Spaceborne precipitation radars are usually designed to operate at attenuating wavelengths, mostly at X, Ku and Ka band. At these frequencies and above, convective rainfall can cause severe attenuation. Moreover, raindrops and precipitating ice can give rise to appreciable multiple scattered radiation which apparently tends to enhance the nominal attenuated reflectivity. In order to properly describe radar observations in such conditions, apparent reflectivity has to be modeled taking into account both path attenuation and incoherent effects. To this aim, a general definition of volume radar reflectivity is introduced, and a Monte Carlo model of backscattered specific intensity is implemented. The numerical model is applied to synthetic profiles, extracted from a mesoscale cloud-resolving model simulation and representing intense and heavy convective precipitation at a developing and mature stage. Realistic appearance of these average profiles is argued by resorting to radar measurements available in literature. Spaceborne apparent reflectivity due to multiple scattering is shown to be significantly different from the attenuated one for the near-surface layers of mature convection at Ku band and even for growing convection at Ka band. A discussion about this discrepancy is carried out at Ku band showing its possible impact for estimated rain rate profiles. If precipitation incoherent effects are formally treated as perturbation factors of the specific attenuation model, constrained single-frequency inversion techniques are shown to be suitable to minimize rain rate retrieval errors due to multiple scattering phenomenon.