Announcements

See the notes for Section 13.

What you will need

Packages:

• New: ggmap and leaflet (and raster, though we loaded it last week)
• Old: lubridate, rgdal, raster, broom, rgeos, GISTools, dplyr, ggplot2, ggthemes, magrittr, and viridis

Data:

• The file chicagoNightLights.tif
• The folder ChicagoPoliceBeats, which contains the shapefile of Chicago’s police beats.
• The file chicagoCrime.rds

R setup

Let’s set up R and then dive in.

# General R setup ----
# Options
options(stringsAsFactors = F)
# Load new packages
pacman::p_load(ggmap, leaflet)
# Load old packages
pacman::p_load(lubridate, rgdal, raster, broom, rgeos, GISTools)
pacman::p_load(dplyr, ggplot2, ggthemes, magrittr, viridis)
# My ggplot2 theme
theme_ed <- theme(
  legend.position = "bottom",
  panel.background = element_rect(fill = NA),
  # panel.border = element_rect(fill = NA, color = "grey75"),
  axis.ticks = element_line(color = "grey95", size = 0.3),
  panel.grid.major = element_line(color = "grey95", size = 0.3),
  panel.grid.minor = element_line(color = "grey95", size = 0.3),
  legend.key = element_blank())
# My directories
dir_12 <- "/Users/edwardarubin/Dropbox/Teaching/ARE212/Spring2017/Section12/"
dir_12b <- "/Users/edwardarubin/Dropbox/Teaching/ARE212/Spring2017/Section12b/"

Loading rasters

We need a raster.³ I’ve decided we are going to look a small subset of the (in)famous night(time) lights dataset.⁴ You can download the night lights data in various ways, but they are all fairly large—like 520 million cells large. I’ve cropped the original night lights raster (for January 2017) so that it covers the Chicago area with a little room to spare.⁵

Let’s read in this raster (named chicagoNightLights.tif). For this task, we will use the raster() function from the raster package.⁶ We will also load the police beats shapefile that we used in the previous section.

# Read the Chicago lights raster
chi_lights <- raster(paste0(dir_12b, "chicagoNightLights.tif"))
# Read the Chicago police beats shapefile
chi_beats <- readOGR(paste0(dir_12, "ChicagoPoliceBeats"), "chiBeats")

## OGR data source with driver: ESRI Shapefile 
## Source: "/Users/edwardarubin/Dropbox/Teaching/ARE212/Spring2017/Section12/ChicagoPoliceBeats", layer: "chiBeats"
## with 277 features
## It has 4 fields

As was the case with vectors (shapefiles), we can quickly and easily plot rasters using R’s base plot() function. Again, this frequent plotting—particularly after loading a new file—is a good policy that helps you avoid errors and better understand what you are looking at/doing. Once again, I am going to use the virids package (and function) for its color palette.

# Plot the Chicago night lights raster
plot(chi_lights, col = viridis(1e3))

Now that we’ve plotted the raster, let’s plot the police beats shapefile over the raster, using the base lines() function. You could also use plot() here with the additional argument add = T. The lwd argument specifies the width of the lines.

# Plot the Chicago night lights raster
plot(chi_lights, col = viridis(1e3))
# Plot the police beats over the night lights raster
lines(chi_beats, col = "white", lwd = 0.8)

Great.⁷ So what’s next?

Raster parts

Before we get too far ahead of ourselves, let’s learn a little about how we can access the different parts of a raster. If you check the names() of our raster, you will find it is simply the name of the file that provided the raster. Unlike shapefiles, we will not learn too much using the slots. Instead, we will use specific functions from the raster package. If you want to access the values of the raster, you can use the values() function or the getValues() function. If you want to change the values within a raster, you should use the setValues() function. Finally, if you want to access the coordinates of the raster’s grid, use the coordinates() function. Examples:

# R's description of the raster
chi_lights

## class       : RasterLayer 
## dimensions  : 115, 124, 14260  (nrow, ncol, ncell)
## resolution  : 0.004166667, 0.004166667  (x, y)
## extent      : -87.98958, -87.47292, 41.59375, 42.07292  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## data source : /Users/edwardarubin/Dropbox/Teaching/ARE212/Spring2017/Section12b/chicagoNightLights.tif 
## names       : chicagoNightLights 
## values      : 0.3693645, 434.6022  (min, max)

