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Visualising spatial exposure

Source: vignettes/visualisation.Rmd
visualisation.Rmd

Introduction

This vignette shows how point-level exposure data can be aggregated to reporting areas and visualised as a choropleth map. Within spatialrisk, this is primarily a reporting and communication workflow.

The fixed-radius concentration workflow answers a local risk question: where is the largest accumulation within a circle of a specified physical radius? Polygon-based visualisation answers a reporting question: how is exposure distributed across administrative or management areas?

Both views are useful, but they should not be interpreted as the same measure.

From point exposures to reporting areas

The example uses two data objects included in spatialrisk:

  • insurance: point-level policy or risk locations with an amount column;
  • nl_gemeente: municipal boundaries for the Netherlands.
library(spatialrisk)
library(sf)

point_exposures <- insurance[, c("lon", "lat", "amount")]

head(point_exposures)
#> # A tibble: 6 × 3
#>     lon   lat amount
#>   <dbl> <dbl>  <dbl>
#> 1  4.48  52.2  20000
#> 2  5.29  51.6 154965
#> 3  4.50  52.0 146078
#> 4  7.00  53.1 129304
#> 5  4.34  52.1  67636
#> 6  4.83  52.3  29971

The amount column represents the exposure measure that will be aggregated. In an applied insurance setting this could be an insured amount, total exposure value, risk premium, or another portfolio quantity.

The reporting polygons define the spatial units used for communication. Municipalities are used here as an example; the appropriate reporting areas depend on the analytical or communication objective.

nl_gemeente[, c("id", "code", "areaname")]
#> Simple feature collection with 352 features and 3 fields
#> Geometry type: MULTIPOLYGON
#> Dimension:     XY
#> Bounding box:  xmin: 3.358378 ymin: 50.75136 xmax: 7.217623 ymax: 53.55362
#> Geodetic CRS:  WGS 84
#> First 10 features:
#>    id   code      areaname                       geometry
#> 1   1 GM0014     Groningen MULTIPOLYGON (((6.772527 53...
#> 2   2 GM0034        Almere MULTIPOLYGON (((5.350772 52...
#> 3   3 GM0037   Stadskanaal MULTIPOLYGON (((7.015446 53...
#> 4   4 GM0047       Veendam MULTIPOLYGON (((6.961735 53...
#> 5   5 GM0050      Zeewolde MULTIPOLYGON (((5.58907 52....
#> 6   6 GM0059 Achtkarspelen MULTIPOLYGON (((6.232173 53...
#> 7   7 GM0060       Ameland MULTIPOLYGON (((5.731096 53...
#> 8   8 GM0072     Harlingen MULTIPOLYGON (((5.472192 53...
#> 9   9 GM0074    Heerenveen MULTIPOLYGON (((5.92758 53....
#> 10 10 GM0080    Leeuwarden MULTIPOLYGON (((5.838649 53...

Aggregate exposure by polygon

The function summarise_points_by_polygon() spatially assigns point locations to polygon geometries and applies a summary function. Here, the total insured amount is calculated for each municipality.

municipality_exposure <- summarise_points_by_polygon(
  polygons = nl_gemeente,
  points = point_exposures,
  value = "amount",
  fun = sum,
  outside = "ignore"
)

sf::st_drop_geometry(municipality_exposure)[
  1:6,
  c("areaname", "amount_sum")
]
#>        areaname amount_sum
#> 1     Groningen   30218869
#> 2        Almere   30905436
#> 3   Stadskanaal    3080895
#> 4       Veendam    3721274
#> 5      Zeewolde    1887282
#> 6 Achtkarspelen    1313688

The result is still an sf object: it retains the municipal geometries and adds the aggregated exposure column. This object can be used directly for mapping.

Create a choropleth

The choropleth() function shades polygons according to a numeric column. The id argument identifies the column used for polygon labels in interactive maps.

choropleth(
  municipality_exposure,
  value = "amount_sum",
  id = "areaname",
  legend_title = "Total insured amount"
)

This map shows how the total point-level exposure is distributed across municipalities. The function returns a tmap object, so the map can be further adjusted with tmap if a report requires additional formatting.

Interpreting the map

A choropleth map represents values attached to predefined polygons. In this example, each municipality is shaded according to the total insured amount of point exposures assigned to that municipality.

This is useful for questions such as:

  • which reporting areas contain the most exposure;
  • how exposure is distributed across administrative areas;
  • which municipalities or regions should be highlighted in a portfolio summary.

It does not directly answer where the highest local accumulation occurs within a fixed physical radius. Polygon-level results depend on the chosen boundaries. Two nearby risks may fall into different municipalities, while exposures spread across a large municipality are aggregated into a single polygon value. Administrative boundaries are therefore reporting choices rather than part of the underlying fixed-radius concentration problem.

Relation to fixed-radius concentration

Polygon-based visualisation and fixed-radius concentration analysis are complementary.

Polygon-based visualisation is useful for:

  • reporting;
  • portfolio summaries;
  • communicating geographic patterns;
  • administrative or management views.

Fixed-radius concentration analysis is useful for:

  • local accumulation;
  • identifying spatial hotspots;
  • analysing concentration independently of administrative boundaries.

For physical accumulation questions, use concentration_hotspot() or the supporting fixed-radius functions described in vignette("fixed-radius-concentration", package = "spatialrisk"). For reporting and communication, aggregate point exposures to relevant polygons and visualise the resulting polygon-level values.

Summary

This vignette demonstrated a complete polygon-based visualisation workflow:

  • start from point-level exposure data;
  • assign points to reporting polygons;
  • aggregate an exposure measure by polygon;
  • visualise the polygon-level result with choropleth();
  • interpret the map as a reporting view rather than a fixed-radius concentration measure.