An Albedic Curiosity

Guest Post by Willis Eschenbach

I had one of my investigations take a curious turn recently. I was going to use as my springboard the most interesting 2015 paper entitled The Albedo Of Earth, by Graeme L. Stephens et al. However, a strange thing happened along the way. I got to thinking about their Figure 5, in particular Panel (a).:

Figure 1. This shows Figure 5(a) of Stephens2015. ORIGINAL CAPTION: Annual cycles of (a) the globally averaged albedo … The solid curves are for all-sky fluxes, and the dashed curves are the clear-sky fluxes. The error bars represent the interannual variability. … Annual means of all quantities have been subtracted.

To start with, a few definitions. The “albedo” of a planet, moon, or other celestial 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 decimal fraction (e.g. 0.30), although I prefer it as a percentage (e.g. 30%). The albedo of the earth is about 0.29, meaning 29% of the sunlight is reflected back to space.

But somehow, their graph didn’t look right to me. I’ve looked at a lot of graphs of the planetary albedo. It’s a curious curve. The maximum albedo occurs on the summer and winter solstices in December and June, when one of the poles are maximally pointed at the sun. At that point, the most ice-covered area is exposed, which makes for a high albedo. In addition, because the snow- and ice-covered area is much larger in the northern hemisphere than in the southern, the December albedo is higher than the June albedo.

And on the other hand, on the equinoxes the sun sees mostly ice-free zones, and so the albedo is lowest around March and September.

The problem is that this means that the two peaks in albedo will be somewhere around the winter and summer solstices (December 21 and June 21) with the two minimum albedo measurements between the two … and their graph shows nothing of the sort. So to see if their graph was correct, I made my own graph using the CERES data. Here’s that result.

Figure 2. Plot of the albedo from the CERES dataset, March 2000 to February 2014 (14 years). 

Note that as expected, the peaks are around the solstices (June and December) with the high peak in December.

To determine which version is correct, the Stephens2015 version or my version, let me offer the following graph from the Encyclopedia of Climate, by Gerald North et al. It shows, not the average, but a single year of the albedo variations of the CERES dataset. However, the albedo varies little from year to year.

Figure 3. The month-by-month albedo cycle as shown in the Encyclopedia of Climate.

Note that the form of the albedo record in the North book is identical to that of my average shown in Figure 2—it peaks around the summer and winter solstices, is highest in December, and is lowest around the two equinoxes. This is in complete contradiction to the Stephens2015 results shown in Figure 1.

This becomes a significant issue because Stephens et al. use the same graph in a later section of their paper to show how different their results are from the output of many climate models. This is shown in Figure 4 below.

Figure 4. This shows Figure 11(a) of the Stephens 2015 paper. ORIGINAL CAPTION: The global mean annual cycle of (a) TOA albedo … The solid lines are CERES observations taken from Figure 5, and the colored lines are 10 year average seasonal cycle of individual CMIP5 models, and the dashed lines are the multimodel mean seasonal cycle.

Based on this graph, the authors of Stephens2015 reasonably say:

From the comparisons presented in these figures, it is evident that models and measurements differ in potentially important ways.

Unfortunately, when we put in the correct values for the albedo variations, a very different picture emerges:

Figure 5. Actual average albedo variations from the CERES data (thick red line) overlaid on Figure 4 (Stephens2015 Fig. 11).

As you can see, while the model average (dotted line) still has problems compared to the red line that shows the CERES albedo variations, at least they generally get the peaks around the solstices (21st of June & December), the low points at the equinoxes, and the larger peak in December.

Now, I noticed this important error back at the end of May, and I was in a bit of a quandary regarding what I should do. In the event, I noted that Peter Webster, an associate of Judith Curry, was one of the authors. Given my respect for Dr. Curry, I didn’t want to blow the whistle on Peter, and I thought I might actually be able to take another path. I didn’t have his email address, so I wrote to Dr. Curry and sent her the above analysis, and I asked her to pass it on to Peter Webster, which she kindly and promptly did.

Dr. Webster was very good about the matter. He responded to me immediately, and said that he had passed my email on to Dr. Stephens because he is the lead author of the paper. So I waited.

After a short while I asked what was happening. Peter said that Dr. Stephens was in England, it would be a week or so. When nothing transpired, I got back in touch with Peter three weeks later. He said that like me, he had heard nothing from Dr. Stephens. Finally, after almost a month and a half had expired with no answer from Dr. Stephens, Peter said that I might as well go ahead and publish, and that I should also send a formal note to Review of Geophysics.

So I am going to take him up on the first half of his suggestion, and any fault in my taking that step is mine alone, not his. I gotta say, this is very frustrating. I tried to do the right thing, even had the backing of one of the co-authors, and I got exactly zip in return. Note that I do not fault Peter Webster in this matter in any way. He has been most responsive and supportive throughout, but his lead author is not replying to the question, which leaves Peter with no options. Ah, well. I’d hoped that a nudge would be as good as a wink to a blind horse, but I guess sometimes that’s not enough, you need a nudge plus a baseball bat.

However, I don’t want to write a dang letter to Rev Geo. I always feel like I have to give myself a lobotomy to write in the black-letter long-paragraph obscurantist style favored by the journals …

So I’ve chosen to make my first (and perhaps only) move by reporting the matter here. At least now, all of the modelers that Stephens claimed were wrong in important ways will know that a) Dr. Stephens was wrong on this particular point, and b) he declined my offer to reveal his mistake himself and correct it in his preferred manner.

We’ll see what comes after that.

Let me add that I think I have acted in this matter with what passes for my best manners. For example, here is what I said to Peter in my earliest emails:

So please take as much time as it needs (within reason) for you to both verify the error, and then decide how you wish to proceed. I am well aware of how difficult it is to be publicly found in error. I’m one of the few bloggers out there with a post entitled Wrong Again.

Let me assume for a moment that your graph is in error, based on my looking at lots and lots of albedo graphs, and based on physics (higher albedo at the solstices when the poles are most exposed to the sun), and based on the Encyclopedia of Climate as I showed, and based on my own calculations shown in Figure 2, and based on the vague but visible similarity to the models.

If that is indeed the case, I’m more than willing to have you and Graeme make the initial announcement, assuming of course that I’m given appropriate credit. I’ll reserve the right to write it up for WUWT if that comes to pass, but you are free to pick the time, place, manner, and content of the announcement.

Like I say, I’ve been there under the spotlight. So I’ll do whatever I can to make it work as best it can for you.

I don’t think I could have been more supportive than that … and I got nothing. People often say something like “Hey, why don’t you write to the authors instead of simply posting your results up at WUWT”. This is one of the many examples of why I’ve generally given up on that approach … it often doesn’t work, and when it doesn’t, it is the source of much delay and frustration.

Despite this error, Stephens2015 is still an interesting paper, don’t let me put you off reading it. I’m sorry that it’s marred by this single problem.

In any case, TGIF, work week’s over. I’ve been up on a scaffolding working on second story windows the last three days, and although I don’t mind the heights, it is still tiring to have to spend the day with the pucker factor up somewhere in the low seventies, safety line or not … I’ll be glad when this part of the job is done.

Regards to all, and my wish is that you get to spend the weekend doing something other than working high up on a scaffolding with your life depending on some overgrown piece of string tying you to safety …

w.

Don’cha Know: If you disagree with someone please have the courtesy to quote the exact words they used. That way we can all be clear exactly what it is that you are objecting to.