Abstract: Unknown boundary conditions for natural waters are estimated using an inverse problem methodology. In the formulation of the inverse problem, expressed as a nonlinear constrained optimization problem, its objective function is given by a square difference term, between experimental and computed data, added to a regularization operator. The computed data are obtained by solving the radiative transfer direct problem using the $LTS_N$ method. A key aspect to get a good reconstruction is played by observed data quality. The reconstruction strategy is examined for {\it in situ} radiance and irradiance data for many arrangements of the experimental grid of the measurement devices, in order to plan good designs for experimental works.