The objective of this study is to develop model order reduction capabilities for high-fidelity off-road mobility simulations. The model reduction technique using the proper orthogonal decomposition (POD) is implemented at the level of the numerical solver in order to decrease the number of equations that need to be solved at each iteration of the solution procedure. The POD is, however, limited in that the modes are dependent on snapshot data collected during the running of a full order model (FOM), limiting the modes to being accurate only for the specific scenario from which they were collected. Due to this limitation, a method of mode adaptation through interpolation on a tangent space of the Grassmann manifold is investigated to allow modes to be predicted for cases in which a full order model has not been run. Modes produced for known values of a simulation parameter are used to predict the modes for a value of the simulation parameter for which POD modes have not been directly produced. For a single tire soil bin mobility model, the POD modes are found to be effective at retaining accuracy with minimal errors while also reducing computational time.