An objective analysis of the evidence for global warming suggests little if any anthropogenic effect, consistent with a direct radiative effect from increased CO2. It is also obvious that global temperature and ocean heat content should be related, so it’s somewhat surprising to see OHC rising so fast around 2002-3 when ocean temperature is relatively stable (upper line below).
Here, out-of-sample tests are used to test the robustness of the linear regression models of natural variation in global temperature. Previous models were developed on the whole data set. Here we develop them on partial data sets and examine how well they predict temperatures on the other part. These are also called independent tests.
The models that do well on the unseen data are in some sense more robust, reliable, and it gives you a feel for the constraints the data are placing on the models. You can see what conditions are needed to give certain results.
The results are placed in the animated gif above, where the blue temperatures are the out-of-sample values.
To continue our excursion into natural variation models of global temperature: What do they predict?
Here are a couple of different models fit with data up to the year 1990. This was in order to compare their projections with out-of-sample reality after 1990. The year 1990 is also the start of the major IPCC projections from the TAR WG1 available here.
One simple way to separate the influence of humans from natural variation is to fit a simple linear regression containing sinusoidal terms, as shown in previous posts.
The figure below shows the result: linear (dotted red), periodic (dashed red) and their sum (solid red) applied to global temperature data sets (A) GISS and (B) HadCRUT and (C) to a selection of simulation models.
Below is quick review of some of the evidence and consequences of a 60 year climate cycle. According to Roy Spencer, the argument that increasing carbon dioxide concentrations alone are sufficient to explain global warming is reasoning in a circle. By ignoring natural variability, they end up claiming that natural variability is insufficient.
However, the recent paper by Craig Loehle finds only a very small linear warming trend is left (potentially attributable to AGW) after subtracting the 60â€“70 yr cycle. While cause of the 60yr cycles is unexplained at present, he claims the small trend disproves AGW because it is:
clearly inconsistent with climate model predictions because the linear trend begins too soon (before greenhouse gases were elevated) and does not accelerate as greenhouse gases continue to accumulate with no acceleration in recent decades.
That oscillations are persistent features of the climate has been known for a long time. Stoker and Mysak in 1992 reviewed ice cores, tree-ring index series, pollen records and sea-ice extents over the last 10,000 years, finding:
The traditional interpretation that decadal-to-century scale fluctuations in the climate system are externally forced, e.g. by variations in solar properties, is questioned. A different mechanism for these fluctuations is proposed on the basis of recent findings of numerical models of the ocean’s thermohaline circulation. The results indicate that this oceanic circulation exhibits natural variability on the century time scale which produces oscillations in the ocean-to-atmosphere heat flux. Although global in extent, these fluctuations are largest in the Atlantic Ocean.
Even a paper by Michael Mann in 2000 identifies the cycle:
Analyses of proxy based reconstructions of surface temperatures during the past 330 years show the existence of a distinct oscillatory mode of variability with an approximate time scale of 70 years.
As far back as 1995 Mann published a paper in Nature stating:
THE recognition of natural modes of climate variability is essential for a better understanding of the factors that govern climate change. Recent models suggest that interdecadal (roughly 15â€“35-year period) and century-scale (roughly 50â€“150-year period) climate variability may be intrinsic to the natural climate system.
The issue is: How large is the cycle relative to potential warming due to AGW?. Klyashtorin and Lyubushin (2003) demonstrated that a 50â€“60 year period temperature signal is dominant from about 1650 (the end of the Little Ice Age) in Greenland ice core records, in several very long tree ring records, and in sardine and anchovy records in marine sediment cores. This result was also reported by Biondi et al. (2001), who also made the pithy remark:
Anthropogenic greenhouse warming may be either manifested in or confounded by alterations of natural, large-scale modes of climate variability.
A wide range of phenomena move in sync with this cycle. Long-term changes of Atlantic spring-spawning herring and Northeast Arctic cod commercial stocks also show 50-70-year fluctuations: sufficient to predict the probable trends of basic climatic indices and populations of major commercial fish species for up to 20-30 years into the future.
Zhen-Shan and Xian (2007) found China temperature from 1881 can be completely decomposed into four quasi-periodic oscillations including an ENSO-like mode, a 6â€“8-year signal, a 20-year signal and also a prominent 60-year timescale oscillation of temperature variation. While they found CO2 concentration contributed a small trend, its influence weight on global temperature variation accounted for no more than 40.19% of the total increase.
Perhaps its all a coincidence. Or perhaps we have yet to see much global warming from CO2, and its all going to suddenly leap out and ambush us in 20 years time.
Maybe, but speculation is a mugs game. Just the facts please. The last 50 years coincides with an upswing in the 60 year cycle, and the recent flat global temperatures coincide with the peak and subsequent downturn.
In tests of the rigor of the Steffen/Wong statement that “not only is the OHC increasing, it is increasing faster“, we previously used a linear regression model including natural cycles. The question was raised about the confounding of an upward trend with part of the quadratic terms representing ‘acceleration’. This risk is increased by the short run of data (only 54 years) and also because the phase of the periodic terms is a free variable. The periodic is free because both sin() and cos() are used.
The phase can be bound easily by the simplification below. I introduce 1976 as a start date for the sin() periodic, the date of the Great Pacific Climate Shift, a widely recognized change in ocean and atmospheric phenomena. The code for obtaining the probability that the model is improved by a quadratic term is then:
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.