Efficiency and Reliability of Probabilistic Based Frequency Ratio

Model (FR) in Urban Growth Modelling

Abubakr A. A. Al-sharif, Biswajeet Pradhan*, Helmi Zulhaidi Mohd Shafri, Shattri

Mansor

Department of Civil Engineering, Faculty of Engineering

University Putra Malaysia, 43400, UPM, Serdang

Email. biswajeet24@gmail.com or biswajeet@lycos.com (Corresponding author)

Abstract

Urban expansion is a dynamic and continuous spatial phenomenon which associates

population growth and economic development. Analysing and understanding urbanization

process require models that capable to simulate, monitor and predict both urban growth and

urban sprawl. In this paper, a probabilistic based frequency ratio model (FR) that has not

applied before in urban growth modelling of cities was employed to simulate and predict the

urban expansion of Tripoli metropolis city, Libya. Three temporal remote sensing data (RS)

of years (1996, 2002 and 2010) and geographic information system (GIS) were used to

extract various urban deriving factors for the study area. The considered urban factors are:

slope, distance to active economic centre, distance to central business district (CBD), distance

to roads, distance to built up areas and distance to educational area. Subsequently, for model

calibration FR model was applied to simulate urban growth for time period 1996 to 2002. For

model validation, temporal data between 2002 to 2010 were used and subsequently future

urban growth suitability map was produced. The relative operating characteristic method

(ROC) was used to validate the FR model. The validation results indicated 83.2% prediction

accuracy. Finally, the results demonstrated that FR model can be used in urban growth

modelling of cities. On the other hand, FR model has temporal and dynamic limitations that

should be considered in urbanization analysis. This research recommended that to improve

FR model performance further, it is necessary to correlate urban expansion rates within the

classified classes and their frequency ratios of particular urban deriving factor with time

change.

Keywords: Urban growth; Frequency ratio; GIS; Remote sensing; Tripoli

1- Introduction

Metropolitan areas in developing countries have grown rapidly as a result of economy

flourishing and population increase. The rapid uncontrolled urban growth causes very

complex problems such as; environment deterioration, decreasing agriculture lands, traffic

congestion, environmental pollution, illegal unplanned urban settlements with poor

infrastructure and ....etc (Al-shalabi et al. 2012; Pathan et al. 1991; Tole 2008; Wu et al.

2012). Sustainable urban development can be achieved by deep understanding of

urbanization process behaviour, understanding urban deriving factors, urban expansion

simulation, prediction of future urban growth patterns and designing suitable alternatives of

urban development (Soffianian et al. 2010; Sandhya Kiran and Joshi 2013; Barredo and

Demicheli 2003). Carrying out experiments to study urban expansion process and to analyse

it is causative factors is not applicable, then rational simulation approaches to model the

dynamicity and complexity of urban expansion are needed (Zhao and Murayama 2011). The

complication of temporal and spatial dynamics is the main aspect of urban growth process

and spatial human activities. Hence, urban driving factors and its spatio-temporal dynamics

should be considered in land use change modelling and urban studies (Veldkamp and Lambin

2001). However, as a result of vast advances in remote sensing and GIS fields; studying,

monitoring and predicting urban expansion dynamics have become more achievable (Masser

2001). Many modelling approaches that capable to incorporate GIS and RS were employed to

examine, analyse, assess, predict future urban growth and to attain sustainable urban

development. For instance, cellular automata model (CA) (Al-shalabi et al. 2012), artificial

neural network model (ANN) (Pijanowski et al. 2002), logistic regression model (LR) (Hu

and Lo 2007), and analytical hierarchal process model (AHP) (Park, Jeon, and Choi 2012).

Moreover, those models are able to consider biophysical factors such as slope, elevation..etc,

and socioeconomic factors like population density, distance to central business district (CBD)

and so on. Urban growth models use factors that affect and derive urban growth process and

it is spatial patterns, to find the optimum coefficients for modelling urban growth, based on

study area conditions, historical data and urban past behaviours. These models estimate

transition rules that govern urban process and assess the role of each factor, to predict amount

and place of future urban expansion occurrence. However, urbanization factors inputs and

calculation methods used for transition rules estimation may result in outcomes variations

depend on used model. Frequency ratio model as a statistical method was applied widely in

landslide modelling. FR model was used to produce landslide susceptibility maps and to

identify and analyse the probability of landslides occurrence (Mohammady, Pourghasemi,

and Pradhan 2012). However, as a unique case study Park et al. (2011) applied FR model to

simulate urban growth patterns of Republic of South Korea and to predict future urban

growth map of whole mentioned country. In simulation process they used data of two time

periods (1980 and 2007) for model calibration and validation. In other words the whole

amount of urbanized area of first time period was used to calculate the coefficients of urban

deriving factors and to produce future suitability map of urban growth. Thereafter, the urban

extent of 2007 time period (which is includes urban extent of 1980) were used to validate the

model performance using relative operating characteristic (ROC). Their (ROC) validation

resulted in 93.72% level of accuracy which is indicating very good model performance.

