This work examines the application of a geometric-optical canopy reflectance model to provide measures of woody shrub abundance in desert grasslands at the landscape scale. The approach is through inversion of the non-linear simple geometric model (SGM) against 631 nm multi-angle reflectance data from the Compact High Resolution Imaging Spectrometer (CHRIS) flown on the European Space Agency's Project for On-Board Autonomy (Proba) satellite. Separation of background and upper canopy contributions was effected by a linear scaling of the parameters of the Walthall bidirectional reflectance distribution function model with the weights of a kernel-driven model. The relationship was calibrated against a small number of sample locations with highly contrasting background/upper canopy configurations, before application over an area of about 25 square kilometers. The results show that with some assumptions, the multi-angle remote sensing signal from CHRIS/Proba can be explained in terms of a combined soil-understory background response and woody shrub cover and exploited to map this important structural attribute of desert grasslands.