J Indian Soc Remote Sens DOI 10.1007/s12524-013-0299-7

RESEARCH ARTICLE

Urban Sprawl Analysis of Tripoli Metropolitan City (Libya) Using Remote Sensing Data and Multivariate Logistic Regression Model Abubakr A. A. Alsharif & Biswajeet Pradhan

Received: 22 April 2013 / Accepted: 27 May 2013 # Indian Society of Remote Sensing 2013

Abstract The main objective of this paper is to analyze urban sprawl in the metropolitan city of Tripoli, Libya. Logistic regression model is used in modeling urban expansion patterns, and in investigating the relationship between urban sprawl and various driving forces. The 11 factors that influence urban sprawl occurrence used in this research are the distances to main active economic centers, to a central business district, to the nearest urbanized area, to educational area, to roads, and to urbanized areas; easting and northing coordinates; slope; restricted area; and population density. These factors were extracted from various existing maps and remotely sensed data. Subsequently, logistic regression coefficient of each factor is computed in the calibration phase using data from 1984 to 2002. Additionally, data from 2002 to 2010 were used in the validation. The validation of the logistic regression model was conducted using the relative operating characteristic (ROC) method. The validation result indicated 0.86 accuracy rate. Finally, the urban sprawl probability map was generated to estimate six scenarios of urban patterns for 2020 and 2025. The results indicated that the logistic regression A. A. A. Alsharif : B. Pradhan (*) Department of Civil Engineering, Faculty of Engineering, University Putra Malaysia, UPM, 43400 Serdang, Malaysia e-mail: [email protected] B. Pradhan e-mail: [email protected]

model is effective in explaining urban expansion driving factors, their behaviors, and urban pattern formation. The logistic regression model has limitations in temporal dynamic analysis used in urban analysis studies. Thus, an integration of the logistic regression model with estimation and allocation techniques can be used to estimate and to locate urban land demands for a deeper understanding of future urban patterns. Keywords Urban modeling . Sprawl analysis . Logistic regression . Remote sensing . GIS . Tripoli

Introduction The complex structure of cities around the world has resulted in complicated patterns of land use. Before 1950s, rapid urbanization occurred in developed countries, which resulted in an increase in urban development and significant reduction in agricultural lands (Firman 1997). However, in recent years, urban development in developing countries has been faster than the developed countries (Youssef et al. 2011). Thus, controlling the urbanization process and creating sustainable development require accurate information about urban growth patterns (Jiang and Yao 2010). Metropolitan areas are growing rapidly worldwide because of the rapid population growth in developing countries. Unfortunately, this rapid growth has resulted in decaying infrastructure, uncontrollable growth (sprawl) of informal settlements (Angotti 1993; Sudhira et al.

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2004), negative socioeconomic and environmental effects (Lambin et al. 2001), global warming, climate and ecosystem changes (López et al. 2001) as well as consumption of agricultural land (Huang et al. 2009). The study of urbanization process and land use change is different from other disciplines because it does not allow experimentation on the ground (Irwin and Geoghegan 2001; Verburg et al. 2006). Thus, rationalizing artificial simulations to model the complexity of land use change dynamics is necessary (Verburg and Overmars 2007; Zhao and Murayama 2011). Implementing various studies and modeling methodologies can lead to understanding the occurrence of urban growth or sprawl (Cheng et al. 2003; Jat et al. 2008; Tv et al. 2012; Al-shalabi et al. 2012, 2013). However, the study of urban growth still calls for considerable attention, particularly in developing parts of the world (Jokar Arsanjani 2011). The complexity of spatial and temporal dynamics of the urbanization process and human activities requires the inclusion of temporal and spatial dynamics as well as urban drivers in land use modeling for urban studies (Veldkamp and Lambin 2001). Gillham (2002) and Helbich and Leitner (2010) reported that urban sprawls formed at the fringes of metropolitan areas, by spreading through commercial and industrial development with low density, and followed by large uncontrolled urban expansion with low quality of services and accessibilities. However, urban sprawl formation in developing countries may follow different growth patterns compared with other parts of the world. The quantity and the location of land use changes are main issues to be addressed by city planners and decision makers, especially in rapidly changing environments. Thus, the main objective of the modeling process is to understand and to predict future urban growth (Knox 1993). In the literature, several modeling methods have been used to study changes in land use and cover. Spatial explicit modeling is a key methodology in explaining the process of change quantitatively, and in examining the understanding of this process (Serneels and Lambin 2001). Monitoring and studying urban growth dynamics have become more manageable owing to enormous developments in the GIS and remote sensing fields. These developments provide powerful tools to predict and to model the direction of urban growth (Masser 2001; Al-shalabi et al. 2012, 2013). Several researchers have used various empirical and theoretical modeling techniques to model, simulate, and predict urban sprawl or growth and land use changes.

