I should have checked. The number given by Stephens et al. is 239.7 +/- 3.3 W/m^2. That is a 90% confidence interval. It is 1.4%, so I stand corrected.

Reference: G. L. Stephens et al., “An update on Earth’s energy balance in light of the latest global observations”, Nature Geoscience, vol 5, 691-696, DOI: 10.1038/NGEO1580, 2012.

One explanation for this problem may lie in the definition of W/m^2 or WPSM as you call it. We might think of a “m^2” as the measure of solid angle extending from the center of the earth through an area 1 m^2 at the surface of the earth and continuing into space where the CERES and ERBE detectors orbit. If we think of a m^2 as a solid angle, the flux would not vary for geometric reasons involving height, but would change only because of absorption and emission. That would make 1 m^2 equal to 2.464E-14 steradian. The scientists working on this project are probably accustomed to analyzing everything in terms of solid angles and viewing angles.

That doesn’t mean scientists always get things right. IIRC, the raw satellite data shows the Earth emitting more energy than it receives. It should be cooling, not warming. The imbalance apparently is within the expected error of the instruments. The Earth’s radiative imbalance is assessed via the rate of ocean warming, not satellite data. One version of CERES data – EBAG? – has been corrected so that the imbalance agrees with ARGO (+0.5 W/m2).

Nic Lewis got his start on climate sensitivity by questioning Gregory Forster about some details in his papers. By the time the IPCC’s zeroeth order draft for AR5 reported a lower limit for the forcing from aerosols, Nic knew exactly what the implications were, including the smaller errors he found in Gregory’s papers and the re-analysis of Gregory’s work used in AR4. His name is now on two of the most important papers on climate sensitivity, Otto (2013) and Lewis and Curry (2014). However, I suspect Nic didn’t get his start by telling Forster that he was wrong!

On the other hand, I got my start here by trying to tell SOD how he was trying to mislead me. Now I find some of my early comments embarrassing. It is hard to be receptive if you aren’t listening. Fortunately, patient replies from SOD convinced me that we were both interested in exploring what was true (or not) about climate science.

]]>*“I think that uncertainty is less than 1%*

Not that it’s of any major relevance, but I highly doubt that. Where are you getting this, BTW?

]]>Is there some reason they calculate the outgoing radiation at the surface rather than measure it directly?

You can’t measure the outgoing radiation at the surface with a satellite.

The outgoing radiation is 4-100 μm (well we could write 4-50, there are diminishing returns as we go to longer wavelengths) but most of this radiation gets absorbed by the atmosphere.

So any satellite can only measure what the “climate system” radiates out. Of course lots of experiments have verified that the surface radiation follows the Stefan-Boltzmann equation, which is why we still find this equation in all heat transfer textbooks.

To calculate surface emitted radiation we only need to know the surface temperature and the emissivity (varies with temperature – it is a material property).

This is how it is easy to determine that the surface emitted radiation is around 390 W/m^{2} (globally, annually averaged)

And the OLR of the climate system is around 240 W/m^{2} (globally, annually averaged) – as measured by satellites.

Someone made a mistake once, somewhere, in another field (astronomy), therefore you are asking someone here to prove that no one in a different field (climate science) has made an elementary high school mistake in calculating the TOA outgoing longwave radiation (OLR) because they are unfamiliar with the inverse square law?

The actual measurement in the instrument is not some W/m^{2} value. That flux value is derived from the temperature of the detector. Maybe we need to prove to you that they measured that correctly, then calculated the correct value of flux from that? Maybe they had the wrong reference temperature? Maybe they pointed the satellite at the wrong planet? The list of possible mistakes is very long.

Consequently, the chances of someone doing everything right is vanishingly small. In fact, the only way they could possibly get the same value of OLR as the previous ERBE satellites, and the same value as the absorbed solar radiation is clearly that they fixed the answer to match..

Well, it’s been a long day. Forgive my random walk down assumption street.

Do you have some reason to pick on the lack of knowledge of the inverse square law in the field of satellite radiation measurements? There are lots of other formulas in this field, way more complicated.

You should comb through all the papers in the field, and the textbooks – and demonstrate the mistakes. Start with *Clouds and Earths Radiant Energy System-CERES-An Earth Observing System Experiment*, Wielicki et al (1998). Look up all the earlier papers referenced and all the subsequent papers that cite it. When you have finished present your results.

Of course, people always do make mistakes, just they are usually quite small in a field crowded with professionals. For example, check out *Reexamination of the Observed Decadal Variability of the Earth Radiation Budget Using Altitude-Corrected ERBE/ERBS Nonscanner WFOV Data*

Takmeng Wong et al (2006). One of the co-authors is Bruce Wielicki of the earlier paper.

Once you have read 10 papers in this specific field you will start to appreciate that they are professionals. Don’t take my word for it. We are skeptics here – test the ideas. But, alternatively, don’t arrive and confidently assume that the field of climate science is full of charlatans. Test your ideas.

If you don’t have access to these papers I will be happy to send them to you, just email me at scienceofdoom – you know what goes here – gmail.com.

