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An adequate characterization of surface roughness is crucial to obtain reliable backscatter simulation results from existing analytical backscattering models. The surface roughness is typically characterized using root mean square height, autocorrelation length, and shape of the autocorrelation function. For the solution of inverse problems it is of interest to reduce the number of unknown surface parameters. Simplified backscattering models are required in this context. The paper introduces a new semiempirical backscattering model in C-band for rough dielectric surfaces which is based on the integral equation model. It is shown that a surface roughness description can be reduced using a single surface roughness parameter. To account for the high variability of autocorrelation function types, the proposed model is based on a generalized power law spectrum approach which mediates between Gaussian and exponential correlated surfaces. The approach is validated against analytical backscatter simulations and laboratory-measured microwave signatures, and the surface parameter retrieval capabilities of the suggested model are investigated.