A Closer Look at Power-Law Scaling Applied to Sea Surface Temperature from Scripps Pier Using Empirical Mode Decomposition
Abstract
The purpose of this study is to extract more information about the scaling exponents we obtain from sea surface temperature (SST) because their information content is limited to a single value. We examine the application of empirical mode decomposition (EMD) to power-law scaling using SST from Scripps Pier, California. The daily observations we employ extend from 1920 to 2009, a period of 90 years. The annual cycle and the long-term trend were first removed. The decomposition produced a total of 15 modes. The scaling exponents were then calculated separately for each mode from the EMD. We have examined the distribution of scaling exponents with respect to the ensemble, and then with respect to the individual modes for the oceanic processes that we may infer from them. The first three modes are antipersistent and contain about one-quarter of the total variance. The pattern of modes that was obtained is continuous and relatively smooth beyond mode 3 with increasing values up to mode 8 and generally decreasing values thereafter. The pattern exhibits intramodal correlation, as expected, and intermodal correlation as well. Intermodal correlation is likely due, for the most part, to long-range persistence. The annual cycle in SST at Scripps Pier is a dominant feature in the record and contains almost 70% of the variance. A method for removing the annual cycle that is not based on removing the mean value is introduced and is recommended for future use.
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