One of these techniques as an empirical estimation model is the logistic regression model. According to the literature, logistic regression in urban growth or sprawl modeling results in a good understanding of the urbanization process, and provides a clear picture of the weight of independent variables and their respective functions (Hu and Lo 2007; Huang et al. 2009; Lin et al. 2010; Eyoh et al. 2012; Jokar Arsanjani et al. 2013). The logistic regression model enables the integration of demographic and socioeconomic factors that are not available in many models (Pradhan 2009, 2010a, b, 2011). Additionally, the logistic regression model considers spatial effects, autocorrelation, and heterogeneity (Jokar Arsanjani et al. 2013; Devkota et al. 2013). However, the logistic regression model requires caution regarding spatial autocorrelations that typically exist in spatially referenced data because such autocorrelations may violate the hypothesis of the logistic regression model (Lin et al. 2010). Statistical relationships between the land-use change and a group of explanatory variables are the main features of most land-use change models, which explain the change (Overmars and Verburg 2005). Understanding and quantifying the interaction between the driving forces of land use/cover change in the logistic regression models is a complex and difficult process. Thus, overcoming the misunderstanding and lack of information about the driving forces is necessary. Certain drawbacks of the logistic regression restrictions should also be considered (Lambin and Geist 2006; Lin et al. 2010). The literature review indicates that there is a need to model and quantify the location and the extent of urban growth in time and space. In this paper, the metropolitan city of Tripoli is chosen as a case study because of its substantial growth in recent decades. Moreover, the urban growth patterns of the city have never been analyzed. Tripoli is classified as multifunctional because it is the political center of the state as well as the economic, industrial, and service capital that communicates with the outside world. In spite of government urban plans in Libya, Tripoli has had rapid but haphazard urban growth over the past decades. Corruption, political unrest, and economic conditions may have affected urban planning, and consequently, led to massive urban sprawl. Thus, the main concern for Tripoli includes the fast and uncontrolled urban expansion, and the conversion of fertile and green lands and environmental reserve areas, which have created socioeconomic and physical problems.

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This study demonstrates the use of logistic regression technique in modeling urban sprawl. The model is used to study and to analyze the urban growth/sprawl in Tripoli. The model aims to facilitate our understanding of urban sprawl as well as biophysical and social econometric factors and their relationships, and to predict different scenarios of future urban expansion.

Study Area Tripoli is the capital and largest city of Libya. The study area is located along the Mediterranean coast in the northwestern part of Libya, and between longitudes (12o 54' 04" E and 13o 26' 38" E) and latitudes (32o 36' 18" N and 32o 54' 17" N). The city occupies a total land area of approximately 1,143.73 sq. km. The Tripoli metropolitan area includes the districts of Tripoli Center, Hey Alandlus, Tajoura, Janzur, Kaser Ben Ghashir, Alswani, Ain Zara, Abuslim, and Suq Ajumma (Fig. 1).

Data and Materials Used The data used in this study were collected from different sources as mentioned in Table 1. The ARC/INFO GIS software package version 10 was used in the different stages of modeling, namely, image processing, generating classified land cover and land use maps, and spatial analysis. For classification, the maximum likelihood classification technique, which is a supervised classification method, was used for Landsat and Spot 5 spaceborne satellite images. These images were classified by selecting accurate polygons as training areas. Three classes, namely, urban, farm/grass, and restricted or excluded areas, were investigated. Next, the classified images were resampled to the same spatial resolution (30 m×30 m). The selection of the pixel size was intended to avoid the decrease in spatial details of the images. Therefore, the resampling step was conducted after image classification. Then, thematic raster maps of all variables were prepared and calculated in the ArcInfo GIS environment, and presented in raster maps with a grid cell size of 30 m× 30 m. For logistic regression model calibration and validation, all data were converted to ASCII format to be further used by a multivariate logistic regression program using the IBM SPSS Statistics 20 software.