# R's summary of the raster
chi_lights %>% summary()

##         chicagoNightLights
## Min.             0.3693645
## 1st Qu.          9.7078307
## Median          33.2180634
## 3rd Qu.         67.7126541
## Max.           434.6021729
## NA's             0.0000000

# The slot names
chi_lights %>% slotNames()

##  [1] "file"     "data"     "legend"   "title"    "extent"   "rotated" 
##  [7] "rotation" "ncols"    "nrows"    "crs"      "history"  "z"

# The first 6 values
chi_lights %>% getValues() %>% head()

## [1] 25.68902 22.61487 26.09766 28.05734 39.12275 47.22555

# The first six coordinates
chi_lights %>% coordinates() %>% head()

##              x        y
## [1,] -87.98750 42.07083
## [2,] -87.98333 42.07083
## [3,] -87.97917 42.07083
## [4,] -87.97500 42.07083
## [5,] -87.97083 42.07083
## [6,] -87.96667 42.07083

A histogram of the raster’s values (logged):

ggplot(data = data.frame(light = getValues(chi_lights)),
  aes(x = log(light))) +
  geom_histogram(bins = 20, fill = viridis(20)) +
  ylab("Count") +
  xlab("log(radiance)") +
  ggtitle("Distribution of light radiance near Chicago",
    subtitle = "January 2017, logged radiance") +
  theme_ed

It’s worth noting that this histogram includes a lot of low light due to Lake Michigan. I took the log of the radiance to get a bit more dispersion in the histogram.

Summarize rasters with polygons

We generally want to take some sort of summary statistics of our raster. Often, we want these summary statistics at the level of some other spatial object—either a polygon or a point. Let’s see how this summarization works for polygons. Specifically, let’s take the average level of light within each of police beats in our police beat shapefile. For this task—and similar tasks—the raster package’s extract() function is your best friend.⁸ The extract() function wants the following arguments:

• x: the raster from which you want to extract values
• y: the points at which you would like to extract values; in the current context, y is our shapefile, but it could also be lines or points
• fun: the function we will use to summarize the raster (here: mean)
• na.rm: do you want to remove missing values (NAs)?
• df: (optional) do you want a data frame (rather than a matrix)
• sp: (optional) do you want the outputted results attached the the data slot of y (requires the y is an sp object, i.e., spatial polygons or spatial lines.)

Because we would end up joining the results of extract() to our spatial polygons data frame (chi_beats), I will go ahead and specify sp = TRUE.

You can also apply extract() over multiple layers of raster stack. Our current raster has one layer, but you will often find multi-layer rasters called raster stacks (or raster bricks). Similar objects but with more layers.⁹

Important note: The extract() function does not always do what you think it is going to do. It is written to be fairly flexible, which means it needs to make decisions. Some of the decisions the function must make:

• What counts as being in a polygon? Must the center of the cell be in the polygon, or is it enough that any part of the cell intersects the polygon?
• If you require the center of the cell to be within the polygon, what happens when a polygon does not intersect with any cells’ centroids?
• Should all cells count equally, or should we weight by the amount of the cell covered by a polygon?

Many of these questions are especially relevant/important when your cells are large relative to your polygons. This is not the case in our current example. Unfortunately, it is often the case in real research.

Alight, let’s summarize our night lights raster by taking the mean within each police beat. Finally, because we loaded the magrittr package after we loaded raster package—and because both packages have a function named extract()—raster’s version of extract has been masked by magrittr’s version. Thus we need to reference the raster package when we call extract(), i.e., raster::extract().

# Take averages of lights raster within each police beat
beat_extract <- raster::extract(
  x = chi_lights,
  y = chi_beats,
  fun = mean,
  na.rm = T,
  sp = T)

Note: extract() can take a little while—particularly when you have a high-resolution raster (many cells in given area) and many, high-resolution polygons.

Summarizing rasters with points

Now let’s carry out a similar task but with points rather than polygons.

First, we need some points. We’ll load the crime locations that we used in our discussion of vector data. And clean them.

