# Rockfall Modelling in Forested Areas: The Role of Digital Terrain Model Grid Cell Size
## 1 Introduction  
Mountainous areas are prone to many mass movement processes, rockfalls being one of the most common [1]. Rockfalls are defined as the detachment of one or several fragments of rocks (blocks) from rock cliffs, followed by rapid down-slope movements by falling, bouncing, rolling, and sliding [2]. Rockfalls can be an important threat to infrastructure, human life, and their property, since they are rapid processes with long runouts [3], and their instantaneous occurrence makes their temporal prediction practically impossible [4]. Rockfall models, especially process-based ones, can be an efficient tool for predicting potential rockfall hazard areas, making it possible to identify rockfall source, propagation, and runout areas as well as model rock trajectories, the kinetic energy of rocks, rock rebound heights and propagation and reach-out probability [1, 5, 6, 7]. By quantifying the potential rockfall hazard, simulation models can be used for planning different protection measures (e.g., technical measures, natural-based solutions) that can significantly reduce the potential risk of rockfall occurrence in high-threat areas [7, 8, 9, 10]. Forests provide a natural solution for protection against rockfalls in alpine regions [11, 12], since they can significantly reduce the intensity (kinetic energy) and propagation probability of falling rocks [13, 14, 15]. Although several rockfall modelling approaches have been proposed in the last two decades [16, 17, 18, 19, 20, 21], only a few consider the protective effect of forest [19, 21, 22]. Models that do consider the protection effect of forest can additionally be used for mapping protection forest and quantifying its protection functionagainst rockfalls [23]. In simulation models [19; 21], the protective effect of forest is considered via the spatial distribution of the forest stand, stem diameter at breast height (_DBH_) distribution, and tree species. Simulation models enable rockfall hazard mapping with and without the effect of forest, and with different forest scenarios [23; 24], and thus, they can be used to quantify the protective effect of forest and different forest stands. Some rockfall models are intended for use on a local scale (individual rockfall events), while others are more appropriate for regional scale (multiple rockfall events on different slopes) [5; 18; 25; 26]. The scale of modelling is an important factor when determining the purpose of the modelled results, as it will affect the choice of the grid cell size of the input data. The most common input data for rockfall simulation models is the digital terrain model (DTM), which carries information about the main morphological properties of the surface. The grid cell size of the DTM can have a significant impact on modelling both potential rockfall source and runout areas, primarily on the lateral dispersion of rockfall trajectories [7; 27; 28] and on the kinetic energy of rocks [29; 30]. In order to achieve the most realistic results, the highest grid cell size is desired in rockfall modelling; however, since individual rockfall models are designed for use at a particular spatial level, a higher DTM grid cell size does not necessarily provide improved modelling results. Different studies have shown that the preferred DTM grid cell size lies between 2 and 10 m [31], since with DTMs that have a grid cell size larger than 10 m, the modelled rockfall trajectories will not be modelled correctly [32]. The impact of the grid cell size will be the most significant in areas with meso-scale roughness, while in the smooth areas, the difference is not as evident [30]. With larger DTM grid cell size, the delineation of rockfall source areas becomes rougher, overestimated, and enhanced, while the majority of the cliffs will still be detected [33]. Modelling with DTMs grid cell size smaller than 5 m can result in too much detail and artefacts in DTM [6; 34; 35], while with larger grid cell sizes, the artificial features such as roads and railway tracks will not be captured [29].