The class of k Nearest Neighbor (kNN) queries is frequently used in geospatial applications. Many studies focus on processing kNN in Euclidean and road network spaces. Meanwhile, with the recent advances in remote sensory devices that can acquire detailed elevation data, the new geospatial applications heavily operate on this third dimension, i.e., land surface. Hence, for the field of databases to stay relevant, it should be able to efficiently process spatial queries given this constrained third dimension. However, online processing of the surface k Nearest Neighbor (skNN) queries is quite challenging due to the huge size of land surface models which renders any accurate distance computation on the surface extremely slow. In this paper, for the first time, we propose an index structure on land surface that enables exact and fast responses to skNN queries. Two complementary indexing schemes, namely Tight Surface Index (TSI) and Loose Surface Index (LSI), are constructed and stored co...