Recent investigations with the photoemission electron microscope showed the formation of spatial patterns (target patterns, spiral waves, disordered patterns) during the NO+H-2 reaction over a Rh(111) single crystal surface. A five-variable mathematical model of the reaction-diffusion type has been developed to describe the experimental observations. A simplified version of this model was originally designed to explain the complex temporal behavior (e.g., oscillatory) found for the NO+H-2 reaction on Rh(111). The simulation results successfully reproduce the main experimental findings and explain the underlying reasons for spatial pattern formation. In addition, the numerical studies predict a variety of self-organization phenomena which should be experimentally verified,