PREDICTING THE PROBABLEIES OF URBAN EXPANSION USING BIVARIATE DEMPSTER-SHAFER MODEL
Abubakr A. A. Sharif
Civil Engineering Department, Faculty of Engineering University Putra Malaysia.
Faesal Alatshan - Abdelmajeed Altlomate
Civil Engineering Department, College of Engineering Technology, Houn.
المؤتمر الدولي للتقنيات الجيومكانية - ليبيا1
International Conference on Geospatial Technologies -Libya1
9-6/ 12 /2015
Abstract :
The urban expansion phenomenon is a dynamic continuous spatiotemporal process associated with growing populations and economic development.
In this paper, the probabilistic Dempster-Shafer (Evidential Belief Functions) (EBF) model was applied to predict the belief, disbelief, plausibility and uncertainty of urban growth maps of the metropolitan area in Tripoli, Libya.
By employing the geographic information system (GIS), three satellite images obtained from 1996, 2002, and 2010 were used to extract seven urban expansion factors for the study area.
The urban factors are distance to central business district (CBD), distance to active economic center, slope, distance to built-up areas, distance to roads, distance to coastal areas, and distance to educational area. For model calibration, the EBF model was applied to simulate urban growth from 1996 to 2002. Data from 2002 to 2010 were used for model validation.
Consequently, four future maps of probable urban expansions were produced. The produced four maps present a new vision in describing probable urban expansions. The validation result indicated 83.2% prediction accuracy for the model.
Keywords: GIS; Remote sensing; Tripoli; Urban growth; Dempster-Shafer
1. Introduction
Urban development is a spatially dynamic phenomenon that indicates population increase, expansion of built-up areas, economic growth, increased importance level of cities, and so on. Urban expansion is characterized and affected by the interactions of many factors in time and space at various scales; for instance, political, economic, social, and cultural. In recent years, urban development in developing countries has been faster than that in developed countries. Hence, controlling the urbanization process and creating sustainable development in emerging countries require accurate information about urban expansion processes and their spatial patterns [1, 2]. However, 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 [3, 4]. But 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 spatiotemporal dynamics should be considered in land use change modelling and urban studies [5]. Moreover, urban expansion analysis using current and historical data is a necessary process in urban spatial studies and future urban planning. However, 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) [6], artificial neural network model (ANN) [7], logistic regression model (LR) [3], and analytical hierarchal process model (AHP) [8].
Urban growth models use factors that affect and drive 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.
To simulate the urban growth process and predict probable spatial patterns in the future, a modeling approach of bivariate statistical model of Evidential Belief Functions (EBF) was applied in this work. The theory of Dempster-Shafer of evidence refers to the generalization of the Bayesian theorem of subjective probability. Proposed by Dempster in1967 and developed by Shafer in1976, this theory has the ability to combine the beliefs from several sources of evidence and the relative flexibility to accept uncertainty [9]. The theory guesses how near the evidence shows the certainty of a hypothesis rather than guessing possibilities that a hypothesis is correct [10]. The Dempster-Shafer theory has been applied effectively by using GIS in many applications. However, in order to model the real problem behavior with GIS, fuzzy-related or probabilistic techniques should be considered [11]. EBF model as a statistical method was used to produce spatial maps and to identify and analyse the probabilities of spatial phenomenons occurrence [12].
Tripoli metropolis, was chosen as the area in which to conduct this research. The general aim of this research is to spatiotemporally present four maps of urban expansion probabilities (belief, disbelief, uncertainty, and plausibility) of Tripoli metropolis by using remotely sensed data through GIS.
2. Study Area
Libya lies along Africa‘s Mediterranean coast and stretches deep into the Saharan region. The study area is located along the Mediterranean coast in the northwestern part of Libya, between longitudes (12o 54' 04" E and 13o 26' 38" E) and latitudes (32o 36' 18" N and 32o 54' 17" N). The Tripoli Agglomeration has the largest concentration of population and economic activities. The studied area occupies a total land area of approximately 1,143.73 km2 . The Tripoli metropolitan area includes the districts of Tripoli Center, Hey Alandlus, Tajoura, Janzur, Kaser Ben Ghashir, Alswani, Ain Zara, Abuslim, and Suq Ajumma Figure 1.
3. Materials and Methods
This work considers some socioeconomic and physical urban growth driving factors to model and to predict probabilities of urban expansion.
The urban development factors considered in the research represented the independent variables of the urban growth process, which are the slope, and the distances to CBD, the active economic centers, built-up areas, roads, coast, and the educational areas. These factors are demonstrated in Figure 2. The slope map was extracted from a digital contour map of Tripoli. Other urban driving factors, such as distances to active economic centers, builtup areas, CBD, educational areas, and to roads were computed by using Euclidean distance function in the Arc-GIS software.
