This article presents a set of artificial surfaces simulating complex terrain types for evaluating the performances of grid-based flow direction algorithms. The proposed artificial surfaces were developed based on sine and cosine functions and thus can simulate four complex terrain
types: a convex-centred slope, concave-centred slope, saddle-centred slope and straight-ridge slope; such features are typical and widespread in real landscapes. We analytically solved the theoretical values of specific catchment area (SCA) for the proposed artificial surfaces. Compared with
existing artificial surfaces for evaluating flow direction algorithms, the proposed artificial surfaces provide a better representation of common terrain types in the real world. To analyse the feasibility of the proposed artificial surfaces, two sets of artificial digital elevation models
(DEMs) were created by sampling the proposed artificial surfaces with different reliefs at a series of resolutions (i.e. 1, 5, 10 and 20 m). Four representative flow direction algorithms were applied to these artificial DEMs: D8, D-inf, FD8 and MFD-md. The root mean square error, mean
error and standard deviation in the computed SCA from flow direction algorithm show that MFD-md generally yielded lower error under simulated terrain conditions than D8, D-inf and FD8. The cumulative frequency distributions of errors from the tested flow direction algorithms with the proposed
artificial DEMs can effectively reflect the inherent characteristics of each algorithm. MFD-md performed more similarly to FD8 in low-relief terrains and more similarly to D-inf in high-relief terrains. The map of errors from each tested algorithm is available for a spatially explicit evaluation
of the occurrence of errors. Over most of the area, the D-inf algorithm underestimated the SCA when FD8 overestimated the SCA.
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