IHISE is comprehensive methodology for generating hydraulic state bounding estimates by considering both measurement and parametric uncertainties. The methodology is based on solving the nonlinear interval hydraulic equations using bounding linearization, a technique that restricts the nonlinearities within a convex set, thus converting the problem in a form which is solvable using linear optimization. An iterative procedure improves the bounding linearization, converging to the tightest possible bounds. Simulation results demonstrate that the proposed methodology produces tight state bounds that can replace Monte-Carlo simulations.