouds just above the Equator. To verify that the oceanic variations we are looking at are a result of cloud albedo rather than ocean surface albedo, we can compare Figure 1 with Figure 2, which shows the surface albedo.

Figure 2. Average surface albedo only.

As you can see, the average albedo of the ocean varies little, other than increasing slightly from equator to pole. The combination of the two figures highlights an albedic mystery—the total albedo of the northern and southern hemispheres are identical to three significant digits. This is clearly the result of the clouds, as the surface albedos of the two hemispheres are quite different. However, the mechanisms involved in the rebalancing are unclear. It does emphasize the responsive nature of the cloud albedo.

Now, as I said above, I wanted to look at the relationship between temperature and albedo. I started by looking at how the relationship breaks out spatially. Figure 3 shows the correlation between average temperature and average albedo. “Correlation” is a number that can vary between -1.0 and +1.0. A correlation of plus one indicates perfect positive correlation (both either go up or go down together). A correlation of minus one indicates perfect negative correlation (when one goes up the other goes down, but still in step with each other).

Figure 3. Correlation between temperature and albedo. The area outlined in red is analyzed separately below in Figures 5 & 6.

As you can see, the northern hemisphere land towards the poles is strongly negatively correlated with temperature. This is because as the northern land warms, the ice and snow melts and the plants grow. Both of these changes lower the solar reflectivity (albedo). In the tropics, on the other hand, there are a number of large areas that are positively correlated with temperature.

Next, I took a look at the general relationship between the temperature and the albedo. I wanted to look in particular at what is happening in the ocean. Figure 4 shows that relationship.

Figure 4. Gridcell by gridcell comparison of average albedo and average ocean temperature. Temperatures below freezing are of ice-covered ocean.

Now, this is most interesting. The warmer the ocean gets, the lower the albedo goes, a negative correlation … except when the temperature gets over about 26°. Above that, the warmer it gets, the higher the albedo goes. This is the tropical area shown in Figure 3 where there is positive correlation between the albedo and the temperature. This is exactly the mechanism that I have proposed, that increasing tropical temperatures cause increasing albedo and thus help to regulate the global temperature. I say that this is due to a combination of both earlier and stronger daily emergence of the cumulus, thunderstorm, and squall line regimes.

However, it could be fairly argued that in Figure 4 we’re not looking at temperature and albedo changes in one location. Instead, we’re looking at average values in a host of different locations. So it might be that the “hook” at the high temperatures doesn’t reflect what is happening as the temperature changes in each individual location.

To see if this is so, I’ve invented a kind of plot that I call a “Lissajous scatterplot”. Or maybe I didn’t invent it, but I’ve never seen one before. It is a combination of Lissajous figures and a scatterplot. Instead of displaying the average for each gridcell, I display the Lissajous figure for that gridcell. And what is a Lissajous figure when it’s just sitting at home by the fire?

A Lissajous figure is a display of two cyclical values, with one shown on the horizontal axis and the other on the vertical axis. As usual there’s a good description at Wolfram Mathworld,  and Wolfram also has an interesting interactive demonstration of the Lissajous figures here.

I use the monthly average values of two cyclical variables to make a Lissajous figure. Here, for example, is the Lissajous figure for temperature and albedo for the gridcell located at 45N 80W:

Figure 5. Lissajous figure, monthly average temperature versus monthly average albedo. The location is near the Great Lakes in North America.

As you can see, in that particular location, as the temperature goes up, the albedo goes down.

So with that as Lissajous prologue, Figure 6 shows a Lissajous scatterplot of the temperature and albedo of an area of the tropical Pacific. This is the area of the Pacific outlined in red in Figure 3. In essence Figure 6 shows the lower right end of the graph shown in Figure 4, but with Lissajous figures for each gridcell rather than dots representing the gridcell averages.

Figure 6. Lissajous scatterplot, showing the monthly changes in tropical Pacific temperatures and albedo. The area of the analysis is outlined in red in Figure 3. Each gridcell is represented by a Lissajous figure showing how monthly average albedo varies with monthly average temperature 

Recall that I am using this method to see if the “hook” in the high-temperature region of Figure 3 was actually reflected in the temperature and albedo changes in each individual location over time. And indeed, the change in the direction of the relationship with the rising temperature shown in Figure 3 is totally borne out by Figure 6. Albedo is dropping as temperatures rise, but only up to about 26°C. As temperatures start rising above 26°C the albedo just goes through the roof.

Finally, how much more sunlight is reflected by this increase in albedo? Figure 7 shows a Lissajous scatterplot of the reflected sunlight versus temperature:

Figure 7. Lissajous scatterplot, as in Figure 6 but showing the monthly changes in tropical Pacific temperatures and reflected sunlight. The area of the analysis is outlined in red in Figure 3.

Figure 7 makes it clear just how much difference the change in albedo makes. The white dashed line shows the approximate trend of the high-temperature section of the graph. The slope of that line is no less than 60W/m2 per °C. In other words, in the warmest tropical regions, for each degree that the temperature warms, the albedo cuts down the incoming sunlight by about 60 W/m2.

My conclusion? The “hook” in the high temperature end of the temperature/albedo graph is evidence that cloud albedo is part of the system that places a limit on how warm the tropical ocean is able to get. When the temperature gets above a certain point, increased clouds cut way back on the incoming energy. The “hook” also provides evidence of some kind of “set point” around 26° – 27°C, with temperatures warmer than that being cooled and temperatures cooler than that being warmed by the variation in albedo.

The albedo data is thus strong support for my hypothesis that the timing and strength of the daily onset of the tropical cumulus and cumulonimbus regimes exercises a strong control on the amount of incoming energy. The presence of large areas of tropical ocean with a positive correlation between temperature and albedo lead to a naturally stable system … which will likely be the subject of my next post, unless I’m once again distracted by … oooh, shiny!

Regards to all, keep the pedal to the metal …

w.

My Customary Request: If you disagree with someone, please QUOTE THEIR EXACT WORDS that you disagree with so we can all understand your precise objections.

Data: Once again I’ve used the CERES EBAF satellite-based radiation dataset.