Reply By Bob Knox And David Douglas To Questions About Their Research On Climate Etc

With their permission, I have reproduced a Reply posted by Bob Knox and David Douglas on Judy Curry’s post

Where’s the “missing” heat?

I have posted on their excellent paper

R. S. Knox, David H. Douglass 2010: Recent energy balance of Earth  International Journal of Geosciences, 2010, vol. 1, no. 3 (November) – In press doi:10.4236/ijg2010.00000

 in my posts

Research Issues On “The Missing Heat”

My Comment On Robert S. Knox And David H. Douglass – Kevin Trenberth On The Climate Etc Post On “Missing Heat”

I would, of course, be glad to post a Response by John Fasullo.

Reply By Robert S. Knox and David H. Douglass

Fasullo in a recent post has commented on the Knox & Douglass paper.

We appreciate John Fasullo’s comment and we welcome the chance to clarify in our minds several of the issues raised by the substantial recent literature on energy balance, to which John and Dr. Trenberth have contributed much.

In our comments we use the following abbreviations to various papers.

TF = Trenberth and Fasullo (2010) Tracking Earth’s Energy, Science 328 p316-317.

TFK = Trenberth, Fasullo and Kiehl (2009) Earth’s Global Energy Budget, Bull Amer Meteorol Soc 90 p 311-323

FT = Fasullo and Trenberth (2008) The annual cycle of the Energy budget. Part1: Global Mean and Land-Ocean Exchanges, J Climate 21 p2297-2312.

H = Hansen et al. (2005) Earth’s Energy balance: Confirmation and implication,
Science 308 1431-1435.

In TF it is stated that FTOA, the net inward energy flux at the top of the atmosphere, exceeds FOHC, the rate of change of ocean heat content per unit area, by 1.2 W/m2, raising the question “where exactly does the energy go?” In a steady state, and because of conservation of energy, FOHC and FTOA should be equal to one another except for a small geothermal component Fgeo. For Earth in energy balance, FOHC should be zero and FTOA nearly zero (actually –Fgeo) .

We summarize some points in TF.

(a) The rate at which energy is stored in Earth’s climate system may be well approximated by FOHC (Pielke, Physics Today 2008); TF show a plot of this quantity, with values ranging from 0.5 W/m2 (year 2000) to 0.3 W/m2 (late 2009). No error bars are given.

(b) For the rate of energy input, TF claim a “post-2000” radiative imbalance at the top of the atmosphere FTOA = 0.9 ± 0.5 W/m2. They show a “heavily smoothed” FTOA curve with values ranging from 0.5 W/m2 (year 2000) to 1.5 W/m2 (late 2009), passing through the value 0.9 in late 2004.

(c) Accordingly, FTOA – FOHC (the claimed rate of production of missing energy) ranges from 0.0 to 1.0 W/m2 over the 2000-10 decade, rising sharply at 2005, according to the TF plot.

The provenance of the TF value FTOA = 0.9 ± 0.5 W/m2 is now explored. The top-of-atmosphere value that they consider “probably [the] most accurately determined” is that of climate models given in H, which is used to scale the measured values to an “acceptable but imposed” 0.9 W/m2. This adjustment is described on page 313 of TFK. While the modeled value according to H has an error bar of ±0.15 W/m2, TF quote the error as ±0.50 W/m2, as derived from their extensive analyses (FT, TFK) of CERES data. These analyses involve obtaining the difference between numbers whose magnitudes are hundreds of W/m2 and whose uncertainties are of the order of several W/m2. One must know the uncertainties in the uncertainties to evaluate the accuracy of the FTOA. We note that in the development of the “imposed” 0.9 estimate in TFK many empirical adjustments were made. For example, one adjustment is made in the longwave component having an “upper error bound” of 1.5 W/m2, in reducing an original quoted 6.4 W/m2 imbalance from CERES data to the imposed value 0.9. The uncertainties in FTOA CERES values alone are estimated to be 2σ = 4.2 W/m2 [N. Loeb et al., J. Climate 22 (2009) 748].

Considering that these calculations on which the TF analysis is based involve an explicit matching to the estimate of H, one cannot possibly regard FTOA = 0.9 W/m2 as a purely empirical result without assigning error bars so large that the “missing energy” is lost in them. This is the basis of our opinion that missing energy is most likely an artifact due to the acceptance, or imposition, of the modeled value FTOA = 0.9 W/m2.

Robert S. Knox
David H. Douglass

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