According to NASA, we have the following exiting news about a new study.

Direct Observations Confirm that Humans are Throwing Earth’s Energy Budget off Balance

Earth is on a budget – an energy budget. Our planet is constantly trying to balance the flow of energy in and out of Earth’s system. But human activities are throwing that off balance, causing our planet to warm in response.

*“Off Balance”* … sounds scary, huh? Plus according to NASA, this isn’t some computer model output, it’s *“direct observations”* …

The paper, sadly paywalled, is entitled “Observational evidence of increasing global radiative forcing” by Kramer et al., hereinafter Kramer2021. It claims that from 2003 through 2018, human actions increased the downwelling longwave infrared radiation from the atmosphere by 0.53 ± 0.11 watts per square meter (W/m2).

So let me see if I can explain the manifold problems with this hot new Kramer2021 study. Let me start by explaining the size of the system we’re talking about, the huge planet-wide heat engine that we call the “climate”. Here is an overview of what happens to the sunlight that warms the planet. The Kramer2021 study has used CERES satellite data, and I am using the same data.

*Figure 1. Solar energy on its path from the top of the atmosphere (TOA) to the surface.*

Note that we are talking about hundreds of watts per square metre of the surface of the earth.

Next, to the same scale, here’s a look at the energy absorbed by the atmosphere that is returned to the surface via downwelling longwave thermal radiation.

*Figure 2. Sources of energy that power the downwelling longwave radiation that is absorbed by the surface. Read it from the bottom up. This is to the same scale as Figure 1.*

So … how much of this downwelling longwave does the new study claim is of human origin during the period 2003 to 2018? See that skinny line to the right of the “300” on the vertical axis? That’s how much the energy is “off balance” …

That’s their claim.

Too big a scale to see how much the study is actually claiming? OK, here’s a detail of Figure 2:

*Figure 3. Detail of Figure 2, to show the size of the amount that we’re claimed to be “off balance”.*

The “whiskers” to the right of the “355” on the vertical axis show the size by which they are claiming that humans have made the downwelling longwave radiation from the atmosphere “off balance” …

So that’s the first problem with their analysis. They are claiming to diagnose an almost invisible change in downwelling longwave, in a very chaotic, noisy, and imperfectly measured system.

The next problem is with the claim that they are using “direct observations” to get their results. Sounds like they’re avoiding the myriad problems with using the global computer models (GCMs) to get results. From the NASA press release linked at the top of the post, we have (emphasis mine):

Climate modelling predicts that human activities are causing the release of greenhouse gases and aerosols that are affecting Earth’s energy budget. Now, a NASA study has confirmed these predictions with

direct observationsfor the first time: radiative forcings are increasing due to human actions, affecting the planet’s energy balance and ultimately causing climate change.

However, what they really mean by* “direct observations” *is that they are using direct observations as inputs to “radiative kernels”. Here’s the abstract to their study, emphasis mine:

ABSTRACTChanges in atmospheric composition, such as increasing greenhouse gases, cause an initial radiative imbalance to the climate system, quantified as the instantaneous radiative forcing. This fundamental metric has not been directly observed globally and previous estimates have come from models. In part, this is because current space-based instruments cannot distinguish the instantaneous radiative forcing from the climate’s radiative response.

We apply radiative kernels to satellite observationsto disentangle these components and find all-sky instantaneous radiative forcing has increased 0.53±0.11 W/m2 from 2003 through 2018, accounting for positive trends in the total planetary radiative imbalance. This increase has been due to a combination of rising concentrations of well-mixed greenhouse gases and recent reductions in aerosol emissions. These results highlight distinct fingerprints of anthropogenic activity in Earth’s changing energy budget, which we find observations can detect within 4 years.

And what are “radiative kernels” when they’re at home? They’re a computer-based analysis of the instantaneous radiative forcing and radiative flux changes due to changes in things like temperature, water vapor, surface albedo and clouds.

