UPDATE #2 June 16 2011: Caroline Katsam has sent us a new paper that has been accepted for publication which addresses the issue of how long lack of warming in the upper ocean should be expected based on the model predictions. The paper is
C. A. Katsman and G. J. van Oldenborgh, 2011: Tracing the upper ocean’s ‘missing heat’. Geophysical Research Letters (in press).
The abstract reads
“Over the period 2003–2010, the upper ocean has not gained any heat, despite the general expectation that the ocean will absorb most of the Earth’s current radiative im- balance. Answering to what extent this heat was transferred to other components of the climate system and by what process(-es) gets to the essence of understanding climate change. Direct heat flux observations are too inaccurate to assess such exchanges. In this study we therefore trace these heat budget variations by analyzing an ensemble of climate model simulations. The analysis reveals that an 8-yr period without upper ocean warming is not exceptional. It is explained by increased radiation to space (45%), largely as a result of El Niño variability on decadal timescales, and by increased ocean warming at larger depths (35%), partly due to a decrease in the strength of the Atlantic meridional overturning circulation. Recently-observed changes in these two large-scale modes of climate variability point to an upcoming resumption of the upward trend in upper ocean heat content.”
“I do agree with you that several years of zero or little radiative imbalance poses some very difficult questions for the modeling community. But I do not think it is grounds for outright rejection of all model results.”
Levitus, S., J.I. Antonov, J. Wang, T.L. Delworth, K.W. Dixon, and A.J. Broccoli, 2001: Anthropogenic warming of Earth’s climate system. Science, 292, 267-269
Pielke Sr., R.A., 2003: Heat storage within the Earth system. Bull. Amer. Meteor. Soc., 84, 331-335.
In a 2008 Climate Science weblog
“The conclusion in Hansen et al. 2005 that the “Earth is now absorbing 0.85 ± Watts per meter squared more energy from the Sun than it is emitting to space” is well supported by their modeling results for the ten years or so ending in 2003.”
With respect to the heating rate, in the 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,
“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/m2 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.”
“Our simulated 1993-2003 heat storage rate was 0.6 W/m2 in the upper 750 m of the ocean.”
He further writes
“The decadal mean planetary energy imbalance, 0.75 W/m2, includes heat storage in the deeper ocean and energy used to melt ice and warm the air and land. 0.85 W/m2 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 value, to calculate the heat change in Joules that should be expected in the upper ocean data from 2003 to the present.
The observed best estimates of the heating and the Hansen et al prediction in Joules in the upper 700m of the ocean are given below:
OBSERVED BEST ESTIMATE OF ACCUMULATION Of JOULES [assuming a baseline of zero at the end of 2002].
2003 ~0 Joules
2004 ~0 Joules
2005 ~0 Joules
2006 ~0 Joules
2007 ~0 Joules
2008 ~0 Joules
2009 ~0 Joules
2010 ~0 Joules
2011 ~0 Joules through May 2011
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] [corrected 6/13/2011 from input from Bob Tilsdale].
2003 ~0.67* 10** 22 Joules
2004 ~1.34* 10** 22 Joules
2005 ~2.01 * 10** 22 Joules
2006 ~2.68 * 10** 22 Joules
2007 ~3.35 * 10** 22 Joules
2008 ~4.02 * 10** 22 Joules
2009 ~4.69 * 10** 22 Joules
2010 ~5.36 * 10** 22 Joules
2011 ~6.03* 10** 22 Joules
2012 ~6.70* 10** 22 Joules
Thus, according to the GISS model predictions, there should have been approximately 5.36 * 10**22 Joules more heat in the upper 700 meters of the global ocean at the end of 2010 than were present at the beginning of 2003.
For the observations to come into agreement with the GISS model prediction by the end of 2012, for example, there would have to be an accumulation 6.7 * 10** 22 Joules of heat over just the next 1 1/2 years. This requires a heating rate over the next 1 1/2 years into the upper 700 meters of the ocean corresponding to a radiative imbalance of ~4 Watts per square meter.