A Tropical Oddity

Guest Post by Willis Eschenbach

I wanted to bring you up to date on my current meanderings in the TAO buoy data that I investigated previously in a post called “Cloud Radiation Forcing in the TAO Dataset“. In my peripatetic inquiries into all things that are ooh, shiny, I ran across a curiosity. First, a very small bit of backstory.

Figure 1. Location of the buoy (red square) which recorded the data used in this study. Solid blue squares show which of all the buoys have the two-minute data. DATA SOURCE

The TAO buoys are strung out across the tropical Pacific, recording a variety of surface and subsurface data. The data I’m looking at now include the solar radiation. From the radiation, it’s possible to tell when the skies are clear and when they are overcast. I wanted to understand the effects of the clouds. So I needed to be able to identify the clear-sky observations, and reliably separate them from the observations made when the sky was overcast. I thought folks might be interested in how I went about doing that.

First, as usual, I eyeballed the data. Figure 2 shows a time slice of the entire dataset for downwelling solar radiation, which covers over 2,000 days at two-minute intervals, or about a million and a half observations. This particular time slice shows the downwelling radiation at local noon for each day of record. I looked at a bunch of the slices, from morning and evening, all times of day, so I could understand what’s going on.

Figure 2. Data taken at local noon over the period. The data exists in five separate chunks. However, this does not matter since I am analyzing daily averages.

The dark wavy line at the top of the data is the record of all of the clear days. The up and down wave reflects the variation in the strength of the sun at the equator. This variation is about 150 W m-2 in amplitude, and has two maxima and two minima per year. So the observations near and above that wavy black line are clear sky observations, while the rest of the observations below that dark wavy line are overcast observations. The question was, how to reliably separate them mathematically.

I started by establishing a breakline. To do that, I took the median of the upper quartile (top 25% of the data). I set the break line at 80% of that median, as shown in Figure 3.

Figure 3. As in Figure 2, and including the breakline.

This left few enough data points in the upper section that I could use a gaussian average to reliably estimate the location of the center of the wavy black line. I used a 73-point gaussian filter, which gives the result shown in Figure 4

Figure 4. As in Figure 3, and including the Gaussian filter.

As you can see, the gaussian average does a very good job of determining the center of the black wavy line demarcating the clear day observations. (Note the differences in the two annual minima of the clear-sky line, due to the earth being closest to the sun in January and furthest away in August.) Finally, I created a new line at 92% of that gaussian average. This line, shown in Figure 5, was the line that I actually used to divide clear-sky observations from overcast observations.

Figure 5. As in Figure 4, and including the final line used to separate clear-sky observations from overcast sky observation.

OK, so that procedure let me reliably distinguish between the clear-sky and the overcast situations. (Note that I didn’t really have to go to that extent, because results don’t change much by just using my first breakline alone to make the cut … but I didn’t know that until I did the gaussian average, did I?. End of digression on methods …)

Now that I had collected and averaged my data, as a first cut in investigating the situation, I took the minute-by-minute average of all of the clear-sky observation, and of all of the overcast-sky observations. I also took the “All Sky” observations, which means the average of all of the observations for that minute of the day.

The results of these are graphed up in Figure 6.

Figure 6. Downwelling solar radiation during daylight hours at the TAO buoy at 0N, 165E. Blue circles are clear sky, green are all sky, and gold are overcast sky. The light red circles show the percentage of sunlight making it through the clouds during just the overcast observations (not all observations). Values following the names are the 24-hour average for each variable.

Now, here is the oddity that I mentioned in the title of this post. The light red circles show, solely for overcast observations, the average amount of sunlight making it through the clouds, as a percentage of the total sunlight available at that time. The oddity is that it is nearly the same all day. That is to say that no matter what time of day the clouds form, on average they intercept about the 45% of the available sunlight, and that’s how it is.

I didn’t expect that. I kind of understand it, in that in my post called The Thermostat Hypothesis I used the point of view of the sun to show that on average it takes less than an hour for the tropical cirrus clouds to set in. Once that happened, there was little change in cloud density for the rest of the day. It appears that a fully developed bank of cirrus/cumulonimbus clouds intercepts about 45% of the sunlight, no matter what time of day it occurs.

Anyhow, that’s the oddity. Like I say, I ascribe it in part to “on/off” nature of the cirrus regime. Seems that either they are there or not there. Still, it doesn’t really explain why the same amount of sunlight would be intercepted on average during overcast periods at any time of day. I would have thought that merely the different angles of the sun hitting the clouds would cause a fairly large variation. The sun angle may be responsible for the slight decline in the afternoon around 4 PM, when the tall towers of the thunderstorms would intercept a larger amount of the slanting afternoon sunlight. Also, it may reflect the increasing thickness of the afternoon clouds.

Let me show one last result of my investigation. This is the average amount of solar energy reflected by the clouds, minute by minute. It is shown by the red circles in Figure 7.

Figure 7. As in Figure 6, and including the amount of energy reflected (on average) by the clouds (red line). This is calculated as the clear sky insolation, minus the all sky insolation (i.e. potential insolation minus actual insolation). This difference is the amount reflected back to space by the clouds.

This result is further evidence supporting my thunderstorm thermostat hypothesis. It does so in two ways. The first way is that the forcing is inversely proportional to the temperature. More sunlight makes it through in the morning (when it is cooler) and less makes it through in the afternoon when it is warmer. The average energy lost to cloud reflection in the morning is 22 W m-2 less than in the afternoon. This warms the mornings, when it is naturally cool, and cools the afternoons, when it is naturally warm.