# Read crime points data file
crime_df <- readRDS(paste0(dir_12, "chicagoCrime.rds"))
# Convert to tbl_df
crime_df %<>% tbl_df()
# Change names
names(crime_df) <- c("id", "date", "primary_offense",
  "arrest", "domestic", "beat", "lat", "lon")
# Drop observations missing lat or lon
crime_df %<>% filter(!is.na(lat) & !is.na(lon))
# Take subset of crimes
crime_df %<>% subset(primary_offense %in% c("HOMICIDE", "NARCOTICS"))
# Convert dates
crime_df %<>% mutate(date = mdy_hms(date))
# Define longitude and latitude as our coordinates
coordinates(crime_df) <- ~ lon + lat
# Assing a CRS to the crime points data
proj4string(crime_df) <- crs(chi_beats)
# Take the union of the beats polygons
chicago_union <- gUnaryUnion(chi_beats)
# Check which crime points are inside of Chicago
test_points <- over(crime_df, chicago_union)
# From 1 and NA to T and F (F means not in Chicago)
test_points <- !is.na(test_points)
crime_df <- crime_df[which(test_points == T), ]

Now we use extract() again, this time applying it so that we get a value from the raster at each of our crime-based points in crime_df.

crime_extract <- raster::extract(
  x = chi_lights,
  y = crime_df,
  fun = mean,
  na.rm = T,
  sp = T)

Rasters in ggplot2

So how does one plot a raster with ggplot2? As with spatial vector data, the problem is that ggplot() wants a data-frame-like object, and the raster is not a data-frame-like object. Lucky for us, raster provides the function rasterToPoints(), which does exactly what its name suggests: it creates a matrix of coordinates and values from a raster.¹⁰ Let’s create a data frame from the night lights data and then plot it in ggplot2 using the geom_raster() function.

# Convert raster to matrix and then to data frame
lights_df <- chi_lights %>% rasterToPoints() %>% tbl_df()
# Plot with ggplot
ggplot(data = lights_df,
  aes(x = x, y = y, fill = chicagoNightLights)) +
  geom_raster() +
  ylab("") + xlab("") +
  ggtitle("Lights at night in Chicago",
    subtitle = "January 2017") +
  scale_fill_viridis(option = "D") +
  theme_ed +
  theme(legend.position = "none", axis.text = element_blank())

Masks

You may have noticed that our raster includes many locations that are not within Chicago’s police beats. The crop() function will only crop the raster to the extent of the police beats shapefile, so we will still end up with a rectangle with many grid squares outside of the polygons.

The mask() function offers a solution to this problem. Masking means that we define any grid square in our raster not covered by some shape as NA. Thus, while we end up with the same extent as before, we now only have values for grid squares within a police beat in Chicago.

Let’s try it. Specifically, we will mask our night lights data with the outline of Chicago (chicago_union).

# Mask night lights raster with Chicago's outline
lights_masked <- mask(x = chi_lights, mask = chicago_union)

Now let’s plot our masked raster to see the result.

# Convert raster to matrix and then to data frame
masked_df <- lights_masked %>% rasterToPoints() %>% tbl_df()
# Plot with ggplot
ggplot(data = masked_df,
  aes(x = x, y = y, fill = chicagoNightLights)) +
  geom_raster() +
  ylab("") + xlab("") +
  ggtitle("Lights at night in Chicago, masked",
    subtitle = "January 2017") +
  scale_fill_viridis(option = "D") +
  theme_ed +
  theme(legend.position = "none", axis.text = element_blank())

Using this masked night lights data, let’s compare the (approximate) densities of (logged) light for (1) all of Chicago, (2) homicide locations, and (3) narcotics offenses’ locations.

# Convert crime_extract to a data frame
crime_extract %<>% tbl_df()
# Density plots
ggplot() +
  geom_density(
    data = masked_df,
    aes(x = log(chicagoNightLights), color = "All of Chicago", fill = "All of Chicago"),
    alpha = 0.6) +
  geom_density(
    data = filter(crime_extract, primary_offense == "HOMICIDE"),
    aes(x = log(chicagoNightLights), color = "Homicide", fill = "Homicide"),
    alpha = 0.6) +
  geom_density(
    data = filter(crime_extract, primary_offense == "NARCOTICS"),
    aes(x = log(chicagoNightLights), color = "Narcotics", fill = "Narcotics"),
    alpha = 0.6) +
  ylab("Density") +
  xlab("Log(Light radiance)") +
  theme_ed +
  scale_color_viridis("", discrete = T) +
  scale_fill_viridis("", discrete = T)

