© 2015 Renosh et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Satellite remote sensing observations allow the ocean surface to be sampled synoptically 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), rarely studied. 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. For that purpose, 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.
Renosh, P. R., Schmitt, F. G., & Loisel, H. (2015). Scaling analysis of ocean surface turbulent heterogeneities from satellite remote sensing: Use of 2D structure functions. PLoS ONE, 10(5). https://doi.org/10.1371/journal.pone.0126975