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).
The figure below extends the empirical models of global temperature data from the previous tests out to the year 2200. The mean and uncertainty in 2200 of the most reliable simple linear regression models (incorporating acceleration and natural variation) appears to be equivalent to the IPCC projections for the year 2100.
CommentsHere, 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.
CommentsZhen-Shan and Xian (2007) (PDF) was mentioned earlier, but here is the abstract in full, because their findings in China apply equally to global temperatures. Read the rest of this entry…
CommentsTo 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.
CommentsIn 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:
CommentsCode 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):
x=time(OHC);
f=x*pi*2/60;
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.
Innovation is not dead as Dyson eliminates the fan (maybe there is one inside though), showing the power of careful attention to shape.
Rational policy analysis is not an oxymoron, as Peter Gallagher deconstructs the emissions trading scheme (ETS).
CommentsWe’ll be watching the drop in ocean heat content (OHC) raised by the brilliant Bob Tisdale for a potential follow-up to the Recent Climate Observations: Disagreement With Projections paper, where observations disproved speculations.
CommentsMy comments on the topical ‘Yamal’ issue:
My AIG article demonstrating reconstruction of a hockey stick with red noise, neatly illustrated the possibility of circular reasoning in screening trees by their response to temperature. Around 20% of random series (or 40% if you count the inverted ones) correlate significantly with the temperature instrument record of the last 150 years, and when averaged back beyond the present create the straight handle of the stick.
CommentsThis numeracy exercise for schools can be adapted to grades pre-up. You need:
1. A number of strong magnets, at least two per group
2. Iron filings
3. Selection of nuts of various metals: iron, copper, brass, some lead sinkers.