SAF Measurement, Analysis & Decision Support Systems 3 — Questions and Answers
Question 1: In forest operations research, the traveling salesman problem (TSP) framework is most directly analogous to which silvicultural planning challenge?
- Scheduling regeneration harvests across a landscape to minimize road travel distance (Correct answer)
- Allocating thinning budgets across stand age classes
- Selecting species mixtures for a reforestation project
- Estimating carbon sequestration under different rotation lengths
Correct answer: Scheduling regeneration harvests across a landscape to minimize road travel distance
TSP seeks the shortest route visiting all nodes once, analogous to routing harvest crews or log trucks across dispersed stands to minimize travel distance.
Question 2: Which remote sensing index is most commonly used to detect forest stress and chlorophyll content because it normalizes near-infrared and red reflectance?
- NDWI (Normalized Difference Water Index)
- NDVI (Normalized Difference Vegetation Index) (Correct answer)
- EVI (Enhanced Vegetation Index)
- SAVI (Soil Adjusted Vegetation Index)
Correct answer: NDVI (Normalized Difference Vegetation Index)
NDVI = (NIR − Red)/(NIR + Red) exploits the contrast between high NIR reflectance and low red reflectance in healthy vegetation to detect stress and biomass.
Question 3: A forester runs a regression of total tree height (Y) on DBH (X) and obtains R² = 0.88. What does this mean?
- DBH explains 88% of the variation in tree height in the sample (Correct answer)
- 88% of trees measured had heights within the prediction interval
- The slope of height on DBH is 0.88
- DBH causes 88% of height growth
Correct answer: DBH explains 88% of the variation in tree height in the sample
R² is the coefficient of determination; it represents the proportion of variance in the dependent variable (height) explained by the independent variable (DBH) in the fitted model.
Question 4: Under the FIA (Forest Inventory and Analysis) national design, what type of sampling design is used for annual inventory?
- Simple random sample with variable plot size
- Systematic grid with rotating panels (Correct answer)
- Cluster sampling with fixed-radius subplots only
- Stratified random sampling by forest type group
Correct answer: Systematic grid with rotating panels
FIA uses a systematic grid of permanent clusters measured on a rotating panel schedule (typically 10-20% remeasured annually), enabling annualized state-level estimates.
Question 5: When constructing a timber harvest schedule using linear programming, which constraint type directly enforces even-flow of volume across planning periods?
- Non-negativity constraints
- Adjacency constraints
- Harvest volume deviation constraints (Correct answer)
- Area control constraints
Correct answer: Harvest volume deviation constraints
Harvest volume deviation constraints limit the percentage by which harvest volume in any period can differ from a target level, enforcing even-flow across the planning horizon.
Question 6: A forest manager uses a decision support system (DSS) that incorporates a stochastic fire risk module. The primary benefit of stochastic over deterministic modeling in this context is:
- Stochastic models run faster on standard hardware
- Stochastic models produce a distribution of outcomes reflecting uncertainty in fire occurrence (Correct answer)
- Stochastic models require less data about fuel loads
- Stochastic models are mandated by NEPA for federal lands
Correct answer: Stochastic models produce a distribution of outcomes reflecting uncertainty in fire occurrence
Stochastic models sample from probability distributions for uncertain inputs (ignition probability, weather), producing a range of outcomes that supports risk-based decision making.
Question 7: The Reineke Stand Density Index (SDI) combines trees per acre and average stand diameter to express density relative to a reference stand. Which relationship defines it?
- SDI = TPA × (QMD/10)^1.605 (Correct answer)
- SDI = TPA × (QMD/10)^0.5
- SDI = Basal Area × (QMD/10)
- SDI = TPA / (QMD × 0.005454)
Correct answer: SDI = TPA × (QMD/10)^1.605
Reineke's SDI = TPA × (QMD/10)^1.605, normalizing observed TPA-QMD combinations to an equivalent 10-inch stand using the self-thinning slope of −1.605.
SAF Measurement, Analysis & Decision Support Systems 3
In forest operations research, the traveling salesman problem (TSP) framework is most directly analogous to which silvicultural planning challenge?