Earths Vitality Imbalance – Watts Up With That?

Guest Post by Willis Eschenbach

I see that there’s a new post up on WUWT claiming that eeevil humans are responsible for the increase in earth’s energy imbalance, which is denoted as ∆EEI in their paper. (The delta, “∆”, means “change in”.) The underlying paper discussed in the post is entitled Anthropogenic forcing and response yield observed positive trend in Earth’s energy imbalance

What do they base this claim of anthropogenic forcing on? Curiously, it’s not the usual claim that it’s due to CO2 absorbing more longwave. Instead, according to their press release, the cause is that:

…we are receiving the same amount of sunlight but reflecting back less, because increased greenhouse gases cause cloud cover changes, less aerosols in the air to reflect sunlight — that is, cleaner air over the U.S. and Europe — and sea-ice decreases.”

I’ve NEVER heard the claim that increased greenhouse gases cause “cloud changes”. How would they possibly know that?

Well, the same way they claim to know everything in their paper—haruspicy, except they use computer models instead of animals. They examine the entrails of climate models, and they compare them to the CERES and other satellite datasets. Color me unimpressed.

In any case, let’s take a closer look at their claims. They are correct that the CERES satellite dataset does indeed show an increasing imbalance. We can start by looking at the relative size of the imbalance. Figure 1 shows the actual size of the changes in incoming and outgoing energy, the two energy fluxes that are compared to give us the changes in Earth’s Energy Imbalance (∆EEI).

Figure 1. The earth receives and radiates about 240 watts per square meter (W/m2)on a globally averaged 24/7 basis.

As you can see, the change is quite small. It’s far less than one percent of the fluxes themselves.


So … given the tiny size of the imbalance compared to the underlying energy fluxes, can the CERES dataset even be used for this question? As you might imagine, this question has been studied. From here we find:

However, the absolute accuracy requirement necessary to quantify Earth’s energy imbalance (EEI) is daunting. The EEI is a small residual of TOA flux terms on the order of 340 W m−2. EEI ranges between 0.5 and 1 W m−2 (von Schuckmann et al. 2016), roughly 0.15% of the total incoming and outgoing radiation at the TOA.

Given that the absolute uncertainty in solar irradiance alone is 0.13 W m−2 (Kopp and Lean 2011), constraining EEI to 50% of its mean (~0.25 W m−2) requires that the observed total outgoing radiation is known to be 0.2 W m−2, or 0.06%. The actual uncertainty for CERES resulting from calibration alone is 1% SW and 0.75% LW radiation [one standard deviation (1σ)], which corresponds to 2 W m−2, or 0.6% of the total TOA outgoing radiation. In addition, there are uncertainties resulting from radiance-to-flux conversion and time interpolation.

With the most recent CERES edition-4 instrument calibration improvements, the net imbalance from the standard CERES data products is approximately 4.3 W m−2, much larger than the expected EEI. This imbalance is problematic in applications that use ERB data for climate model evaluation, estimations of Earth’s annual global mean energy budget, and studies that infer meridional heat transports.

So that is the uncertainty in the imbalance … ± 4.3 W/m2. Makes determining the top-of-atmosphere (TOA) energy imbalance somewhat problematic, given that it is less than 1 W/m2 …

Then there’s the question of drift. Over time, satellites shift slightly in their orbits, instruments age, and reported values drift slowly over time. Basically, the authors of the paper just shine this on, in the following fashion:

Although there is excellent agreement between the individual satellites CERES derives its data from, there is, however, the potential for systematic errors associated with the observed trend due to instrument drift. We attach an estimate of 0.20 Wm−2decade−1 (assuming a normal distribution) to CERES trends, based on best realistic appraisals of observational uncertainty (N. Loeb, CERES Science Project Lead, personal communication)

Call me skeptical, but I find that far less than satisfying … seems to me that the CERES dataset is not at all fit for looking for the purpose of diagnosing trends of less than half a W/m2 per decade in the residual difference of two large values.


