Abstract: Exponential integrators, among them the Exponential Time Differencing (ETD) methods, have been widely used for solving stiff, nonlinear equations due to their accuracy, stability and ability of maintaining exponential behavior. The cost of these methods is dominated by the computing of matrix exponentials and their products with vectors. In this talk, we will use domain decomposition methods to enhance the efficiency (in terms of computational cost) of ETD schemes. In particular, we will present localized ETD Runge-Kutta schemes for the rotating shallow water equations and discuss their numerical performance compared to the explicit Runge-Kutta or strong stability preserving Runge-Kutta (SSP-RK) algorithms.