J. Geogr. Sci. 2015, 25(2): 196-210 DOI: 10.1007/s11442-015-1162-2 © 2015 Science Press Springer-Verlag Received: 2013-06-05 Accepted: 2014-04-20 Author: Rafaello Bergonse, E-mail: rafaellobergonse@gmail.com www.geogsci.com www.springerlink.com/content/1009-637x Reconstructing pre-erosion topography using spatial interpolation techniques: A validation-based approach Rafaello BERGONSE, Eusébio REIS Center for Geographical Studies, University of Lisbon, Portugal Abstract: Understanding the topographic context preceding the development of erosive landforms is of major relevance in geomorphic research, as topography is an important factor on both water and mass movement-related erosion, and knowledge of the original surface is a condition for quantifying the volume of eroded material. Although any reconstruction implies assuming that the resulting surface reflects the original topography, past works have been dominated by linear in- terpolation methods, incapable of generating curved surfaces in areas with no data or values out- side the range of variation of inputs. In spite of these limitations, impossibility of validation has led to the assumption of surface representativity never being challenged. In this paper, a validation-based method is applied in order to define the optimal interpolation technique for reconstructing pre-erosion topography in a given study area. In spite of the absence of the original surface, different techniques can be nonetheless evaluated by quantifying their ca- pacity to reproduce known topography in unincised locations within the same geomorphic contexts of existing erosive landforms. A linear method (Triangulated Irregular Network, TIN) and 23 parameterizations of three distinct Spline interpolation techniques were compared using 50 test areas in a context of research on large gully dynamics in the South of Portugal. Results show that almost all Spline methods produced smaller errors than the TIN, and that the latter produced a mean absolute error 61.4% higher than the best Spline method, clearly establishing both the better adjustment of Splines to the geomorphic context considered and the limitations of linear ap- proaches. The proposed method can easily be applied to different interpolation techniques and topographic contexts, enabling better calculations of eroded volumes and denudation rates as well as the in- vestigation of controls by antecedent topographic form over erosive processes. Keywords: pre-erosion topography; surface reconstruction; spatial interpolation; spline interpolation; triangu- lated irregular networks; erosive landforms; gully erosion 1 Introduction Topographic form is both a cause and a consequence of erosive processes. Concerning water erosion, slope (i.e. the first derivative of altitude) controls the velocity of flow, and hence the shear stress it exerts. Relations between slope and shear stress are explicit in the shear stress equation (e.g. Poesen et al., 2003; Yao et al., 2008):