As hydrogen demand in the refineries is increasing, hydrogen management strategies are of great interest for the refiners. Hydrogen management deals with the optimal distribution, routing, and flow allocation of hydrogen gas within a refinery linking the hydrogen producing and consuming units. This is also known as the hydrogen network synthesis or design. Due to uncertainty in the crude feedstock or final product specification in a refinery, there exists variations or uncertainties in the operating conditions (parameters) required for hydrogen network design. Hence there is a need to incorporate these uncertainties while designing hydrogen networks. In this paper, we address the issue of optimal hydrogen network design under uncertainty or uncertain operating parameters. For this, we develop a nonconvex multiscenario Mixed Integer Nonlinear Programming (MINLP) model which is the deterministic equivalent of mathematical two stage stochastic model. The purpose is to develop a network design that is optimal for different operating conditions of a refinery constituted by multiple scenarios of operation. The superstructure for this hydrogen network design under uncertainty includes hydrogen reuse, recycle, and purification options. It also has hydrogen gas stream conditioning equipment, like compressors and valves, to cater to the nonisobaric conditions and heaters and coolers to deal with the nonisothermal conditions. The size of this multiscenario two stage mathematical model builds with increase in the number of scenarios. For this, standard optimization solvers may not be able to guarantee global optimality within reasonable computational time. We propose a specific solution strategy to solve this mathematical model to global optimality by convexifying the nonlinear terms. This strategy is found to exhibit exceptional computational time savings compared to the conventional branch and bound based global optimization approaches. Two case studies are solved to illustrate the applicability of the proposed model and solution strategy.