A soil scientist measures lead contamination at 50 sample points and needs to produce a continuous contamination map. Why might kriging be preferred over inverse distance weighting (IDW)?
AKriging is computationally faster than IDW
BKriging uses the variogram to model the actual spatial structure of the data and provides prediction uncertainty estimates, while IDW uses an arbitrary distance-weighting function and gives no uncertainty information
DKriging produces smoother maps that look better in reports
Kriging models the specific spatial correlation structure of the data (via the variogram), weights nearby samples optimally, and produces a standard error map showing where predictions are reliable and where they are uncertain. IDW applies a generic distance-decay function regardless of the data's actual spatial behavior and gives no uncertainty quantification. For environmental contamination assessment, knowing the uncertainty is as important as the prediction itself.
Question 2 True / False
A variogram that reaches a constant value (the sill) at a certain distance (the range) indicates that observations separated by more than the range are no longer spatially correlated.
TTrue
FFalse
Answer: True
The range is the distance at which the variogram reaches its sill (plateau). Beyond this distance, pairs of observations are no more similar than random pairs -- spatial autocorrelation has decayed to zero. The sill represents the total variance of the data. The nugget (variogram value at distance zero) represents very short-range variability plus measurement error. These three parameters -- nugget, sill, range -- characterize the spatial structure.
Question 3 Short Answer
Explain what the nugget effect in a variogram represents physically.
Think about your answer, then reveal below.
Model answer: The nugget is the variogram value extrapolated to zero separation distance. Theoretically, two observations at the same location should be identical (zero variance), but the nugget captures two real-world effects: (1) measurement error -- repeat measurements at the same point will differ due to instrument precision and sampling variability; (2) micro-scale spatial variation at distances smaller than the sampling interval that the survey cannot resolve. A large nugget relative to the sill indicates that much of the total variance is either noise or occurs at scales finer than the sampling design can capture.
The nugget represents the irreducible uncertainty in the data -- the variance that cannot be explained by spatial structure at the scale of observation.