# Chapter 32 Activity 15: Spatially Continuous Data I

NOTE: The source files for this book are available with companion package {isdas}. The source files are in Rmarkdown format and packed as templates. These files allow you execute code within the notebook, so that you can work interactively with the notes.

## 32.1 Practice questions

1. What is the difference between spatially continuous data and a spatial point pattern?
2. What is the purpose of spatial interpolation?
3. In your own words describe the method of Inverse Distance Weighting.
4. Consider the following spatial interpolation algorithms: Voronoi polygons and k-point means. How do they differ when the number of points used to calculate means is 1?

## 32.2 Learning objectives

In this activity, you will:

1. Explore a dataset with area data using visualization as appropriate.
2. Discuss a process that might explain any pattern observed from the data.
3. Conduct a modeling exercise using appropriate techniques. Justify your modeling decisions.

• Bailey TC and Gatrell AC (1995) Interactive Spatial Data Analysis, Chapters 5 and 6. Longman: Essex.
• Bivand RS, Pebesma E, and Gomez-Rubio V (2008) Applied Spatial Data Analysis with R, Chapter 8. Springer: New York.
• Brunsdon C and Comber L (2015) An Introduction to R for Spatial Analysis and Mapping, Chapter 6, Sections 6.7 and 6.8. Sage: Los Angeles.
• Isaaks EH and Srivastava RM (1989) An Introduction to Applied Geostatistics, Chapter 4. Oxford University Press: Oxford.
• O’Sullivan D and Unwin D (2010) Geographic Information Analysis, 2nd Edition, Chapters 9 and 10. John Wiley & Sons: New Jersey.

## 32.4 Preliminaries

It is good practice to clear the working space to make sure that you do not have extraneous items there when you begin your work. The command in R to clear the workspace is rm (for “remove”), followed by a list of items to be removed. To clear the workspace from all objects, do the following:

rm(list = ls())

Note that ls() lists all objects currently on the workspace.

Load the libraries you will use in this activity (load other packages as appropriate).

library(isdas)
library(tidyverse)
library(spatstat)
library(spdep)
library(plotly)

Load the data that you will use in this activity:

data("aquifer")

The data is a set of piezometric head (watertable pressure) observations of the Wolfcamp Aquifer in Texas (https://en.wikipedia.org/wiki/Hydraulic_head). Measures of pressure can be used to infer the flow of underground water, since water flows from high to low pressure areas.

These data were collected to evaluate potential flow of contamination related to a high level toxic waste repository in Texas. The Deaf Smith county site in Texas was one of three potential sites proposed for this repository. Beneath the site is a deep brine aquifer known as the Wolfcamp aquifer that may serve as a conduit of contamination leaking from the repository.

The data set consists of 85 georeferenced measurements of piezometric head. Possible applications of interpolation are to determine sites at risk and to quantify uncertainty of the interpolated surface, to evaluate the best locations for monitoring stations.

Create an a unique identifier variable:

aquifer\$ID <- factor(c(1:nrow(aquifer)))

## 32.5 Activity

NOTE: Activities include technical “how to” tasks/questions. Usually, these ask you to practice using the software to organize data, create plots, and so on in support of analysis and interpretation. The second type of questions ask you to activate your brainware and to think geographically and statistically.

Activity Part I

1. Map the Wolfcamp Aquifer data.

2. Create a surface using Voronoi polygons.

3. Create a surface using IDW.

4. Create a surface using $$k$$-point means.

Activity Part II

1. What is the effect of changing the power of the inverse distance function?

2. What is the effect of changing the number of points used in this algorithm?

3. Discuss the limitations of these approaches. How can you calculate the uncertainty in the predictions?

### References

Bailey, T. C., and A. C. Gatrell. 1995. Interactive Spatial Data Analysis. Book. Essex: Addison Wesley Longman.
Bivand, R. S., E. J. Pebesma, and V. Gómez-Rubio. 2008. Applied Spatial Data Analysis with r. Book. New York: Springer Science+Business Media.
Brunsdon, Chris, and Lex Comber. 2015. An Introduction to r for Spatial Analysis and Mapping. Book. Sage.
Isaaks, E. H., and R. M. Srivastava. 1989. Applied Geostatistics. Book. New York: Oxford University Press.
O’Sullivan, David, and David Unwin. 2010. Geographic Information Analysis. Book. 2nd. Edition. Hoboken, New Jersey: John Wiley & Sons.