In a discussion concerning Kevin Trenberth’s ‘missing heat’ on John Cook’s sceptical science blog, the following comment was posted by Péter Berényi:
Berényi Péter at 10:48 AM on 22 April, 2010
Well, I think I have found the solution. OHC reconstructions before mid 2003 are simply wrong.
Otherwise satellite TOA energy imbalance measurements have low accuracy but reasonable precision while ARGO OHC measurements are just the opposite.
Therefore I have calculated the integral of CERES FLASHFlux net TOA radiation imbalance between the fourth quarter of 2003 and third quarter of 2009. The linear component of this integral is arbitrary due to low precision. So I have calculated a least square fit linear approximation to the difference of the integral above and the NODC OHC reconstruction for the same period.
It gives the correct offset for TOA net radiation imbalance. With this correction we get the graph below:
The match is pretty good. I think the fluctuations of OHC around the TOA energy accumulation curve are not real, it’s just measurement noise.
Thermal energy content of the climate system has decreased in this 6 years long period at a 0.19 × 1022 J/year rate. It corresponds to a -118 mW m-2 radiative imbalance at TOA.
CERES FLASHFlux only goes back to 2000. If I take all ten years and apply the same procedure it looks like this:
The fit is awful because of the huge step-like change of OHC in early 2003 and also the high noise level before. I guess these features are measurement errors due to changing coverage & instrumentation.
The dimension is 1022 J for both columns, offsets arbitrary, slope of TOA radiation imbalance as well (being the temporal integral of a function with offset unknown). Time resolution is three months.
Net TOA flux should be very close to proportional to the time derivative of OHC, because there is no other heat reservoir in the climate system with comparable storage capacity. Rapid large scale (back & forth) heat exchange between the upper 700 m of oceans and the abyss has no know mechanism, turnover time being several millenia.
If climate system heat content is calculated from net TOA fluxes, only the second derivative is measured by CERES with reasonable accuracy, therefore heat content history has a free additive linear term.
With OHC, on the other hand, the temporal inegral itself is measured. What I did was to choose the free term for best fit.
It can be done for the last six years, but not before first half of 2003. This is the same period when ARGO float deployment was still at an early stage with poor global coverage and rather few floats compared to the target of 3000. At the same time older systems were already phased out almost completely.
The systematic error is large and unknown. Net flux at TOA is estimated to be 2 ± 5 W m-2, i.e. even the sign is doubtful. In this sense TOA flux is not measured at all by CERES.
However, interannual variation is much better constrained.
The large difference between figures in #60 & #62 comes from OHC. The transition around 2003 from MBT/XBT stuff to ARGO has a huge intercalibration problem. That is how the “missing heat” was produced.
If the unknown offset of CERES FLASHFlux is aligned to the early 21th century OHC data, one gets a positive slope but poor fit with much missing thermal energy by the end of this decade. On the other hand, if it is done the other way around and FLASHFlux is aligned to the late part of OHC, the fit is excellent except before mid 2003. In this case we do not have any recent “missing heat”, but excess heat before 2003.
My guess is the thermal energy was there, in the upper 700 m of oceans, just was not measured properly (e.g. in southern Pacific). In this case one does not have to invent mysterious processes transferring heat into the abyss directly through a 700 m deep cooling layer. What is more, this process would only carry heat, but not dissolved carbon dioxide. After all CO2 deep mixing is supposed to be extremely slow.
So far so good. However, we still have a problem. Not with measurement, but with theory. OHC and net TOA flux measurements can be made consistent, but at a price. We have a negative energy balance for the last six years. The climate system is not gaining energy, but losing it. A -118 mW m-2 rate may not sound much, but is enough to bring havoc to standard greenhouse theory.
It is about the decrease in TSI (Total Solar Irradiance) due to weak and late cycle 24.
But wait, CO2 has increased from 375 ppmv to 389 ppmv between 2003 & 2010. The change in radiative forcing during this period is about 5% of a CO2 doubling. Effective temperature of Earth as seen from space should have decreased by 0.15 °C if climate sensitivity is 3 °C for carbon dioxide doubling as claimed. It is equivalent to a positive energy imbalance of 560 mW m-2 at TOA, which is not seen.