Talk given at Wisconsin Land Information Association Annual Meeting, Feb 2015.

2. Problem: Mapping units may be a poor match to the spatial distribution
of the phenomenon being mapped.
Example: Distribution of cropland variable within a county.
Solution: Reapportion the variable spatially based on knowledge (or
assumptions) about its spatial distribution.
Example: Reapportion total county cropland to zones based on land use.
Limiting or related variable: Variable that controls, that we think has an
effect on, or is statistically related to, the phenomenon being mapped.
Example: Land use (for cropland).
Why do this? Should produce a better map, with more accurate spatial
distribution of the phenomenon.
What is Dasymetric Mapping?

3. Robinson Example
Source:
Arthur H. Robinson et
al, Elements of
Cartography, 6th Edition,
New York: Wiley, 1995.

4. Early Example
Source:
John K. Wright, “A Method
of Mapping Densities of
Population: With Cape Cod
as an Example,”
Geographical Review, Vol.
26, No. 1 (Jan., 1936), pp.
103-110.

5. Favorite Example

6. Goal: Create dasymetric map of Wisconsin population based on census
tract populations.
~1400 census tracts in Wisconsin
Tracts can be quite large
Population density not uniform within tracts
We’d like a better map
Wisconsin Case Study

7. Average area of tracts: > 10 sq. miles

8. Why not used census blocks?
Blocks are much smaller than tracts, on average.
But in rural areas, blocks can still be very large.
A problem when there are population concentrations in rural areas,
such as unincorporated communities.
Wisconsin Case Study

9. Blocks are much smaller on average: > 1/10 sq. mile

11. Controlling variable:
Landcover
NLCD 2006…most current at the time
Resolution of 30 meters
Maybe not the best choice…more later
Starting point is to intersect the tract layer and the land cover layer
Wisconsin Case Study

14. Let Pi,j be the population of polygon “i,j” (formed by
intersection of tract i and land cover polygon j)
Dasymetric Equation

15. Then
Pi,j = dj x ai,j
where
dj = population density of land cover polygon j
ai,j = area of polygon “i,j”
Dasymetric Equation

16. Note that dj (population density of land cover polygon j)
depends on the land cover class of polygon j.
The most complex part of dasymetric mapping is estimating
population densities for each land cover class.
To generate estimates, use the polys
created by intersected tract and land
cover layers to get the ai,j values.
Sum all areas within each tract that
belong to the same land cover class.
Density Estimation

17. Set up the following regression model:
Pi = ď1 x ai,1 + ď2 x ai,2 + … + ďK x ai,K
Where:
Pi = observed population of tract i
ai,k = observed area of all land cover polys within tract i
for which the land cover class = k
ďk = pop density for cover class k (unknown coefficients)
K = number of unique land cover classes
Density Estimation

18. Analogous to “hedonic” regression, the classic example of
which is: estimate the increase in market value (in $) of
specific characteristics of a home (bathroom, deck, garage…).
In our case, estimate the increase in population of a tract
associated with a unit-area increase in each land cover class.
Many ways to implement this. We use Generalized Reduced
Gradient (GRG) optimization to constrain ďk > 0.
Regression Analysis

20. Final Map

21. Map Detail: Legend

22. Map Detail: Pipe

23. Map Detail: Explanation

24. Land cover data not a good proxy for population density.
 NLCD includes transportation in “low intensity developed” causing population
to be reapportioned from census tracts to the transportation network.
 NLCD mixes residential and non-residential in “high intensity developed”
causing high-population areas to be mixed with low-population areas such as
malls and parking lots.
 Should try to combine land cover with land use, zoning, parcels…
Data-intensive. Even after simplification, the intersection of
tracts and land cover generates about 3 million polys.
Small-scale depiction of the population distribution over the
state; not accurate for large-scale mapping.
Issues

25. CREDITS
RESEARCH TEAM
Blaine Hackett
Co-Founder and President, Flat Rock Geographics
Tom Cox
Minnesota Power; formerly a UW-Madison student
Howard Veregin
Wisconsin State Cartographer
PHOTO CREDITS
Making a map for the blind. Stefan Kühn
(http://hdl.loc.gov/loc.pnp/ggbain.19023)
[Public domain], via Wikimedia Commons.
Image of an officer and soldier making maps in France, 1917-1918.
US Army Signal Corps (US Army Center of Military History, Carlisle, PA)
[Public domain], via Wikimedia Commons
Staff Sergeant Blake Ellis, Sheel Creek, Tennessee, inking in the pencil tracings.
Culture, Hydrography, and Contours are shown. England , 01/11/1943. Department of Defense.
Department of the Army. Office of the Chief Signal Officer. (09/18/1947 - 02/28/1964) [Public
domain], via Wikimedia Commons