13. Spatial Joins

Spatial joins are the bread-and-butter of spatial databases. They allow you to combine information from different tables by using spatial relationships as the join key. Much of what we think of as „standard GIS analysis“ can be expressed as spatial joins.

In the previous section, we explored spatial relationships using a two-step process: first we extracted a subway station point for ‚Broad St‘; then, we used that point to ask further questions such as „what neighborhood is the ‚Broad St‘ station in?“

Using a spatial join, we can answer the question in one step, retrieving information about the subway station and the neighborhood that contains it:

SELECT
  subways.name AS subway_name,
  neighborhoods.name AS neighborhood_name,
  neighborhoods.boroname AS borough
FROM nyc_neighborhoods AS neighborhoods
JOIN nyc_subway_stations AS subways
ON ST_Contains(neighborhoods.geom, subways.geom)
WHERE subways.name = 'Broad St';

 subway_name | neighborhood_name  |  borough
-------------+--------------------+-----------
 Broad St    | Financial District | Manhattan

We could have joined every subway station to its containing neighborhood, but in this case we wanted information about just one. Any function that provides a true/false relationship between two tables can be used to drive a spatial join, but the most commonly used ones are: ST_Intersects, ST_Contains, and ST_DWithin.

13.1. Join and Summarize

The combination of a JOIN with a GROUP BY provides the kind of analysis that is usually done in a GIS system.

For example: „What is the population and racial make-up of the neighborhoods of Manhattan?“ Here we have a question that combines information from about population from the census with the boundaries of neighborhoods, with a restriction to just one borough of Manhattan.

SELECT
  neighborhoods.name AS neighborhood_name,
  Sum(census.popn_total) AS population,
  100.0 * Sum(census.popn_white) / Sum(census.popn_total) AS white_pct,
  100.0 * Sum(census.popn_black) / Sum(census.popn_total) AS black_pct
FROM nyc_neighborhoods AS neighborhoods
JOIN nyc_census_blocks AS census
ON ST_Intersects(neighborhoods.geom, census.geom)
WHERE neighborhoods.boroname = 'Manhattan'
GROUP BY neighborhoods.name
ORDER BY white_pct DESC;

  neighborhood_name  | population | white_pct | black_pct
---------------------+------------+-----------+-----------
 Carnegie Hill       |      18763 |      90.1 |       1.4
 North Sutton Area   |      22460 |      87.6 |       1.6
 West Village        |      26718 |      87.6 |       2.2
 Upper East Side     |     203741 |      85.0 |       2.7
 Soho                |      15436 |      84.6 |       2.2
 Greenwich Village   |      57224 |      82.0 |       2.4
 Central Park        |      46600 |      79.5 |       8.0
 Tribeca             |      20908 |      79.1 |       3.5
 Gramercy            |     104876 |      75.5 |       4.7
 Murray Hill         |      29655 |      75.0 |       2.5
 Chelsea             |      61340 |      74.8 |       6.4
 Upper West Side     |     214761 |      74.6 |       9.2
 Midtown             |      76840 |      72.6 |       5.2
 Battery Park        |      17153 |      71.8 |       3.4
 Financial District  |      34807 |      69.9 |       3.8
 Clinton             |      32201 |      65.3 |       7.9
 East Village        |      82266 |      63.3 |       8.8
 Garment District    |      10539 |      55.2 |       7.1
 Morningside Heights |      42844 |      52.7 |      19.4
 Little Italy        |      12568 |      49.0 |       1.8
 Yorkville           |      58450 |      35.6 |      29.7
 Inwood              |      50047 |      35.2 |      16.8
 Washington Heights  |     169013 |      34.9 |      16.8
 Lower East Side     |      96156 |      33.5 |       9.1
 East Harlem         |      60576 |      26.4 |      40.4
 Hamilton Heights    |      67432 |      23.9 |      35.8
 Chinatown           |      16209 |      15.2 |       3.8
 Harlem              |     134955 |      15.1 |      67.1

What’s going on here? Notionally (the actual evaluation order is optimized under the covers by the database) this is what happens:

1. The JOIN clause creates a virtual table that includes columns from both the neighborhoods and census tables.

2. The WHERE clause filters our virtual table to just rows in Manhattan.

3. The remaining rows are grouped by the neighborhood name and fed through the aggregation function to Sum() the population values.

4. After a little arithmetic and formatting (e.g., GROUP BY, ORDER BY) on the final numbers, our query spits out the percentages.

Bemerkung

The JOIN clause combines two FROM items. By default, we are using an INNER JOIN, but there are four other types of joins. For further information see the join_type definition in the PostgreSQL documentation.

We can also use distance tests as a join key, to create summarized „all items within a radius“ queries. Let’s explore the racial geography of New York using distance queries.

First, let’s get the baseline racial make-up of the city.

SELECT
  100.0 * Sum(popn_white) / Sum(popn_total) AS white_pct,
  100.0 * Sum(popn_black) / Sum(popn_total) AS black_pct,
  Sum(popn_total) AS popn_total
FROM nyc_census_blocks;

    white_pct     |    black_pct     | popn_total
------------------+------------------+------------
 44.0039500762811 | 25.5465789002416 |    8175032

So, of the 8M people in New York, about 44% are recorded as „white“ and 26% are recorded as „black“.

