Forecasting the motion and evolution of tropical cyclones is a challenging, computationally expensive task. Complex, interacting physical processes on a wide range of scales need to be considered. Adaptive techniques, such as local mesh refinement, are a promising way to improve the efficiency of numerical models for such multi-scale problems. We investigate the interaction of two tropical cyclones in a barotropic model assuming exact initial conditions and discuss how the impact of discretization errors on the prediction of storm tracks can be minimized using adjoint-based goal-oriented adaptivity. We propose suitable functionals for the prediction of storm tracks, interpret the associated sensitivity from a meteorological point of view and discuss its relation to sensitivity measures commonly used in meteorological applications. We present numerical results of adaptive simulations on optimized meshes and adaptive time stepping controlled by a posteriori error estimators that exploit the sensitivity information. Using goal-oriented adaptivity, the storm tracks can be determined about one order of magnitude more precisely, compared ... mehrto uniform discretizations with the same number of unknowns. The highest improvement in accuracy (up to two orders of magnitude) can be observed for meshes with comparatively low number of cells.