Setting that large uncertainty aside, let’s look at the two datasets that make up the EEI. These are the top-of-atmosphere (TOA) outgoing longwave and incoming solar radiation. I often use “breakpoint analysis” to investigate what is going on. There’s a description of the breakpoint analysis functions that I use here. Figure 2 shows the breakpoint analysis of the outgoing longwave.

Figure 2. Breakpoint analysis, TOA longwave radiation. Blue lines show individual trends of sections of the data, yellow line shows the overall trend.

Now, this is interesting. Outgoing longwave runs basically level up until about 2015 (plus or minus about half a year), when there is a shift upwards combined with a rapidly increasing trend.

Why? I can’t guarantee that nobody knows … but that is certainly my belief. We can speculate, but cause and effect in the climate system are like sand in your hands …

How about the incoming solar? Figure 3 shows that result.

Figure 3. Breakpoint analysis, TOA longwave radiation. Blue lines show individual trends of sections of the data, yellow line shows the overall trend.

This one is a bit more complex. Initially, incoming solar was increasing rapidly. Then it went level, followed by an upwards jump around 2015 (the same time as the jump in the longwave).

Why would the solar and the longwave fluxes both have breakpoints at the start of 2015? It may be related to the large 2015-2016 El Nino/La Nina … or it may not be related, given that there are more Nino/Nina alternations during the period of record, and given that the El Nino peak is not until the very end of 2015. It may be due to a change in instrumentation. Again, a very elusive question.

We can take a couple of other kinds of looks at the energy imbalance. First, here’s a graph showing both incoming and outgoing energy, along with LOWESS smooths of the two datasets.

Figure 4. Same datasets as in Figure 1 but at a different scale, including LOWESS smooths of both datasets.

This is curious. At times the incoming and outgoing radiation fluxes move in harmony, and at other times they move in opposition. In particular, they move in harmony after the breakpoints in 2015. At a minimum, we can say that we are looking at some complex processes in both cases …

Finally, here’s the difference between the LOWESS smooths, which give the actual changes in the TOA earth energy imbalance (∆EEI). Figure 5 shows those changes.

Figure 5. Earth’s Energy Imbalance, March 2000 – February 2021

Now, this is most interesting. The imbalance starts out at about 0.4 W/m2. Shortly thereafter, it drops to half of that amount. It then goes up, down, and back up to 1.2 W/m2 … before rapidly dropping all the way back to 0.2 W/m2. Then it jumps all the way back up to 1.2 W/m2, wanders around for a bit, goes up to a peak at 1.4 W/m2 … and then drops all the way down to about 0.4 W/m2. So it ends up right about where it started.

I’m sorry, but anyone claiming to see a “human fingerprint” in Figure 5 has curious fingers.

Let me close with a map showing the complexity of the overall energy imbalance.

Figure 6. Energy imbalance at the top of the atmosphere, on a 1°latitude by 1° longitude basis.

Some things of note. The numbers involved are very large. In the tropics, there is much more solar energy entering the system than longwave energy leaving the system. The opposite is true near the poles, where far less solar energy enters the system than longwave energy leaving the system. This is an indication of the “advection”, the huge constantly ongoing horizontal movement of sensible and latent heat from the tropics to the poles. In addition, the ocean generally receives more solar energy than it loses in longwave, and the reverse is true for the land. This difference is visible, for example, around the Mediterranean.

Me, I find it highly unlikely that our instruments can determine the overall total of that to the nearest tenth of a watt per square meter … yes, that’s the answer we get, but the slightest error, the slightest drift in the system, the slightest shift in the line of zero imbalance, and we’d be out by much more than the imbalance itself, much less the even smaller change in the imbalance.

My best regards to everyone,


Nota Bene: PLEASE quote the exact words that you are discussing. This makes it clear who and what you are talking about, which avoids much misunderstanding.


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