Accuracy, Precision, and One Watt per Square Metre

Guest Post by Willis Eschenbach

I’ve been investigating one of my favorite datasets in the last few days, the CERES satellite-based top-of-atmosphere (TOA) radiation dataset. In particular, I’ve taken month-by-month global and hemispheric averages of the data. The dataset consists of observations of three variables—downwelling solar radiation, upwelling longwave (infrared) radiation, and upwelling shortwave radiation (reflected sunlight). From these I derive a further dataset. This is the top-of-atmosphere (TOA) imbalance. It is calculated as downwelling solar minus upwelling (reflected) solar minus upwelling longwave. That gives a fascinating look at the overall radiation picture.

I got to thinking about this because of a curious claim in a recent paper published in Nature Climate Change entitled Model-based evidence of deep-ocean heat uptake during surface-temperature hiatus periods (paywalled). I did love the whole concept of “model-based evidence”, but that wasn’t what caught my eye. It was this statement (emphasis mine):

There have been decades, such as 2000–2009, when the observed globally averaged surface-temperature time series shows little increase or even a slightly negative trend (a hiatus period). However, the observed energy imbalance at the top-of-atmosphere for this recent decade indicates that a net energy flux into the climate system of about 1 W m−2 (refs 2, 3) should be producing warming somewhere in the system (refs 4, 5). Here we analyse twenty-first-century climate-model simulations that maintain a consistent radiative imbalance at the top-of-atmosphere of about 1 W m−2 as observed for the past decade. [References are listed at the bottom of this post.]

Anyhow, here’s some news regarding that claim of a consistent TOA imbalance, from the CERES satellite dataset:

Figure 1. CERES satellite-measured top-of-atmosphere (TOA) radiation levels, starting in January 2001. Numbers on the horizontal axis are months. Shown are the solar energy entering the system (red line), solar energy leaving the system (dark blue line) and longwave (infrared) energy leaving the system (light blue line). The overall monthly imbalance at the TOA is shown at the bottom in purple. The 12-month running average for each variable is shown as a thin line. Curiously, the variations in upwelling longwave are about 6 months out of phase with the downwelling radiation. All radiation values are positive. TOA Imbalance is solar less reflected solar less outgoing longwave, i.e. inflow less outflow. Twelve-month averages vary too little for the changes to be visible at this scale. 

Now, there are a number of things of interest in this chart. The first is the fact that while the seasonal variations are fairly large, tens of watts per square metre, the annual variations are so small. At this scale we can hardly see them. So let’s expand the scale, and take a more close-up look at just the variations in the overall TOA energy imbalance (purple line at bottom of Figure 1). Figure 2 shows that result.

Figure 2. Closeup of the overall energy imbalance. Horizontal scale is months. Narrow line shows running centered 12-month averages of the TOA imbalance data. All radiation values are positive. TOA Imbalance is solar less reflected solar less outgoing longwave, i.e. inflow less outflow.

Here, we can begin to see the small variations in the 12-month running average. However, the average itself is around five watts per square metre … not good. That much out of balance is not credible.

This shows the difference between precision and accuracy. You see that the measurements are obviously quite precise—the 12-month running average only varies by about three-quarters of a degree over the whole period.

However, in absolute terms they’re not that accurate, we know that because they don’t balance … and it’s very doubtful that the earth is out of balance by five watts per square metre. That’s a very large amount, it would be noticed.

Now, I’ve previously discussed how James Hansen deals with this problem. He says:

The precision achieved by the most advanced generation of radiation budget satellites is indicated by the planetary energy imbalance measured by the ongoing CERES (Clouds and the Earth’s Radiant Energy System) instrument (Loeb et al., 2009), which finds a measured 5-year-mean imbalance of 6.5 W/m2 (Loeb et al., 2009). Because this result is implausible, instrumentation calibration factors were introduced to reduce the imbalance to the imbalance suggested by climate models, 0.85 W/m2 (Loeb et al., 2009).

As a result, Hansen used the Levitus data rather than the CERES data to support the claims of a ~ one watt per square metre radiation imbalance. However, all is not lost. The precision of the CERES data very good. In Figure 2 we can see, for example, how one year’s TOA radiation imbalance  is different from another. So let’s expand the scale once again, and take an even closer look at just the 12-month running averages, for all four of the radiation measurements shown in Figure 1.

Figure 3. An even closer look, this time at just the tiny variations in the 12-month running averages of the CERES data as shown in Figure 1. All radiation values are positive. TOA Imbalance is solar less reflected solar less outgoing longwave.

Now we’re getting somewhere.

The first thing I noticed is the precision of the measurements of the downwelling solar radiation (red line). As you might expect, the sun is quite stable, it doesn’t vary much compared to the variations in reflected solar and upwelling longwave radiation. And the observations reflect that faithfully. So it seems clear that their instruments for measuring  radiation are quite precise.