A couple of books I recommend where you might appreciate that there are solid professionals in the field:

– Radiation & Climate, Vardavas & Taylor (2007) – F.W.Taylor is a professor of physics at Oxford University.

– A First Course in Atmospheric Radiation – Grant Petty (2006) – this is much much easier than Vardavas & Taylor and yet, you will see many pages explaining for novices, the inverse square law.

You can see the second reviewed in Find Stuff Out and Book Reviews along with some extracts of an earlier much cited work by Goody and Yung (Atmospheric Radiation: Theoretical Basis) that the excellent Vardavas and Taylor work improves on.

]]>Sure, smart people make mistakes. They also cross check their work and catch their mistakes. Although these numbers are expressed as W/m^2, the fundamental quantity is total radiation out, integrated over the globe and averaged over time, since that must balance total radiation in, to within experimental uncertainty. If they did that calculation while making some silly error in the radius of the surface used, it would not balance and the error would have been caught. So we can be confident that any such error must be small enough to be lost in the measurement uncertainty. I think that uncertainty is less than 1%, so any error in radius must be no more than about 30 km. Given the fact that issues like the radius of the surface are integral to doing the calculations, I doubt that they have overlooked even such a small factor.

]]>The altitude matters 240 wpsm at a height of 2,000 m is four times the total energy if they measure 240 wpsm at a height of 1,000 m

Hi Mike M

I assume they are very smart and well credentialed but people make mistakes, you may remember the Hubble telescope. A simple conversion error to metric.

Apparently the level to calculate the outgoing energy from is 5 k above the surface. TOA is in other sources is 100 k above the surface, though perhaps the 20 k in the very interesting site you posted has its reasons and I like the ellipsoid description of the TOA. I shall do some more reading there.

Nevertheless the statement above is that CERES is measuring the energy and the orbit appears to be at 700 k above the surface. They mention that they calculate the surface temperature but don’t mention a correction to the CERES measurement.

Is there some reason they calculate the outgoing radiation at the surface rather than measure it directly? Put CERES in a balloon at a 5 k altitude perhaps. send it around the world and take an average as a check.

Hi Frank

I may have led you astray. My question is whether they adjusted the measurement of the outgoing radiation that was measured at +700k. Your calculation of 1% loss at 30k is correct but they are measuring it at 700 k and the loss there would be almost 19%

This is a passage from the dissertation above.

“The average for 2009 is 239 W/m². This average includes days, nights and weekends. The average can be converted to the total energy emitted from the climate system over a year like this:

Total energy radiated by the climate system into space in one year = 239 x number of seconds in a year x area of the earth in meters squared

= 239 x 60 x 60 x 24 x 365 x 4 x 3.14 x (6.37 x 10^6 )²

= 239 x 3.15 x 10^7 x 5.10 x 10^14

ETOA= 3.8 x 10^24 J”

WPSM x seconds in a non leap year x 4 x PI x Earths Radius squared.

Look closely and you see he is using the energy measured from

CERES =239 WPSM which is either at TOA +30 or 700k above the surface but he has used the radius at the Earth at the surface (6.37E6).

If WPSM is the measurement at +700 ETOA would be 4.74E+24 J including a quarter day for a leap year. So where it is measured is very important. I will keep checking.

I also agree that the systems are more complex than implied above, there is also convection sending hot air closer to TOA and the GHG’s also screen out some of the Sunlight EM on the way in as it is 50% + IR radiation.

Cheers

]]>So where is the TOA? One pragmatic definition might be above 99% of the atmosphere. Surface pressure is about 1000 m, so only 10% of the atmosphere is above 100 mb (16 km) and 1% of the atmosphere is above 10 mb (30 km). However, water vapor, a major GHG, is not evenly distributed. It’s saturation vapor pressure drops at higher altitudes where it is colder. So less than 10% and 1% of the GHGs in the atmosphere lie above 16 and 30 km.

You can calculate the drop in OLR with altitude using MODTRAN, a program that uses absorption coefficients for all of the GHGs in the atmosphere and temperature and humidity profiles for the atmosphere. Using the US Standard Atmosphere, OLR drops about 1 W/m2 (or 0.4%) between 30 km and 70 km. (Between those altitudes, we go from being above about 99% of the atmosphere to above about 99.99%. So OLR doesn’t change much above 30 km.

http://climatemodels.uchicago.edu/modtran/

You can try other altitudes, but you’ll find the situation is more complicated than implied above. OLR actually increases very slightly traveling upward through the stratosphere because the temperature (and therefore emission by GHGs) rises with altitude there. Nevertheless, most of the reduction in OLR occurs in the troposphere and the change above about 20 or 30 km is tiny.

]]>Sounds like you are assuming that the teams processing the satellite data are composed of idiots. I am pretty sure that assumption is wrong, I’m sue they understand that the flux per square meter depends on the radius of the surface in question and adjust to some conventional radius. Sounds like they use TOA, which they define as 20 km above the surface of the Earth. https://ceres.larc.nasa.gov/faq_main.php#ceres_toa

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