POPULATIONDENSITY MAPPINGUSING THEDASYMETRICMETHODBACKGROU

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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?

Robinson Example

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

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.

Favorite Example

Goal: Create dasymetric map of Wisconsin population based on census tract populations.

~1400 census tracts in WisconsinTracts can be quite largePopulation density not uniform within tractsWe’d like a better map

Wisconsin Case Study

Average area of tracts: > 10 sq. miles

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

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

Controlling variable: LandcoverNLCD 2006…most current at the timeResolution of 30 metersMaybe not the best choice…more laterStarting point is to intersect the tract layer and the land cover layer

Wisconsin Case Study

POPULATIONDENSITY MAPPING

USING THEDASYMETRIC

METHODPROCEDURE

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

Dasymetric Equation

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

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 thatbelong to the same land cover class.

Density Estimation

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 iai,k = observed area of all land cover polys within tract i

for which the land cover class = kďk = pop density for cover class k (unknown coefficients)K = number of unique land cover classes

Density Estimation

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

POPULATIONDENSITY MAPPINGUSING THEDASYMETRICMETHODRESULTS

Final Map

Map Detail: Legend

Map Detail: Pipe

Map Detail: Explanation

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

CREDITSRESEARCH TEAM

Blaine HackettCo-Founder and President, Flat Rock Geographics

Tom CoxMinnesota Power; formerly a UW-Madison student

Howard VereginWisconsin 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

THANKYOU!