It actually looks like the crimes occur in locations with a bit more light.¹¹ We can also check out the means:¹²

# Compare means
masked_df %>%
  dplyr::select(chicagoNightLights) %>%
  summary()

##  chicagoNightLights
##  Min.   :  8.418   
##  1st Qu.: 69.079   
##  Median : 89.395   
##  Mean   : 87.474   
##  3rd Qu.:105.267   
##  Max.   :434.602

crime_extract %>%
  filter(primary_offense == "HOMICIDE") %>%
  dplyr::select(chicagoNightLights) %>%
  summary()

##  chicagoNightLights
##  Min.   : 13.36    
##  1st Qu.: 85.61    
##  Median : 96.42    
##  Mean   : 99.05    
##  3rd Qu.:109.40    
##  Max.   :434.60

crime_extract %>%
  filter(primary_offense == "NARCOTICS") %>%
  dplyr::select(chicagoNightLights) %>%
  summary()

##  chicagoNightLights
##  Min.   : 10.25    
##  1st Qu.: 89.73    
##  Median : 99.98    
##  Mean   :103.29    
##  3rd Qu.:113.39    
##  Max.   :434.60

These numerical summaries are consistent with what we observed in the density plot above: the recorded crimes tend to happen in places that are brighter than the average point in Chicago. Of course, this observation is not causal and does not include standard errors/inference (or even a formal point estimate), so I wouldn’t recommend any policy decisions quite yet.

Creating a raster

As we’ve discussed thus far, rasters are really just grids with values assigned to the grid cells. Thus, they are fairly simple to create.

First, we need a grid. The function expand.grid() is a very nice function for creating a grid—it takes all possible combinations of the given variables and then returns an (ordered) matrix. Let’s create an 11-by-11 grid by taking all combinations of [-5, 5] and [-5, 5] (by 1).

# Creating an 11-by-11 grid
our_mat <- expand.grid(x = -5:5, y = -5:5)
# Check out the head
our_mat %>% head(10)

##     x  y
## 1  -5 -5
## 2  -4 -5
## 3  -3 -5
## 4  -2 -5
## 5  -1 -5
## 6   0 -5
## 7   1 -5
## 8   2 -5
## 9   3 -5
## 10  4 -5

Let’s now convert the matrix to a data frame and then add a column of random numbers (standard normal).

# Convert to data frame
our_df <- our_mat %>% tbl_df()
# Set seed
set.seed(12345)
# Add random numbers
our_df %<>% mutate(value = rnorm(nrow(our_df)))

Because ggplot2 actually wants a data frame—rather than a raster—we can check our soon-to-be raster before it is finished.

# Plotting our raster data
ggplot(our_df, aes(x, y, fill = value)) +
  geom_raster() +
  ggtitle("Our (random) raster data") +
  scale_fill_viridis("Value") +
  coord_equal() +
  theme_ed +
  theme(
    legend.key.width = unit(2, "cm"),
    legend.key.height = unit(3/4, "cm"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank())

Beautiful! I think someone should make a quilt out of this bad boy.

Let’s finish converting this data frame into a raster. Once we have a data frame with coordinates and values (which we do), we can use the function rasterFromXYZ() (raster package) to convert the data frame into a raster object. rasterFromXYZ() will assume your x and y variables are the x and y coordinates. The function allows you to specify the resolution (res) and coordinate-reference system (crs), but because our raster is based in an imaginary world, we’ll ignore these arguments. rasterFromXYZ() also requires that the points are on a regular grid; if you cannot meet this requirement, see the function rasterize().

# Finish creating our raster
our_raster <- rasterFromXYZ(our_df)
# See if it worked
our_raster

## class       : RasterLayer 
## dimensions  : 11, 11, 121  (nrow, ncol, ncell)
## resolution  : 1, 1  (x, y)
## extent      : -5.5, 5.5, -5.5, 5.5  (xmin, xmax, ymin, ymax)
## coord. ref. : NA 
## data source : in memory
## names       : value 
## values      : -2.380358, 2.477111  (min, max)

It worked! A final check:

plot(our_raster, col = viridis(1e3),
  xlim = c(-5,5), ylim = c(-5,5))