18-Geom-B1 Digital Terrain Modelling · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2015 — 3 hours, closed book (an approved Casio or Sharp calculator permitted). TWELVE numbered questions constitute a complete paper; each is of varying value and the margin 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).
Note: this December 2015 paper is the same twelve-question essay set as the December 2014 04-Geom-B1 exam, re-ordered and with one definition changed (Q3(e) asks for the contour interval where the 2014 paper asked for the interpolation method). The margin marks are internally consistent this year — every sub-part annotation matches its header weight and the schedule sums to 100.
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 DEM (grid or point set) possibly containing gross errors (spikes, wells, mismatched strips).
Find. A mathematical procedure to detect and remove them.
Method. Blunders are located as statistical outliers against a locally predicted surface: (1) for each point, fit a local surface (a plane or low-order polynomial, or interpolate from a robust neighbourhood) using the surrounding points; (2) form the residual $v_i = z_i - \hat z_i$ between the observed height and the predicted height; (3) estimate the residual spread with a robust scale (median absolute deviation or a trimmed standard deviation $\hat\sigma$, so the blunders themselves do not inflate it); (4) apply a rejection test—flag any point with a standardized residual $|v_i|/\hat\sigma$ exceeding a threshold (commonly $3\sigma$, i.e. data-snooping / Baarda's test at a chosen significance). Detected spikes and pits are then eliminated by deletion and the location re-interpolated from the accepted neighbours, or replaced by the local prediction. Because removing one blunder changes the local statistics, the process is iterated (one point per pass, re-estimating $\hat\sigma$) until no residual exceeds the threshold. Robust estimators (least-median-of-squares, RANSAC-type surface fitting) are preferred so a cluster of gross errors cannot mask itself.
