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18-Geom-B1 Digital Terrain Modelling · December 2014

Question 2 of 12: Definitions in Digital Terrain Modelling

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

Notes on this paper

Paper format: National Exams, December 2014 — 3 hours, closed book (any non-communicating calculator permitted). TWELVE numbered questions constitute a complete paper; each is of varying value and the schedule totals 100 marks. Most answers are required in essay format, so clarity and organization are graded. All twelve questions are solved below for completeness.

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); Natural Resources Canada High-Resolution DEM (HRDEM) and CDEM product specifications. Canadian datums throughout (NAD83(CSRS), CGVD2013).

Check / source note. The Question 1 header carries 9 marks but its annotation reads “(3 × 2 marks)” = 6. The header value is authoritative because it is the figure that makes the printed schedule sum to the stated 100 Total marks; the “3 × 2” is a typographic error for 3 × 3. Answers are graded on all three parts of Q1 equally.

Question 2: Definitions in Digital Terrain Modelling (10 marks)

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. Five terms central to building and describing a terrain model.

Find. A precise definition of each.

(a) Breaklines. Linear features along which the terrain slope changes abruptly—ridge lines, valley/drainage lines, the tops and toes of banks, road crowns, curbs, retaining walls and shorelines. They are stored as constraints so that interpolation and triangulation are not allowed to cross them, preserving the discontinuity. A hard breakline marks a true slope break (a ditch); a soft breakline enforces a feature edge without a slope change (a mapped boundary).

(b) Spot heights. Discrete, individually measured points of known elevation placed at locally significant locations—summits, depressions (pits), saddles, and other points the grid would otherwise miss. They supplement the systematic samples and anchor the surface at critical morphological points.

(c) Sampling interval. The spacing (ground distance) between adjacent elevation samples—the grid post-spacing or the mean point spacing of an irregular set. It governs the spatial resolution of the model, the smallest terrain feature that can be represented (a Nyquist-type limit), the data volume, and the achievable accuracy.

(d) Elevation data accuracy. The closeness of the modelled heights to their true values, i.e. the vertical accuracy, usually quantified as a root-mean-square error $\text{RMSE}_z$ or, following the U.S. NSSDA / ASPRS convention, as a 95%-confidence value ($\text{RMSE}_z\times1.96$ in open terrain). It is a function of the source technique, the sampling interval, the terrain and the interpolation.

(e) Interpolation method. The mathematical rule used to estimate the elevation at an unsampled location from surrounding known heights—e.g. linear interpolation within a TIN facet, bilinear/bicubic on a grid, inverse-distance weighting (IDW), splines, or geostatistical Kriging. The choice controls how faithfully the continuous surface is reconstructed and how noise is treated (exact vs. smoothing interpolators).