And as a result, they can never be any more accurate than the underlying temperature, water vapor, surface albedo, and cloud etc. datasets …

Not only that, but to give an accurate result regarding human influence, the “radiation kernels” have to include * all* of the factors that go into the radiation balance. From Figure 2 above, we can see that these include the amount of solar radiation absorbed by the atmosphere (including the clouds), the sensible heat lost by the surface, the latent heat lost by the surface, and the longwave radiation emitted by the surface.

However, I find no indication that they have included all of the relevant variables.

And in any case, how accurately do we know those values? Not very well. Let me return to that question after we discuss the next problem.

The next problem with their study is that they seem totally unaware of the issues of long-term persistence (LTP). “Long-term persistence” in terms of climate means that today’s climate variables (temperature, rainfall, pressure, etc.) is not totally different from yesterday, this year is somewhat similar to last year, and this decade is not unrelated to the previous decade. Long-term persisitence is unmentioned in their study. Long-term persistence is characterized by something called the “Hurst Exponent”. The value of this exponent ranges from 0.0 to 1.0. Purely random numbers have a Hurst Exponent of 0.5. An increasing Hurst Exponent indicates increasing long-term persistence.

And natural climate variables often show high long-term persistence.

What’s the problem with this? Well, the uncertainty in any statistical analysis goes down as the number of observations increases. The number of observations is usually denoted by capital N. If I throw a die (one of a pair of dice) four times (N=4) and I average the answer, I might get a mean (average) value of 4.2, or of 1.6. But if I throw the die ten thousand times (N=10,000), I’ll get something very near to the true average of 3.5. I just tried it on my computer, and with N=10,000, I got 3.4927.

The problem is that if a dataset has high long-term persistence, it acts like it has fewer observations than it actually has.

To deal with this, we can calculate an “Effective N” for a dataset. This is the number of observations that the dataset acts as though it has.

The general effect of long-term persistence is that it greatly increases the uncertainty of our results. For example, finding longer-term trends in a random normal dataset is unusual. But because of long-term persistence, as the saying goes, “Nature’s style is naturally trendy.” Longer-term trends in natural datasets are the rule, not the exception. As that linked article in Nature magazine says, *“trend tests which fail to consider long-term persistence greatly overstate the statistical significance of observed trends when long-term persistence is present.”*

So let’s take for example the CERES downwelling longwave dataset, the one that they say humans are affecting. It is indeed trending upwards. Looking at the period they studied, it increased by 1.1 W/m2, and they claim about half of that (0.53 W/m2) is from human actions.

And if we ignore long-term persistence, the “p-value” of that trend is 0.0003, which is very small. This means that there is almost no chance that it’s just a random fluctuation. Ignoring long-term persistence, the trend in that data is highly statistically significant.

But that’s calculated with the actual number of datapoints, N = 192. However, once we adjust for long-term correlation, we see that particular dataset has a Hurst Exponent of 0.88, which is very high.

*Figure 4. Hurst Exponent analysis of the 16-year CERES dataset used in the Kramer2021 study. The diagonal line is what we’d see if there were no long-term persistence.*

This means that there is so much long-term persistence that the Effective N is only 3 data points … which in turn means that the apparent trend is not statistically significant at all. It may be nothing more than another of nature’s many natural trends.

**To summarize the problems with the Kragen2021 study:**

• The way that they are isolating the human contribution is to measure every single other variable that affects the downwelling longwave radiation, and subtract them from the total downwelling longwave radiation. The residual, presumably, is the human contribution. To do that, we’d need to measure every single variable that either adds to or removes energy from the atmosphere.

- These include:
- CO2
- all other non-condensing greenhouse gases
- water vapor
- aerosols such as sulfur dioxide and black carbon
- surface temperature
- surface albedo
- solar absorption/reflection by clouds
- solar absorption/reflection by the atmosphere
- solar absorption/reflection by aerosols
- sensible heat loss from the surface
- latent heat loss from the surface by evaporation and sublimation
- sensible heat gain by the surface from the atmosphere
- latent heat gain by the surface from dew
- solar wind
- long-term melting of glacial and sea ice
- long-term changes in oceanic heat content
- transfer of cold water from the atmosphere to the surface via snow, rain, and other forms of precipitation

I do not see evidence that all of these have been accounted for.

