Solar Statistics

There are various ways to analyse time series data such as the annual average global temperature. A common way is to decompose it into its cyclic components using Fourier analysis. This is very useful for long datasets, but not so good for the post-1860 so-called instrumental period of earth temperature readings – there hasn’t been enough time to determine its components. Fourier analysis has its limitations for certain kinds of time series that are technically described as non-linear and non-stationary.About a decade ago a new approach was being developed to analyse time series that, in a way, is a more general technique than Fourier analysis. It’s called Empirical Mode Decomposition (EMD). It can isolate any cyclic components of a time series. In technical terms it decomposes a time series into a finite sum of so-called ‘basis functions’ whose amplitude and frequency are functions of time.It has been used to analyse rainfall, heart rhythms, radar echoes and water waves, to give a few examples.A new paper (Barnhart, B.L., Eichinger, W.E., Empirical Mode Decomposition applied to solar irradiance, global temperature, sunspot number, and.... Journal of Atmospheric and Solar-Terrestrial Physics (2011), doi:10.1016/j.jastp.2011.04.012) uses EMD to look at the earth’s global temperature, the number of sunspots, the total radiation coming from the sun and the carbon dioxide concentration in the Earth’s atmosphere. It produces some surprising results.The way it works is to find and subtract a ‘Intrinsic Mode Function (IMF)’ in the data and keep repeating the procedure until it cannot be done any more. The last IMF will be the longest-term trend in the data (its lowest frequency component), the first IMF will be the changes that occur at the highest frequency, i.e. the most rapidly.The researchers perform EMD analysis on;1. Sunspot numbers between 1749 and 2009. 2. Total Solar Irradiance (TSI) reconstructed between 1749 up to the 1970’s when satellite measurements are available.3. Nasa’s land ocean temperature index, LOTI.4. Carbon dioxide concentrations as measured since 1959 at Mauna Loa.Carbon dioxide is the most straightforward analysis. Click on the image to enlarge. The IMF’s show three components, high frequency noise, an annual oscillation and an upward trend. This is as one would expect.The analysis of the other datasets are more interesting. The sunspot and TSI data are about the same. This is to be expected as the TSI outside the satellite era is estimated using the sunspot number.IMF1 of the sunspot data show high frequency noise that, curiously, is more apparent in the past 50 years. There is less high frequency noise when the sunspot number is low. (Note that according to the IPCC before 50 years ago the sun was the dominant influence on Earth’s temperature. Post 50 years ago it is greenhouse gasses that are the main driver.)IMF6 shows the lowest frequency component – the trend in the data – that shows sunspot activity had a low in 1850 and since then has been increasing to 2009. This is interesting as an analysis of solar activity by smoothing the number of sunspots shows that sunspot activity peaked in the 1950’s, declined a bit and then peaked in the 1980’s before declining again.The possibility of a correlation between TSI and the global mean temperature has been discussed widely in the scientific literature. In this analysis TSI and temperature fluctuates between being correlated and being not.Specifically, between 1880 – 1945 it was not correlated (or it has been small or negative). Between 1940 – 2009 it has been. The researchers call this a “dramatic increase in correlation.”This work is in its infancy but it shows that there are other ways to look at solar activity that just smoothing the sunspot number count with a running mean and comparing it to the global temperature. These new results will take some time to digest. But they do throw new light on the changing behaviour of the sun and its possible link to the Earth’s temperature.Feedback: david.whitehouse@netzerowatch.com