499c Lab 8 (Spatial Interpolation): Todd Mitchell

Todd Mitchell

GEOG-499c

Lab 8: Spatial Interpolation

1. What is a Thiessen polygon?

Thiessen polygons are a kind of nearest neighbor indicator. The points of each polygon are defined by the perpendicular bisectors of the lines between all points.

2. What is the major difference between Hand-in 2 and Hand-in 3? Why?

Simple Density shows large areas, whereas Kernel Density shows smaller areas. Simple Density adds and divides cells to calculate the emissions, and Kernel Density is a convolution from each emission location to the search radius, resulting in a smaller area.

3. What is the major difference between Hand-in 4 and Hand-in 5? Why?

Hand-In 5 shows a slightly finer division between classes than Hand-In 4. The exponential difference between ì2î and ì3î is barely noticeable.

4. What is the major difference among Hand-ins 6-8? Why?

The regularized spline (#6) is smoother in the area of study versus the tension splines of #7 and #8. The regularized spline creates smooth, gradual surfaces with values which may lie outside the data range. A tension spline adjusts the surface based on trends in the data and has values corresponding more closely to the data range.

5. What is histogram? What does the histogram on page 20 tell you?

A histogram is a graph of the distribution of data. Individual values are shown on the x-axis and frequency (density) of those values is shown on the y-axis. The close approximation of a bell shape on the page 20 histogram shows a normal distribution of data.

6. What is the QQplot?

This compares the distribution of data to a standard normal distribution, allowing an easy appraisal of the data.

7. Define the terms: Sill, Range, Nugget, and variogram. Estimate the value of sill range and nugget for the variogram after step 10 on page 28.

Sill ñ represents the value in a variogram when distances are very large.

Range ñ represents the lag distance in a variogram.

Nugget ñ represents minute variations and measurement error in the variogram.

Variogram ñ a graph showing the variance of the difference between two variables at two locations.

The estimated value of sill would be 29.28 x 10⁵ g, range would be 1.2 x 10^-5 h, and nugget would be around 10 x 10⁵ g.

8. What do the graphs tell you when you conduct cross-validation analysis (page 35-36)?

This shows me how closely the measured data matches the predicted values. The closer the model falls to the line, the better the result.

9. Which is model is better after doing the comparison in Exercise 4? Why?

The Trend Removed model was the best because it had less microstructure error than Indicator Kriging.

10. What does the map Indicator Kriging mean?

The map shows values contained within a user defined threshold (0.12) as 1 and values falling outside that threshold as 0. It is not representing the measured data as the Trend Removed model.

Maps:

Hand-In 1