GIS Analyses of Snow's Map

Snow's map, demonstrating the spatial clustering of cholera deaths around the Broad Street well, provided strong evidence in support of his theory that cholera was a water-borne disease. Snow used some proto-GIS methods to buttress his argument: first he drew Thiessen polygons around the wells, defining straight-line least-distance service areas for each. A large majority of the cholera deaths fell within the Thiessen polygon surrounding the Broad Street pump, amd a large portion of the remaining deaths were on the Broad Street side of the polygon surrouding the bad-tasting Carnaby Street well. Next, using a pencil and string, Snow redrew the service area polygons to reflect shortest routes along streets to wells. An even larger proportion of the cholera deaths fell within the shortest-travel-distance area around the Broad Street pump.

Try replicating and extending Snow's analysis with ArcGIS. The pumps and deaths datapoints were digitized by Rusty Dodson at the National Center for Geographic Information & Analysis (NCGIA) at UC Santa Barbara, using an arbitrary (not geo-referenced) scan of Snow's map. These data locate 578 cholera deaths and the 13 public wells in an arbitrary XY coordinate system.   I edited these plain text files so they are directly importable to Arc:  deaths.txt and pumps.txt. I edited a high-resolution JPEG-format scan of Snow's map, correcting some broken lines and converting it to a large PNG image:

  1. Click and download the full-size image of this map along with the pumps and deaths datafiles, add them into a blank Arc map session.
  2. Use File--Add Data--Add XY Data to display the pumps and deaths as points on your map. 
  3. Georeference the map image to the well points, and save a rectified version of the map image.

    wells and cholera deaths

  4. Use Arc's Euclidean Allocation tool to define zones of cells (Theissen polygons) closest to each pump.  What percent of cholera deaths fall within the Broad Street well's Theissen polygon?

    theissen polygons

  5. Use Arc's Kernel Density tool to calculate the spatial densities of deaths around each of the wells.  What are the density measures at each pump?

    kernel density map

  6. The Euclidean allocation implies travel through walls and buildings rather than only on streets. Use an image editor program (Paint or GIMP) fill the just streets in the map image with a distinct color.  (If the color leaks into any blocks, you will have to edit the image to close line breaks.)  Add this revised image to your map.  Use the Raster Calculator on this image (or one of its bands) to create a raster in which street cells have a value of 1 (a low travel cost), and "not street" cells have a high travel cost like 100.

    Then use the Cost Allocation tool to identify the area served by each well according to shortest travel cost distance (via streets).  What percent of the cholera deaths occurred in the Broad Street well's shortest-travel cost area?

    cost-weighted allocation of deaths to wells

  7. The very first cholera death was an infant in the house nearest the Broad Street pump; the house's cesspool actually leaked directly into the well.  But once the epidemic got going, there may have been secondary sources of infection.  Some of the subsequent deaths were not directly traceable to the Broad Street pump.  Unfortunately we don't know the dates of the deaths, just their locations, so we need some forensic analysis of the spatial clustering of deaths to infer the presence or absence of secondary infection points.  Assuming the population density was uniform across the map, use Arc's Spatial Statistics tools to see if you can identify secondary clusters indicating likely secondary infection points.

  8. Here's a Google Earth image of the area today:

    Try georeferencing a large version of this image to your cholera map. How much alteration have the streets undergone in 150 years? The Broad Street well used to be at what is now the intersection of Broadwick and Lexington Streets. The building at that corner is now a pub named The John Snow.

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