This paper explores the question of creating and maintaining terrain maps in environments where the terrain changes. The specific example explored is the construction of terrain maps from 3D LiDAR measurements on an electric rope shovel. The approach extends the height grid representation of terrain to include a Hidden Markov Model in each cell, enabling confidence-based mapping of constantly changing terrain. There are inherent difficulties in this problem, including semantic labelling of the LiDAR measurements associated with machinery and determining the pose of the sensor. Solutions to both of these problems are explored. The significance of this work lies in the need for accurate terrain mapping to support autonomous machine operation.