SLEUTH model has been developed by its author, Keith Clarke, as general model, suitable for all kinds of urban growth, in order to define a sort of DNA of urban systems (constituted by particular sets of model parameters). To be really general, we think that this model has to fit two general aspects: the urban sprawl and the rank-size rule. We present an evaluation of Sleuth model through European case studies, showing the calibrated set of parameters which fit each city we have analysed, and showing how this model can predict urban growth and in particular the dynamic process of the sprawl, through the output maps of the Sleuth software. Moreover it’s possible to apply this model not only at single cities, but also to a wide territory (due to scale invariance), in order to predict the evolution of a system of cities; to do this we considered an ideal territory, built by ourselves, respecting the rank-size rule, evaluating the ability of the model to fit this aspect. We will present also the sensitivity analysis conducted on the 5 parameters of the model (see below), in order to establish how these parameters influence the growth of urbanized areas. The goal is a contribution for the ambitious Project Gigalopolis, investigating the meaning of the parameters of the model, and the common aspects among different type of urbanized areas, in order to build a “DNA of city” through the analysis of the outgoings produced by Sleuth.

1. The SLEUTH Urban CA-BasedThe SLEUTH Urban CA-Based
Model: an evaluationModel: an evaluation
ing. Matteo Caglioniing. Matteo Caglioni
prof. Giovanni Rabinoprof. Giovanni Rabino
Università di PisaUniversità di Pisa
Dipartimento di Ingegneria CivileDipartimento di Ingegneria Civile
Politecnico di MilanoPolitecnico di Milano
Dipartimento di Architettura eDipartimento di Architettura e
PianificazionePianificazione

2. CA-based modelCA-based model
 X:X: number of cells of the grid (map)number of cells of the grid (map)
 S:S: number of possible states for the cellsnumber of possible states for the cells
 N:N: number of cells which defines thenumber of cells which defines the
neighbourhoodneighbourhood
 f(…):f(…): function of state transition, whichfunction of state transition, which
gives the state at time t+1gives the state at time t+1

3. SLEUTH CA-based modelSLEUTH CA-based model
 It is a probabilistic 2D cellular automata based model that simulates urbanIt is a probabilistic 2D cellular automata based model that simulates urban
growth through time.growth through time.
 Constituted by 2 modules (sub-models):Constituted by 2 modules (sub-models):
1. UGM 2. DELTATRON1. UGM 2. DELTATRON
1. The Urban Growth Model (UGM) simulates the effect of topography,1. The Urban Growth Model (UGM) simulates the effect of topography,
adjacency, and transportation networks on the patterns of urbanizationadjacency, and transportation networks on the patterns of urbanization
through time. It uses Boolean logic (urbanized/not urbanized)through time. It uses Boolean logic (urbanized/not urbanized)
2. The Deltatron Land Use/Land Cover Model uses CA-based rules, class2. The Deltatron Land Use/Land Cover Model uses CA-based rules, class
transition probabilities (Markov matrixes), and local topography in order totransition probabilities (Markov matrixes), and local topography in order to
define land use changes.define land use changes.

4. SLEUTH CA-based modelSLEUTH CA-based model
 4 sequential phases for each module4 sequential phases for each module
 Time step: 1 yearTime step: 1 year
 5 parameters to calibrate5 parameters to calibrate
UGMUGM
• Spontaneous growth
• New spreading centres
• Edge growth
• Road influence growth
DeltatronDeltatron
• Initial Change
• Cluster Change
• Propagate Change
• Age Deltatrons

5. 19001900 1925 19501925 1950 1975 20001975 2000
 SSlopelope
 LLand Coverand Cover
 EExcludedxcluded
 UUrbanrban
 TTransportationransportation
 HHillshadeillshade

6. SLEUTH CA-based modelSLEUTH CA-based model
Changes are driven by 5 parameters:Changes are driven by 5 parameters:
 DispersionDispersion (determines the smallest, spontaneous, global(determines the smallest, spontaneous, global
urbanization probability)urbanization probability)
 SpreadSpread (defines the part of the growth that starts from existing(defines the part of the growth that starts from existing
spreading centres)spreading centres)
 BreedBreed (defines the probability for each new urbanized cell to(defines the probability for each new urbanized cell to
become a new spreading centre)become a new spreading centre)
 Slope ResistanceSlope Resistance (urbanization decrease with slope)(urbanization decrease with slope)
 Road GravityRoad Gravity (urbanization follows road network)(urbanization follows road network)

7. Spontaneous growthSpontaneous growth
 Urban settlements may occur anywhere on a landscape
 f (diffusion coefficient, slope resistance)

8.  Some new urban settlements will become centers of further growth.
 Others will remain isolated.
 f (spontaneous growth, breed coefficient, slope resistance)
Creation of new spreading centersCreation of new spreading centers

9.  The most common type of development
 It occurs at urban edges and as in-fill
 f (spread coefficient, slope resistance)
Organic growthOrganic growth

