Extended target models often approximate complex structures of real-world objects. Yet, these structures can have a significant impact on the interpretation of the measurements. A prime example for such a scenario is a dimensional reduction, i.e. a target that generates three-dimensional measurements is estimated by a two-dimensional model. We present an approach that introduces asymmetric surface noise to the Random Hypersurface Model (RHM). This allows for a different generation interpretation of measurements depending on their location relative to the target surface, and in turn provides a way to model extended targets that generate measurements primarily but not exclusively at the surface. The benefits of this model are demonstrated on automotive LIDAR data and a large-scale comparison to the literature approach is provided on the Nuscenes data set.