Isochrones

1. Introduction

An isochrone map shows how far one can travel from a given place within a certain amount of time. In other other words, it shows all the areas reachable from that place within a maximum travel time. This vignette shows how to calculate and visualize isochrones in R using the r5r package using a reproducible example. In this example, we will be using a sample data set for the city of Porto Alegre (Brazil) included in r5r. Our aim here is to calculate several isochrones departing from the central bus station given different travel time thresholds.

There are two ways to calculate / visualize isochrones using r5r. The quick and easy option is using the r5r::isochrone() function. The other alternative requires one to first calculate travel time estimates, and then to do some spatial interpolation operations. We will cover both approaches in this vignette.

Before we start, we need to increase Java memory + load a few libraries, and to build routable transport network.

Warning: If you want to calculate how many opportunities (e.g. jobs, or schools or hospitals) are located inside each isochrone, we strongly recommend you NOT to use the isochrone() function. You will find much more efficient ways to do this in the Accessibility vignette.

2. Build routable transport network with setup_r5()

Increase Java memory and load libraries

First, we need to increase the memory available to Java and load the packages used in this vignette. Please note we allocate RAM memory to Java before loading our libraries.

options(java.parameters = "-Xmx2G")

library(r5r)
library(sf)
library(data.table)
library(ggplot2)
library(interp)

To build a routable transport network with r5r, the user needs to call setup_r5() with the path to the directory where OpenStreetMap and GTFS data are stored.

# system.file returns the directory with example data inside the r5r package
# set data path to directory containing your own data if not running this example
data_path <- system.file("extdata/poa", package = "r5r")

r5r_core <- setup_r5(data_path)

3. Isochrone: quick and easy approach

The quick and easy approach to estimate / visualize an isochrone is to use the isochrone() function built in the r5r package. In this example, we will be calculating the isochrones by public transport from the central bus station in Porto Alegre. The isochrone() function calculates isochrones considering the travel times from the origin point to a random sample of 80% of all nodes in the transport network (default). The size of the sample can be fine tuned with the sample_size parameter.

With the code below, r5r determines the isochrones considering the median travel time of multiple travel time estimates calculated departing every minute over a 120-minute time window, between 2pm and 4pm.

# read all points in the city
points <- fread(file.path(data_path, "poa_hexgrid.csv"))

# subset point with the geolocation of the central bus station
central_bus_stn <- points[291,]

# isochrone intervals
time_intervals <- seq(0, 100, 10)

# routing inputs
mode <- c("WALK", "TRANSIT")
max_walk_time <- 30      # in minutes
max_trip_duration <- 100 # in minutes
time_window <- 120       # in minutes
departure_datetime <- as.POSIXct("13-05-2019 14:00:00",
                                 format = "%d-%m-%Y %H:%M:%S")

# calculate travel time matrix
iso1 <- r5r::isochrone(r5r_core,
                       origins = central_bus_stn,
                       mode = mode,
                       cutoffs = time_intervals,
                       sample_size = 1,
                       departure_datetime = departure_datetime,
                       max_walk_time = max_walk_time,
                       max_trip_duration = max_trip_duration,
                       time_window = time_window,
                       progress = FALSE)

As you can see, the isochrone() functions works very similarly to the travel_time_matrix() function, but instead of returning a table with travel time estimates, it returns a POLYGON "sf" "data.frame" for each isochrone of each origin.

head(iso1)

Now it becomes super simple to visualize our isochrones on a map:

# extract OSM network
street_net <- street_network_to_sf(r5r_core)
main_roads <- subset(street_net$edges, street_class %like% 'PRIMARY|SECONDARY')
  
colors <- c('#ffe0a5','#ffcb69','#ffa600','#ff7c43','#f95d6a',
            '#d45087','#a05195','#665191','#2f4b7c','#003f5c')

ggplot() +
  geom_sf(data = iso1, aes(fill=factor(isochrone)), color = NA, alpha = .7) +
  geom_sf(data = main_roads, color = "gray55", size=0.01, alpha = 0.2) +
  geom_point(data = central_bus_stn, aes(x=lon, y=lat, color='Central bus\nstation')) +
  # scale_fill_viridis_d(direction = -1, option = 'B') +
  scale_fill_manual(values = rev(colors) ) +
  scale_color_manual(values=c('Central bus\nstation'='black')) +
  labs(fill = "Travel time\n(in minutes)", color='') +
  theme_minimal() +
  theme(axis.title = element_blank())

4 Isochrone alternative

This second approach to calculating isochrones with r5r takes a few more steps because it requires the spatial interpolation of travel time estimates, but it generates more refined maps. It takes two steps.

4.1 Calculate travel times

First, we calculate the travel times by public transport from the central bus station in Porto Alegre to multiple destinations we input to the function. Here, we input the points data frame, which comprises the centroids of a hexagonal grid at a fine spatial resolution.

# calculate travel time matrix
ttm <- travel_time_matrix(r5r_core,
                          origins = central_bus_stn,
                          destinations = points,
                          mode = mode,
                          departure_datetime = departure_datetime,
                          max_walk_time = max_walk_time,
                          max_trip_duration = max_trip_duration,
                          time_window = time_window,
                          progress = FALSE)

head(ttm)

4.2 Spatial interpolation of travel times

Now we need to bring the spatial coordinates information to our travel time matrix output ttm, and do some spatial interpolation of travel time estimates.

# add coordinates of destinations to travel time matrix
ttm[points, on=c('to_id' ='id'), `:=`(lon = i.lon, lat = i.lat)]

# interpolate estimates to get spatially smooth result
travel_times.interp <- with(na.omit(ttm), interp(lon, lat, travel_time_p50)) |>
                        with(cbind(travel_time=as.vector(z),  # Column-major order
                                   x=rep(x, times=length(y)),
                                   y=rep(y, each=length(x)))) |>
                            as.data.frame() |> na.omit()

With just a few more lines of code, we get our isochrones on a map:

# find isochrone's bounding box to crop the map below
bb_x <- c(min(travel_times.interp$x), max(travel_times.interp$x))
bb_y <- c(min(travel_times.interp$y), max(travel_times.interp$y))

# plot
ggplot(travel_times.interp) +
  geom_sf(data = main_roads, color = "gray55", size=0.01, alpha = 0.7) +
  geom_contour_filled(aes(x=x, y=y, z=travel_time), alpha=.7) +
  geom_point(aes(x=lon, y=lat, color='Central bus\nstation'),
             data=central_bus_stn) +
  # scale_fill_viridis_d(direction = -1, option = 'B') +
  scale_fill_manual(values = rev(colors) ) +
  scale_color_manual(values=c('Central bus\nstation'='black')) +
  scale_x_continuous(expand=c(0,0)) +
  scale_y_continuous(expand=c(0,0)) +
  coord_sf(xlim = bb_x, ylim = bb_y) +
  labs(fill = "Travel time\n(in minutes)", color='') +
  theme_minimal() +
  theme(axis.title = element_blank())

Cleaning up after usage

r5r objects are still allocated to any amount of memory previously set after they are done with their calculations. In order to remove an existing r5r object and reallocate the memory it had been using, we use the stop_r5 function followed by a call to Java’s garbage collector, as follows:

r5r::stop_r5(r5r_core)
rJava::.jgc(R.gc = TRUE)

If you have any suggestions or want to report an error, please visit the package GitHub page.