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. [email protected] or [email protected] (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.
8-References
Al-shalabi, Mohamed, Lawal Billa, Biswajeet Pradhan, Shattri Mansor, and Abubakr A. A. Al-Sharif. 2012. Modelling urban growth evolution and land-use changes using GIS based cellular automata and SLEUTH models: the case of Sana’a metropolitan city, Yemen. Environmental Earth Sciences:1-13.
Barredo, José I, and Luca Demicheli. 2003. Urban sustainability in developing countries’ megacities: modelling and predicting future urban growth in Lagos. Cities 20 (5):297-310.
Hu, Zhiyong, and CP Lo. 2007. Modeling urban growth in Atlanta using logistic regression. Computers, Environment and Urban Systems 31 (6):667-688.
Masser, Ian. 2001. Managing our urban future: the role of remote sensing and geographic information systems. Habitat International 25 (4):503-512.
Mohammady, Majid, Hamid Reza Pourghasemi, and Biswajeet Pradhan. 2012. Landslide susceptibility mapping at Golestan Province, Iran: A comparison between frequency ratio, Dempster–Shafer, and weights-of-evidence models. Journal of Asian Earth Sciences 61 (0):221-236.
Park, Soyoung, Seongwoo Jeon, and Chuluong Choi. 2012. Mapping urban growth probability in South Korea: comparison of frequency ratio, analytic hierarchy process, and logistic regression models and use of the environmental conservation value assessment. Landscape and Ecological Engineering 8 (1):17-31.
Pathan, SK, VK Shukla, RG Patel, BR Patel, and KS Mehta. 1991. Urban land use mapping: A case study of ahmedabad city and its environs. Journal of the Indian Society of Remote Sensing 19 (2):95-112.
Pijanowski, Bryan C, Daniel G Brown, Bradley A Shellito, and Gaurav A Manik. 2002. Using neural networks and GIS to forecast land use changes: a land transformation model. Computers, Environment and Urban Systems 26 (6):553-575.
Pontius Jr, R. Gil, and Laura C. Schneider. 2001. Land-cover change model validation by an ROC method for the Ipswich watershed, Massachusetts, USA. Agriculture, ecosystems & environment 85 (1–3):239-248.
Sandhya Kiran, G, and Usha B Joshi. 2013. Estimation of variables explaining urbanization concomitant with land-use change: a spatial approach. International Journal of Remote Sensing 34 (3):824-847.
Soffianian, A, M Ahmadi Nadoushan, L Yaghmaei, and S Falahatkar. 2010. Mapping and Analyzing Urban Expansion Using Remotely Sensed Imagery in Isfahan, Iran. World Applied Sciences Journal 9 (12):1370-1378.
Tole, Lise. 2008. Changes in the built vs. non-built environment in a rapidly urbanizing region: A case study of the Greater Toronto Area. Computers, Environment and Urban Systems 32 (5):355-364.
Veldkamp, Antonie, and Eric F Lambin. 2001. Predicting land-use change. Agriculture, ecosystems & environment 85 (1):1-6.
Wu, Kai-ya, Xin-yue Ye, Zhi-fang Qi, and Hao Zhang. 2012. Impacts of land use/land cover change and socioeconomic development on regional ecosystem services: The case of fast-growing Hangzhou metropolitan area, China. Cities.
Zhao, Yaolong, and Yuji Murayama. 2011. Urban Dynamics Analysis Using Spatial Metrics Geosimulation. In Spatial Analysis and Modeling in Geographical Transformation Process: Springer.