Spatial scaling and Multi-Scale analysis of remote sensing reflectance, Chlorophyll-a and Sea Surface Temperature

Abstract:

Satellite remote sensing is a powerful tool for understanding many of oceanic processes synoptically. The images provided by the ocean colour satellites are widely used in physical, biological and ecological aspects of oceanography, but the scaling properties of satellite images are too rarely studied. In the present work we aim to understand the scaling properties of the satellite ocean colour products obtained from the MODIS-Aqua using tools from turbulence. We identify some regions which experience high spatial heterogeneity in Chlorophyll-a (Chl-a) and Sea Surface Temperature (SST). We also study the remote sensing reflectance at two wavelengths (R_rs443 and R_rs555 nm) which has direct link to the phytoplankton biomass. We have selected four regions of various water types for the present methodology study. Here we use 1D and 2D Fourier power spectra to understand the spatial scaling of R_rs, Chl-a and SST. The 2D power specrum is derived from the radially averaged power spectrum of R_rs, Chl-a and SST. The power spectra derived for 1D and 2D follow power law behaviour with specific slope values, and it varies with region.

The multi-scaling properties of these images are also studied using the Structure Function (SF) and Coarse graining (CG) method. SF is analysed from the R_rs, Chl-a and SST maps and the CG is done using their gradient modulus. The moment scaling functions (ζ(q) for SF and K(q) for CG) are also derived for these images. Using simulations of 2D fBm, 2D beta model and lognormal cascades, we test both methods and show that, for nonstationary cascades (when the Hurst value is not zero) the CG method applied to the small scale laplacian field, is not adequate to characterize fully the image scaling statistics. The advantage of using the SF method is also that it can be applied to an instantaneous image with missing pixels, due to cloud coverage.

Keywords: Power spectra, Scaling; Structure Function, Coarse graining, Multifractalilty, Beta model, Lognormal cascades