Duke Ellington once sang that „You / must take the A-train / To / go to Sugar Hill way up in Harlem.“ As we saw earlier, Harlem has far and away the highest African-American population in Manhattan (80.5%). Is the same true of Duke’s A-train?

First, note that the contents of the nyc_subway_stations table routes field is what we are interested in to find the A-train. The values in there are a little complex.

SELECT DISTINCT routes FROM nyc_subway_stations;

A,C,G
4,5
D,F,N,Q
5
E,F
E,J,Z
R,W

Bemerkung

The DISTINCT keyword eliminates duplicate rows from the result. Without the DISTINCT keyword, the query above identifies 491 results instead of 73.

So to find the A-train, we will want any row in routes that has an ‚A‘ in it. We can do this a number of ways, but today we will use the fact that strpos(routes,'A') will return a non-zero number only if ‚A‘ is in the routes field.

SELECT DISTINCT routes
FROM nyc_subway_stations AS subways
WHERE strpos(subways.routes,'A') > 0;

A,B,C
A,C
A
A,C,G
A,C,E,L
A,S
A,C,F
A,B,C,D
A,C,E

Let’s summarize the racial make-up of within 200 meters of the A-train line.

SELECT
  100.0 * Sum(popn_white) / Sum(popn_total) AS white_pct,
  100.0 * Sum(popn_black) / Sum(popn_total) AS black_pct,
  Sum(popn_total) AS popn_total
FROM nyc_census_blocks AS census
JOIN nyc_subway_stations AS subways
ON ST_DWithin(census.geom, subways.geom, 200)
WHERE strpos(subways.routes,'A') > 0;

    white_pct     |    black_pct     | popn_total
------------------+------------------+------------
 45.5901255900202 | 22.0936235670937 |     189824

So the racial make-up along the A-train isn’t radically different from the make-up of New York City as a whole.

13.2. Advanced Join

In the last section we saw that the A-train didn’t serve a population that differed much from the racial make-up of the rest of the city. Are there any trains that have a non-average racial make-up?

To answer that question, we’ll add another join to our query, so that we can simultaneously calculate the make-up of many subway lines at once. To do that, we’ll need to create a new table that enumerates all the lines we want to summarize.

CREATE TABLE subway_lines ( route char(1) );
INSERT INTO subway_lines (route) VALUES
  ('A'),('B'),('C'),('D'),('E'),('F'),('G'),
  ('J'),('L'),('M'),('N'),('Q'),('R'),('S'),
  ('Z'),('1'),('2'),('3'),('4'),('5'),('6'),
  ('7');

Now we can join the table of subway lines onto our original query.

SELECT
  lines.route,
  100.0 * Sum(popn_white) / Sum(popn_total) AS white_pct,
  100.0 * Sum(popn_black) / Sum(popn_total) AS black_pct,
  Sum(popn_total) AS popn_total
FROM nyc_census_blocks AS census
JOIN nyc_subway_stations AS subways
ON ST_DWithin(census.geom, subways.geom, 200)
JOIN subway_lines AS lines
ON strpos(subways.routes, lines.route) > 0
GROUP BY lines.route
ORDER BY black_pct DESC;

 route | white_pct | black_pct | popn_total
-------+-----------+-----------+------------
 S     |      39.8 |      46.5 |      33301
 3     |      42.7 |      42.1 |     223047
 5     |      33.8 |      41.4 |     218919
 2     |      39.3 |      38.4 |     291661
 C     |      46.9 |      30.6 |     224411
 4     |      37.6 |      27.4 |     174998
 B     |      40.0 |      26.9 |     256583
 A     |      45.6 |      22.1 |     189824
 J     |      37.6 |      21.6 |     132861
 Q     |      56.9 |      20.6 |     127112
 Z     |      38.4 |      20.2 |      87131
 D     |      39.5 |      19.4 |     234931
 L     |      57.6 |      16.8 |     110118
 G     |      49.6 |      16.1 |     135012
 6     |      52.3 |      15.7 |     260240
 1     |      59.1 |      11.3 |     327742
 F     |      60.9 |       7.5 |     229439
 M     |      56.5 |       6.4 |     174196
 E     |      66.8 |       4.7 |      90958
 R     |      58.5 |       4.0 |     196999
 N     |      59.7 |       3.5 |     147792
 7     |      35.7 |       3.5 |     102401

As before, the joins create a virtual table of all the possible combinations available within the constraints of the JOIN ON restrictions, and those rows are then fed into a GROUP summary. The spatial magic is in the ST_DWithin function, that ensures only census blocks close to the appropriate subway stations are included in the calculation.

13.3. Function List

ST_Contains(geometry A, geometry B): Returns true if and only if no points of B lie in the exterior of A, and at least one point of the interior of B lies in the interior of A.

ST_DWithin(geometry A, geometry B, radius): Returns true if the geometries are within the specified distance of one another.

ST_Intersects(geometry A, geometry B): Returns TRUE if the Geometries/Geography „spatially intersect“ - (share any portion of space) and FALSE if they don’t (they are Disjoint).

round(v numeric, s integer): PostgreSQL math function that rounds to s decimal places

strpos(string, substring): PostgreSQL string function that returns an integer location of a specified substring.

sum(expression): PostgreSQL aggregate function that returns the sum of records in a set of records.