spatialrisk

spatialrisk is a R-package for spatial risk calculations. It offers an efficient approach to determine the sum of all observations within a circle of a certain radius. This might be beneficial for insurers who are required (by a recent European Commission regulation) to determine the maximum value of insured fire risk policies of all buildings that are partly or fully located within a circle of a radius of 200m. The key functions in spatialrisk are written in C++ (using Rcpp), and are therefore very fast.

Installation

Install spatialrisk from CRAN:

install.packages("spatialrisk")

Or the development version from GitHub:

# install.packages("remotes")
remotes::install_github("MHaringa/spatialrisk")

Example 1

Find all observations in data.frame Groningen that are located within circle of a radius of 100m from the point (lon,lat) = (6.561561,53.21326):

library(spatialrisk)
circle <- points_in_circle(Groningen, lon_center = 6.571561, lat_center = 53.21326, radius = 100)
circle

## # A tibble: 14 x 10
##    street  number letter suffix postal_code city     lon   lat amount distance_m
##    <chr>    <int> <chr>  <chr>  <chr>       <chr>  <dbl> <dbl>  <dbl>      <dbl>
##  1 Heresi…      5 <NA>   <NA>   9711EP      Groni…  6.57  53.2      5       31.4
##  2 Heresi…     11 <NA>   <NA>   9711ER      Groni…  6.57  53.2     11       47.8
##  3 Zuider…   1003 <NA>   <NA>   9724AK      Groni…  6.57  53.2   1003       57.6
##  4 Heresi…     13 <NA>   <NA>   9711ER      Groni…  6.57  53.2     13       68.1
##  5 Herepl…     10 <NA>   <NA>   9711GA      Groni…  6.57  53.2     10       74.6
##  6 Heresi…     16 <NA>   <NA>   9711ES      Groni…  6.57  53.2     16       84.1
##  7 Heresi…      6 <NA>   <NA>   9711ES      Groni…  6.57  53.2      6       86.2
##  8 Heresi…      6 a      <NA>   9711ES      Groni…  6.57  53.2      6       87.8
##  9 Heresi…      6 b      <NA>   9711ES      Groni…  6.57  53.2      6       90.9
## 10 Heresi…     20 <NA>   <NA>   9711ET      Groni…  6.57  53.2     20       91.5
## 11 Heresi…     20 a      <NA>   9711ET      Groni…  6.57  53.2     20       93.0
## 12 Heresi…     15 a      <NA>   9711ER      Groni…  6.57  53.2     15       95.1
## 13 Zuider…   1007 <NA>   <NA>   9724AK      Groni…  6.57  53.2   1007       97.2
## 14 Zuider…     25 a      <NA>   9724AJ      Groni…  6.57  53.2     25       97.8

The sum of all observations within a circle of a radius of 100m is equal to:

sum(circle$amount)

## [1] 2163

The next example shows how to determine the sum of all observations within a circle with a certain radius for multiple points.

Example 2

concentration() determines the sum of all observations within a circle of a certain radius for multiple points. Find for each row in df the sum of all observations in Groningen within a circle of a radius of 100m from the (lon,lat) pair:

df <- data.frame(location = c("p1", "p2", "p3"), 
                 lon = c(6.561561, 6.561398, 6.571561), 
                 lat = c(53.21369, 53.21326, 53.21326))

conc <- concentration(df, Groningen, value = amount, radius = 100)
conc

##   location      lon      lat concentration
## 1       p1 6.561561 53.21369           775
## 2       p2 6.561398 53.21326          2271
## 3       p3 6.571561 53.21326          2163

Show that result is indeed equal to the result from Example 1:

isTRUE(sum(circle$amount) == conc$concentration[3])

## [1] TRUE

Example 3

Example 2 shows how to determine the sum of all observations within a circle of certain radius for multiple points. highest_concentration() can be used to find the coordinates of the center of a circle for which the sum of the observations within the circle is the highest. This example gives an application to data set Groningen. highest_concentration() uses Gustavo Niemeyer’s wonderful and elegant geohash coordinate system. Niemeyer’s Geohash method encodes latitude and longitude as binary string where each binary value derived from a decision as to where the point lies in a bisected region of latitude or longitudinal space.

Note that all functions are written in C++, and are therefore very fast. It takes about 5-10 seconds to find the highest concentration for a portfolio with 500,000 objects.

