Interpolation
Content for Monday, October 23, 2023
Point patterns give us the foundation for beginning geostatistical analyses. In geostatistical analyses, we have observations or a spatial process from a limited sample of locations, but would like to be able to infer the values of that process across the entire study region (or at least an area larger than we initially sampled). Interpolation provides one simple way of doing this that relies on the notion that we can learn something about the process simply from our measurements and the location those measurements were taken. We can extend these approaches by adding additional covariates and model structures, but we’ll start simple for now.
Resources
Chapter 2: Scale in (Fletcher and Fortin 2018) provides a thorough introduction to the ecologist’s conceptualization of scale with
Rexamples.This article by Steven Manson (Manson 2008) provides a more comprehensive view of conceptualizations of scale.
The Hypothesis Testing and Autocorrelation chapters of Manuel Gimond’s Introduction to GIS and Spatial Analysis
bookdownproject provide concrete examples of attempts to find process from spatial patterns.Chapter 12: Spatial Interpolation in Spatial Data Science by Edzer Pebesma and Roger Bivand provides examples of different types of kriging and interpolation using
sfandstars.
Objectives
By the end of today you should be able to:
Distinguish deterministic and stochastic processes
Define autocorrelation and describe its estimation
Articulate the benefits and drawbacks of autocorrelation
Leverage point patterns and autocorrelation to interpolate missing data