1. ----- Calculating Urban Density Profiles----- Calculating Urban Density Profiles
Using Population Surface ModelsUsing Population Surface Models
Zunqiu ChenZunqiu Chen
New Opportunities for Urban Analysis

2. 1.1. Background of this research workBackground of this research work
The analysis of urban morphology to furtherThe analysis of urban morphology to further
understanding of urban sustainability is becomingunderstanding of urban sustainability is becoming
more important.more important.
The traditional analysis of urban morphology canThe traditional analysis of urban morphology can
be done through one or more of the followingbe done through one or more of the following
ways:ways:

Identification of built formsIdentification of built forms

Identification of human activity pattern, for example:Identification of human activity pattern, for example:
residential densitiesresidential densities

Measures of dynamicsMeasures of dynamics

3. 1.1. Background of this research workBackground of this research work
Residential density represents a key dimension of anyResidential density represents a key dimension of any
social-environmental interface (Jarvis, 2001).social-environmental interface (Jarvis, 2001).

It is instructive to undertake a household residential approach toIt is instructive to undertake a household residential approach to
analyse urban morphology as a premise for questions of urbananalyse urban morphology as a premise for questions of urban
social and environmental sustainability.social and environmental sustainability.
Traditional methods, such as RS approaches andTraditional methods, such as RS approaches and
analysis based on Census data provide difficultanalysis based on Census data provide difficult
challenges (challenges (Mesev, 1997).Mesev, 1997). to complete the target aboto complete the target aboveve
because:because:

Remote Sensing can not provide the critical interface betweenRemote Sensing can not provide the critical interface between
urban form analysis and routine population characteristics .urban form analysis and routine population characteristics .

UK Census geography lacks any ‘natural’ units of aggregationUK Census geography lacks any ‘natural’ units of aggregation
and land use data at a fine scale (and land use data at a fine scale (Openshaw, 1984, Harris,Openshaw, 1984, Harris,
2000)2000) ..

4. 2.2. The New Opportunity in Urban AnalysisThe New Opportunity in Urban Analysis
The increasing availability of some point datasets withThe increasing availability of some point datasets with
finer resolution and certain population characteristicsfiner resolution and certain population characteristics
compared to Census data and RS data has appeared incompared to Census data and RS data has appeared in
Britain. Such as:Britain. Such as:

Code-Point datasetCode-Point dataset
There also exist some popular methods which haveThere also exist some popular methods which have
been widely applied in geographic urban analysisbeen widely applied in geographic urban analysis
associated with point dataset such as Population surfaceassociated with point dataset such as Population surface
model (PSM).model (PSM).
Code-Point Dataset and PSM provide a positive potentialCode-Point Dataset and PSM provide a positive potential
perspective for making possible new kinds of urbanperspective for making possible new kinds of urban
analysis and modeling at a fine scale.analysis and modeling at a fine scale.

5. 3.3. Research objectivesResearch objectives
Research issue --- “Can new sources of micro-levelResearch issue --- “Can new sources of micro-level
data associated with PSM offer new insights intodata associated with PSM offer new insights into
understanding urban morphology/urban process?”understanding urban morphology/urban process?”

To evaluate the sensitivity of parameters embedded in PSMTo evaluate the sensitivity of parameters embedded in PSM
when we apply PSM on estimates of the total residential areaswhen we apply PSM on estimates of the total residential areas
of UK citiesof UK cities..

To develop the density profiles for the investigation ofTo develop the density profiles for the investigation of
residential land useresidential land use

To answer the question: whether our work can provide a newTo answer the question: whether our work can provide a new
opportunity for better understanding of urban morphologyopportunity for better understanding of urban morphology

6. 4.4. Code-point dataset andCode-point dataset and
Study areasStudy areas
Code-PointCode-Point is an Ordnance Survey data product andis an Ordnance Survey data product and
provides a precise geographical location for eachprovides a precise geographical location for each
postcode units.postcode units.
Code-Point
Date vendor Ordnance Survey (GB)
First data collection 1997 (as Data-Point)
Geography GB
Frequency of updates 3 months
Sampling unit Unit Postcode
Average number of households per unit About 12 (GB)
Data-type Attributed point
Resolution Most postcode centroids precise to 1m
Content Total number of residential and commercial
mail delivery points per postcode

7. Four cities’ code-points were used in this study:Four cities’ code-points were used in this study:

Bristol, Norwich, Peterborough, and Swindon.Bristol, Norwich, Peterborough, and Swindon.
Bristol Swindon
Peterborough
Norwich