Logistic Regression Model Logistic regression is one of the most popular approaches to modeling. This model can be used in modeling and explaining the relationship of a number of (Xs) independent variables to a dichotomous single dependent variable (Y), which represents the occurrence or non-occurrence of an event (Kleinbaum and Klein 2010). Logistic regression finds the relationship between the independent variables and the function of the probability of an event happening empirically (Sweet and Grace-Martin 1999). Logistic regression also describes the combined effects of several factors (Kleinbaum and Klein 2010). The use of logistic regression can find the coefficients of independent variables (both continuous and categorical), whereas the dependent variable is a binary categorical variable (Huang et al. 2009). The binary dependent variable value is either 1 or 0, and can be computed by using the well-known logistic regression equation (Mahiny and Turner 2003). The aforementioned literature review indicates the application of logistic regression model in urban expansion modeling and land use change analysis. The model gives the probability of the existence or the nonexistence of each type of land use/cover in every location based on their driving factors, and quantifies the interaction between the different land use types and their drivers (Lin et al. 2010; Eyoh et al. 2012). Logistic regression is a powerful empirical method to use when the outcome dependent variable is dichotomous (Peng et al. 2002). The spatial urban expansion is the dependent variable represented in a raster binary map. A value of 1 on the produced probability map indicates the presence of urban growth, and a value of 0 indicates the absence of urban growth. The probability of urbanization for each cell in the raster map was produced based on the following logistic regression equation: f ðzÞ ¼ 1

.

ð1 þ e−z Þ

PðY ¼ 1jX 1 ; X 2 ; ……; X k Þ ¼ 1

.

 X

1þe

− αþ

βi X i

!

ð1Þ

where Xi is an independent variable representing a driving factors of urban process, which can be continuous or categorical by nature;;α is the coefficient of

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Fig. 1 Area of study

J Indian Soc Remote Sens Table 1 Data used and its source Data

Source of data

Land Sat Image 1984

Biruni Remote Sensing Center

Spot 5 Image 2002

Biruni Remote Sensing Center

Spot 5 Image 2010

Libyan Centre For Remote Sensing And Space Science

Roads Network

Urban Planning Agency, Libya

Population Data

General Information Authority, Libya

Digital Contour Map & Topographic Map Detailed Land Use Map

Biruni Remote Sensing Center Urban Planning Agency, Libya

the model formula; P(Y=1|X1, X2,……,Xk) is the probability of the dependent variable Y being 1 given (X1, X2,……,Xk), i.e., the probability of a cell being changed to built-up (urbanized); and βi is the coefficient of variable Xi. The regression coefficient βi reflects the function of independent explanatory variables. A negative sign indicates that the variable tends to decrease the possibility of change, and a positive sign indicates the opposite effect. The selection of independent variables was based on information provided by the Urban Planning Agency (UPA) in Tripoli, and on the results of a field survey. The choice of variables conforms to previous urban modeling and simulation studies (Hu and Lo 2007; Huang et al. 2009). These variables reflect socioeconomic factors, biophysical conditions, and spatial effects (Dietzel and Clarke 2006; Hu and Lo 2007; Huang et al. 2009; Poelmans and Van Rompaey 2010; Wang and Mountrakis 2011; Eyoh et al. 2012; Jokar Arsanjani et al. 2013). Figure 2 and Table 2 indicate the independent variables used in this study. Figure 3 shows the dependent variable Y that represents the urban growth from 1984 to 2002 and from 2002 to 2010. In the modeling process, data from 1984 to 2002 were used firstly for model calibration, and for verification of the spatial autocorrelation of regression results. Validation was conducted by using the actual growth map of 2010, whereas prediction of future patterns used data from 2010.

Model Results Analysis and Interpretation Table 3 indicates the modeling results of the behavior of urban sprawl. The logistic regression model checks

the multicollinearity, which verifies the correlation of independent variables. The modeling results demonstrate the tolerance and the variance inflation factor (VIF) that examines the multicollinearity. The tolerance value ranges from 0.141 to 0.956, and the VIF (1/tolerance) varies from 1.046 to 7.069. The general rule of thumb is that the VIF should not exceed 10. According to the results shown in Table 3, the model works extremely well as per the multicollinearity assessment (Menard 2004; Bui et al. 2011). The model illustrates that urban growth has been affected by main active economic centers. This finding reflects the polycentric aspect of the study area. The distance to the main active economic center (X1) has a coefficient equal to −1.563 and an odds ratio of 0.210. This result indicates the odds of the urbanization process in the area nearer to an active economic centre is 1/0.210, i.e., 4.76 times as great as that of an region 1 km further away from main active economic center. The model results show the distance to CBD (X2) has a probability ratio equivalent to 0.151, which means that the probability of urban expansion of the region closer to CBD is equal to 6.622 times the odds of the area further away by 1 km from CBD. The easting coordinate variable (X3) has a coefficient value of −0.169 and an odds ratio of 0.844. This result demonstrates that the urban sprawl is not similar in the east and west directions because urban expansion to the east direction is more probable. The northing coordinate variable (X4) has a coefficient of −1.983, and an odds ratio of 0.138 or 1/7.246. The odds ratio indicates that increasing 1 km in the south direction decreases the urban expansion odds by 7.246. The probability of urban expansion in a lower slope area is larger than the probability of urbanization in an area that has a higher slope degree. This finding is a reasonable effect of the slope variable (X5). The remarkable point is that the restricted area variable (X6) and the urbanized area variable (X11) have the highest coefficients, and their signs are negative. The odds ratio of the two variables is zero, which indicates that the possibility of urban expansion in those regions is almost zero. These areas are either restricted or controlled against the urbanization process, or have been urbanized previously. The urbanization process and urban sprawl are more likely to occur in areas nearer the urbanized clusters, i.e., the variable of distance to the nearest urbanized

