Towards a seascape topology II: Zipf analysis of one-dimensional patterns

Large temporal and spatial data series are increasingly available and easy to produce. This paper uses Zipf analysis to evaluate serial data sets from the HOTS, BATS, EquaPac and high-resolution vertical profiles of FluoroMAP. Zipf analysis produced Zipf exponents from best-fit lines that permitted comparison among data sets. It allows comparison of one-dimensional series despite differences in scale and missing data. Zipf exponents ranged from 0.043 to 0.83. Serial data with sampling intervals of milliseconds and months showed exponents that ranged around 0.3. To the extent that Zipf exponents measure structure and variation, the indication is that structure of distributions is similar over millimeters and hundreds of kilometers. Zipf analysis provides a means to quantify similarities and differences, and suggests that variation is linked across many length scales for phytoplankton.