Global optimization models in many problems suffer from high computational costs due to the need for performing high-fidelity simulation models for objective function evaluations. Metamodeling is a useful approach to dealing with this problem in which a fast surrogate model replaces the detailed simulation model. However, training of the surrogate model needs enough input-output data which in case of absence of observed data, each of them must be obtained by running the simulation model and may still cause computational difficulties. In this paper a new metamodeling approach called adaptive sequentially space filling (ASSF) is presented by which the regions in the search space that need more training data are sequentially identified and the process of design of experiments is performed adaptively. Performance of the ASSF approach is tested against a benchmark function optimization problem and optimum basin-scale water allocation problems, in which the MODSIM river basin decision support system is approximated. Results show the ASSF model with fewer actual function evaluations is able to find comparable solutions to other metamodeling techniques using random sampling and evolution control strategies.