This paper introduces a grid-based approach to reduce the time to deliver local meteorological forecast information. The computation of local meteorological forecasts relies on the execution of both regional and local scale Numerical Weather Prediction models. Typically, such models require extensive computation on large compute clusters. Moreover, the models are commonly executed sequentially, since local models rely on the output of a regional model. The approach introduced in this paper, modifies the computational dependencies in order to compute the models more in parallel while ensuring that computational results are appropriately synchronized. We evaluate the method in a high performance computing grid using the Brazilian Regional Atmospheric Modelling System (BRAMS). The experimental results show a reduction of up to 71 % in the time to deliver local meteorological information with this approach. The approach is sufficiently general that it can be useful with other large distributed applications.