Comparison of the Mean Global Ocean Anomaly Warming with the Record

  I forgot to include a plot of the mean warming rate with the record of the global ocean temperature anomaly in the last blog.

The zigzag in the record may be a little to regular to be considered purely random.

Ancient Arctic Ice Pack

   I redid the estimate of the rate of global warming for the oceans more carefully and found a value of 1.57 °C per 1000 years.

Taking into account a mean ocean temperature of 13.9 °C for the 20th Cent. and that seawater freezes at -1.89 °C we find that much of the worlds oceans would have been frozen over about 10,000 years ago. 

So, we have to assume that the Arctic Ice Pack would have been much greater during the last ice age. The land bridges for North America could have been farther south in the Pacific and the Atlantic.

The Global Ocean Anomaly and Its Rate of Change

  One can do a similar comparison of polynomial predictors for the global ocean temperature anomaly and the results are not much better even if one bases the prediction on a 100 year interval which better constrains the higher order polynomials.

If one starts with the global ocean anomaly for 1880.0 and asks what slope is the best predictor of the change in the anomaly one gets a surprisingly low value of 1.5 °C per 1000 years as these least squares fits show.

Since the mean temperature estimates indicate that the average for the twentieth century is 13.9 °C one would expect much of the world's oceans to be near freezing about 9000 years ago.

Using the Polynomials as Predictors of Global Warming

  The lower degree polynomials make better predictors since the higher degree polynomials tend to diverge from mean value in an interval as one moves father forward in time. In the following example the data from the 40 years prior to 1980 were used predict the subsequent global land anomaly. The black horizontal line is the average for the interval. The blue line is the linear fit and the cyan and brown are the best 2-degree and 3-degree polynomials.

If the change was determined by a stochastic variable the horizontal line would be the best predictor. In this case it seems to be the best "predictor" of prior anomalies. The horizontal line and linear fit seem to be the best long term predictors. The quadratic curve is capable of detecting some curvature in the interval but it can go astray more quickly. Smaller intervals for the fit tend to result in higher curvatures and sometimes produces unlikely results.

Separating Signal from Noise in the Global Warming Data

  I stumbled upon an interesting way of doing a curve fit a few days ago that is a variant of the idea behind Chebyshev polynomials. Instead of using fixed polynomials though one finds a series of best fitting polynomials of increasing degree to the successive remainders of the data fits. One also needs to re-scale the time about a mean value to keep the powers involved in the polynomials manageable. In the case of the global land anomaly the fit soon reaches the point of diminishing returns.

I found that an 8-degree polynomial gives a reasonably good fit for the anomaly with an approximately linear start and finish. To limit the sensitivity of the fit to the ends I used 5 year buffers with a lower statistical weight (0.25 vs 1) in the sums involved. 

The quick approach to a limiting value for the rms error as one increases the degree of the polynomial seems to indicate that most of the data is "noise." As one increases the degree of the polynomial a point is reached where the any remaining global warming is masked by the fluctuations present present in the data. The 6-degree polynomial shows a sharp downturn in the fitted curve on the right side. The 10-degree polynomial shows a rapid change on the left side. The results are similar to the 20-year average used for the prediction made in October 2013 but much easier to do. But effects analogous to the Gibbs phenomenon and large fluctuations interfere with making an accurate prediction of what will happen.

  It's been reported in the news lately that the global warming anomaly will pass the 1°C mark this year. It appears the global land anomaly has already done so.