Estimation of the likelihood function for non-linear optimization problems: Applications to the radiative transfer model in shallow water

Hyperspectral sensors provides informative data in many fields related to Earth observation. On the coastal zone, the inversion of radiative transfer models of the light has shown the ability to estimate parameters characterizing the water column. Particularly the water column depth, its concentration in non-algal particles, in phytoplankton, the bottom reflectance can be retrieved. Nevertheless the reliability of these estimations are difficult to clearly assess. In this paper a methodology based on interval arithmetic is presented to estimate the likelihood function. This allows to describe the behavior of this function around its maximum and therefore to evaluate the reliability of the solution. This methodology is applied to describe the influence of the noise level.