How Much Sunlight Actually Enters The System?

Guest Post by Willis Eschenbach

There’s a new study in PNAS, entitled “Observational determination of albedo decrease caused by vanishing Arctic sea ice” by Pistone et al. Let me start by registering a huge protest against the title. The sea ice is varying, it isn’t “vanishing”, that’s just alarmist rhetoric that has no place in science.

In any case, here’s their figure 4B, showing the decrease in albedo from the “vanishing” sea ice:

Figure 1. Graph from Pistone2014 showing CERES albedo data (green, solid line) for the ocean areas of the Arctic.

The authors say:

Using the relationship between SSM/I and CERES measurements to extend the albedo record back in time, we find that during 1979–2011 the Arctic darkened sufficiently to cause an increase in solar energy input into the Arctic Ocean region of 6.4 ± 0.9 W/m2, equivalent to an increase of 0.21 ± 0.03 W/m2 averaged over the globe. This implies that the albedo forcing due solely to changes in Arctic sea ice has been 25% as large globally as the direct radiative forcing from increased carbon dioxide concentrations, which is estimated to be 0.8 W/m2 between 1979 and 2011.

The present study shows that the planetary darkening effect of the vanishing sea ice represents a substantial climate forcing that is not offset by cloud albedo feedbacks and other processes. Together, these findings provide direct observational validation of the hypothesis of a positive feedback between sea ice cover, planetary albedo, and global warming.

So … how are they going about making that case?

Let me start by saying that looking at albedo as they are doing is a very roundabout and inaccurate way of handling the data. The CERES dataset doesn’t have an “albedo” dataset. Instead, they have a dataset for downwelling solar, and another dataset for upwelling solar. The problem is that when the numbers get very small, the values of the calculated albedos get more and more inaccurate. Albedo is reflected solar divided by downwelling solar. So when you get down to where there’s almost no sunshine, you can get things like a gridcell that averages 0.2 W/m2 of incoming sunlight over some month, and reflects 0.4 W/m2 … giving us an impossible albedo of 2.0 …

It’s not clear how Pistone et al. have handled this issue. The way I work around the problem is to calculate the average upwelling reflected sunlight for the Arctic ocean area, and divide that by the average downwelling sunlight for the Arctic ocean area. This gives me an overall average albedo. I get slightly different numbers from theirs, and I am unable to replicate their results. However, I do get about the same trend that they get over the period, a decrease in the albedo of about 1.5% per decade. However, I don’t particularly trust those albedo numbers, averages of ratios make me nervous.

For this reason, I use a different and simpler measure, one which Pistone et al. mention and quantify as well. This is the actual amount of sunlight that makes it into the climate system. The authors call this the “total solar energy input”, and I will follow the practice. And qualitatively, my results agree with theirs—the amount of sunlight absorbed by the arctic has indeed increased over the period of the CERES data, 2000-2013. Figure 2 shows both the clear-sky and the all-sky arctic total energy input:

Figure 2. Increase in solar energy input to the Arctic ocean areas, 2000-2012. Clear sky in black, all sky in red. Units are area-weighted watts/m2.

In addition to the overall trend in all sky solar input (green line), you can see the peak in energy input in 2007, with the high solar input corresponding to very low ice areas. Overall, Figure 2 shows an even greater increase in energy input than Pistone2014 have estimated over the entire period. They report an increase in Arctic solar energy input over the ocean of 0.21 W/m2 over 32 years … and the CERES data shows an increase of 0.3 W/m2 per decade.

So we’ve established that their first claim, of increasing solar energy input to the Arctic ocean area 2000-2012, is true, and perhaps even underestimated. And this is quite reasonable, since we know the sea ice has decreased over the period … but what about their second claim? As you may recall, this was (emphasis mine):

The present study shows that the planetary darkening effect of the vanishing sea ice represents a substantial climate forcing that is not offset by cloud albedo feedbacks and other processes. Together, these findings provide direct observational validation of the hypothesis of a positive feedback between sea ice cover, planetary albedo, and global warming.

