**UPDATE: Decmber 28 2009:** **The source of the descrepancy between the 0.77 Watts per meter squared reported by von Schuckmann et al and the 0.47 Watts per meter squared that I calculated is that my value distributed this heating over the global area [thanks to David Douglas and Robert Knox for solving this decrepancy!]. I have updated the text below as needed. There is the question as to whether the same flux of heat that enters the ocean should be assumed to be the large majority of heating of the climate system or if the same flux of heat occurs over land and in the melting of sea and continental ice.**

In my post Comment On EPA Response To Reviewer Comments On Ocean Heat Content, the EPA presented the paper

von Schuckmann, K., F. Gaillard, and P.-Y. Le Traon (2009), Global hydrographic variability patterns during 2003–2008, J. Geophys. Res., 114, C09007, doi:10.1029/2008JC005237

as refuting the claims that the climate system is not accumulating heat. As I report in this post, the EPA response is in error [thanks to Ron Cram and Leonard Ornstein for encouraging me to write this post]

The EPA reported

“…..(von Schuckmann et al., 2009) indicates the global ocean accumulated (between the surface and 2,000 meter depth) 0.77 (plus or minus 0.11) watts per square meter of heat between 2003 and 2008, which is roughly consistent with the 0.86 (plus or minus 0.12) watts per square meter of heat (between the surface and 750 meter depth) accumulated between 1993 and 2003 as documented in Willis et al. (2004); and Hansen et al. (2005). These studies suggest the ocean has and continues to accumulate heat, contributing to an overall imbalance in the Earth’s energy budget.”

The abstract of the von Schuckmann et al 2009 paper reads

*“Monthly gridded global temperature and salinity fields from the near-surface layer down to 2000 m depth based on Argo measurements are used to analyze large-scale variability patterns on annual to interannual time scales during the years 2003–2008. Previous estimates of global hydrographic fluctuations have been derived using different data sets, partly on the basis of scarce sampling. The substantial advantage of this study includes a detailed summary of global variability patterns based on a single and more uniform database. In the upper 400 m, regions of strong seasonal salinity changes differ from regions of strong seasonal temperature changes, and large amplitudes of seasonal salinity are observed in the upper tropical and subpolar global ocean. Strong interannual and decadal changes superimpose long-term changes at northern midlatitudes. In the subtropical and tropical basin, interannual fluctuations dominate the upper 500 m depth. At southern midlatitudes, hydrographic changes occur on interannual and decadal time scales, while long-term changes are predominantly observed in the salinity field. Global mean heat content and steric height changes are clearly associated with a positive trend during the 6 years of measurements. The global 6-year trend of steric height deduced from in situ measurements explains 40% of the satellite-derived quantities. The global freshwater content does not show a significant trend and is dominated by interannual variability.*

The figure (Figure 11 top) which was presented in their paper to document this heating rate in the ocean from the surface to 2000m is reproduced below.

I have tried to reproduce the linear trend that is plotted on this figure (of 0.77 Watts per meter squared), but cannot reproduce the value (I have requested clarification from von Schuckmann but there, as of yet, has been no reply).

My calculation is presented below, and I welcome e-mails if you can find the source of the discrepancy [or any errors in my calculations]. The units in the above figure are in Joules per meter squared. To convert to total Joules, the value in Joules per meter squared are multiplied by the area of the ocean [3.35 x 10^{8} kilometers squared]. Thus, for example, 1 x 10^{8}Joules per meter squared becomes 3.35 x 10^{22} Joules [0.56 x 10^{22} Joules per year if this heat accumulates over 6 years].

Since, 0.6 Watts per meter squared is equal to 0.98 x 10^{22} Joules per year when the heat is distributed globally (see), 0.56 x 10^{22} Joules per year is equal to 0.34 Watts per meter squared. From the above figure, the change of heat content for the 6 years is estimated as about 1.4 x 10^{8 }Joules per meter squared [4.69 x 10^{22} Joules] which is equal to 0.47 Watts per meter squared. This is 0.30 Watts per meter squared (39%) less than what is presented in the von Schuckmann et al Figure due to how the heating is distributed globally.

In order to further analyze the data, we can estimate the heating rate for each year from the above figure;

**From the von Schuckmann et al Figure 11 (top) of the heat accumulation in the ocean layer 0 to 2000m**

2003 +0.5 x 10^{8 }Joules per meter squared

2004 0.0 x 10^{8 }Joules per meter squared

2005 +0.5 x 10^{8 }Joules per meter squared

2006 0.0 x 10^{8 }Joules per meter squared

2007 +0.4 x 10^{8 } Joules per meter squared

2008 0.0 x 10^{8 } Joules per meter squared

Total over the 6 years is about 1.4 Joules per meter squared which yields **4.69 x 10 ^{22} Joules**.