Urban expansion maps representing the dependent variable were extracted from three satellite images of Tripoli during different time periods (1996, 2002, and 2010) using the maximum likelihood supervised classification technique, as illustrated in Figure 2. Lastly, all thematic maps of the urban expansions and urban driving factors were clipped with study area boundary vector map and resampled to a grid size of 30 m × 30 m.
Figure 1: Study Area
Figure 2: Thematic maps of independent and dependent variables; Slope; Distance to active economy centres; Distance to CBD; Distance to roads; Distance to nearest urbanized area; Distance to educational area; Distance to coast; Urban growth from 1996 to 2002; Urban growth from 2002 to 2010.
To apply the EBF model in urban expansion modeling, we assume the existence of a set of urban growth driving factors 𝐶 = (𝐶𝑖 , 𝑖 = 1,2,3, …… … 𝑛), comprising of mutually exhaustive and exclusive factors 𝐶𝑖 ,. is named the frame of discrimination. A simple probability assignment is the function m: 𝑃(𝐶) → [0,1] where 𝑃(𝐶) is the set of whole subsets of as well as of the empty set, and of set itself. The m function can be named as a mass function and satisfies 𝑚(Ф) = 0 and ∑𝐴 𝐶 𝑚(𝐴) = 1 where Ф is the empty set and A could be any subset of . 𝑚(𝐴) estimates the level to which the evidence support A, and is a belief function 𝐵𝑒𝑙(𝐴).
Figure 3 demonstrated that there are four basic EBF functions namely: 𝐷𝑖𝑠 (degree of disbelief),𝐵𝑒𝑙 (degree of belief), 𝑃𝑙𝑠 (degree of plausibility),and 𝑈𝑛𝑠 (degree of uncertainty). Dis represents the belief of the suggestion being untrue based Figure 2: Thematic maps of independent and dependent variables; Slope; Distance to active on given evidence. 𝐵𝑒𝑙 and 𝑃𝑙𝑠 give the upper and lower bounds of the probability, respectively, for the suggestion [12]. Unc means ignorance, i.e.,the difference between the plausibility and the belief.
1−Unc − Bel or Dis = 1 – Pls, and always Dis + Bel+ Unc =1. For cases of Cij with no urban expansion demonstrating that 𝐵𝑒𝑙 = 0, 𝐷𝑖𝑠 is reset to 0 even if 𝐷 is not [13].
By overlaying the urban growth map (𝐿) on every thematic urban deriving factor map, we determined the quantity of pixels with urban growth and pixels without urban growth for each factor class.
Suppose𝑁(𝐿) is the total number of urban growth pixels and 𝑁(𝐶) is the total number of pixels in the whole area of study. Cij is the 𝑗 𝑡ℎ class attribute of the urban growth driving factors 𝐶 = (𝐶𝑖 , 𝑖 = 1,2,3, … … … 𝑛).𝑁(𝐶𝑖𝑗)is the total number of pixels in class 𝐶𝑖𝑗 and 𝑁(𝐿 ∩ 𝐶𝑖𝑗 ) is the quantity of urban growth pixels in 𝐶𝑖𝑗. The data driven estimation of EBF could be obtained by: ....
5. Conclusion
In this study, the future urban growth probability maps of Tripoli in Libya were produced by using a bivariate statistical model, namely EBF. The modeling result demonstrate that the applied model is valid for analyzing the urban growth process, and the prediction of probable urban expansion trends. The validation result shows that the evidential belief function model (the predicted belief map) presented very acceptable level of accurcy with 83.2%. Hence, the probabilistic bivariate data-driven approach such as EBFs is promising in such spatial application. The integrated map of degrees of belief represent the probable urban growth. The integrated map of degrees of uncertainty reflects areas where the spatial evidences are insufficient to provide a prove for urban expansion occurance, and the map provides guide for further urban developemets preperations and planning. The field assessment verification, exploration and analysis work should be carried out on the urban expansion map of belief integration. The degree of plausibility map demonstrates expected urban expansion and the area where more spatial evidences exsit because it represents all the integrated evidence except the disbelief. Also it shows that spatial evidences are sufficient to provide support for the urban growth existance, and the evidence are inefficient to prove more that urban growth factor will effect on the dependent (urban expansion) factors. The EBF model provides a quick comprehensive prediction and assessment for future urban expansions and a guide for urban planner. Moreover, the research result offers maps with very good degree of confidence which can be used for urban developement planning and management. However, applying the EBF model to more areas will generalize the usage of this model.
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