8. 5.5. Population Surface ModelingPopulation Surface Modeling
The PSM method is described fully by Harris and Longley (2000;The PSM method is described fully by Harris and Longley (2000;
after Bracken and Martin, 1989 and Martin and Bracken, 1991).after Bracken and Martin, 1989 and Martin and Bracken, 1991).
The formula based on Cressman (1959) but modified by the alphaThe formula based on Cressman (1959) but modified by the alpha
parameter is:parameter is:
2 2
2 2
( )
0{
j ij
j ij
w d
w d
ijW
α−
+
=
d wij j<
d wij j≥
… for
… for
WWijij: the weighting associated with distance: the weighting associated with distance ddijij
ddijij: the distance between a point: the distance between a point jj and the centre of anand the centre of an
output grid celloutput grid cell ii
wwjj : is the local kernel width around that point: is the local kernel width around that point
αα:: distance decay functiondistance decay function

9. i
jwj

10. What parameters in PSM are we going toWhat parameters in PSM are we going to
investigate?investigate?

Two parameters that most govern the PSMTwo parameters that most govern the PSM
outputsoutputs

The search window sizeThe search window size ww

The output grid cell sizeThe output grid cell size ll
**Distance-decay parameter: α which are relativelyDistance-decay parameter: α which are relatively
unimportant based on empirical evidence including ourunimportant based on empirical evidence including our
own investigations. So, the analysis of α won’t beown investigations. So, the analysis of α won’t be
presented here.presented here.

11. 6.6. The effects on the density profiles ofThe effects on the density profiles of
altering search window,altering search window, ww, process, process
ProcessProcess

Using fixed cell sizeUsing fixed cell size ll, various search window size to produce, various search window size to produce
the estimated residential area.the estimated residential area.

giving an estimate of the total residential area at or above thegiving an estimate of the total residential area at or above the
density threshold.density threshold.

showing the linear pattern of the estimate of the totalshowing the linear pattern of the estimate of the total
residential area at or above a series of density thresholds.residential area at or above a series of density thresholds.

13. It is clear from Figures1 and 2 that the estimatedIt is clear from Figures1 and 2 that the estimated
total residential areas of both Bristol andtotal residential areas of both Bristol and
Norwich are scale dependent: at each densityNorwich are scale dependent: at each density
threshold, as the search window,threshold, as the search window, ww, changes, changes
then so too does the estimated residential area.then so too does the estimated residential area.

14. 7.7. Comparing the effects ofComparing the effects of ww andand ll onon
estimates of urban extent at thresholdestimates of urban extent at threshold
densitiesdensities
Recall that we expect the shape of the density profilesRecall that we expect the shape of the density profiles
to be dependent not only onto be dependent not only on ww but also the output cellbut also the output cell
lengthlength ll. We compared the effects of. We compared the effects of ww andand ll onon
estimates of urban extent at threshold densities.estimates of urban extent at threshold densities.

