  Environmental management optimizing a long-run objective is an ergodic
control problem whose resolution can be achieved by solving an associated
non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective
Hamiltonian. Focusing on sediment storage management as a modern engineering
problem, we formulate, analyze, and compute a new ergodic control problem under
discrete observations: a simple but non-trivial mathematical problem. We give
optimality and comparison results of the corresponding HJB equation having
unique non-smoothness and discontinuity. To numerically compute HJB equations,
we propose a new fast-sweep method resorting to neither pseudo-time integration
nor vanishing discount. The optimal policy and the effective Hamiltonian are
then computed simultaneously. Convergence rate of numerical solutions is
computationally analyzed. An advanced robust control counterpart where the
dynamics involve uncertainties is also numerically considered.
