Scaling Analysis of Ocean Surface Turbulent Heterogeneities from Satellite Remote Sensing: Use of 2D Structure Functions, methodology and applications

Abstract:

Satellite remote sensing observations allow the ocean surface to be sampled over large spatio-temporal scales. The images provided from visible and thermal infrared satellite observations are widely used in physical, biological, and ecological oceanography. The present work proposes a method to understand the multi-scaling properties of satellite products such as the Chlorophyll-a (Chl-a), and the Sea Surface Temperature (SST). The specific objectives of this study are to show how the small scale heterogeneities of satellite images can be characterised using tools borrowed from the fields of turbulence. We show how the structure function, which is classically used in the frame of scaling time series analysis, can be used also in 2D. The main advantage of this method is that it can be applied to process images which have missing data. Based on both simulated and real images, we demonstrate that coarse-graining (CG) of a gradient modulus transform of the original image does not provide correct scaling exponents. We show, using a fractional Brownian simulation in 2D, that the structure function (SF) can be used with randomly sampled couple of points, and verify that 1 million of couple of points provides enough statistics.

After this methodological study, some applications are presented: the nonlinear moment function ζ(q) is fitted using the lognormal model with 2 parameters, the Hurst index H and the intermittency μ. The values of H and μ are discussed for 4 different parameters (Chl-a, SST, Rrs-443 and Rrs-555) and for different locations, chosen among different contrasted regions of the ocean, characterized by high spatial heterogeneity in Chl-a and SST.