1

Sample 50 points that fall within the boundaries of the city of Cologne. You will find the shapefile in the ./data folder.

The shapefile is not a raster file, so you need the sf::read_sf() function to load the data. Sampling is straightforward: Apply the sf::st_sample to the loaded shapefile, but make sure to apply the sf::st_as_sf() function afterward to receive a full-fledged data table (with a geometry column only).

solution 

library(dplyr)

cologne <- sf::read_sf("./data/cologne.shp")

cologne_50_points <-
  cologne |>  
  sf::st_sample(50) |> 
  sf::st_as_sf()

2

Create a new raster layer comprising Cologne’s immigrant rates based on the raster layers from the previous exercises.

You would need the immigrants_cologne.tif and inhabitants_cologne.tif files in the ./data folder.

solution 

library(terra)

immigrant_rates <-
  terra::rast("./data/immigrants_cologne.tif") * 100 /
  terra::rast("./data/inhabitants_cologne.tif")

3

Extract the immigrant rate value at each position of the previously sampled points as a vector. What is your observation?

Remember that the German Census 2011 data could be more sparse due to some severe data protection measures.

solution 

immigrant_rates_at_point <- terra::extract(immigrant_rates, cologne_50_points)

immigrant_rates_at_point
##    ID immigrants_cologne
## 1   1                 NA
## 2   2                 NA
## 3   3                 NA
## 4   4           7.017544
## 5   5                 NA
## 6   6                 NA
## 7   7                 NA
## 8   8                 NA
## 9   9                 NA
## 10 10                 NA
## 11 11                 NA
## 12 12                 NA
## 13 13                 NA
## 14 14           6.060606
## 15 15                 NA
## 16 16                 NA
## 17 17                 NA
## 18 18                 NA
## 19 19                 NA
## 20 20                 NA
## 21 21                 NA
## 22 22                 NA
## 23 23                 NA
## 24 24           9.708738
## 25 25                 NA
## 26 26           9.523810
## 27 27                 NA
## 28 28                 NA
## 29 29                 NA
## 30 30                 NA
## 31 31          15.116279
## 32 32                 NA
## 33 33          18.343195
## 34 34                 NA
## 35 35                 NA
## 36 36                 NA
## 37 37                 NA
## 38 38                 NA
## 39 39                 NA
## 40 40          22.826087
## 41 41          30.769231
## 42 42                 NA
## 43 43                 NA
## 44 44                 NA
## 45 45                 NA
## 46 46                 NA
## 47 47          25.000000
## 48 48          12.500000
## 49 49                 NA
## 50 50           4.545455
# There are a lot of missing values.

4

Use an adequate method of raster extraction to gather information in the geographic surroundings of a point. What is your observation now?

Assume that people move in a 1,000-meter radius around their location. Thus, extracting information on buffers of 1,000 meters around the points might be interesting using the option sf::st_buffer() function. In that case, you should also set a descriptive statistics function, e.g., with the option fun = mean and its helpful companion option to consider missing values na.rm = TRUE.

solution 

immigrant_rates_1000m_buffer <-
  terra::extract(
    immigrant_rates, 
    sf::st_buffer(cologne_50_points, 1000), 
    fun = mean,
    na.rm = TRUE
    )

immigrant_rates_1000m_buffer
##    ID immigrants_cologne
## 1   1           19.94206
## 2   2           10.86003
## 3   3           24.60711
## 4   4           14.76968
## 5   5           41.19776
## 6   6            9.57958
## 7   7           16.66667
## 8   8           10.47115
## 9   9                NaN
## 10 10                NaN
## 11 11                NaN
## 12 12           12.31503
## 13 13                NaN
## 14 14           11.32721
## 15 15           12.56422
## 16 16           23.35796
## 17 17                NaN
## 18 18           19.11399
## 19 19           20.21938
## 20 20           10.07462
## 21 21           15.46473
## 22 22           12.01796
## 23 23           12.00779
## 24 24           18.82225
## 25 25           29.17175
## 26 26           30.28828
## 27 27           13.63636
## 28 28           15.35337
## 29 29           15.88380
## 30 30                NaN
## 31 31           18.26736
## 32 32                NaN
## 33 33           17.13602
## 34 34           11.13494
## 35 35           22.32109
## 36 36                NaN
## 37 37           15.40239
## 38 38           19.64879
## 39 39           17.75252
## 40 40           19.56511
## 41 41           20.06646
## 42 42           12.32524
## 43 43           16.97988
## 44 44           26.13186
## 45 45           41.42228
## 46 46           14.66044
## 47 47           15.21124
## 48 48           12.14026
## 49 49           13.99355
## 50 50           15.31588