Not surprisingly, Watts up With That (WUWT) has a post mocking John Cook’s recent quote that the increase in energy associated anthropogenic global warming (AGW) is the same as 4 Hiroshima bombs per second. As I showed in yesterdays’s post, this comparison is actually quite accurate.
So, what does Anthony say in this post? He quotes Willis Eschenbach who apparently has said
400,000 Hiroshima bombs per day works out to 0.6 watts per square metre … in other words, Hansen wants us to be very afraid because of a claimed imbalance of six tenths of a watt per square metre in a system where the downwelling radiation is half a kilowatt per square metre … we cannot even measure the radiation to that kind of accuracy.
The Hansen mentioned is James Hansen (who initially made the comparison with atom bombs) and, indeed, the energy imbalance is equivalent to 0.6 Wm-2. That’s what everyone is concerned about. So Willis has calculated the same energy excess as is observed (good for him) but decided it’s insignificant. Really? All these scientists are just being melodramatic? Just because Willis thinks this is a small number doesn’t mean that it isn’t going to lead to significant changes in our climate.
Anthony then goes on to say
So imagine the output of a 0.6 watt light bulb, 1/100th the power of a common household 60 watt light bulb.
Could you even see it?
So I think this analogy is wrong. The correct analogy would be a house full of 60 Watt lightbulbs, but in which 0.6 J of energy per square metre per second nevers leaves the house. So a typical house has a footprint of about 200 m-2. This means the house would gain 120 J of energy every second. If the house has a volume of 2000m-2, then the mass of the air in the house is about 2300 kg. From what I can find, the specific heat capacity of air is 1000 J kg-1 K-1. The temperature of the air in the house would therefore increase by 5.22 x 10-5 K every second. Sounds like a tiny amount doesn’t it? Well, in fact, this means the temperature in the house would increase by 4.5 degrees per day. Unless my calculation is wrong, the house would reach boiling point within a month. Maybe Anthony thinks this is insignificant. Personally, I would disagree.
Anthony then includes the figure below and says
Note the figure on the Earth that I highlighted in yellow: Surface imbalance 0.6 ± 17 Wm-2
Energy balance figure from Stephens et al. (2011)
So, Anthony highlights the surface energy imbalance and suggests that such a large uncertainty (2 orders of magnitude greater than the estimated imbalance) means that we can’t even be sure that such an imbalance exists or that it will lead to anything in the future. Well, that isn’t the energy imbalance that James Hansen or John Cook are talking about. They’re talking about the top-of-the-atmosphere (TOA) energy imbalance. This is the energy imbalance that tells us how much excess energy is entering the climate system. Have a look at the top of the figure above and you will see “TOA imbalance 0.6 +- 0.4” Wm-2. Okay, so the error is still quite large but indicates that there is indeed a positive energy imbalance. So, Anthony’s argument that the large uncertainty in this imbalance means we can’t make claims about the future is based on highlighting the incorrect energy imbalance.
Anyway, Anthony thinks that the analogy with atom bombs suggests that the energy imbalance is insignificant simply because the number associated with this imbalance happens to be a small number. However, extending his lightbulb analogy suggests that he would be happy living in a house that reached boiling point in less than a month. He then goes on to say that on top of this, the energy imbalance is so uncertain that we shouldn’t be basing anything on this estimate, but bases this on the incorrect energy imbalance (surface rather than TOA). Don’t really know what else to say? I suspect those who read this can draw their own conclusions.
Wotts Up With That Blog 
I was going to add that the errors shown in the figure above are not (I believe) measurement errors, but indicators of variability. ENSO events can cause rapid rises in surface temperature while volcanoes can act to produce rapid drops in surface temperature. Hence, the surface energy imbalance can vary considerably. Similarly for the TOA imbalance; the long-term mean is around 0.6 Wm-2 but variations in surface temperature and solar irradiance can produce variations around this mean. So, these errors don't indicate that climate scientists can't measure them accurately, they simply indicate that the values can vary. If I'm wrong about this, happy to be corrected by others who know more than me.
For what it is worth, the given surface imbalance uncertainty is just the rounded square root of the squares of the uncertainties of each individual component. Likewise, the TOA imbalance uncertainty is the rounded square root of the squares of the uncertainties of outgoing short wave and long wave radiation. As such, they represent measurement or estimation errors on individual components.
That being said, the surface imbalance is far more tightly constrained by measurements of ocean heat content. The recent (post 1996 to avoid the effects of Mount Pinatubo) 0-2000 meter increase in ocean heat content reflects a 0.5 W/m^2 mean forcing with approx a 1 W/m^2 standard error. Of that error, a significant portion will be due to fluctuations in the imbalance due to ENSO and other natural variations. One standard error of measurement error is about 0.7 W/m^2 over that period, but as you have noted in a prior blog, that is the error on the trend in OHC increase, and hence on the average annual forcing is much smaller.
I consider it a significant weakness of Steven’s et al that they do not use OHC to contrain the uncertainty of the energy imbalance terms.
Okay, so the errors are simply the errors of each component added in quadrature. However, if the errors in each component is determined by the standard deviation of the measurements over the time interval considered, doesn’t that still suggest that it incorporates the variability as well as any measurement error (unless the time interval happens to be short).
I agree, that the OHC can provide a much better estimate of the uncertainties in the energy imbalance.
Stevens et al say:
I take it from this that the error represent measurement errors (including calibration errors) rather than inter-annual variability. I assume the same is also true of the surface flux. Given that the reported values are a mean over an eleven year interval, my intuition is that it would be inappropriate to include the variability within that period in the error estimate. This is different from the case where you show an annual value but must indicate the range of variation of annual values. Given that I am neither a mathematician nor a scientist, however, my intuition may be way of on this point.
On another point, I must withdraw my comment about Stevens et al on the OHC. They write:
Clearly they are aware of the more tightly constrained imbalance from OHC, and are merely trying to quantify the uncertainty of alternate means of estimating the TOA and surface imbalances. Given that, it is a significant misrepresentation of the paper to treat, as Watts does, the 0.6 +/-17 W/m^2 as representing the actual uncertainty as reported in the paper.
Thanks, that seems fairly clear. I assumed that Anthony using 0.6 +- 17 Wm-2 was him simply not realising which flux he should be using (surface rather than TOA).
A bit more than that. He could have chosen from the paper, Surface (0.6 +/-17), TOA as measured with satellites (0.6 +/-4), or TOA as measured from OHC (0.6 +/-0.4). The last is the one he should have used. The first allows a better spin for his cause.
Yes, it does appear that he has chosen the one with the largest error so as to make the measurements appear somewhat ridiculous even though it’s clear that OHC data constrains it much better than his choice indicates.
Giving Watts the benefit of the doubt, he is probably merely misinformed in this case due to:
1) Not understanding the theory of the greenhouse effect, and therefore thinking the surface imbalance is the important quantity; and
2) Not having read Stevens et al, and so not knowing about the OHC data.
Yes, to be fair I had indeed assumed that he was simply mistaken, rather than choosing to make the wrong comparison and to make a big deal of the errors despite knowing the caveats.
On the other hand, when it does appear to be so disparate, he doesn’t seem to stop and consider that maybe he’s misunderstood what he is evaluating.