A computationally efficient hybrid method, that combines the characteristic basis function method and the physical optics as well as the forward backward method, is applied for the solution of integral equations used to investigate the electromagnetic scattering from and propagation over large scale rough terrain problems. The method utilizes high-level basis functions defined on macro-domains (named as blocks) namely characteristic basis functions that are constructed by aggregating low-level basis functions (i.e., conventional sub-domain basis functions). In the construction of the abovementioned characteristic basis functions, forward backward method as well as the physical optics approach (when applicable) are used. The conventional characteristic basis function method originally developed by Prakash et al. is slightly modified to handle large terrain problems, and is further embellished by accelerating it and by reducing its storage requirements via the use of an extrapolation procedure. Numerical results for the induced currents, total fields and path loss are presented and compared with either measured or previously published reference solutions to assess the efficiency and the accuracy of the method. Besides, certain parametric studies and convergence tests have been carried out.