Generalized Cauchy model of sea level fluctuations with long-range dependence

This article suggests the contributions with two highlights. One is to propose a novel model of sea level fluctuations (sea level for short), which is called the generalized Cauchy (GC) process. It provides a new outlook for the description of local and global behaviors of sea level from a view of fractal in that the fractal dimension D that measures the local behavior of sea level and the Hurst parameter H which characterizes the global behavior of sea level are independent of each other. The other is to show that sea level appears multi-fractal in both spatial and time. Such a meaning of multi-fractal is new in the sense that a pair of fractal parameters (D, H) of sea level is varying with measurement sites and time. This research exhibits that the ranges of D and H of sea level, in general, are 1≤D<2 and 0.50.96 for all data records at all measurement sites, implying that strong LRD may be a general phenomenon of sea level. On the other side, regarding with the local behavior, we will reveal that there appears D=1 or D≈1 for data records at a few stations and at some time, but D>0.96 at most stations and at most time, meaning that sea level may appear highly local irregularity more frequently than weak local one.