Guest Post by Willis Eschenbach
I got to looking at the numbers for how much energy is exported from the tropics each month by this great heat engine we call the climate. As I discussed in The Magnificent Climate Heat Engine, at all times the tropics are receiving more energy than they are radiating to space. The excess is exported from the tropics to the poles, and radiated to space from there. Ruminating about the numbers, I realized that I could use the satellite data to check the oceanographers data regarding the flow of energy into and out of the ocean. Here’s how.
The actual situation we’re looking at is that what is exported from the tropics is equal to what is radiated back out to space from the poles, plus what goes into storage in the ocean. From the CERES data we know how much is exported from the tropics, and we also know what is radiated to space from the poles. So the difference between what is exported from the tropics and the amount received by the poles must be the change in the ocean heat storage. What was surprising to me, however, was the amount of energy that goes into and out of the ocean every year. Seeing the size of that swing in ocean heat content, I realized that we should be able to use the CERES data as an independent check on the Levitus upper ocean heat content data. Figure 1 shows the results of the analysis:
Figure 1. Sizes of the flows (in 1022 joules/month), and the ocean heat content (OHC) anomaly (in 1022 joules). The top panel shows the total amount of energy exported every month from the tropics, in units of 1022 joules per month . Panel 2 shows the imports of energy into the polar regions. Panel 3 shows the change in storage for that month (exports minus imports). Panel 4 shows the annual changes in ocean heat content (OHC) in units of 1022 joules (NOT joules/month). Panel 4 is calculated from the flows shown in Panel 3.
In the top two panels, we see the amount of heat being exported from the tropics, and the amount imported into the polar regions. The third panel shows the storage, calculated as the exports minus imports. And the bottom panel shows the cumulative sum of the monthly changes in OHC, which gives us the ocean heat content anomaly.
The beauty of climate science is that I’m continually being surprised. I certainly didn’t expect that there would be two cycles per year in the imports and the exports (top two panels), but only one cycle per year in the storage (bottom panel). Nothing more fun than discoveries. I also would never have guessed that the storage cycle would peak in January and bottom out in June … is this related to the earth being closer to the sun in January? Who knows. In any case, it’s the fourth panel that lets us compare satellites and oceanographers. Oh, yeah … as I’m writing this, I still don’t know what I’ll find out.
Now, there’s an oddity about this method for calculating the OHC anomaly. You can’t use it to establish the trend in the OHC data (Panel 4). This is because even a tiny systematic error in one of the three datasets (solar, upwelling longwave, and upwelling reflected solar) results in a very large trend in the ocean heat content. So while the annual changes will be valid in terms of swing and timing, and they can be compared to the adjacent years, the overall trend is meaningless. As a result, all we can see are the relative sizes of the annual swings in OHC data. Because we don’t know what the trend is, I’ve set the trend in the OHC (Fig. 1, bottom panel) to zero.
However, this calculation of OHC from the CERES data is very interesting despite its limitations. We can extract the “climatology” (the average seasonal changes) of the OHC from the data. The CERES data establishes that we should see an annual swing in OHC of about 4e+22 joules … and that is large enough that I figured it should be quite visible in the Levitus ocean heat content data. We can also see the month-by-month changes in the ocean heat content, and compare the various years.
So I went and got the Levitus OHC climatology (quarterly average actual temperature) data so I could compare the Levitus and CERES data (see note below for data sources). The Levitus data is quarterly, so I have averaged the CERES OHC anomaly data shown in Panel 4 above to convert it to quarterly data. Figure 2 shows the comparison of Levitus and CERES OHC climatologies, the average changes from quarter to quarter in the ocean heat content:
Now, I have long been critical of the Levitus data for a couple of reasons. One is the steep rise from 2001 to 2004 (see Fig. 3 below), which coincides with the full introduction of the Argo floats for collecting ocean temperatures. Another reason is that I don’t think that they have the kind of accuracy that they claim, as described here. Next, the large rise that they show at the end of 2001 seems unphysical. Finally, my sense overall is that they are claiming greater changes than are actually occurring.
Figures 2 and 3 show some of those difficulties. One of the problems with the Levitus climatological data (Fig. 2 above) is the very large change in OHC from the first quarter (Q1) to the second quarter (Q2) of the year. In Fig. 2, the Levitus climatology data claims that the OHC changes by 6.9 e+22 joules/quarter. This is a change in storage of 2.3 e+22 joules per month.