The task now is to compare with the models. In their paper

Hansen, J., L. Nazarenko, R. Ruedy, Mki. Sato, J. Willis, A. Del Genio, D. Koch, A. Lacis, K. Lo, S. Menon, T. Novakov, Ju. Perlwitz, G. Russell, G.A. Schmidt, and N. Tausnev, 2005: Earth’s energy imbalance: Confirmation and implications. Science, **308**, 1431-1435, doi:10.1126/science.1110252,

they wrote

*“Our climate model, driven mainly by increasing human-made greenhouse gases and aerosols among other forcings, calculates that Earth is now absorbing 0.85±0.15 W/m ^{2} more energy from the Sun than it is emitting to space. This imbalance is confirmed by precise measurements of increasing ocean heat content over the past 10 years.”*

In the response by Jim Hansen to a comment by Christy and Pielke Sr Hansen wrote me with respect to their GISS model predictions that

*“Our simulated 1993-2003 heat storage rate was 0.6 W/m ^{2} in the upper 750 m of the ocean.”*

He further writes

*“The decadal mean planetary energy imbalance, 0.75 W/m ^{2}, includes heat storage in the deeper ocean and energy used to melt ice and warm the air and land. 0.85 W/m^{2} is the imbalance at the end of the decade.”*

Thus, the best estimate value of 0.60 Watts per meter squared given in Hansen et al. can be used as a conservative lower estimate [since it is just for the upper 750m while the von Schuckmann et al analysis includes the depths down to 2000m] to compare with each other.

The observed best estimates of the observed heating and the Hansen et al. prediction in Joules in the upper 700 m of the ocean are given below:

**HANSEN PREDICTION OF THE ACCUMULATION OF JOULES** [ at a rate of 0.60 Watts per meter squared] assuming a baseline of zero at the end of 2002 for the upper 750m of the oceans].

2003 ~0.98 x 10^{22}Joules

2004 ~1.96 x10^{22}Joules

2005 ~2.94 x10^{22}Joules

2006 ~3.92 x10^{22}Joules

2007 ~4.90 x 10^{22}Joules

2008 ~5.88 x10^{22}Joules

2009 ~6.86 x10^{22}Joules

2010 ~7.84 x10^{22}Joules

2011 ~8.82 x 10^{22}Joules

2012 ~9.80 x 10^{22}Joules

Thus, according to the GISS model predictions, there should be approximately 5.88 * 10^{22 }Joules more heat in the upper 700 meters of the global ocean at the end of 2008 than were present at the beginning of 2003.

The von Schuckmann et al 2009 paper, using their value of 0.77 Watts per meter squared **for the entire 2000 depth**, shows an accumulation of 7.2 x 10^{22 } Joules from 2003 to 2008 (a rate of 1.26 x 10^{22 }Joules per year) which is in good agreement with the Hansen prediction.

However, using the rate 0.47 Watts per meter squared diagnosed from the von Schuckmann et al 2009 paper gives an accumulation of 4.69 x 10^{22} Joules. For this estimate to come into agreement with the GISS model prediction by the end of 2012, for example, **there would have to be an accumulation 5.1 x 10 ^{22}Joules of heat over just the next three years**. This requires a heating rate over the next 3 years into the upper 700 meters of the ocean of 1.70 x 10

^{22}Joules per year, which corresponds to a radiative imbalance of ~+1.0 Watts per square meter.

Since von Schuckmann et al examined a deeper layer, the actual heating to compare with the GISS model predictions of heating in the upper 750m would have to be, conservatively, about 10% larger if we split the o.15 Watts per meter squared added heating in the deeper ocean, from melted ice, and input into the land and atmosphere that Jim Hansen listed in his e-mail to me.

There is also another issue. How accurate are the estimates of heating in the earlier period of the von Schuckmann et al analysis? In an e-mail from Josh Willis of JPL, he writes

*“The Agro Science Team continues to improve the accuracy of the float pressure data for the entire historical Argo dataset. As it strives to achieve the array-averaged accuracy of 1-2 db that is necessary for estimates of global sea level and ocean heat content, small but significant revisions in estimates based on Argo should be expected, partiularly in the early years of the array prior to 2005.”*

There is a paper which supports his finding, as well as provides further confidence in the analysis of Josh Willis. It is

Leuliette, E. W., and L. Miller (2009), Closing the sea level rise budget with altimetry, Argo, and GRACE, *Geophys. Res. Lett.*, 36, L04608, doi:10.1029/2008GL036010.

Figure 2 from that paper is reproduced below which shows the close agreement between the Leuliette and Miller analysis and the Willis et al analyses, except for the period prior to 2005 [note: the steric sea level change is that part of sea level change from thermal expansion and salinity changes; globally averaged the salinty changes must be small on this time period].

**This figure also clearly documents that since 2005 there has not been the 0.77 Watts per meter squared heating that was claimed in the EPA Response. Moreover, even the von Schuckmann et al analysis does not support this large of a heating rate. **

**The EPA failed to critically assess their response, and have misled policymakers on the actual rate of global warming.**