The deep water chlorophyll concentration fluctuation from 2003 to 2007 has been studied using fractal analysis. The SeaWiFS global daily mean chlorophyll concentration time series were used. The Higuchi fractal algorithm was used to calculate fractal dimension, which is given by the slope of an associated length versus the lag. Short range fluctuation investigation using a six point slope gives fractal dimensions from 1.80 to 1.85, suggesting the presence of correlation, which was confirmed by computer simulations. The gradual increase of fractal dimension to 1.9 in about 15 lag-days suggests that a long-range de-correlation mechanism favoring random fluctuation is present. The 2007 times series shows a relatively low overall fractal dimension and exhibits a peculiar multi-fractal behavior. This phenomenon and the observed low accumulated cyclone energy in 2007 support the interpretation that cyclone energy can promote deep-water chlorophyll concentration fluctuation. A regression of fractal dimension at 10 lag-days versus the log of cyclone energy gives an R 2 value of 0.75 (N = 5)., which suggests the presence of additional or related de-correlation mechanisms.

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Exoplanet transit time series photometric data usually contain noise levels that are comparable to the transit signal jumps. The analysis that assumes Gaussian noise and extensive data averaging calibrated to a reference star has been the traditionally used algorithm. This paper studied the fractal property of the time series and found that the fractal dimension changes for time series data that contain transits. The Higuchi fractal method, where the length of the increment in various time lags is plotted against the lags, was used in this study. (Higuchi, T., "Approach to an irregular time series on the basis of fractal theory", Physica D, vol 31, 277-283, 1988). The fractal algorithm was calibrated with the Weierstrass function. Simulations using Gaussian noise suggested that a transit jump signal at about 1-sigma noise level would produce changes in fractal dimension, while non-Gaussian noise simulations suggested a higher transit jump signal. The fractal algorithm was applied to data collected on HD 209458 as well as on published data. The transit caused a fractal dimension change of about 0.06. An over-exposed CCD dataset with much noise was also analyzed and a fractal dimension change of about 0.02 was obtained. The result suggests that fractal dimension analysis, without the assumption of error normality, is an alternative method for identifying transits in time series photometric data.

The Pacific Ocean deep sea height data around latitude 20 N from Jason-1 satellite was analyzed in terms of standard deviation (std) and fractal dimension during a 90-day period that included the coronal mass ejection event of 2003 Oct 29 where a peak solar energetic particles of about 30,000 pfu was measured. The surface height standard deviation series was observed to have two peaks that corresponded to two typhoon events of Oct 25 and Nov 26, 2003. The cross correlation of the height-std series and average-height series showed a positive correlation with time delay. The fractal dimension of the height series peaked on Nov 1 (fractal dimension ~1.96 with a background 90-day average of ~ 1.81) and no corresponding peak was observed in the other time series data. Computer simulation of the fractal dimension of a finite random series suggested a standard deviation of about 0.071. Annual and long-term trends of the fractal dimensions were also found and investigated. The possible contribution of coronal mass ejection to the surface height series fractal dimension and the height correlation to chlorophyll were discussed.