Code and figures to quantify the answer to the question “Is ocean heat content is accelerating?” are below. The idea is that ‘acceleration’ is synonymous with the significance of a quadratic term in a regression:
1. Annual OHC data from NODC.
2. Fit a regression model (M1) incorporating linear and periodic terms of period 60 years (to account for Pacific Decadal Oscillation):
M1 = lm(OHC~x+sin(f)+cos(f))
3. Fit another regression model with the addition of a quadratic term,
M2 = lm(OHC~x+sin(f)+cos(f)+I(x^2))
4. Compare the reduction in the regression sum of squares due to the incorporation of the quadratic term, taking into account the loss of degrees of freedom due to autocorrelation (see http://en.wikipedia.org/wiki/F-test for tests of nested models)
The result below shows M1 as a solid line and M2 as a dashed line. The p value for the F test is a marginally significant 0.052 (not significant at the 95% CL) for an improvement in the model due to addition of a quadratic term.
For interest, I appended a value of 5 onto the end of the series, to anticipate the case of a precipitous fall in OHC this year. The result is below, with a non-significant p value of 0.467 for an improvement in the model due to addition of a quadratic term.
So based on these tests, taking into account the oscillation of the PDO and the autocorrelation, the empirical evidence does not strongly support an ‘acceleration’ in OHC and if it continues to decline as it appears to be doing, what support there is will vanish.
The turnkey R script and data as a zip file is here.