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18-Geom-B1 Digital Terrain Modelling · December 2017

Question 10 of 12: Flow Directions, Flow Lines and Watershed from a DEM

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: National Exams, December 2017 — 3 hours, closed book (one approved Casio or Sharp calculator permitted). The schedule prints TWELVE questions and states that "10 questions constitute a complete paper": Part A (Q1–Q8) is compulsory, Part B requires ONE of Q9–Q10, and Part C requires ONE of Q11–Q12, for a 100-mark paper. All twelve questions are solved below for completeness (a candidate would answer only Q1–Q8 plus one from each of Parts B and C).

Reference texts: Li, Zhu & Gold, Digital Terrain Modeling — Principles and Methodology (CRC Press, 2005); Maune (ed.), Digital Elevation Model Technologies and Applications: The DEM Users Manual (2nd ed., ASPRS, 2007); Wilson & Gallant, Terrain Analysis — Principles and Applications (Wiley, 2000); Wolf, Dewitt & Wilkinson, Elements of Photogrammetry with Applications in GIS (4th ed., McGraw-Hill, 2014); Isaaks & Srivastava, An Introduction to Applied Geostatistics (Oxford, 1989). Canadian datums throughout (NAD83(CSRS), CGVD2013).

Question 10: Flow Directions, Flow Lines and Watershed from a DEM (10 marks — Part B, answer one of Q9/Q10)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A bare-earth DEM of a drainage basin.

Find. (10.1) how the DEM yields flow directions and flow lines; (10.2) how it yields a watershed boundary.

Watershed boundary (ridge)Stream networkOutlet (pour point)
Hydrologic terrain analysis on a DEM: each cell drains to its steepest-descent neighbour (flow directions), flow accumulates into channels (flow lines), and the set of cells draining to an outlet, bounded by ridge divides, is the watershed.

10.1 Flow directions and flow lines. Flow is inferred from the DEM by the rule that water runs downhill along the steepest gradient. First the DEM is hydrologically conditioned by filling spurious sinks/pits (single-cell depressions from noise) so every cell can drain. Then a flow-direction grid is computed: in the standard D8 algorithm each cell is assigned the one of its eight neighbours that gives the steepest downslope gradient, $\max\big[(z_0 - z_i)/d_i\big]$ (with $d_i = \Delta$ for cardinal, $\sqrt{2}\,\Delta$ for diagonal neighbours). Chaining each cell to its downstream neighbour traces the flow lines (flow paths). Accumulating, for every cell, the number of upstream cells that drain through it gives a flow-accumulation grid; cells whose accumulation exceeds a threshold form the drainage/stream network — the principal flow lines of the basin.

10.2 Watershed boundary. A watershed (catchment) is the area that drains to a chosen point. Using the flow-direction grid: (1) select an outlet (pour point) on the stream network; (2) trace upstream — recursively collect every cell whose downslope flow path eventually reaches that outlet; (3) the union of all contributing cells is the catchment, and its outer edge is the watershed boundary. Geometrically the boundary follows the ridge lines (drainage divides), where flow directions on either side diverge into different basins. The delineation is only as good as the DEM: unfilled sinks fragment the catchment, and on flat terrain a small vertical error can shift the divide a long way horizontally.