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David Whitehouse: Solar Statistics
Monday, June 6th 2011, 2:25 PM EDT
Co2sceptic (Site Admin)
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.

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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.

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