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area (X7) has a coefficient of −4.576, which means that increasing the distance from the urban area decreases urbanization probability. The odds ratio is equal to 0.010, which reflects that the prospect of urban expansion in a region will be 100 times larger than the probability of urban expansion in a region further away by 1 km from the nearest urbanized zone. The urban expansion tends to take place in a region that has an increment in population density (X8). The probability ratio result is 4.737, which is more than 1, i.e., the probability of urban expansion in some areas will increase 4.737 times with the unit increment in population density. The significance and function of

distance to the educational areas variable (X9) is shown by the modeling output. The odds ratio value is 0.250 or 1/4. Thus, the possibility of urban growth in a region nearer the educational area is estimated as four times the probability of urbanization in an area further away by 1 km. For the variable of distance to roads (X10), the model demonstrates that roads have a significant effect on urban development, and that the probability ratio of distance to roads variable (X10) is 0.014 or 1/71.428. This odds ratio reflects the strong influence of roads on urban spatial patterns, i.e., roads cause the strip and ribbon urban expansion patterns.

Fig. 2 Thematic raster maps of independent variables; a Distance to active economy centers; b Distance to CBD; c Easting coordinate; d Northing coordinate; e Slope; f Restricted areas; g Distance

to nearest urbanized area; h Population density; i Distance to educational area; j Urban area; and k Distance to roads

J Indian Soc Remote Sens Fig. 2 (continued)

Table 2 List of variables included in the model Variable

Description

Type of variable

Dependent (Y)

0 – no urban expansion; 1 – urban expansion

Dichotomous

Independent (X1)

Distance to main active economy centres

Continuous

Independent (X2)

Distance to CBD

Continuous

Independent (X3)

Easting coordinate

Continuous

Independent (X4)

Northing coordinate

Continuous

Independent (X5)

Slope (%)

Continuous

Independent (X6)

1 – restricted area; 0 – not restricted area

Design

Independent (X7)

Distance to nearest urbanized area

Continuous

Independent (X8)

Population density

Continuous

Independent (X9)

Distance to educational area

Continuous

Independent (X10)

Distance to roads

Continuous

Independent (X11)

1 – urbanized area; 0 – not urbanized area

Design

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Fig. 3 Dependent variable (Y); a urban growth from 1984 to 2002; and b urban growth from 2002 to 2010

J Indian Soc Remote Sens Table 3 Estimated coefficients of implemented logistic regression model Variable

Coefficient (βi)

Odds ratio

Tolerance

VIF

Independent (X1)

−1.563

0.210

0.230

4.351

Independent (X2)

−1.889

0.151

0.180

5.563

Independent (X3)

−0.169

0.844

0.760

1.315

Independent (X4)

−1.983

0.138

0.269

3.719

Independent (X5)

−3.004

0.050

0.925

1.082

Independent (X6)

−19.188

0.000

0.956

1.046

Independent (X7)

−4.576

0.010

0.399

2.505

Independent (X8)

1.555

4.737

0.495

2.019

Independent (X9)

−1.386

0.250

0.141

7.069

Independent (X10)

−4.305

0.014

0.785

1.274

Independent (X11)

−21.415

0.000

0.730

1.370

Constant

0.850

–

–

–

spatial agreement exists between the real urban expansion and the predicted urban probability maps (Pontius and Schneider 2001). To confirm the model capability, the model validation was conducted by comparing the probability image map of future urban expansion produced from the logistic regression model alongside the real urban expansion from 2002 to 2010. The ROC curve is based on several two by two contingency tables. These tables are based on the comparisons between the actual and the predicted probability images. Table 4 shows the contingency table form where:

