GIS Section 4.2

Question 1

What is spatial interpolation?

Answer 1

process of predicting/estimating calues for unsampled or un-visited locations using measured values

Question 2

Why is spatial interpolation so common?

Answer 2

because it is impossible to measure all of the infinite measurements and locations in an area

Question 3

What types of features can be interpolated?

Answer 3

• point, line, small areas

Question 4

What is the output of spatial interpolation?

Answer 4

raster

Question 5

What are the two main types of spatial interpolation?

Answer 5

• Deterministic
• Probabilistic

Question 6

What types of fitting methods can be used for interpolation (depending on scale)?

Answer 6

• Global fitting methods
• Local estimation (neighbourhood)

Question 7

What is a Global Fitting Method for interpolation?

Answer 7

Trend Surface Analysis - polynomial regression on coordinate pairs
- probabilistic

Question 8

What are the 4 types of local fitting methods for interpolation?

Answer 8

• Inverse Distance Functions (IDW)
• Plate Surface (bi-cubic splines)
• Nearest Neighbour interpolation
• moving averages with arbitrary weights

Question 9

What is the geostatistical spatial interpolation method?

Answer 9

Kriging!!!

Question 10

How does Global polynomial interpolation (trend surface analysis) work?

Answer 10

• fits a smooth surface defined by a polynomial to the sample points
• fits over the full extent of the data (‘global’)
• multiple regression of coordinate pairs

Question 11

What is the result of global polynomial interpolation?

Answer 11

• smooth surface representing gradual changes

Question 12

What can be said of complex polynomials produced through Global polynomial interpolation?

Answer 12

the more complex, the harder it is to ascribe physical meaning to it

Question 13

What is the Thiessen Polygon Method of interpolation?

Answer 13

• split an area into zones
• each zone represents areas that are closer to the central point than any other point
• all parts of a Thiessen polygon have the same value

Question 14

How does Inverse Distance Weighting (IDW) interpolation work?

Answer 14

• uses measured values close the a location to give the location a value
• assumes every nearby point has a local influence that decreases with distance
• known points are given weights that diminish as a function of distance

Question 15

What is an assumption of IDW interpolation?

Answer 15

things that are close together are more alike

Question 16

What two factors are important in IDW interpolation?

Answer 16

SIZE and SHAPE of neighbourhood

• neighbourhood generally circular, but could make adjustments depending on site specifics

Question 17

How is IDW an ‘exact interpolator’?

Answer 17

known input points define the maximum and minimum values that will appear in the interpolation

Question 18

How does a spline work?

Answer 18

• two-dimensional minimum curvature spline
• cubic polynomials are fitted as ‘panels’ that are smoothed together

Question 19

What are the two kinds of spline?

Answer 19

• regularized
• tension

Question 20

What is the optimal interpolation method?

Answer 20

Kriging

Question 21

How does kriging work?

Answer 21

• uses calculated semi-variance to find how distance affects change in a given area

Question 22

What two tasks are necessary for kriging?

Answer 22

• uncover dependancy rules (by semi-variogram)
• make the predictions

Question 23

What are the two steps in kriging?

Answer 23

1. Estimate the semi-variogram
2. Fit a mathematical model to those values

(then it can use the model to make a prediction)

Question 24

What are the structural components of variability in kriging?

Answer 24

• C = maximum ‘sill’ variance
• Co = ‘nugget’ variance (chance)
• C-Co = variability due to spatial dependence
  b = range of influence
  points = experimental semi-variance values

Question 25

What is the semi-variogram?

Answer 25

graph depicting the spatial autocorrelation of measured sample points

Question 26

What competing models might fit to a semi-variogram?

Answer 26

• Gaussian
• Spherical
• exponential

Question 27

What is the recommended procedure for kriging?

Answer 27

1. plot the experimental semi-variogram
2. choose candidate models
3. Check Residual Sum of Squares (RSS) and RMS in predicitions (ie do the kriging a bunch and check errors)
4. Select midel that minimizes RMS
5. Inspect visually
6. select model and parameters that minimize RMS

Question 28

Essentially, what is kriging?

Answer 28

a weighted local moving average of variable Z which has been measured at points within a neighbourhood

Question 29

What is ‘cross-validation’ of a semi-variogram model fit?

Answer 29

trying models iteratively and comparing the RMS values
- the best indicator for finding the best model!

Question 30

What is a major shorrtcoming of kriging?

Answer 30

takes a long time to fit semi-variogram models

Question 31

What can Empirical Bayesian Kriging do?

Answer 31

• compare dozens of models at once using empirical simulation (checking a family/’ensemble’ of similar models at once
• select the average/best of a family of models

Question 32

What’s so great about Empirical Bayesian Kriging?

Answer 32

saves a lot of time!
- uses the mean model of the ‘ensemble’ of models