A Search for Periodic and Quasi-Periodic Patterns in Select Proxy Data with a Goal to Understanding Temperature Variation

In this work over 200 temperature proxy data sets have been analyzed to determine if periodic and or quasi-periodic patterns exist in the data sets. References to the journal articles where data are recorded are provided. Chapter 1 serves an introduction to the problem of temperature determination in providing information on how various proxy data sources are derived. Examples are given of the techniques followed in producing proxy data that predict temperature for each method used. In chapter 2 temperature proxy data spanning the last 4000 years, from 2,000 BCE to 2,000 CE, are analyzed to determine if overarching patterns exist in proxy data sets. An average of over 100 proxy data sets was used to produce Figure 4. An overview of the data shows that several “peaks” can be identified. The data were then subjected to analysis using a series of frequency modulated cosine waves. This analysis led to a function that can be expressed by equation 3. The literature was examined to determine what mathematical models had been published to fit the experimental proxy data for temperature. A number of attempts have been made to fit data from limited data sets with some degree of success. Some other papers have used a sinusoidal function to best fit the changes in the temperature. After consideration of many published papers and reviewing long time streams of proxy data that appeared to have sine wave patterns, a new model was proposed for trial. As the patterns observed showed “almost” repeating sine cycles, a frequency modulated sine wave was chosen to obtain a best fit function. Although other papers have used a sinusoidal function to best fit the changes in the temperature, the “best fit” was limited. Thus, it was decided that a frequency modulated sine wave may be a better model that would provide a more precise fit. This proved to be the case and the more than 240 temperature proxy data sets were analyzed using Equation 3. In chapter 3 the time span for the proxy data was extended to cover the period of time 12,000 BCE to 2000 CE. The data were then tested by using the equation above to search for periodic/quasi-periodic patterns. These results are summarized under select conditions of time periods. In chapter 4 the interval of time is extended over 1,000,000 years of time to test for long period “periodic” changes in global temperature. These results are provided for overall analysis. The function f(x) as described above was used to test for periodic/quasi-periodic changes in the data. Chapter 5 provides an analysis of temperature proxy data for an interval of time of 3,000,000 years to establish how global temperature has varied during the last three million years. Some long-term quasi-periodic patterns are identified. Chapter 6 provides a summation of the model proposed for global temperature that can be expected if similar trends continue over future years as have prevailed for the past few million years. Data sets that were used in this work are tabulated in the appendices of this paper