<p>This paper addresses the identification of the leak bound function <i>g</i> in the Stokes system with threshold leak boundary conditions, where <i>g</i> varies spatially. The state problem is solved using the dual formulation of the algebraic system, and the resulting optimization problem is formulated as a nonsmooth optimization problem. We establish the existence of solutions for both the continuous and discrete formulations of the problem. The theoretical developments are complemented by numerical experiments, which compare the performance of the nonsmooth optimization approach with traditional regularization-based methods and global optimization techniques.</p>