Model Validation Using the ROC Technique To evaluate the performance of the logistic regression model and to assess the resulting probability maps employed in this study, the relative operating characteristic (ROC) technique is used. The ROC technique has been applied in land use/cover change modeling studies, and is considered as a reliable method to check and to validate models (Pontius and Schneider 2001; Hu and Lo 2007; Wang and Mountrakis 2011; Jokar Arsanjani et al. 2013). The ROC technique measures the relationship between expected and real changes. This method calculates the percentage of false-positives, the truepositives for a range of thresholds, and relates them to each other in a chart (Pontius and Schneider 2001). The ROC computes the area under the curve, which varies from 0.5 to 1. A value of 0.5 indicates the random assignment of the probabilities, i.e., the expected agreement is due to chance. A value of 1 indicates perfect probability assignment, i.e., an ideal

(A) is the amount of true positive cells, i.e., cells predicted as urban expansion and agree with the actual image. (B) is the amount of false positive cells, i.e., cells predicted as urban expansion but disagree with the actual image. (C) is the amount of false negative cells, i.e., cells predicted as non-urban expansion but disagree with the actual image.

Table 4 Two-by-two contingency table showing the number of grid cells in an actual map vs. a predicted map Actual map Urban expansion (1) Predicted Probability map Total

Total No urban expansion (0)

Urban expansion (1)

A

B

A+B

No urban expansion (0)

C

D

C+D

A+C

B+D

A+B+C+D

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(D) is the amount of true negative cells, i.e., cells predicted as non-urban expansion and agree with the actual image. From every contingency table, single data point (x, y) is created, where X and Y are the rate of false positives and the rate of true positives respectively. ðtrue positive %Þ ¼ A=ðA þ CÞ

ð2Þ

ðfalse positive %Þ ¼ B=ðB þ DÞ

ð3Þ

Those data points are joined to form the relative operating characteristic (ROC) curve from which the ROC value is computed. The ROC value is the area under the curve that is created by the plotted points. The ROC curve is illustrated in Fig. 4. The result value of the ROC is 0.86. Urban Expansion Probability Map To produce an urbanization probability map, the coefficients of the logistic regression model were used and applied in Eq. 1. For better model performance, temporal dynamics were considered. The thematic raster maps of following independent variables, distance to nearest urbanized area (X7), population density (X8), distance to educational area (X9), distance to roads (X10), and urbanized area (X11) were updated by using 2010 data, whereas the other independent variables were kept without any change.

Fig. 4 ROC Curve

Figure 5 illustrates the predicted urban expansion probability map. The darker red color indicates a higher probability of urban expansion, whereas the darker blue color specifies the lowest urbanization probability. The trend of future urban expansion process patterns is based on the future probability map (Fig. 5). The urban development would occur probably near roads and existing urbanized areas, particularly those areas associated with population growth.

Urban Spatial Patterns in the Future Based on the urbanization probability map produced by the model, knowing where urban expansion will happen is possible. Thus, by generating several maps, one can demonstrate future urban distribution patterns based on the current demand for land for urban use. For the estimation of future urbanization patterns, Eq. 4 was used (Campbell et al. 2007). Equation 4 requires knowing the size of the existing urbanized area, the anticipated future population, and the growth ratio, which is equal to the ratio of urbanized land to population growth.    Pfuture −Pexisting Afuture ¼ Aexisting 1 þ R ð4Þ Pexisting where: Afuture Aexisting

is the future area of urbanized land. is the existing area of urbanized land.

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Fig. 5 Urbanization probability map of Tripoli in future

R

Pfuture Pexisting

is the growth ratio, which is equal to the ratio of change in urbanized land/ratio of population growth. is the expected population in the future. is the existing population.

The population and its growth rate data were obtained from the General Authority of Information, Libya. The population growth rate was 1.41 % per year. The ratio of the urbanized area growth was calculated based on situations in 2002 and 2010, and equaled to 8.57 % per year. Thus, the growth ratio was approximately 6. To forecast the population in the future, we assumed that the population growth rate would not change significantly, and the growth rate was used to estimate the future population. To predict the area of urbanized land for 2020 and 2025, various scenarios were considered. In the first scenario, the calculated

growth ratio of 6 was used, while in the second scenario, the growth ratio was assumed to decrease to 5. In the third scenario, the growth ratio was assumed to increase to 7. The reason for assuming different scenarios is the instability of economic, social, and political conditions. Urban planning policies were also unclear. Thus, different scenarios were expected to provide different perspectives to manage unexpected and uncontrolled urban growth. Table 5 summarizes the size of the predicted urbanized area (sq. km.) in the future. Spatial patterns in the future were determined by allocating the estimated size of the urban area to the urban probability map. The increase of urbanized land was calculated by comparing the estimated area to the 2010 base year map. Subsequently, the increased urbanized area was converted to a number of cells. The quantity of predicted urbanized cells was allocated to the predicted urban probability map starting from the

J Indian Soc Remote Sens Table 5 Predicted demand of urban land use in future (km2) Year Growth Ratio

2020

2025

5

471

568

6

509

626

7

548

685

highest probability cells to the lowest, until the total area was equal to the estimated future area. The generated urban spatial patterns in the future are presented in Figs. 6 and 7.