• The uncertainty in any and all of these measurements presumably adds “in quadrature”, meaning as the square root of the sum of their squares. Their claim is that the total uncertainty of their result is about a tenth of a watt per square metre (±0.11 W/m2) … I’m sorry, but that is simply not credible. For example, even without accounting for long-term persistence, the uncertainty in the mean of the CERES 2003 – 2018 downwelling LW radiation data is more than half of that, ±0.08 W/m2. And including long-term persistence, the uncertainty of the mean goes up to ±0.24, more than twice their claimed uncertainty.

• And it’s not just that longwave radiation dataset, that’s only one of the many uncertainties involved. Uncertainties are increased in all of the datasets by the existence of long-term persistence. For example, using standard statistics, the uncertainty in the mean of the atmospheric absorption of solar energy is ±0.02 W/m2. But when we adjust for long-term persistence, the uncertainty of the mean of the absorption is twice that, ±0.04 W/m2, which alone is a third of the claimed uncertainty of their “human contribution”, which is said to be 0.53 ± 0.11 W/m2.

• They are claiming that they can measure the human contribution to the nearest hundredth of a W/m2, which is far beyond either the accuracy of the instruments or the uncertainty of the measurements involved. And they claim that they can measure human influence as being about 0.15% of the total downwelling longwave … which means that all of their underlying calculations must be even more accurate than that.

Let me close by saying that I DO think that human-generated increases in CO2 alter the energy balance. That much seems reasonable based on known physics.

However, I don’t think changes in CO2 alter the temperature, because the changes are very small and more importantly, they are counteracted by a host of emergent climate phenomena which act to keep the temperature within narrow bounds. In other words, I think that the authors of Kramer2021 are correct in principle* (humans are increasing the downwelling LW radiation by a small amount)*, but I think that they are very far from substantiating that claim by their chosen method.

Not only that, but the change in downwelling LW radiation from increasing CO2 is trivially small, even over the long term.

*Figure 5. Using the IPCC figures of an increase of 3.5 W/m2 for each doubling of CO2, the yellow/black line shows the increase in total downwelling radiation (longwave + shortwave) since the year 1700 due to increasing CO2. See here for details on the data used.*

As you can see, over the last full three centuries the theoretical increase in downwelling radiation from CO2 is not even four-tenths of one percent of the total.

Now, when I analyze a system, my method is to divide the significant variables into three groups.

**Categories of Variables****First order variables:**these cause variations in the measurement of interest which are greater than 10%. If the measurement of interest is instantaneous downwelling radiation (LW + SW), this would include say day/night solar variation, or the formation of tropical cumulus fields.**Second order variables:**these cause variations in the measurement of interest which are between 1% and 10%. If the measurement of interest is instantaneous downwelling radiation (LW + SW), this would include say nighttime clouds.**Third order variables:**these cause variations in the measurement of interest which are less than 1%. If the measurement of interest is long-term changes in downwelling radiation (LW + SW), this would include say incremental changes in CO2.

In general, I’ve found that third-order variables can be ignored in all but the most detailed of analyses …

TL;DR Version? They claim far greater accuracy and far smaller uncertainty than they can demonstrate.

Here on the hill, I spent most of my day cleaning up and fixing up my old Peavey Classic amplifier, using windex, a dish scrubby sponge, a wire wheel on my grinder to clean the rust off the corner protectors, and Rustoleum Wipe-New to restore the black finish … and then using the amp to do further damage to my eardrums and the general peace of the house.

I’d been wondering why it was hissing so badly, and then duh, I found out that somewhere along the line the ground prong on the plug had broken off. So I cut off and replaced the plug, and it’s good as new.

Keep the music flowing, dear friends. …

w.

**Technical Note:** I describe the method I use to determine “Effective N” in a post called “A Way To Calculate Effective N“. It turns out that I had independently discovered a method previously found by the brilliant Greek hydrologist Demetris Koutsoyiannis, whose work is always worth reading.

**My Usual Note:** To avoid the misunderstandings that bedevil the intarwebs, when you comment please **quote the exact words** you are discussing. This allows us all to understand just who and what you are referring to.