Assessing the accuracy of hexagonal versus square tilled grids in preserving DEM surface flow directions

Luís de Sousa, Fernanda Nery, Ricardo Sousa and João Matos
Departamento de Engenharia Civil e Arquitectura
Instituto Superior Técnico (IST)
Avenida Rovisco Pais
1049-001 Lisbon, Portugal
Tel. +351-218418350, Fax: +351-218419765
lads@mega.ist.utl.pt; nery@ist.utl.pt; rts@civil.ist.utl.pt; jmatos@civil.ist.utl.pt

Abstract
The theoretical advantages of hexagonal grids over rectangular grids have been known for a large number of years. Among these, two can be stressed out: the higher spatial resolution achieved with the same number of samples and the isotropy of local neighbourhoods. This work explores such advantages in the representation of flow directions used in hydrologic modeling. The 3 arc-second resolution DEM data collected by the Shuttle Radar Topography Mission (SRTM) was resampled to increasingly  lower resolution grids, both of squares and hexagons. The flow direction vectors where computed in each of these grids using the steepest down slope neighbour criteria; for the hexagonal grids an equivalent model was used. Reference data was obtained from  the original full resolution DEM, calculating the resulting flow direction vectors of the samples contained  inside each of the lower resolution cells. The accuracy of each model in preserving the original DEM flow direction characteristics was assessed by comparing the angles defined by  lower resolution flow vectors with the resulting vectors of the corresponding full resolution samples. In the data analysis phase, the influence of local terrain morphology and variability was evaluated. A set of tests where conducted in the Minho River basin (ca. 16950 Km2 in the northwest of the Iberian Peninsula). The results obtained suggest a superior capacity of the hexagonally tilled grids in maintaining the original flow directions, as given by the resulting vector of the original samples.

Keywords: regular tessellation, hexagonal grid, flow direction

In: Caetano, M. and Painho, M. (eds). Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 5 – 7 July 2006, Lisboa, Instituto Geográfico Português

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