Measurements of radar pulse return waveforms are known to provide information on properties of the observed surface, and are commonly used in oceanographic altimetry. In such applications, the convolution model (also called the “Brown model”) is widely applied for waveform analysis. This model describes pulse return waveforms as a multiple convolution of the “flat surface impulse response”, the surface's height probability density function, and the radar's point target response. The flat surface impulse response is typically determined by an integration of scattering contributions from incremental surface elements weighted by a geometrical optics (GO) prediction of the normalized radar cross-section of the elemental surfaces. Recent interest in the analysis of pulse return waveforms at VHF and lower frequencies for ice sheet sensing applications motivate reconsideration of the convolution model. While the ultimate goal of this effort is the development of a model to be utilized for interpreting VHF radar measurements over ice sheets, it is important first to establish the validity of the convolution model for these applications. Such an investigation, which involves the comparison of convolution model predictions with those of a method that does not require a separation of surface length-scales into “elemental” and large-scale regions, is most easily performed for one-dimensional surfaces. This paper describes a derivation of the convolution model for one-dimensionally rough surfaces that is applicable at low frequencies, primarily through the replacement of GO surface scattering coefficients with those of a physical optics theory. The method is validated by comparing its predictions with a Monte Carlo physical optics approach. Results show the convolution model to provide reasonable estimates of the pulse return waveform, so that a similar method can be utilized to develop a convolution model for two-dimensional surface pulse return waveforms in ice-sheet sensing applications. The results also suggest the possibility of retrieving surface profile statistical information from waveform measurements.