10.  Urbanization has a tendency to follow transportation network.
 f (breed coefficient, road gravity coefficient, slope resistance,
diffusion coefficient)
Road Influenced GrowthRoad Influenced Growth

11. TT00 TT11
ForFor nn time periods (years)time periods (years)
spontaneous
spreading
center organic
road
influenced deltatron
f (slope
resistance,
diffusion
coefficient)
f (slope
resistance,
breed
coefficient)
f (slope
resistance,
spread
coefficient)
f (slope resistance,
diffusion coefficient,
breed coefficient,
road gravity)

12. pastpast
presentpresent
For
For mm
M
onte Carlo iterations
M
onte Carlo iterations
For
For nn
coefficient sets
coefficient sets
CALIBRATION:CALIBRATION:
Predicting the presentPredicting the present
from the pastfrom the past

13. SLEUTH CA-based modelSLEUTH CA-based model
 CalibrationCalibration (brute force calibration)(brute force calibration)
1) Set initial conditions:1) Set initial conditions:
• coefficient values (D; S; B; SR; RG)
• 6 kinds of input images
2)2) Apply GrowthApply Growth
Rules:Rules:
• UGM (4 phases)
• Deltatron (4 phases)
3)3) Self-Modification:Self-Modification:
• Calculate growth rate (GR)
• If (GR > CRITICAL_HIGH), modify coefficients
for BOOM state  rapid growth
• If (GR < CRITICAL_LOW), modify coefficients
for BUST state  depressed growth

15. http://www.ncgia.ucsb.edu/projects/gig/ncgia.htmlhttp://www.ncgia.ucsb.edu/projects/gig/ncgia.html

16. Simulation of ideal casesSimulation of ideal cases
 Validity of information we can get from modelValidity of information we can get from model
prediction is directly proportional with the abilityprediction is directly proportional with the ability
of the model to adapt itself to the system… itsof the model to adapt itself to the system… its
ability in reproducing reality.ability in reproducing reality.
 In order to evaluate this model ability we analyseIn order to evaluate this model ability we analyse
two ideal cases:two ideal cases:
- Zipf’s Rank Size Rule- Zipf’s Rank Size Rule
- Urban Sprawl- Urban Sprawl

17. Road NetworkRoad Network
(from Fulong Wu’s studies about spontaneous and self-organized urban growth)
Urbanized areaUrbanized area
19901950 19701930
1950 1970

18. rank-size
1
10
100
1000
1 10 100 1000
rango
dimensione
R2 = 0,9949
0
10
20
30
40
50
60
70
80
0 1 2 3
rango
numerocentri
Rank Size Rule is verified with the following set of calibrated parameters:Rank Size Rule is verified with the following set of calibrated parameters:
(DI=0, BR=2, SP=0, SR=7, RG=60)(DI=0, BR=2, SP=0, SR=7, RG=60)

19. Rank Size Rule is verified with the following set of calibrated parameters:Rank Size Rule is verified with the following set of calibrated parameters:
(DI=0, BR=2, SP=0, SR=7, RG=60)(DI=0, BR=2, SP=0, SR=7, RG=60)
3200
3220
3240
3260
3280
3300
3320
3340
3360
3380
1991 1994 1997 2000 2003 2006 2009
anni
celle
0
10
20
30
40
50
60
70
80
90
100
area urbana [n° celle] nuclei urbani

20. rank-size, analisi parametrica: areaurbanizzata
3000
4000
5000
6000
7000
8000
1991 1994 19 97 2000 2003 2006 20 09
anni
[celle]
valori dacalibrazione di=10, br=0, spr=1, s.r.=1, r.g.=61
di=10, br=10, spr=1, s.r.=1, r.g.=61 di=10, br=10, spr=10,s.r.=1, r.g.=61
di=0, br=10, spr=0, s.r.=1, r.g.=61 di=0, br=0, spr=10, s.r.=1, r.g.=61
di=25, br=0, spr=1, s.r.=1, r.g.=61 di=25, br=25, spr=1, s.r.=1, r.g.=61
di=25, br=25, spr=25, s.r.=1, r.g.=61
Sensitivity analysis for model parametersSensitivity analysis for model parameters
• Dispersion parameter determines the level of urbanization.Dispersion parameter determines the level of urbanization.
• Breed and Sprawl parameters increase Dispersion effects.Breed and Sprawl parameters increase Dispersion effects.

21. (di=10, br=10, spr=10, s.r.=1, r.g.=61)(di=10, br=10, spr=10, s.r.=1, r.g.=61) (di=25, br=25, spr=25, s.r.=1, r.g.=61)(di=25, br=25, spr=25, s.r.=1, r.g.=61)
When DI, BR, SPR are higher than 25 we loose the hierarchical structureWhen DI, BR, SPR are higher than 25 we loose the hierarchical structure
and we obtain something similar to urban sprawl.and we obtain something similar to urban sprawl.