Next, I noticed that the change in the imbalance (purple) is more related to the change in reflected solar (dark blue) than to the variations in upwelling longwave. I’ve highlighted the reflected solar (dark blue) in the graph above. This is confirmed by the correlation. The R^2 between TOA imbalance and reflected solar is 0.67; but between TOA imbalance and upwelling longwave, R^2 is only 0.07.

This seems like an important finding, that the imbalance is mostly albedo related, and that because of variation in the albedo, the variations in the reflected solar energy were on the order of ± three tenths of a watt within a few years.

Finally, I am once again surprised by the overall stability of the system. Twelve-month averages of all three of the variables (the TOA balance, reflected solar, and upwelling longwave) are all stable to within about ± 0.3 watts per square metre. Out of a total of 340 watts per square metre going each way, that’s plus or minus a tenth of one percent … I call that extremely stable. Yes, with a longer sample size we’d likely see greater swings, but still, that’s very stable.

And that brings me back to the quotation from the paper where I started this post. They say that there is

… a consistent radiative imbalance at the top-of-atmosphere of about 1 W m−2 as observed for the past decade …

Now, according to their references [2] and [3], this claim is based on the idea that the excess energy is being soaked up by the ocean. And this claim has been repeated widely. I’ve discussed these claims here. The claims are all based on the Levitus ocean temperature data, which shows increasing heat in the ocean. Here’s my graph of the annual forcing needed to give the changes shown by Levitus in ocean heat content:

Figure 4. Annual forcing in watts per square metre needed to account for the energy going into or coming out of the ocean in the Levitus data. Data is for the top 2,000 metres of water. Note that despite average values being used, both by Hansen and also in the study under discussion, neither the mean nor the trend are statistically significant. Further discussion here.

For current purposes, let me point out that Figure 4 shows that in order for the ocean to gain or lose the energy that is shown in the Levitus data, it requires a very large year to year change in the amount of energy entering the ocean. That energy has to come from somewhere, and it has to go to somewhere when it leaves the ocean. Since the solar input is about constant over the period, that energy has to be coming from a change in either the upwelling longwave or the reflected solar … and we have precise (although perhaps inaccurate) data from CERES on those. Fortunately, the lack of accuracy doesn’t matter in this case, because we’re interested in the year to year changes. For that all we need is precision, and the CERES data is very precise.

So … let me compare the forcing shown by the Levitus ocean heat content in Figure 4, with the CERES data. Figure 5 shows the difference.

Figure 5. Forcing given by the Levitus ocean heat content data, compared to the CERES data shown in Figure 3.

As you can see, they have a couple of big problems with their claims of a consistent 1 W/m2 imbalance over the last decade.

First, it is contradicted by the very data that they claim establishes it. There is nothing “consistent” about what is shown by the Levitus data, unless you take a long-term average.

The second problem is with the Levitus data itself … where is the energy coming from or going to? While the CERES TOA imbalance is not accurate, it is very precise, and it would certainly show a fluctuation of the magnitude shown in the Levitus data. If that much energy were actually entering or leaving the ocean, the CERES satellite would surely have picked it up … so where is it?

I’ve discussed what I see as unrealistic error bars in the Levitus data here. My current comparison of Levitus with the CERES data does nothing to change my previous conclusion—the precision of the Levitus data is greatly overestimated.

Finally, the idea that we have sufficiently accurate, precise, and complete observations to determine the TOA imbalance to be e.g. 0.85 watts per square meter is … well, I’ll call it premature and mathematically optimistic. We simply do not have the data to determine the Earth’s energy balance to an accuracy of ± one watt per square metre, either from the ocean or from the satellites.

Best regards to all,

w.

MY OTHER POSTS ON THE CERES DATA:

Observations on CERES TOA forcing versus temperature

Time Lags In The Climate System

A Demonstration of Negative Climate Sensitivity

DATA:

CERES data: Unfortunately, when I go to verify it’s still available, I get:

The Atmospheric Science Data Center recently completed a site wide redesign.  

It is possible that the page you are looking for is being transitioned.  Please try back later.

If the page you have requested is still not available, it may have been renamed or deleted.

It is recommended that you use the Search interface on the ASDC Web Site to find the information you were looking for.

Since I got there via the aforementioned “Search interface on the ASDC Web Site”, I fear we’re temporarily out of luck.

[UPDATED TO ADD] I’ve collated the global and hemispheric monthly averages from R into a “.csv” (comma separated values) Excel file available here.

Levitus data

REFERENCES FOR THE NATURE CLIMATE CHANGE ARTICLE:

2. Hansen, J. et al. Earth’s energy imbalance: Confirmation and implications.

Science 308, 14311435 (2005).

3. Trenberth, K. E., Fasullo, J. T. & Kiehl, J. Earth’s global energy budget.

Bull. Am. Meteorol. Soc. 90, 311323 (2009).

4. Trenberth, K. E. An imperative for climate change planning: Tracking Earth’s

global energy. Curr. Opin. Environ. Sustain. 1, 1927 (2009).

5. Trenberth, K. E. & Fasullo, J. T. Tracking Earth’s energy. Science 328,

316317 (2010).