Show all points in data set Groningen:

plot_points(Groningen, value = amount)

Find the highest concentration:

hconc <- highest_concentration(Groningen, amount, radius = 200, grid_distance = 50)

For a portfolio of about 25,000 it takes about 0.5 second to find the highest concentration.

microbenchmark::microbenchmark(
  highest_concentration(Groningen, amount, radius = 200, grid_distance = 50), 
  times = 10)

## Unit: milliseconds
##                                                                        expr
##  highest_concentration(Groningen, amount, radius = 200, grid_distance = 50)
##       min       lq     mean   median       uq      max neval
##  607.0512 609.9632 619.7995 611.0177 614.7176 696.1569    10

The two highest concentrations are found in geohash u1kwug:

head(hconc)

##    concentration      lon      lat geohash
## 1:         63485 6.547372 53.23650  u1kwug
## 2:         61075 6.547372 53.23695  u1kwug
## 3:         57121 6.523147 53.23101  u1kwu6
## 4:         57009 6.589809 53.20534  u1kwtv
## 5:         56336 6.589809 53.20579  u1kwtv
## 6:         55631 6.523897 53.23145  u1kwu6

The following gives an illustration of this. The yellow parts show the areas with the highest concentrations.

plot(hconc) 

highest_concentration() returns the highest concentration within a portfolio based on a grid. However, higher concentrations can be found within two grid points. neighborhood_gh_search() looks for even higher concentrations in the neighborhood of the grid points with the highest concentrations. This optimization is done by means of Simulated Annealing.

Look for higher concentrations in the geohash with the highest concentration found by highest_concentration():

hconc_nghb <- neighborhood_gh_search(hconc, max.call = 7000)

The highest concentration is found in:

hconc_nghb

##   highest_concentration      lon      lat geohash
## 1                 64438 6.547329 53.23658  u1kwug

The concentration 64,438 is higher than the highest concentration of 63,485 on the grid points. This concentration is the highest in data set Groningen.

Show the highest concentration on a map (the highest concentration includes two apartment buildings with many objects):

plot(hconc_nghb)

Its also possible to show the coordinates for more than one concentration. To show the second and third highest concentration:

nb3 <- neighborhood_gh_search(hconc, max.call = 7000, highest_geohash = 3) 
nb3

Create interactive map:

plot(nb3)

Show objects in the highest geohash:

points_in_circle(Groningen, lon_center = nb3$lon[1], lat_center = nb3$lat[1], radius = 200)

## # A tibble: 208 x 10
##    street   number letter suffix postal_code city    lon   lat amount distance_m
##    <chr>     <int> <chr>  <chr>  <chr>       <chr> <dbl> <dbl>  <dbl>      <dbl>
##  1 Elzenla…    135 <NA>   <NA>   9741ND      Gron…  6.55  53.2    135       3.81
##  2 Elzenla…    139 <NA>   <NA>   9741ND      Gron…  6.55  53.2    139       8.13
##  3 Elzenla…     70 <NA>   <NA>   9741NG      Gron…  6.55  53.2     70      30.7 
##  4 Elzenla…     68 <NA>   <NA>   9741NG      Gron…  6.55  53.2     68      34.1 
##  5 Duindoo…      1 <NA>   <NA>   9741NM      Gron…  6.55  53.2     12      35.2 
##  6 Duindoo…     17 <NA>   <NA>   9741NM      Gron…  6.55  53.2     17      44.3 
##  7 Duindoo…     15 <NA>   <NA>   9741NM      Gron…  6.55  53.2     15      48.2 
##  8 Duindoo…     21 <NA>   <NA>   9741NM      Gron…  6.55  53.2     21      48.6 
##  9 Duindoo…     13 <NA>   <NA>   9741NM      Gron…  6.55  53.2     13      52.3 
## 10 Ranonke…     38 <NA>   <NA>   9741LT      Gron…  6.55  53.2     38      59.5 
## # … with 198 more rows

Example 4

spatialrisk also contains functionality to create choropleths. Typically in R it is difficult to create choropleths. points_to_polygon() attempts to elegantly solve this problem.

The common approach is to first aggregate the data on the level of the regions in the shapefile, and then merging the aggregated data with the shapefile. Despite it being common, it is problematic in case the names in the data and the names in the shapefile do not match. This is for example the case when there are differences in punctuation marks in the area names. Therefore, points_to_polygon() uses the longitude and latitude of a point to map this point to a region. This approach makes it easy to create choropleth maps on different region levels.

This example shows how points_to_polygon() is used to map the total sum insured on the municipality level in the Netherlands:

gemeente_sf <- points_to_polygon(nl_gemeente, insurance, sum(amount, na.rm = TRUE))

choropleth() creates a map based on the simple feature object obtained in the previous step. There are two options to create a choropleth map. When mode is set to plot a static map is created. The given clustering is according to the Fisher-Jenks algorithm. This commonly used classification method for choropleths seeks to reduce the variance within classes and maximize the variance between classes.

choropleth(gemeente_sf, mode = "plot", legend_title = "Sum insured (EUR)", n = 5)

If mode is set to view an interactive map is created:

choropleth(gemeente_sf, mode = "view", legend_title = "Sum insured (EUR)")

The following simple feature objects are available in spatialrisk: nl_provincie, nl_corop, nl_gemeente, nl_postcode1, nl_postcode2, nl_postcode3, nl_postcode4, world_countries, and europe_countries.