Our approach so far has been to model natural climate variation of global temperature with sinusoidal curves, and potential AGW as increasing trends. A new algorithm called EMD (Empirical Mode Decomposition) promises to more robustly identify cyclical natural variation (NV), showing the contribution of NV and AGW to global temperature, and testing the IPCC claim that most of the recent warming is due to AGW.

Underestimation of natural variation (NV) is a crucial flaw in the IPCC’s logic, according to Dr Roy Spencer:

They ignore the effect of natural cloud variations when trying to diagnose feedback, which then leads to overestimates of climate sensitivity. … By ignoring natural variability, they can end up claiming that natural variability does not exist. Admittedly, their position is internally consistent. But then, so is all circular reasoning.

The relative contribution of AGW to temperature increase in the late 20th century underpins the IPCC global warming claims, according to the Wiki page on Scientific Opinion on Climate Change:

National and international science academies and scientific societies have assessed the current scientific opinion, in particular on recent global warming. These assessments have largely followed or endorsed the Intergovernmental Panel on Climate Change (IPCC) position of January 2001 that states:

An increasing body of observations gives a collective picture of a warming world and other changes in the climate system… There is new and stronger evidence that most of the warming observed over the last 50 years is attributable to human activities.[1]

Since 2007, no scientific body of national or international standing has maintained a dissenting opinion.

So estimating the relative proportion of natural variation vs. trend is very important. While widely used in other fields, EMD is relatively little used in climate science.

As an example, Lin and Wang (2004) used EMD for analysis of solar insolation. They claim that the solar eccentricity signal is much larger than previously estimated, more than 1% of solar irradiance, and adequate for controlling the formation and maintenance of quaternary ice sheets. This is a potential resolution of the 100,000 year problem, that has also been used to justify the necessity of CO2 feedback in producing ice ages.

Conventional spectral methods are strictly periodic — the period is constant in both frequency and amplitude. EMD relaxes these assumptions, allowing quasi-periodicity, which might explain why more variation is potentially explained. The EMD algorithm proceeds by first extracting out the highest frequency, called an intrinsic mode function (IMF) and leaving a residual. It does this to the next highest frequency, and so on, until only a trend is left.

While it is possible the residual is also part of a cycle — it is always possible to model a trend with a sinusoidal of long enough period — we treat this as AGW trend in order to estimate the maximum possible contribution of AGW to global warming.

Here are the results of applying EMD to the CRU global temperature series. Figure 1 below shows each of the 5 IMF’s and the residual, the remainder after subtracting out the periodics.

Each of the IMF’s is shown, with mean periods of 4.0, 6.6, 11.9, 23.4, and 55.1 years respectively. Most readers would be well aware of the similarity of these periods to major solar and oceanic cycles.

Below the CRU temperatures are plotting against the series, adding in each of the IMF’s sequentially to the residual, and we estimate the relative contribution of AGW and natural variation over a specific period from 1975 to 2000.

Here is the first IMF, showing the residual (solid red thin line), the largest IMF with a period of around 60 years (dashed thin red line), and the sum of the two (solid, thick red line) overlaid on the temperature in black.

The blue lines deliniate 1975 and 2000. The residual rises 0.157C during this time, but the first IMF rises 0.243C, giving a percentage contribution by the trend of only 39% of the overall rise during this period, suggesting most of the contribution is due to natural variation, and not anthropogenic factors.

Adding in the next IMF, the AGW is 0.157C, and the NV is 0.31 giving a contribution of only 33.8%.

Next is the residual plus 3 IMF’s. Here the AGW is 0.157C and the NV is 0.42C giving a contribution of only 27.1%.

You get the idea. Here is 4 and 5. AGW=0.157C, NV=0.49 is 24%, and AGW=0.157C NV=0.62 and 20%.

If we look at 1950 as the starting point, there is more time for the trend to increase, relative to the NV. Even so, the relative percentage contributions of the trend is 57%, 49%, 43%, 39%, and 34% for the IMF 1-5 respectively.

These results, based on the EMD algorithm at least, would seem to directly contradict the IPCC claim for which, since 2007, “no scientific body of national or international standing has maintained a dissenting opinion, that most of the warming observed over the last 50 years is attributable to human activities.”

Granted, we don’t know why natural variation could contribute almost 0.5C to global temperature over the space of 25 years, when solar insolation changes suggest a contribution of only as much as 0.1C from external forcing. I have a few ideas that I hope to pursue. However, its clear that strong claims about the contribution of AGW while NV is not understood is very premature, as according to Dr Roy Spencer:

In my experience, the public has the mistaken impression that a lot of climate research has gone into the search for alternative explanations for warming. They are astounded when I tell them that virtually no research has been performed into the possibility that warming is just part of a natural cycle generated within the climate system itself.

Turnkey R code for this analysis is here.