# Chapter 38 Activity 18: Spatially Continuous Data IV

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.

## 38.1 Practice questions

1. What does “Best” in BLUP mean?
2. What is the advantage of kriging over other interpolation approaches?
3. How is the the autocovariance used to produce optimal predictions?

## 38.2 Learning objectives

In this activity, you will:

1. Conduct variograpic analysis.

2. Use kriging to interpolate a field.

• 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 12. 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.

## 38.4 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(gstat)
library(sf)
library(tidyverse)
library(stars)

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.

Convert to a SpatialPointsDataFrame:

aquifer.sf <- aquifer %>%
st_as_sf(coords = c("X", "Y"),
remove = FALSE)

## 38.5 Activity

Capstone Activity

This is a capstone activity where you can work free-style on a data set of your choice, and put in practice what you have learned with respect to the analysis of spatially continuous/ field data.

1. Partner with a fellow student to analyze the dataset provided.

2. Use kriging to interpolate the underlying field. Justify your modeling choices.

4. Imagine that you had to compare different modeling approaches (e.g., kriging, IDW). Propose a protocol to decide which method is more accurate.

Anselin, Luc. 1988. Spatial Econometrics: Methods and Models. Book. Dordrecht: Kluwer.
———. 1995. “Local Indicators of Spatial Association - LISA.” Journal Article. Geographical Analysis 27: 93–115.
Baddeley, Adrian, Ege Rubak, and Rolf Turner. 2016. Spatial Point Patterns: Methodology and Applications with r. Book. Chapman; Hall/CRC.
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, C., A. S. Fotheringham, and M. E. Charlton. 1996. “Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity.” Journal Article. Geographical Analysis 28 (4): 281–98. ISI:A1996VL03500001.
Brunsdon, Chris, and Lex Comber. 2015. An Introduction to r for Spatial Analysis and Mapping. Book. Sage.
Cressie, N. A. C. 1993. Statistics for Spatial Data. Book. Wiley Series in Probability and Mathematical Statistics. New York: John Wiley & Sons.
Farber, S., and A. Páez. 2007. “A Systematic Investigation of Cross-Validation in GWR Model Estimation: Empirical Analysis and Monte Carlo Simulations.” Journal Article. Journal of Geographical Systems 9 (4): 371–96. C:/Papers/Journal of Geographical Systems/Journal of Geographical Systems (2007) 9 (4) 371-396.pdf.
Fotheringham, A. S., and C. Brunsdon. 1999. “Local Forms of Spatial Analysis.” Journal Article. Geographical Analysis 31 (4): 340–58.
Getis, A., and J. K. Ord. 1992. “The Analysis of Spatial Association by Use of Distance Statistics.” Journal Article. Geographical Analysis 24 (3): 189–206. ISI:A1992JF93400001 C:/Papers/Geographical Analysis/Geographical Analysis (1992) 24 (3) 189-206.pdf.
Geyer, Charles J, and Jesper Møller. 1994. “Simulation Procedures and Likelihood Inference for Spatial Point Processes.” Scandinavian Journal of Statistics, 359–73.
Griffith, D. A. 1988. Advanced Spatial Statistics: Special Topics in the Exploration of Quantitative Spatial Data Series. Book. Dordrecht: Kluwer.
Haase, P. 1995. “Spatial Pattern Analysis in Ecology Based on Ripley’s k-Function: Introduction and Methods of Edge Correction.” Journal of Vegetation Science 6 (4): 575–82.
Haining, R. 1990. Spatial Data Analysis in the Social and Environmental Sciences. Book. Cambridge: Cambridge University Press.
Isaaks, E. H., and R. M. Srivastava. 1989. Applied Geostatistics. Book. New York: Oxford University Press.
Lloyd, Christopher D. 2010. Local Models for Spatial Analysis. CRC press.
Lovelace, Robin, Jacub Nowosad, and Jannes Muenchow. 2019. Geocomputation with r. Book. CRC Press.
McElreath, Richard. 2016. Statistical Rethinking: A Bayesian Course with Examples in r and Stan. Book. Vol. 122. CRC Press.
McGrew Jr, J Chapman, and Charles B Monroe. 2009. An Introduction to Statistical Problem Solving in Geography. Book. 2nd. Edition. Long Grove, Illinois: Waveland Press.
McMillen, D. P. 2003. “Spatial Autocorrelation or Model Misspecification?” Journal Article. International Regional Science Review 26 (2): 208–17. ISI:000181958400007 C:/Papers/International Regional Science Review/International Regional Science Review (2003) 26 (2) 208-217.pdf.
Moller, Jesper, and Rasmus Plenge Waagepetersen. 2003. Statistical Inference and Simulation for Spatial Point Processes. Chapman; Hall/CRC.
O’Sullivan, David, and David Unwin. 2010. Geographic Information Analysis. Book. 2nd. Edition. Hoboken, New Jersey: John Wiley & Sons.
Paez, A., S. Farber, and D. Wheeler. 2011. “A Simulation-Based Study of Geographically Weighted Regression as a Method for Investigating Spatially Varying Relationships.” Journal Article. Environment and Planning A 43 (12): 2992–3010. https://doi.org/10.1068/a44111.
Paez, A., F. Long, and S. Farber. 2008. “Moving Window Approaches for Hedonic Price Estimation: An Empirical Comparison of Modelling Techniques.” Journal Article. Urban Studies 45 (8): 1565–81. https://doi.org/10.1177/0042098008091491.
Plant, Richard E. 2012. Spatial Data Analysis in Ecology and Agriculture Using r. Book. cRc Press.
Rey, S. J. 2009. “Show Me the Code: Spatial Analysis and Open Source.” Journal Article. Journal of Geographical Systems 11 (2): 191–207. ISI:000266249500007.
Ripley, B. D. 1976. “2nd-Order Analysis of Stationary Point Processes.” Journal Article. Journal of Applied Probability 13 (2): 255–66. ISI:A1976CA37400007.
Tomlin, C Dana. 1990. A Map Algebra. Harvard Graduate School of Design Cambridge, MA.
Tong, Daoqin, and Alan T. Murray. 2012. “Spatial Optimization in Geography.” Journal Article. Annals of the Association of American Geographers 102 (6): 1290–1309. https://doi.org/10.1080/00045608.2012.685044.
Wickham, Hadley. 2015. R Packages: Organize, Test, Document, and Share Your Code. " O’Reilly Media, Inc.".
———. 2017. Tidyverse: Easily Install and Load the ’Tidyverse’. https://CRAN.R-project.org/package=tidyverse.
Wickham, Hadley, and Garrett Grolemund. 2016. R for Data Science: Import, Tidy, Transform, Visualize, and Model Data. " O’Reilly Media, Inc.".
With, Kimberly A, and Anthony W King. 1997. “The Use and Misuse of Neutral Landscape Models in Ecology.” Oikos, 219–29.

### 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.