Reconstructing pre-erosion topography using spatial interpolation techniques: A validation-based approach

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 interpolation methods, incapable of generating curved surfaces in areas with no data or values outside 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 capacity 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 approaches. 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 investigation of controls by antecedent topographic form over erosive processes.

Paleotopographic controls on loess deposition in the Loess Plateau of China

“…The initial accuracy results (Table ) suggest that the Kriging method is suitable for paleotopography reconstruction. However, the interpolated result could also be influenced by the input parameters (Bergonse and Reis, ), such as the Semivariogram models and the number of points in a radius. Figure shows the results for different input parameters for the Kriging evaluation.…”

“…Hence, there is a need to examine the effect of scale on the spatial variation of loess deposition in relation to paleotopography. With the development of the multiple data source acquisition and digital terrain analysis method (Geomorphometry; Evans, 2012), it is possible to reconstruct pre-existing underlying paleotopography (Alexander et al, 2008;Campani et al, 2012;Perron and Fagherazzi, 2012;Castillo et al, 2014;Xiong et al, 2014c;Bergonse and Reis, 2015). A comparative analysis of both dual-layer terrains, including modern terrain and paleotopography, could help to reveal the landform evolution process.…”

Topographic Spatial Variation Analysis of Loess Shoulder Lines in the Loess Plateau of China Based on MF-DFA

“…In recent years, the development of Digital Elevation Model (DEM) applications and Geographic Information System (GIS) spatial analysis techniques has greatly promoted the study of the land surface analysis of the Loess Plateau. Digital land surface analysis has been used to extract the basic terrain derivatives (e.g., slope and aspect) [15,16] and to study complicated applications (e.g., paleo-topographic reconstruction and landform classification) [17][18][19][20][21] of the Loess Plateau. The terrain points [22][23][24], lines [25][26][27], and surfaces [28][29][30] studies mainly focused on research with the view of developing and evaluating technologies and methods, and there is a lack of research and discussion on the role of terrain data in the study of the topography and geomorphology of the Loess Plateau.…”

Comparative analysis of SRTM, TanDEM-X and UAV-SfM DEMs to estimate lavaka (gully) volumes and mobilization rates in the Lake Alaotra region (Madagascar)

“…Two interpolation methods were used: i) Triangulated Irregular Network (TIN) and ii) spline interpolation. TIN interpolation is based on a linear method where triangles are constructed from the nearest neighbour points, resulting in non-smooth surfaces (Bergonse and Reis, 2015; QGIS, 2020) (Fig. 2b).…”