A numerically efficient methodology for the optimal design of monitoring networks aiming at the surveillance of accidental atmospheric release is proposed in this paper. In a realistic context, the design of such a network requires the knowledge of a database of potential dispersion accidents occurring in the domain of the study. An objective function measures the ability of a potential network to provide measurements in order to reconstruct any accidental plume taken from the database. In the optimisation of such cost functions with respect to networks, most of the computational time is spent in the evaluation of the function, especially if the accidents database is large. In this paper we show how to optimally reduce this database and how this affects the design via a mathematical expansion in the cost function. We introduce methods based on principal component analysis, which are rigorous when the cost function is of least-squares type. These methods are then tested and validated with success on the design of a radionuclides monitoring network to be deployed over France. This is the so-called Descartes network which will be operated by the French Institute for Radiation and Nuclear Safety. These techniques are then applied on Descartes to solve several issues that are computationally demanding, but are also of more general interest, such as: how should one sequentially deploy the stations of the network? How is affected the optimal network when other European potential radiological sources are taken into account?