Use RStudio to perform the calculations for the homework assignment.

Data set sic97 in R package gstat includes the rainfall measurements of a specific day in Switzerland at 467 locations. After loading the data set, there should be two point pattern shapefiles: sic_obs (contains coordinates and rainfall for 100 stations) and sic_full has coordinates and rainfall for all 467 stations. There is also a spatial grid dataframe called demstd. This contains the elevation of a bounding box that covers all of Switzerland.

The goal of the homework is to create a spatial interpolation of rainfall across the demstd grid based on the 100 stations in sic_obs. You should validate the interpolation results on the remaining 367 stations.

HINTS:

1. Be sure to make a validation data set by stating with sic_full and removing any control points including in sic_obs:

sic_valid <- sic_full[is.element(sic_full$ID, sic_obs$ID) == F,]

2. And load useful packages listed below and any others that help.

library(gstat) library(raster) library(lattice) library(sp)

QUESTION:

Using the sic97 data set, fit an inverse distance weighting interpolation using inverse distance weighting powers of idp = 1,2,5, and 10. Which idp results in an interpolation most closely matches the validation data set? Show numerical and written justification.