But as you can see in Figure 1 (third panel), the CERES data don’t show any monthly change in ten years that is much greater than 1 e+22 J/mo. This casts doubt on the accuracy of the Levitus data.
And things only get worse when we look, not at the climatologies, but at the actual quarter by quarter measured changes in OHC reported by both Levitus and CERES. Figure 3 shows those results
Figure 3. Measured quarterly OHC anomalies, Levitus (oceanographic) and CERES (satellite) data. I have adjusted the trend of the CERES OHC results to match the trend of the Levitus OHC data so that they can be compared. Levitus data is the sum of their anomaly data and the climatology.
Now, here’s the thing … as I mentioned above, we cannot trust the trend of the CERES OHC data. Even a tiny error in the underlying data, while not affecting the year-to-year changes, makes a huge difference in the trend of the results. However, there’s still a lot revealed by the CERES OHC data. Solely in order to be able to compare the CERES and Levitus data, I’ve adjusted the trend in the CERES actual OHC results so that the slope matches that of the Levitus data. Several issues are apparent.
The first issue is that the cycle of the CERES ocean heat content data doesn’t vary much from year to year. There are indeed variations year to year, but the CERES OHC data swings about the same amount from year to year. The Levitus data, on the other hand, shows huge variations from one year to the next.
Here’s the problem. The largest swing per quarter in the Levitus actual data is 7.3 e+22 J/quarter at the end of 2001, or about 2.5 e+22 joules per month max over the time. But where is that energy coming from? The annual average export of energy from the tropics is only about 5 e+22 joules per month … so the Levitus data is saying that somehow, half the average export from the tropics, which is a huge number, has been sequestered in the ocean.
Now while the CERES data is admittedly only accurate to a few W/m2, which is why the CERES calculated OHC trend can’t be trusted, a 50% error in the CERES measurements seems highly unlikely. And that is what the Levitus data is claiming, that somehow half the average tropical energy export was diverted into the ocean at the end of 2001.
My conclusion? Well, my main conclusion is that the satellite data are likely better than the ocean measurements.
My second conclusion is that the jump in the last quarter of 2001 in the Levitus data is not correct.
My final conclusion is that year over year, the variations in the energy flows into and out of the ocean are nowhere near as large as the Levitus data suggests. Where would the energy be coming from?
[UPDATE] There is another graph of interest. This is the graph showing the OHC data in the normal way. This is after removal of the average seasonal swings, leaving only the anomalies.
Figure 4. OHC data from the CERES (gold) and Levitus (blue) datasets. Both datasets have had the seasonal averages subtracted from the data. The trend of the CERES data is nominal, and has been adjusted to the trend of the Levitus data.
Figure 4 is one of the clearest examples of the problem with the Levitus data. The deviations in OHC in the Levitus data represent huge swings in energy … but these claimed swings simply are not visible in the CERES data.
Onwards, the world is a magical place.
METHODS: Unfortunately, the Levitus data doesn’t seem to contain an OHC climatology (averages for the value for each month or quarter of a year). Instead, what they provide is a temperature climatology, in 33 depth levels from 0 to 5,500 metres of depth. This means we have to take a roundabout route to get to the OHC climatology.
First we need the data about the size and thickness of each of the levels at which the variables are measured (see data list below). The Levitus climatology data measures the temperatures at depth levels of 0, 10, 20, 30, 50, 75, 100, 125, 150, metres and so on, with thicker layers as they go deeper, down to 9,000 metres. To get the volume of each layer, you need to average the area of the top and bottom depth levels that define the thickness. Then you multiply that by the thickness of the layer to get the volume. To convert that to tonnes, multiply by 62/60. To get the energy needed to raise the temperature of the layer by 1°C, multiply the tonnage by 4 e+6 joules/tonne of seawater/°C.
Then from the quarterly temperature climatologies, calculate the average temperature of each of the layers as the average of the temperatures at the levels at the top and bottom of each layer. Then calculate the quarterly change in temperature for each of the layers. Multiply those layer-by-layer changes by the energy needed to change each layer by 1°, add up the energy needed for each the layers for their particular temperature change, and that’s the change in OHC over the quarter given the temperature climatology.
DATA: Levitus climatology
CERES data (I note that the CERES folks have added another three years to the dataset, 2010-2013. This is good news, more data is always a good thing … except for the part where I need to redo my various previous analyses … not enough time in the day.)