Discussions and Conclusion In this study, a logistic regression model has been used in modeling and analyzing urban expansion, and in investigating the functions of spatial driving factors as well as their level of significance in the urban expansion process in Tripoli. A logistic regression model was employed to produce a probability map that showed where urban expansion would probably occur in the future. The results indicated that the population density factor has the highest odds ratio, which means that the population increase will result in a spread pattern of urban expansion in the absence of a clear policy on urban planning.

Fig. 6 Predicted urban patterns in 2020 with various growth ratios; a with growth ratios 1:5; b with growth ratios 1:6; and c with growth ratios 1:7

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Fig. 7 Predicted urban patterns in 2025 with different growth ratio scenarios; a with growth ratios 1:5; b growth ratios 1:6; and c growth ratios 1:7

The UPA in Libya reported that residential use accounted for over 67 % of the urban land requirement in Tripoli. This critical demand for houses resulted in a severe urban sprawl, which the UPA did not anticipate. This fact is in accordance with the model results, which reflected the significance of the population density factor. Based on the model of future urban development, this study found that the biophysical variables affected urbanization process. Thus, urbanization was more likely to be close to existing urbanized areas and roads, and to avoid areas with higher slopes. This finding indicates the function and significance of these variables in the present study. Moreover, these variables are extremely significant in other

urban modeling techniques such as the SLEUTH and Cellular Automata models (Clarke and Gaydos 1998; Yang and Lo 2003). Econometric variables such as distances to CBD, to active economic centers, and to educational areas were included in the model to obtain a deeper understanding of how urban expansion happens. This method provides the logistic regression model an advantage over other modeling methods such as the CA model. The modeling results demonstrated that the variables have a less significant effect on urbanization process compared with roads and existing urban areas. Nevertheless, their functions are remarkable. For this reason, these variables should be considered in achieving

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a higher modeling accuracy rate and a more reliable urbanization assessment. The use of the northing and the easting coordinate variables minimizes and corrects spatial autocorrelation. The results illustrated that urban land use is expanding in an unbalanced pattern in all directions, i.e., the odds ratio of the northing coordinate factor was higher than that of the easting coordinate factor. The existing urban and restricted areas will not change, and their percentage of probability in the final probability map is zero. The logistic regression model cannot allocate and specify where urbanization will occur. Thus, different scenarios of future urbanization patterns are predicted by allocation cells that represent the estimated size of the required urban land on the predicted probability map. The prediction of future urban patterns for different years and the use of different growth ratios are extremely useful in associating the temporal urban expansion process and the population growth. This method provides information about future urbanization trends, and alerts the planners and decision makers so that they can manage the unexpected sprawl. The future urban extent maps show that the urban expansion will be concentrated in the southwest more than other directions. Finally, the quantitative relationships between urban sprawl and causative factors distinguished between the effectiveness of variables and their functions in urban sprawl. The main limitations of the logistic regression model are temporal determination of change, and change quantification within an acceptable limit. All three scenarios of future urbanization patterns considered in this study demonstrated that the situation might worsen in future. Furthermore, the urban history of Tripoli has shown a continuous increase of land consumption per capita. This finding should raise the alarm for urban planners and decision makers. Therefore, the city urgently needs the implementation of an effective urban plan, strict urban development regulations, and reduction of urban growth ratio to save fertile agriculture lands and to protect the environment. A recommendation is for Tripoli to consider a compact city strategy to accommodate its growing population, and to ensure a low rate of land consumption. Acknowledgments The first author greatly acknowledges Libyan government for providing data and financial support for this work.

