Authors' comment in response to the RCs

Abstract

<strong class="journal-contentHeaderColor">Abstract.</strong> 4D topographic point cloud data contain information on surface change processes and their spatial and temporal characteristics, such as the duration, location, and extent of mass movements, e.g., rockfalls or debris flows. To automatically extract and analyse change and activity patterns from this data, methods considering the spatial and temporal properties are required. The commonly used M3C2 point cloud distance reduces uncertainty through spatial averaging for bitemporal analysis. To extend this concept into the full 4D domain, we use a Kalman filter for point cloud change analysis. The filter incorporates M3C2 distances together with uncertainties obtained through error propagation as Bayesian priors in a dynamic model. The Kalman filter yields a smoothed estimate of the change time series for each spatial location, again associated with an uncertainty. Through the temporal smoothing, the Kalman filter uncertainty is, in general, lower than the individual bitemporal uncertainties, which therefore allows detection of more change as significant. In our example time series of bi-hourly terrestrial laser scanning point clouds of around 6 days (71 epochs) showcasing a rockfall-affected high-mountain slope in Tyrol, Austria, we are able to almost double the number of points where change is deemed significant (from 14.9 % to 28.6 % of the area of interest). Since the Kalman filter allows interpolation and, under certain constraints, also extrapolation of the time series, the estimated change values can be temporally resampled. This can be critical for subsequent analyses that are unable to deal with missing data, as may be caused by, e.g., foggy or rainy weather conditions. We demonstrate two different clustering approaches, transforming the 4D data into 2D map visualisations that can be easily interpreted by analysts. By comparison to two state-of-the-art 4D point cloud change methods, we highlight the main advantage of our method to be the extraction of a smoothed best estimate time series for change at each location. A main disadvantage of not being able to detect spatially overlapping change objects in a single pass remains. In conclusion, the consideration of combined temporal and spatial data enables a notable reduction in the associated uncertainty of the quantified change value for each point in space and time, in turn allowing the extraction of more information from the 4D point cloud dataset.