18-Geom-A7 Geospatial Information Systems · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, December 2018 — 04-Geom-A7, Geospatial Information Systems. Closed book (one approved Casio or Sharp calculator permitted); duration 3 hours. Fifteen (15) questions are provided and any ten (10) constitute a complete paper; each question is of equal value (10 marks), so a complete paper totals 100 marks. Most answers are essay-format; clarity and organization count. All fifteen questions are solved below for completeness.
Longley, Goodchild, Maguire & Rhind, Geographic Information Systems and Science (4th ed.); P. Bolstad, GIS Fundamentals (5th ed.); Worboys & Duckham, GIS: A Computing Perspective (2nd ed.); Burrough, McDonnell & Lloyd, Principles of Geographical Information Systems (3rd ed.); de Smith, Goodchild & Longley, Geospatial Analysis; OGC Simple Feature Access (ISO 19125); ISO 19157 Geographic information — Data quality; ISO 19115 Metadata.
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.
Overlay combines two or more spatially coincident layers cell-by-cell (raster) or region-by-region (vector) to produce a new layer; the four operators differ in the rule used to combine coincident values.
a) Arithmetic overlay. Coincident values are combined by ordinary arithmetic — addition, subtraction, multiplication, division or a weighted sum. It is the basis of raster map algebra and of weighted-overlay suitability models, e.g., Suitability = w1·Slope + w2·Soil + w3·Access. It requires the inputs to be measured on interval/ratio scales.
b) Logical (Boolean) overlay. Inputs are treated as binary (true/false — meets criterion or not) and combined with the Boolean operators AND, OR, NOT (and XOR). It produces a crisp in/out result, e.g., Suitable = (slope < 10°) AND (soil = good) AND NOT(flood zone). It answers strict "all/any/none of these conditions" questions with hard boundaries.
c) Probabilistic overlay. Each input expresses a probability (or likelihood/weight of evidence) of an outcome, and the layers are combined using probability theory — typically Bayes' rule or weights-of-evidence — to yield a posterior probability that accounts for the reliability of each evidence layer. It is used where inputs are uncertain, e.g., Bayesian mineral- or landslide-potential mapping, and outputs a graded probability surface rather than a yes/no map.
d) Fuzzy overlay. Inputs are expressed as fuzzy membership values in [0, 1] (degree of belonging to a set such as "steep" or "suitable") instead of crisp 0/1, and are combined with fuzzy operators — fuzzy AND (minimum), fuzzy OR (maximum), fuzzy algebraic product/sum, or the gamma operator. Fuzzy overlay handles gradational boundaries and vague classes gracefully, producing a continuous suitability score; it is preferred when class transitions are gradual and rigid Boolean cut-offs would be arbitrary.
