Inferring missing data in satellite chlorophyll maps using turbulent cascading

Abstract

Oceanic turbulent flows develop complicated patterns, with eddies, filaments and shear currents. Although usually referred as chaotic, their inner organization is strongly hierarchical: turbulent flows develop cascades, which transfer properties such as energy or scalar density from larger to smaller scales. In this work, we present a novel algorithm based on the cascade and able to fill data gaps in satellite images (particularly, chlorophyll concentration maps). The first step is to show that cascade processes for chlorophyll-a concentration images take a simple, explicit form when an appropriate wavelet (here Battle–Lemarié of order 3) representation is used. A reconstruction algorithm exploiting the cascade structure is then given with a detailed description. We discuss the validity and quality of this algorithm when applied to SeaWiFS and MODIS-Aqua ocean color images. An application to merging data from multiple satellite missions is presented together with a demonstration of the benefit of this algorithm over two other merging methods