15. BRISTOL w l ρ≥t t = 4 t = 5 t = 6 t = 7 t = 8 t = 12 t = 16 t = 20 t = 24
TRA = A (ha.)*
1
100 100 7246 6951 6701 6472 6245 5386 4600 3872 3220 A
TRA = A + B% *
2
200 100 26.66 26.79 26.03 24.86 24.15 18.62 12.80 2.82 -9.53 B
TRA = A + (B+C)% *
3
200 50 0.69 -0.17 0.66 -0.70 -0.34 0.42 C
TRA = A + (B+D)% *
4
200 200 6.71 5.91 5.18 5.61 4.85 8.52 3.72 1.63 -2.76 D
TRA = A + E% 400 100 50.65 50.28 48.98 46.94 44.28 34.14 17.54 -8.60 -34.69 E
TRA = A + (E+F)% 400 50 0.10 0.19 0.32 -0.40 0.16 -0.17 F
TRA = A + (E+G)% 400 200 0.17 0.20 -1.00 -1.76 -0.86 0.80 0.72 -0.08 -0.47 G
TRA = A + (E+H)% 400 400 8.11 6.47 4.55 3.37 5.60 5.48 2.46 -5.45 -10.65 H
TRA = A + I% 800 100 72.23 70.26 67.84 64.18 61.10 42.46 7.63 -33.86 -65.31 I
TRA = A + (I+J)% 800 50 1.78 1.26 -0.16 -0.83 -1.83 -2.24 J
TRA = A + (I+K)% 800 200 -0.33 0.01 0.79 0.40 0.30 -0.98 0.98 -0.03 0.47 K
TRA = A + (I+L)% 800 400 0.66 0.53 0.49 0.71 -0.98 -0.46 2.28 -1.68 -6.37 L
NORWICH w l ρ≥t t = 4 t = 5 t = 6 t = 7 t = 8 t = 12 t = 16 t = 20 t = 24
TRA = M (ha.) 100 100 2821 2693 2575 2455 2331 1913 1543 1257 1028 M
TRA = M + N% 200 100 32.22 30.78 28.08 25.30 24.11 16.68 8.23 -0.24 -14.49 N
TRA = M + (N+O)% 200 50 -0.86 0.38 -0.13 0.91 -1.05 1.41 O
TRA = M + (N+P)% 200 200 5.88 6.02 7.22 8.15 8.88 6.48 3.76 0.48 -2.63 P
TRA = M + Q% 400 100 59.31 56.55 53.83 49.53 46.85 25.98 2.85 -19.01 -42.12 Q
TRA = M + (Q+R)% 400 50 0.55 -0.06 0.30 0.71 0.12 0.00 R
TRA = M + (Q+S)% 400 200 0.92 1.78 -0.35 -0.29 -1.16 -0.52 -0.97 -1.75 0.49 S
TRA = M + (Q+T)% 400 400 9.15 10.40 5.24 6.23 7.59 0.31 -0.19 -7.16 -11.19 T
TRA = M + U% 800 100 82.84 77.65 71.61 66.76 60.53 23.37 -17.04 -47.26 -72.47 U
TRA = M + (U+V)% 800 50 1.29 1.05 -0.52 -2.61 -2.27 -2.65 V
TRA = M + (U+W)% 800 200 0.07 0.15 -0.43 1.22 -0.09 -0.63 0.52 -1.51 0.10 W
TRA = M + (U+X)% 800 400 0.35 -1.78 1.13 -4.48 1.46 1.25 -1.04 -3.10 8.27 X
*1 For example, the total estimated residential area (TRA) of Bristol with a population density equivalent to 4 or more Code-Points per hectare (10,000m2) is
7246 ha given a search radius of 100m and output cell length of 100m. The estimated TRA with 5 or more Code-Points per ha. is 6951 ha.
*2 Doubling the search radius (and leaving the output cell length constant) raises the estimated TRA at density 4 or above by 26.66% (giving a new total of
0.2666 × 7246 + 7246 ha.). It raises the estimated TRA at density 5 or above by 26.79% (giving a new total of 0.2679 × 6951 + 6951 ha).
*3 Doubling the search radius and halving the cell length raises the estimated TRA at a density equivalent to 4 or more Code-Points per hectare (i.e. 1 Code-
Point per 2,500m--2 cell) by 27..35% above the original estimate of 7246 ha. The 27.35% is made-up of 26.66% due to the doubled search radius and 0.69%
due to the halved cell size.
*4 Doubling the search radius and also doubling the cell length raises the estimated TRA at a density equivalent to 4 or more Code-Points per hectare (i.e. 16
Code-Points per 40,000m--2 cell) by 33.37% above the original estimate of 7246 ha. The 33.37% is made-up of 26.66% due to the doubled search radius
and 6.71% due to the doubled cell size. The estimated TRA at 5 or more Code-Points per hectare is raised by 32.70% above the original estimate of 6951 ha.
(26.79% is due to the search window change, 5.91% to the cell length).
=7246+7246×26.66%
=7246+7246× (26.66+0.69)%
=7246+7246× (26.66+6.71)%
Further investigation proves that the impact of l is much less than that of w in PSM.
% change
caused by w
% change
caused by l
N/A N/A
26.66
26.66 0.69
22.66 6.71
=7246

16. 8.8. Using the density profiles toUsing the density profiles to
investigate residential land useinvestigate residential land use
The result and analysis in previous slides also provide the evidenceThe result and analysis in previous slides also provide the evidence
of self-similarity insofar as they are found to fill the same proportionof self-similarity insofar as they are found to fill the same proportion
of space. However, it does not provide sufficient information for usof space. However, it does not provide sufficient information for us
to support the notion.to support the notion.
A more persuasive method of comparing the density profiles of eachA more persuasive method of comparing the density profiles of each
area is sought based on plotting the estimated area as a percentagearea is sought based on plotting the estimated area as a percentage
increase above a benchmark calculated at density threshold 25 forincrease above a benchmark calculated at density threshold 25 for
each value ofeach value of ww..

17. 26%
1315%

18. Our focus has been changed:Our focus has been changed:
a single scale methoda single scale method
multiple scales in combination methodmultiple scales in combination method

To use an analogy from Remote Sensing, are we able to treat the fourTo use an analogy from Remote Sensing, are we able to treat the four
sets of values for each settlement ((sets of values for each settlement ((mmww100,100, mmww200,200, mmww400 and400 and mmww800) as800) as
separate bands of information that together offer insight into the urbanseparate bands of information that together offer insight into the urban
structures?structures?

20. 9.9. ConclusionConclusion
Search window radius -- the most significantSearch window radius -- the most significant
parameter in PSM which affects the output hasparameter in PSM which affects the output has
been identified and evaluated to tell us howbeen identified and evaluated to tell us how
sensitive it will affect PSM modeling output.sensitive it will affect PSM modeling output.
More locally sensitive representations of urbanMore locally sensitive representations of urban
extent and density can be investigated byextent and density can be investigated by
fitting separate surface model to differentfitting separate surface model to different
locations within cities .locations within cities .
This new approach offers potential forThis new approach offers potential for
modeling different types of land use and themodeling different types of land use and the
possible premise of questions of urban socialpossible premise of questions of urban social
and environmental sustainability.and environmental sustainability.