However, the reason behind this accuracy level is that the calibration data (i.e. urban area in

1980) was duplicated within validation data (i.e. urban area in 2007). Hence, the rising

questions are to which extent FR model is reliable in urban growth modelling?, how to be

applied in proper way? and is it efficient in urban expansion modelling of smaller areas like

metropolitan cities? The main objectives of this research are: 1) To apply and assess FR

model in urban growth prediction of Tripoli metropolitan area; 2) Apply FR model in novel

different way to reflect urban growth dynamicity.

2-Study area

Tripoli is the capital of Libyan state, it is the most important economic, political, commercial

centre in the country. Tripoli metropolis city is located at (N 32o 53′ and E 13

o 10′) and

covers area about 1147sq.km, with population more than 1.3 million individuals as shown in

Figure 1 . It has experienced rapid dispersed urban expansion in last decades.

Figure: 1 Study area.

3- Materials used

In this work socioeconomic, physical and environmental urban deriving factors are

considered to predict urban growth probability map. The used urban factors that represent the

independent variables of urbanization process are: slope, distance to active economic centres,

distance to CBD, distance to road, distance to built up areas and distance to educational areas

as shown in Figure 2.The slope map was generated from digital contour map of study area.

Distances to: roads, active economic centre, CBD, built up areas and to educational areas

were calculated in Arc-GIS platform using Euclidean distance function. Urban growth maps

which represent the dependent variable were extracted from three satellite images of study

area in different time periods (1996, 2002 and 2010) using maximum likelihood supervised

classification method as shown in Figure 2-g,h. As last step in data preparation all thematic

maps of urban factors and urban expansions were clipped with study area boundary vector

map and resampled to grid size 30m × 30m.

Figure 2: Thematic maps of independent and dependent variables; (a) Slope; (b) Distance to

active economy centers; (c) Distance to CBD; (d) Distance to roads; (e) Distance to nearest

urbanized area; (f) Distance to educational area; (g) Urban growth from 1996 to 2002; (h)

Urban growth from 2002 to 2010.

4- Methodology

Frequency ratio (FR) model is one of univariate probability analysis methods. The FR model

was employed in this study to analyse the spatial correlation among the location of urban

growth occurrence and each urban expansion deriving factor. i.e. FR model is based on the

recorded associations among allocation of urban expansions and classified classes of deriving

factors. The frequency ratio of urban growth is the ratio of the probability of urbanization

occurrence to the probability of a non-occurrence for given attributes. In order to produce

urban growth probability map the FR model was applied using GIS technique which able to

represent the information spatially. The frequency ratios were computed for all classes of

urbanization factors, then the frequency ratios distribution maps were summed to get the

urban growth probability map.

For FR values lower than 1 indicate lower relationship with urban growth, whereas values

larger than 1 mean higher correlation with urban expansion, value of 1 reflects average

condition.

Urban Growth Probability Map =∑ FR...................................................................................(1)

where FR is the rating of the range of each urban factor.

5-Analysis and Results

FR model analysis results are showed in Figure 2 where the whiter the tone, the larger FR

ratio and the darker, the lower FR ratio. The illustrated maps show the spatial relationship

between each factor and the occurrence of urban growth.

Figure 3 illustrate the behaviour of urban expansion and frequency ratios variation during

different time periods and their relationship with urbanization factors. The slope in study area

is ranged from 0 degree to 17

degree, in this study slope was classified into 7 quantile classes.

The values of FR are ranged from 0.79 to 1.13 in time period 1996-2002 and 0.67 to 1.31 in

time period 2002-2010. This result demonstrates that the slope factor has low effect on urban

growth process in Tripoli, especially when the low slope domains become very saturated with

urban area, consequently, the urban area will extend to higher slope domains . Hence one can

say that the slopes of all domains in the study area allow urban expansion with little

variations. The influence of distance to active economic centres can be noticed from FR

values, the highest growth was happened in distance range 0m to 630m from active economic

centres in time period 1996-2002 with FR value 1.64; In time period 2002-2010 the largest

