18-Geom-B1 Digital Terrain Modelling · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
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 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. An airborne laser-scanning (lidar) system used to measure terrain.
Find. (7.1) how such a system works; (7.2) single- versus multiple-return sensing and the extra information multiple returns provide.
7.1 Operational principle. Airborne lidar (LiDAR / airborne laser scanning) measures the 3-D position of ground points by active laser ranging from a moving aircraft. A pulsed near-infrared laser fires tens to hundreds of thousands of pulses per second; a scanning mirror sweeps the beam across-track while the aircraft advances, painting a swath of ground. For each pulse the system measures the two-way travel time $t$ and computes the slant range $R = \tfrac{1}{2}c\,t$ to the reflecting surface. Three subsystems are fused to turn that range into a georeferenced coordinate: (i) an onboard GNSS receiver (differential to a ground base) gives the aircraft position; (ii) an inertial measurement unit (IMU) gives the aircraft attitude (roll, pitch, heading); and (iii) an angle encoder gives the instantaneous scan angle. Combining sensor position, attitude, scan angle and range in a rigorous geolocation equation yields an accurate $(X,Y,Z)$ for every return — a dense, irregular 3-D point cloud. The raw cloud is a DSM; ground filtering separates bare-earth returns to build the DEM/DTM. Precise time synchronization across GNSS/IMU/scanner and system calibration (boresight) are essential to the cm-level accuracy.
7.2 Single vs multiple returns. A single laser pulse has a finite footprint and can strike several surfaces at different heights on its way down (canopy top, branches, understorey, ground). A single-return sensor records only one echo per pulse (typically the first or the strongest), so over vegetation it captures mainly the canopy and cannot see the ground. A multiple-return sensor records several discrete echoes per pulse — commonly first, intermediate and last returns — because partial reflections come back from each surface the beam partly penetrates. Additional information from multiple returns: the last return (which has penetrated gaps in the foliage) supplies genuine bare-earth heights for the DEM, while the first return gives the DSM; the difference (DSM − DEM) is the canopy / object height, from which vegetation height, forest biomass and building heights are derived. The vertical distribution of intermediate returns profiles the canopy structure (multiple storeys), and return count/intensity aids land-cover classification. In short, multiple returns let one flight yield both the surface and the terrain, plus the vegetation in between.
