We consider the Variational Data Assimilation (VarDA) problem in an operational framework, namely, as it results when it is employed for the analysis of temperature and salinity variations of data collected in closed and semi closed seas. We present a computing approach to solve the main computational kernel at the heart of the VarDA problem, which outperforms the technique nowadays employed by the oceanographic operative software. The new approach is obtained by means of Tikhonov regularization. We provide the sensitivity analysis of this approach and we also study its performance in terms of the accuracy gain on the computed solution. We provide validations on two realistic oceanographic data sets.