22. Growth of the urban sprawlGrowth of the urban sprawl
19901950 19701930
Urbanization probability in forecastUrbanization probability in forecast
DI=2, BR=6, SP=26, SR=1, RG=1DI=2, BR=6, SP=26, SR=1, RG=1
Calibrated parameters show an higherCalibrated parameters show an higher
value of spread coefficient.value of spread coefficient.
Sleuth model recognises the sprawlSleuth model recognises the sprawl
dynamics acting on territory.dynamics acting on territory.

23. Simulation of real casesSimulation of real cases
 The model has been calibrated using historicalThe model has been calibrated using historical
data coming from MOLAND project (Monitoringdata coming from MOLAND project (Monitoring
of Land-use Dynamics).of Land-use Dynamics).
 PalermoPalermo (1955, 1963, 1988, 1997)(1955, 1963, 1988, 1997)
 Padova – MestrePadova – Mestre (1955, 1963, 1989, 1997)(1955, 1963, 1989, 1997)
 HelsinkiHelsinki (1950, 1966, 1984, 1998)(1950, 1966, 1984, 1998)
 BilbaoBilbao (1956, 1972, 1984, 1997)(1956, 1972, 1984, 1997)

24. PalermoPalermo
1955 1963 1988 19971955 1963 1988 1997

25. PalermoPalermo
Excluded areaExcluded area
SlopeSlope
HillshadeHillshade

26. PalermoPalermo
growth rate - Palermo 1997 - 2017
0
0,5
1
1,5
2
2,5
3
3,5
19981999200020012002200320042005200620072008200920102011201220132014201520162017
years
[%]
urban area - Palermo 1997-2007
30000
35000
40000
45000
50000
55000
19981999200020012002200320042005200620072008200920102011201220132014201520162017
year
[ha]

27. PalermoPalermo

28. Padova - MestrePadova - Mestre
HelsinkiHelsinki BilbaoBilbao

29. Velocità di crescita urbana (normalizzata)
0
0,002
0,004
0,006
0,008
0,01
0,012
0,014
0,016
0,018
1 4 7 10 13 16 19
anni di simulazione
[1/anno]
Padova Mestre Palermo Helsinki Bilbao
Growth rate for European cities after 20 years of simulationGrowth rate for European cities after 20 years of simulation

30. Valorimedideiparametrineidiversipaesi
2
18 21
36
90
8
47
27
38
65
40 42
47
20
42
10
31
71
22
31
0
10
20
30
40
50
60
70
80
90
100
Diffusion Breed Spread Slope Road
italia europa usa altri
• min DI and max RG for
Italian cases, opposite to
USA (for historical
reasons and different
space competition)
• BR maximum in Europe
• SP is higher when faster
is the development (i.e.
economical boom)

31. Observing different cases allows us to trace a kind of “DNA of cities” using particular sets ofObserving different cases allows us to trace a kind of “DNA of cities” using particular sets of
parameters:parameters:
• RG and DI are different for coastal/inland citiesRG and DI are different for coastal/inland cities
• SP is higher for growing and more populated cities (Mexico City, Tijuana, Houston,SP is higher for growing and more populated cities (Mexico City, Tijuana, Houston,
Palermo)Palermo)
• BR high and DI low for strictly planned areas (Netherlands, Helsinki…)BR high and DI low for strictly planned areas (Netherlands, Helsinki…)
Parameter valuesParameter values
UrbanisationUrbanisation DIDI BRBR SPSP RGRG SRSR
New metropolitan areaNew metropolitan area 25-4025-40 >50>50 >80>80 >50>50
urban sprawlurban sprawl 10-2010-20 10-3010-30 10-3010-30 >50>50
Strictly planned cityStrictly planned city <5<5 >90>90 <10<10 40-6040-60
Urban constrainsUrban constrains <5<5 100100 <10<10 <10<10
Metropolis with satellite citiesMetropolis with satellite cities 5-105-10 30-4030-40 10-3010-30 >90>90
Possible range of parameter values in order to describe different kind of urban growthPossible range of parameter values in order to describe different kind of urban growth
(SR independent by cities).(SR independent by cities).

32. Conclusive remarksConclusive remarks
 Sleuth model is really useful for simulationSleuth model is really useful for simulation
and comparison of urban growth.and comparison of urban growth.
 It’s possible to use parallel computing toIt’s possible to use parallel computing to
solve the calibration problem (highsolve the calibration problem (high
execution time).execution time).

33. Conclusive remarksConclusive remarks
 It’s just a descriptive model (parametersIt’s just a descriptive model (parameters
are shape indices).are shape indices).
 It isn’t explicative, it doesn’t explain theIt isn’t explicative, it doesn’t explain the
shape of the city.shape of the city.
 The same shape can derive from differentThe same shape can derive from different
urban sprawl dynamics acting on territory.urban sprawl dynamics acting on territory.