References Al-shalabi, M., Billa, L., Pradhan, B., Mansor, S., & Al-Sharif, A. A. A. (2012). Modelling urban growth evolution and landuse changes using GIS based cellular automata and SLEUTH models: the case of Sana’a metropolitan city, Yemen. Environmental Earth Sciences. doi:10.1007/s12665-012-2137-6. Al-shalabi, M., Pradhan, B., Billa, L., Mansor, S., & Althuwaynee, O. F. (2013). Manifestation of remote sensing data in modeling urban sprawl using the SLEUTH model and brute force calibration: a case study of Sana’a City, Yemen. Journal of the Indian Society of Remote Sensing. doi:10.1007/s12524-012-0215-6. Angotti, T. (1993). Metropolis 2000: Planning, poverty and politics. London: Routledge. Bui, D. T., Lofman, O., Revhaug, I., & Dick, O. (2011). Landslide susceptibility analysis in the Hoa Binh province of Vietnam using statistical index and logistic regression. Natural Hazards, 59, 1413–1444. Campbell, C. E., Allen, J., & Lu, K. S. (2007). Modeling growth and predicting future developed land in the upstate of South Carolina. Report submitted to the Saluda-Reedy Watershed Consortium. Strom Thurmond Institute, Clemson University, Clemson, South Carolina. Cheng, J., Ottens, H., Masser, I., & Turkstra, J. (2003). Understanding urban growth: a conceptual model. International Journal of Urban Sciences, 7, 83–101. Clarke, K. C., & Gaydos, L. J. (1998). Loose-coupling a cellular automaton model and GIS: long-term urban growth prediction for San Francisco and Washington/ Baltimore. International Journal of Geographical Information Science, 12, 699–714. Devkota, K. C., Regmi, A. D., Pourghasemi, H. R., Yoshida, K., Pradhan, B., Ryu, I. C., Dhital, M. R., & Althuwaynee, O. F. (2013). Landslide susceptibility mapping using certainty factor, index of entropy and logistic regression models and their comparison at a landslide prone area in Nepal Himalaya. Natural Hazards, 65(1), 135–165. doi:10.1007/ s11069-012-0347-6. Dietzel, C., & Clarke, K. (2006). The effect of disaggregating land use categories in cellular automata during model calibration and forecasting. Computers, Environment and Urban Systems, 30, 78–101. Eyoh, A., Olayinka, D. N., Nwilo, P., Okwuashi, O., Isong, M., & Udoudo, D. (2012). Modelling and predicting future urban expansion of lagos, nigeria from remote sensing data using logistic regression and GIS. International Journal of Applied Science and Technology, 2, 116–124. Firman, T. (1997). Land conversion and urban development in the northern region of West Java, Indonesia. Urban Studies, 34, 1027–1046. Gillham, O. (2002). The limitless city: A primer on the urban sprawl debate (pp. 328). Washington, DC, USA: Island Press. Helbich, M., & Leitner, M. (2010). Postsuburban spatial evolution of Vienna's urban fringe: evidence from point process modeling. Urban Geography, 31, 1100–1117. Hu, Z., & Lo, C. P. (2007). Modeling urban growth in Atlanta using logistic regression. Computers, Environment and Urban Systems, 31, 667–688.

J Indian Soc Remote Sens Huang, B., Zhang, L., & Wu, B. (2009). Spatiotemporal analysis of rural–urban land conversion. International Journal of Geographical Information Science, 23, 379–398. Irwin, E. G., & Geoghegan, J. (2001). Theory, data, methods: developing spatially explicit economic models of land use change. Agriculture, Ecosystems & Environment, 85, 7–24. Jat, M. K., Garg, P. K., & Khare, D. (2008). Monitoring and modelling of urban sprawl using remote sensing and GIS techniques. International Journal of Applied Earth Observation and Geoinformation, 10, 26–43. Jiang, B., & Yao, X. (2010). Geospatial analysis and modelling of urban structure and dynamics (Vol. 99, p. 440). Springer: Netherlands. Jokar Arsanjani, J. (2011). Dynamic land use/cover change modelling: Geosimulation and multiagent-based modelling (hardback)(series: springer theses) (XVII, p. 139), Springer: Berlin Heidelberg. Jokar Arsanjani, J., Helbich, M., Kainz, W., & Darvishi Boloorani, A. (2013). Integration of logistic regression, Markov chain and cellular automata models to simulate urban expansion. International Journal of Applied Earth Observation and Geoinformation, 21, 265–275. Kleinbaum, D. G., & Klein, M. (2010). Logistic regression: A self-learning text. New York: Springer. Knox, P. L. (1993). The restless urban landscape. Englewood Cliffs: Prentice Hall. Lambin, E. F., & Geist, H. J. (2006). Land-use and land-cover change: Local processes and global impacts. Berlin Heidelberg: Springer. Lambin, E. F., Turner, B. L., Geist, H. J., Agbola, S. B., Angelsen, A., Bruce, J. W., et al. (2001). The causes of land-use and land-cover change: moving beyond the myths. Global Environmental Change, 11, 261–269. Lin, Y.-P., Chu, H.-J., Wu, C.-F., & Verburg, P. H. (2010). Predictive ability of logistic regression, auto-logistic regression and neural network models in empirical land-use change modeling – a case study. International Journal of Geographical Information Science, 25, 65–87. López, E., Bocco, G., Mendoza, M., & Duhau, E. (2001). Predicting land-cover and land-use change in the urban fringe: a case in Morelia city, Mexico. Landscape and Urban Planning, 55, 271–285. Mahiny, A. S., & Turner, B. J. (2003). Modeling past vegetation change through remote sensing and GIS: a comparison of neural networks and logistic regression methods. In Proceedings of the 7th international conference on geocomputation. University of Southampton, UK. Masser, I. (2001). Managing our urban future: the role of remote sensing and geographic information systems. Habitat International, 25, 503–512. Menard, S. (2004). Six approaches to calculating standardized logistic regression coefficients. The American Statistician, 58, 218–223. Overmars, K. P., & Verburg, P. H. (2005). Analysis of land use drivers at the watershed and household level: linking two paradigms at the Philippine forest fringe. International Journal of Geographical Information Science, 19, 125– 152. Peng, C.-Y. J., Lee, K. L., & Ingersoll, G. M. (2002). An introduction to logistic regression analysis and reporting. The Journal of Educational Research, 96, 3–14.