The CERES data agrees that the increase in solar energy input from reduced ice cover is not counteracted by Arctic clouds … nor would I have expected it to be counteracted by clouds in the Arctic. As I have discussed, well, more than once, the main climate control system is in the tropics. So if this increase in absorbed energy were counteracted by clouds, my hypothesis is that it would happen be in the tropics. I’ll return to this in a moment.

First, however, they’ve claimed that their results establish the existence of “a positive feedback between sea ice cover [and] planetary albedo”. Since the planetary albedo controls the total solar energy input to the globe, let’s take a look at the same data as Figure 2, total solar energy input, but this time for the entire planet …

Figure 3. Available solar energy at the top of atmosphere (red) and total solar energy input to the globe (blue), 2000-2012. Units are area-weighted watts/m2.

So their claim of increased solar energy input to the Arctic from reduced sea ice is true … but their claim that there is “a positive feedback between sea ice cover [and] planetary albedo” is falsified by the CERES data. The total solar energy input (blue line above), and thus the planetary albedo, is amazingly stable over the time period. There is no feedback at all from the changes in the ice.

To illustrate the stability, Figure 4 shows a breakdown of the total solar input data (blue line above). It’s divided into panels that from top to bottom show the data itself, the seasonal pattern, the trend, and the residuals of the global solar energy input:

Figure 4. Decomposition of the solar energy input signal into trend, seasonal, and residual components. Red scale bars on the right indicate the relative scale of the individual panel. Units are area-adjusted W/m2.

I’ve written before about the amazing stability of the climate system. This is another example. In the past people have objected that the system is forced to be stable, because over time, energy out must generally equal energy in.

But the global solar energy input, the amount of the available solar energy that actually makes it into the climate system, is under no such constraint. There is nothing that it must balance to. Solar energy input is a function of the albedo, which is determined by clouds, snow, ice, vegetation, and wind, and all of these are constantly varying in all parts of the planet … and despite that, the swings of the trend are no greater than ±0.3 w/m2 over the period. The maximum monthly deviation from the seasonal average is a mere one W/m2, and the standard deviation of the residuals (data minus seasonal) is half a watt/m2.

So … how does it happen that we have a strong increase in solar energy input in the Arctic, but the global energy input stays the same?

Well … as I mentioned above, the tropics. Over the period 2000-2012, during which the Arctic received increased solar energy input, here’s what’s happened in the tropics:

Figure 5. Total solar energy input, all skies, tropics. Units are area-adjusted W/m2

As I hypothesized, the control is happening in the tropics. Pistone et al. note that the Arctic solar input is going up because of decreased sea ice … but they did not notice that at the same time, the tropical solar input is going down because of increased clouds. And the net sum of all of the changes, of more energy being absorbed in the extra-tropical areas and less energy being absorbed in the tropics, is … well … no change at all for the globe. It all averages out perfectly, with little change in either the monthly, annual or decadal data.

Coincidence? Hardly.

This is about as neat a demonstration as I can imagine in support of my hypothesis that the system is not ruled by the level of the forcings—instead, it is regulated by a system of interlocking emergent climate phenomena. A number of these phenomena operate in the tropics, and they have a curious property—the warmer the planet gets, the more that they cut down on the incoming solar energy.

So at the end of the day, we find that the claim of the authors that increased solar input to the Arctic is connected to the planetary albedo to be true … except that it is true in exactly the opposite of the direction that they claimed. When more energy is absorbed in the Arctic, less energy is absorbed elsewhere.

In closing, I want to highlight what it was that got me interested in climate science to begin with. I wasn’t interested in finding out why the global temperature had changed by something like ± 0.3°C over the 20th century.

Instead, I was interested in finding out why the global temperature had only changed by ± 0.3°C over the 20th century. I was amazed by the stability of the system, not the fact that it had varied slightly. So let me close with a graph showing the total global solar input residuals, what remains after the seasonal cycle in total solar input is removed.