The second way that it supports my hypothesis is that the morning to afternoon difference in this analysis (22 W m-2) is of the same order of magnitude as that of my previous analysis done in the post “The Thermostat Hypothesis”. That data indicated a morning to afternoon difference (across the Pacific) of just over 40 W m-2. Since they are not measuring exactly the same thing, and my previous data was proxy-based and much cruder, I find that amount of agreement encouraging. Here is the figure showing the previous data:

Figure 8. Average of one year of GOES-West weather satellite images taken at satellite local noon. The Intertropical Convergence Zone is the bright band in the yellow rectangle. Local time on earth is shown by black lines on the image. Time values are shown at the bottom of the attached graph. Red line on graph is solar forcing anomaly (in watts per square meter) in the area outlined in yellow. Black line is albedo value in the area outlined in yellow.

I have no big conclusions out of this, other than to note that once again we see a strong thermostatic temperature governing mechanism in action. It is not simple feedback. It adds more energy to the surface in the morning when it is cool, and it reflects more energy to space in the afternoon when it is warm … just one of the many homeostatic mechanisms that keep the planet from overheating. It is a fairly powerful mechanism. As a measuring stick, 22 W m-2 is the expected change in forcing from CO2 increasing from its present value (~390 ppmv) to about 24,000 ppmv … just providing a sense of scale here …

In any case, that’s the news from my latest investigations. I was marveling today that I have that rare opportunity, with both the freedom to look into whatever might interest me at the moment, plus a host of wicked-smart folks to discuss my findings with. What more could a man want … except longer days. Somehow, it’s slipped past midnight again.

In between paroxysms of writing I frequently walk out to take the measure of the night. It’s crisp and cold this evening. The moon is up in the sky about 30°. I know because using a trick I learned doing celestial navigation with a sextant, I measured it using my hand at arm’s length with my thumb like this:

I know from experiment that from the top of my thumb knuckle to the bottom of my fist is 15° (for me, YMMV), which is a useful measurement because it is the distance that the sun or moon travels in the sky in one hour. I can measure up from the horizon and estimate how long it will be until sunset, one hand per hour. So I know the moon is about two hours above the horizon. That means it rose about 10:30.

Sunset these days is at 5:30. At full moon, the moon rises just as the sun sets, that’s why it is full, because it is exactly opposite the sun. (In fact, the full moon traces out the same path in the sky that the sun will take in six months … again because it is about directly opposite the sun. But I digress from my digression…)

Now, every day after the full moon, the moon rises after dark, and just under an hour later. So if it rose at 10:30 tonight that’s about five hours after dark, so we’re about five days past full … I check the moon tables to see how well I’ve done. Moonrise was 10:35 but that’s just luck to hit it that close, and we’re just starting the sixth day past full. Works for me …

The moon can also be used to determine the position of the sun. If you look at a half moon and you imagine it as a drawn bow, you’ll see it shoots its arrow directly at the sun … why do I bring this arcana up? Mostly to remind myself why I do this—because I love observing the oddities and iniquities of this most mysterious and enigmatic universe.

Tonight, Jupiter and Sirius the Dog Star frame the constellation of the hunter Orion in the southern sky. Jupiter’s a planet so it doesn’t twinkle, it’s a serene peaceful white, like a ship’s anchor light. Sirius is a star so it flashes and flickers, in shades of crimson. I take it as a channel marker for the course out of the harbor. Because it is red and I’m leaving harbor for the open sea, I’ll take it on the left, following of the “Red Right Returning” rule for channel markers …

… and in the distance, from my house I can see a tiny triangle of ocean glistening under the moon. And like the poet I long to go down to the sea again, but not to this cold green Northern sea that lies moon-bound in my night vision. The ebbing tide calls me much further afield, it’s angling on a long glance off of the horizon and out to a proper warm tropical sea of viridian and azure, with the sunlight far-reaching across the sparkling surface and lighting the color-drenched reef below, and my friends and I laughing and chaffing on our surfboards waiting for the next set … like the man said;

... The long day wanes:

                        the slow moon climbs:

                                               the deep

Moans round with many voices.

                               Come, my friends,

'Tis not too late to seek a newer world.

Push off, and sitting well in order smite

The sounding furrows;

                       for my purpose holds

To sail beyond the sunset, and the baths

Of all the western stars,

                           until I die. ...

I wish the best of that wildering road for all of you, the finest of that side-winding path half seen through that hidden door you occasionally redismember in your wainscoting. You know the one, that unacknowledged door into summer that beckons and tickles at your mind in the gloaming, calling for you to slip once more through that fugitive crack like when you were only three but you forgot, daring you to slide unseen through that opening into whatmight, beckoning you to make a spectacular of yourself and go a-yondering far and away beyond that boringly flat event horizon you resignedly contemplate through your quotidian expectacles …

I know that road calls for me, but I’m at anchor here for a while, as I am bound at this time by family obligation to stay where I am, and I will honor that obligation fully and joyously until it ends, but hey, let’s get real here. Someone should be taking my place in the ocean, investigating the mysteries of the thermal stratification and overturn of the warm tropical waters and their relationship with climate, suntans, and bikinis … so why not you now? I mean … who better, and what better time?

Hele on …

w.