Ground-based remote sensing instruments are often operated in a vertically pointing mode, producing time-height cross-section images (THIs) of the atmosphere. However, THIs are not Lagrangian observations: they cannot track the evolution of a single particle directly. Instead, several assumptions are required to derive the particle evolution from THI. We discuss these assumptions and show how their validity can be assessed using elevation scans. For demonstration, we analyze two intense riming cases. Since rimed particles exhibit enhanced sedimentation velocities, we first present a method to derive the vertical target velocity from scanning cloud radar observations. This method allows to study the spatial distribution of riming. The first case is comprised of several horizontally homogeneous, descending layers of rimed particles. Under these conditions, one can safely study the particle evolution in a "traditional" way by evaluating subsequent vertical profiles. The second case is more heterogeneous. For the analysis, we introduce the new spectral column vertical profile (SCVP) technique. SCVPs allow to trace the evolution of a single particle population's Doppler spectrum in space and time, thereby representing true Lagrangian observations. Our results demonstrate the value of scanning observations and show that downsides, for example regarding the use of Doppler velocity, can be overcome. Our results also raise the question whether the typically very high time resolution of THI is actually required for the common type of analyses performed on THI, and whether a combination of scanning and vertical observations could be the better observational strategy for ground-based remote sensing instruments.