Figure 5. Residual total solar input after the seasonal cycle is removed. Dotted lines show the inter-quartile range. Smooth curve is the loess trend line.

The monthly deviation from the seasonal cycle is tiny. Half the months are within a third of a W/m2 of the seasonal average … a third of a watt, to me that’s simply amazing.

Now, you might disagree with my hypothesis that the planet is thermoregulated by emergent climate phenomena such as thunderstorms, El Nino, and the PDO.

But the stability shown in the above graphs surely argues strongly for the existence of some kind of regulatory system …

My regards, as usual to everyone.

w.

AVISO: If you disagree with what I or anyone says, please quote the exact words you disagree with. It allows everyone to understand exactly what you are objecting to.

DATA AND CODE: You’ll need the CERES data (227 Mb) , the CERES surface data (117 Mb) and two support files (CERES Setup.R and CERES Functions.R) in your R workspace. The code is Arctic Albedo.R, it should be turnkey.

[UPDATE]

Well, y’all will find this funny, I assume … following up on the question of the net effect of the loss of the sea ice that came up below in the comments, I decided to see what was happening with the upwelling longwave. We’ve established that the loss of the ice increases the total solar energy input … but what about the energy loss via longwave? (Yr. humble author slaps forehead for not thinking of this sooner …)

As you can see, the change in solar energy input is more than offset by increased losses … so the net effect of the melting sea ice is a net energy loss of 0.05 W/m2 per decade.

Note again the stability over time. Note also that this part of the system is not constrained by any need for solar input and longwave output to be stable, or to have the configuration they have. The average solar input is 30 W/m2, and the average longwave loss to space is 63 W/m2 … and despite the marked changes in ice cover over the period, they’ve only changed about 1% per decade over the period …

Gotta love the climate, always more surprises … 

w.

[UPDATE II] 

Some folks have said that there is a problem with my area-weighting, so let me explain exactly what I did.

The data exists in 180 latitude bands. The center of the bands start at -89/5° (south) and end up at 89.5° (north). To area-weight the data, we want to adjust the results for each gridcell by the area.

What we want to do is adjust the results to give what you would get if they had the size of the average gridcell. Now the area is proportional to the cosine of the mid-latitude. So what we do is multiply each gridcell result by

area of the gridcell / area of the average gridcell

This give each gridcell the value it would have if it were of average size. The effect of tiny gridcells is reduced, and the effect of large gridcells is increased.

Now, what is the average cell size? Well, if we integrate Cos(x) from zero to pi/2, we get 1. So the average gridcell size is 1/(pi/2) = 2/pi ≈ 0.637.

As a result, the weighting factor by which we multiply the gridcell value is, as you recall:

area of the gridcell / area of the average gridcell

which is equal to

cosine of the gridcell midlatitude / 0.637

Once you’ve multiplied the data by those weighting factors, you can compare them directly, as they are all adjusted to the average gridcell size.

The way to test if you’ve done this correctly is to see if the plain vanilla average of the newly-weighted dataset is correct. For example, see the average available solar (~340 W/m2) and solar input (~240 W/m2) values in Figure 3. They are simple averages of weighted data.

Note that there are two ways to do the weighting.

The first is to do all calculations (trends, etc) using the unadjusted variables. Then to get an average, you use what is called an “weighted mean”, which weights the data on the basis of gridcell area as it calculates the average.

The other way to do it is the way I described above, which converts all of the data to what an average sized gridcell would show. Once you’ve done that, you no longer need to do an area-weighted average, because the data itself is weighted. This means that you can use a normal average, and compare things like trends directly.

So … what I do to check my work is to compare the normal mean of the area-weighted data, with the weighted mean of the original data. They should be the same, and that is the case in this analysis.

Finally, an area-weighted mean uses different weights, where the sum of all of the weights is 1. This allows you to calculate the weighted mean as the sum of the product of the data and the weights. These weights are different than the weights I used to area-weight the data itself. These weights which do not sum to 1. However, the end result is the same.