Flow direction algorithms in a Hierarchical Hexagonal Surface Model

Abstract

Motivated by the need for hydrologically adaptive representations of urban environments for hydrological modelling, this paper proposes a Hexagonal Hierarchical Surface Model (HHSM) and an equivalent Rectangular Hierarchical Surface Model (RHSM). The HSMs are point-based Level of Detail (LoD) models that store values in array trees. Both HSMs use an intrinsically hierarchical indexing system across both the tree and array components of the data structure, which facilitates neighbourhood operations, adaptive surfaces and multi-level analysis. An investigation of variable resolution flow direction arrays using a mathematically defined cone surface shows that at the highest levels of detail, rotation between LoDs in the HHSM causes significant loss of accuracy if flow directions are restricted to the directions of a cell's neighbours. There is no such effect in the RHSM. These findings suggest unrestricted flow direction algorithms such as D∞ are required for adaptive hexagonal flow direction arrays.

Keywords::

• digital elevation model
• flow direction
• level of detail
• hexagonal image processing
• hierarchical surface model

Acknowledgements

We thank the two anonymous reviewers whose comments and suggestions helped improve and clarify this manuscript.