Poelmans, L., & Van Rompaey, A. (2010). Complexity and performance of urban expansion models. Computers, Environment and Urban Systems, 34, 17–27. Pontius, R. G., Jr., & Schneider, L. C. (2001). Land-cover change model validation by an ROC method for the Ipswich watershed, Massachusetts, USA. Agriculture, Ecosystems & Environment, 85, 239–248. Pradhan, B. (2011). Manifestation of an advanced fuzzy logic model coupled with Geo-information techniques to landslide susceptibility mapping and their comparison with logistic regression modelling. Environmental and Ecological Statistics, 18(3), 471–493. doi:10.1007/s10651-010-0147-7. Pradhan, B. (2010a). Remote sensing and GIS-based landslide hazard analysis and cross-validation using multivariate logistic regression model on three test areas in Malaysia. Advances in Space Research, 45(10), 1244–1256. doi:10.1016/j.asr.2010.01.006. Pradhan, B. (2010b). Landslide susceptibility mapping of a catchment area using frequency ratio, fuzzy logic and multivariate logistic regression approaches. Journal of the Indian Society of Remote Sensing, 38(2), 301–320. doi:10.1007/s12524010-0020-z. Pradhan, B. (2009). Flood susceptible mapping and risk area estimation using logistic regression, GIS and remote sensing. Journal of Spatial Hydrology, 9(2), 1–18. Serneels, S., & Lambin, E. F. (2001). Proximate causes of land-use change in Narok District, Kenya: a spatial statistical model. Agriculture, Ecosystems & Environment, 85, 65–81. Sudhira, H. S., Ramachandra, T. V., & Jagadish, K. S. (2004). Urban sprawl: metrics, dynamics and modelling using GIS. International Journal of Applied Earth Observation and Geoinformation, 5, 29–39. Sweet, S. A., & Grace-Martin, K. (1999). Data analysis with SPSS (Vol. 1, p. 204): Allyn & Bacon. Tv, R., Aithal, B. H., & Sanna, D. D. (2012). Insights to urban dynamics through landscape spatial pattern analysis. International Journal of Applied Earth Observation and Geoinformation, 18, 329–343. Veldkamp, A., & Lambin, E. F. (2001). Predicting land-use change. Agriculture, Ecosystems & Environment, 85, 1–6. Verburg, P., & Overmars, K. (2007). Dynamic simulation of land-use change trajectories with the clue–s model. Modelling Land-Use Change, 321–335. Verburg, P. H., Kok, K., Pontius, R. G., & Veldkamp, A. (2006). Modeling land-use and land-cover change. Land-Use and Land-Cover Change, 117–135. Wang, J., & Mountrakis, G. (2011). Developing a multi-network urbanization model: a case study of urban growth in Denver, Colorado. International Journal of Geographical Information Science, 25, 229–253. Yang, X., & Lo, C. (2003). Modelling urban growth and landscape changes in the Atlanta metropolitan area. International Journal of Geographical Information Science, 17, 463–488. Youssef, A. M., Pradhan, B., & Tarabees, E. (2011). Integrated evaluation of urban development suitability based on remote sensing and GIS techniques: contribution from the analytic hierarchy. Arabian Journal of Geosciences, 4(3–4). doi:10.1007/s12517-009-0118-1. Zhao, Y., & Murayama, Y. (2011). Urban dynamics analysis using spatial metrics geosimulation. Spatial Analysis and Modeling in Geographical Transformation Process, 153–167.