This paper discusses the challenges of executing a long-term application on a computational grid, which generates the climatology of the atmospheric numerical model BRAMS (Brazilian development on Regional Atmospheric Modeling System) using ensemble members. We have developed a workflow that submits climatology to the computational grid composed by three different grid middlewares (OurGrid, OAR/CiGri and Globus) and three clusters (situated in Porto Alegre, São José dos Campos and Cachoeira Paulista-Brazil). The application characteristics demand a processing grid, rather than a data grid, due to intensive computation and data transfer between the geographically distributed grid nodes. We achieved the goal of generating the climatology using a computational grid. However, we observed problems on application performance due data transfer and non-availability of the computational grid. Questions related to data storage/transfer and grid failures must be better treated to ensure application performance.