Generation of kth-order random toposequences

The model presented in this paper derives toposequences from a digital elevation model (DEM). It is written in ArcInfo Macro Language (AML). The toposequences are called kth-order random toposequences, because they take a random path uphill to the top of a hill and downhill to a stream or valley bottom from a randomly selected seed point, and they are located in a streamshed of order k according to a particular stream-ordering system. We define a kth-order streamshed as the area of land that drains directly to a stream segment of stream order k. The model attempts to optimise the spatial configuration of a set of derived toposequences iteratively by using simulated annealing to maximise the total sum of distances between each toposequence hilltop in the set.The user is able to select the order, k, of the derived toposequences. Toposequences are useful for determining soil sampling locations for use in collecting soil data for digital soil mapping applications. Sampling locations can be allocated according to equal elevation or equal-distance intervals along the length of the toposequence, for example.We demonstrate the use of this model for a study area in the Hunter Valley of New South Wales, Australia. Of the 64 toposequences derived, 32 were first-order random toposequences according to Strahler's stream-ordering system, and 32 were second-order random toposequences.The model that we present in this paper is an efficient method for sampling soil along soil toposequences. The soils along a toposequence are related to each other by the topography they are found in, so soil data collected by this method is useful for establishing soil–landscape rules for the preparation of digital soil maps.