FR was recorded in distance range 630m to 1260m with FR value of 1.8. It is worth to

mention that the distance range 0 to 630m had increased FR value equals 1.74. However, this

increase means that this distance range is going to be very crowded. For that the higher

urbanization suitability expanded to the next domain, i.e. from 630m to 1260m. The factor of

distance to CBD showed higher FR value at distance range from 8000m to 9150m in time

periods 1996-2002 and 200-2010 with values of 2.46 and 2.32 respectively. The decrease in

FR value refers to the decrease of growth with time increase, i.e. this range is becoming more

compact. However, distance ranges less than 8000 m demonstrated dramatic decrease in

growth from 2002 to 2010, i.e. became very dense. At the same time the distance ranges from

8000m until 19500m indicated remarkable increase of FR, i.e. increased urban growth which

may indicated uncontrolled growth. The model results showed that FR values (i.e. urban

growth) are increased gradually with the increase of the distance from roads with time

progress, the reason is that the earlier urban expansions tend to occur near the roads, after that

the urban area will expand away from roads with time increase. The general trend of FR

values for distance to built up areas factor demonstrates that the probability of growth is

increasing with the decrease of the distance to urbanized areas in all time periods. The factor

of distance to educational areas almost showed behaviour similar to the distance to roads

factor; that in case of compact urban domains nearer to educational areas the growth will

occur in next further domains. Finally, to get urban growth probability map equation 1 was

applied , thereafter the restricted areas and last built up area extents were excluded to produce

final map as shown in Figure 4.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1996 to 2002

2002 to 2010

(a)

0.000.200.400.600.801.001.201.401.601.802.00

1996 to 20022002 to 2010

(b)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

1996 to 20022002 to 2010

(c)

0.000.200.400.600.801.001.201.401.601.80

1996 to 2002

2002 to 2010

(d)

Figure 3: Variation of urban growth frequency ratios in urbanization factors domains in two

time periods; (a) Slope; (b) Distance to active economy centers; (c) Distance to CBD; (d)

Distance to roads; (e) Distance to nearest urbanized area; (f) Distance to educational area.

Figure 4: Predicted urban growth probability map.

6-Model validation using the ROC technique

To validate and assess applied FR model performance the receiver operating characteristic

(ROC) method was used. The ROC technique is considered as a dependable technique in land

use/cover change modelling studies, ROC method measures the relationship among real and

expected changes (Pontius Jr and Schneider 2001).In ROC curve, the model sensitivity (true

positive) is plotted against 1-specificity (false positive). Higher sensitivity means larger

amount of correct predictions while higher specificity refers larger amount of false positives.

The predicted urban growth probability map produced based on the data of time period 1996-

2002 is compared against real urban growth in time period 2002-2010 rather than whole

urbanized area. The model validation result indicated (83.2%) prediction accuracy as shown

in Figure 5, which reflects good performance of used model.

0

0.5

1

1.5

2

2.5

1996 to 2002

2002 to 2010

(e)

0.000.200.400.600.801.001.201.401.601.802.00

1996 to 20022002 to 2010

(f)

Figure 5: FR model prediction accuracy (83.2%) using ROC.

7-Conclusion and discussion

In this paper future urban growth probability map of Tripoli-Libya was produced using FR

statistical model. The analysis results demonstrate that FR model can be used for analysing

urban expansion, it's deriving forces and prediction urban future trends in metropolitan areas

and cities. FR model is powerful in assessing the relationship between urban growth and each

causative factor individually, that gives superior understanding about the role of each factor.

The urban growth is a dynamic, temporal, continuous and not repetitive phenomenon.

However, Park et. al (2012) used the whole urban extent area to calculate the frequency ratio

for each urban deriving factor (i.e. model calibration). Moreover, in model performance

validation they used again whole urban extent of next time period which already includes

urban area of previous time period. This implementation way could be suitable for urban

patterns analysis and assess present urban situations, but it does not explain real urban

expansion dynamicity and urban growth as a progressive process. The approach used in this

research for FR model implementation was based on the use of actual urban growth quantity

rather than all urbanized area, to understand the actual effect of urbanization process factors.

The use of actual urban growth quantity gives better understanding of urban expansion

process and reflects clearer picture about the dynamicity of urban growth. The major concern

in implement FR model are urban growth dynamicity with temporal change (i.e. urban areas

increase with time and these urban areas will not be urbanized again). This characteristic of

urban expansion process may leads to inaccurate frequency ratios. To improve FR model

further, it is recommended to correlate urban expansion rates within the classified classes of

each urban factor and their frequency ratios with time change based on past urban tendencies.

Thus, next changes of frequency ratios in next time period can be estimated.

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