Methods of Analysis

Lesson

Empirical estimation: biology

Because some biological and ecological field are dominated by turbulent flow (ocean , lakes, reservoir), there exists some relationship between the structure of the phytoplankton population and their physical environment. There exists in literature a wide researches in this domain, and because theses studied fields possess the scale invariant property, the multifractal analysis seems the most adequate tool to characterize their statistical behavior. In order to illustrate the application of the UM framework in this domain, we present an analysis performed in marine system by Seuront et al, 1999^[1]. They used of Double Trace Moment technique to perform the estimation of UM parameters. As for the velocity an temperature field they defined a flux for the fluorescence field:

$\phi_\lambda \approx \Delta f_\lambda^{3}$

Where denotes the fluorescence field.

Double trace moment as a function of the resolution in a log-log plot, showing the scale invariance for the temperature field (a) and fluorescence field (b).

Log K(q, eta) as function of log eta : (a) temperature field, (b) fluorescence field

For the temperature field they found and for fluorescence field .

[Seuront et al , 1999]
Seuront, L., Schmitt, F., Lagadeuc, Y., Schertzer, D., & Lovejoy, S. (1999). Universal multifractal analysis as a tool to characterize multiscale intermittent patterns: example of phytoplankton distribution in turbulent coastal waters. Journal of Plankton Research, 21(5).

Homepage