Cumulative Model

The first half of this post by Willis Eschenbach is valid, but not interesting to me. The second half is very interesting and should stand alone, so I've reproduced it here:

In any case, let me move on to the more serious topic I mentioned above, regarding Dr. Trenberth’s infamous “missing heat”. Let me suggest where some of it is going. It’s going back out to space.

One of the main thermal controls on the planet’s heat balance is the relationship between surface temperature on one hand, and the time of day of cumulus and cumulonimbus formation in the tropics. On days when the surface is warmer, clouds form earlier in the day. The opposite is true when the surface is cooler, clouds form later. This control operates on an hourly basis. I’ve shown how this affects the daily evolution of tropical temperature here and here using the TAO moored buoy data. Here’s a bit of what I demonstrated in those posts. Figure 2, from the second citation, shows how cold mornings and warm mornings affect the evolution of the temperature of the ensuing day.

Figure 2. Average of all TAO buoy records (heavy black line), as well as averages of the same data divided into days when dawn is warmer than average (heavy red line), and days when dawn is cooler than average (heavy blue line) for each buoy. Light straight lines show the difference between the previous and the following 1:00 AM temperatures.

The control of the surface temperature is exerted in two main ways: 1) in the morning, cumulus cloud formation reduces incoming solar radiation by reflecting it back to space, and 2) in the afternoon, thunderstorms both increase cloud coverage and remove energy from the surface and transport it to the upper troposphere. We can see both of these going on in the average temperatures above.

The black line in Figure 2 shows the average day’s cycle. The onset of cumulus is complete by about 10:00. The afternoon is warmer than the morning. As you would expect with an average, the 1 AM temperatures are equal (thin black line).

The days when the dawn is warmer than average for each buoy (red line) show a different pattern. There is less cooling from 1AM to dawn. Cumulus development is stronger when it occurs, driving the temperature down further than on average. In addition, afternoon thunderstorms not only keep the afternoon temperatures down, they also drive evening and night cooling. As a result, when the day is warmer at dawn, the following morning is cooler.

In general, the reverse occurs on the cooler days (blue line). Cooling from 1 AM until dawn is strong. Warming is equally strong. Morning cumulus formation is weak, as is the afternoon thunderstorm foundation. As a result, when the dawn is cooler, temperatures continue to climb during the day, and the following 1AM is warmer than the preceding 1 AM.

Regarding the reduction in incoming solar energy, in a succeeding post called “Cloud Radiation Forcing in the TAO Dataset“, I provided measurements of the difference between the shortwave and longwave radiation effects of tropical clouds, based on the same TAO buoy data. The measurements showed that around noon, when cumulus usually form, the net effect of cloud cover (longwave minus shortwave) was a reduction of half a kilowatt per square metre in net downwelling radiative energy.

In addition to that reduction in downwelling radiation, there is another longer-term effect. This is that we lose not only the direct energy of the solar radiation, but also the subsequent “greenhouse radiation” resulting from the solar radiation. In the TAO buoy dataset, the 24/7 average downwelling solar radiation reaching the surface is about 250 W/m2. Via the poorly-named “greenhouse effect” this results in a 24/7 average downwelling longwave radiation of about 420 w/m2. So for every ten W/m2 of solar we lose through reflection to space, we also lose an additional seventeen W/m2 of the resulting longwave radiation.

This means that if the tropical clouds form one hour earlier or later on average, that reduces or increases net downwelling radiation by about 50 W/m2 on a 24/7 basis. This 100 W/m2 swing in incoming energy, based solely on a ± one-hour variation in tropical cloud onset time, exercises a very strong daily control on the total amount of energy entering the planetary system. This is because most of the sun’s energy enters the climate system in the tropics. As one example, if the tropical clouds form on average at five minutes before eleven AM instead of right at eleven AM, that is a swing of 4 W/m2 on a 24/7 basis, enough to offset the tropical effects of a doubling of CO2 …

Not only that, but the control system is virtually invisible, in that there are few long-term minute-by-minute records of daily cloud onset times. Who would notice a change of half an hour in the average time of cumulus formation? It is only the advent of modern nearly constant recording of variables like downwelling long and shortwave radiation that has let me demonstrate the effect of the cloud onset on tropical temperatures using the TAO buoy dataset.

While writing this here on a cold and foggy night, I realized that I had the data to add greatly to my understanding of this question. Remember that I have made a curious claim. This is that in the tropics, as the day gets warmer, the albedo increases. This means that we should find the same thing on a monthly basis—warmer months should result in a greater albedo, there should be a positive correlation between temperature and albedo. This is in contrast to our usual concept of albedo. We usually think of causation going the other way, of increasing albedo causing a decrease in temperature. This is the basis of the feedback from reduced snow and ice. The warmer it gets, the less the snow and ice albedo. This is a negative correlation between albedo and temperature, albedo going down with increasing temperature. So my theory was that unlike at the poles, in the tropics the albedo should be positively correlated with the temperature. However, I’d never thought of a way to actually demonstrate the strength of that relationship at a global level.

So I took a break from writing to look at the correlation of surface temperature and albedo in the CERES satellite dataset. Here’s that result, hot off of the presses this very evening, science at its most raw:

Figure 3. Correlation between albedo and temperature, as shown by the CERES dataset. Underlying data sources and discussion are here.

Gotta confess, I do love results like that. That is a complete confirmation of my claim that in the tropics, as the temperature increases, the albedo increases. Lots of interesting detail there as well … fascinating.

My conclusion is that Dr. Trenberth’s infamous “missing heat” is missing because it never entered the system. It was reflected away by a slight increase in the average albedo, likely caused by a slight change in the cloud onset time or thickness.

My regards to everyone,

w.

# posted by aaron @ 6:58 AM 8 comments