Previous measurements have shown that there is a marked change in the attenuation of an acoustic impulse above grassland as it propagates into a meteorological shadow zone. This paper extends the theoretical calculations by considering penetration of the boundary by creeping waves. Calculated pulse waveforms for various ground impedance models are compared with the experimental results. Discrepancies between the pulse shapes and overprediction of the excess attenuation may be caused by the restrictive approximations used in applying the theory or imply that other mechanisms contribute to the sound penetration.