Urban growth modeling using cellular automata model and AHP (case study: Qazvin city)
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Abstract
Irregular growth in the surrounding lands is one of the most important issues for the city managers and programmers at various levels. Whereas nowadays study the process of land use changes to urban use plays the main role in long time decisions and programs, predicting the process of city growth and its modeling in future with precise methods for management and urban expansion control will be necessary more than other times. One of urban growth modeling is cellular automata model. This model has been used widely in urban studies because of its dynamic nature, ability of Integration with other models, ability to modify the model and required data availability. In this article, to maximize the efficiency of the cellular automata model and its constraints, the integration of the AHP automated cell model and cellular automata model have been used; and its accuracy has been evaluated. This article has been practical because its related principles has been collected in a documentary manner and has been used to analyses the issue in comparative and quantitative methods. Initially, the unplanned growth of Qazvin city has been investigated by Holdern and Shannon model. Then main parameters including distance from roads, land prices, distance from faults, distance from the rivers, soil gender, slope, permission to build land, topography, landscape, view to gardens and forest park as parameters involved in the development of Qazvin city are considered. The input data used in this research are Landsat tm and DEM images of the city of Qazvin in 1996 and 2016. Also, to evaluate the correctness of the model responses, the map of the developed regions in 2016 and the Kappa coefficient have been used. The Kappa coefficient is 92.3%, which is considered significant and appropriate and gave the fact that the Kappa number is acceptable. The Qazvin simulation was made in 2026. The results show that the proposed integrated model is suitable for studying urban growth.
Keywords
Urban simulation Shannon’s and Holdern entropy model’s Urban growthcellular automata Analytic hierarchy processIntroduction
Key driving factors to urban growth extracted from existing CA models (Wahyudi and Liu 2013)
Geomorphology  Connectivity  Facilities  Environment 

Slope Elevation Hillshade  Highway Tollgate/ramp Road Waterways Railways Intersection  Station Airport Major towns Shopping centre Business centre Industrial Existing developed areas School Health facilities Thematic Recreational  Greenery Other 
Government  Constraints  Demography  Land  Economy 

Zoning Institutional factor  Water bodies National parks, forest Wetlands Protected areas  population size Annual growth rate Population density Migration  Land suitability Land availability Land genetic  Gross domestic products (GDP) Land value Economic trends 
Factors affecting urban growth based on resources provided in table
Environmentalnatural  Demographicsocial  Economic  Physical 

Protected areas Slope Distance from faults Elevation Type of soil Distance from river  Population changes, population density, population growth  Price and value of land, distance from the main roads, distance from the city centre  Permission to build land, limitation of artificial limits, infrastructure network, expansion to sensitive and protected open spaces, distances from parks and other green spaces 
Hasse (2002), Cheng and Masser (2003), AlKheder (2006), Bhatta (2010), Foroutan et al. (2012), Moghadam and Helbich (2013), Wahyudi and Liu (2013), Mohammady et al. (2014), Ahmadi and Rahmani (2016), Hoseinpour et al. (2017), Nowrouzifar et al. (2017)  Cheng and Masser (2003), AlKheder (2006), Olajoke (2007), Bhatta (2010), Hoseinpour et al. (2017)  White and Engelen (1997), Barnes et al. (2001), Barredo et al. (2003), Cheng and Masser (2003), AlKheder (2006), Olajoke (2007), Bhatta (2010), Geshkov (2010), Wahyudi and Liu (2013), Deep and Saklani (2014), Hoseinpour et al. (2017)  Barnes et al. (2001), Cheng and Masser (2003), Bhatta (2010), Moghadam and Helbich (2013), Mohammady et al. (2014), Hoseinpour et al. (2017) 
Materials and methods
Urban sprawl
Sprawl definition could be the increase in builtup and paved area with impact on loss of agricultural land, open space and ecologically sensitive habitats (Liu and Phinn 2001). The sprawl mainly causes population growth, economy and the template and preparation of infrastructure (Sudhira et al. 2003; Sudhira 2004) sprawl development is accomplished in three ways which are ribbon sprawl, leapfrog sprawl and lowdensity (radial) sprawl. Consumptive use of land is highly affected by provision of public infrastructures such as water, sewer, power, Telecommunication and roads. The ribbon sprawl is developed along the main transportation network that joins urban areas. The main point is that the Lands without direct access to the network remains rural or undeveloped. The leapfrog sprawl is a discontinuous pattern of urbanization in which the developed lands are widely separated from each other and it costs more than two other ways. The inherent causal and dynamics involved in the rapid changes of landuse because of urban sprawl are the most important factors, which are considered as a fit case to apply Cellular Automata models and AHP logic for simulating future scenarios (Sudhira et al. 2004).
Cellular automata
CA modelling is one of the suitable ways for urban sprawl modelling (Feng et al. 2011).
Lattice: according the shape similarity to square at raster data in GIS, square shape of lattice was selected in which the size of each cell equals 10 m by 10 m.
Cell state: the definition of three cell states is in the offered model, the urban state, constraint state and the nonurban state with the values of 1, 0 and between 0 and 1 respectively.
Neighbourhood: the Moore neighbourhood was selected for this study.
 1.
There is not any changing in state of the cell at simulation periods if the state of a cell is urban.
 2.
There is not any changing in state of the cell at simulation periods if the state of a cell is constrained.
 3.
Probability of a cell for transformation to the urban state will increase if affecting factors are closer to the cell.
 4.
The probability for transformation to urban state will increase if cells have more urban state neighbours.
 5.
The state of the cell will transform to urban state if calculated of a cell has the maximum value between the other cells (Mohammad et al. 2013).
Analytic hierarchy process (AHP) model
In general, it has a set of issues that are evaluated on the basis of metrics. Multiple criteria decision making (MCDM) analysis is a set of analysis methods which helps decision makers to solving complex problems with poor or incomplete structure and use their knowledge to solve these problems (Sardari and Rafieian 2008).
Analytic hierarchy process is one of the most famous multiple criteria decision making methods (Saaty 1980) which has been suggested in year time and It has been widely used in various sciences as yet (Zebardast 2001). The process consists of four steps of creating hierarchy, determining the Importance factor of the criteria and subcriteria, determine the Importance factor of the options, final rating and compatibility check in judgments (Zebardast 2001). By using this method, the appropriate weights of the affecting factors for urban growth are calculated and it is used in the production of land suitability map and formulation of transfer laws in the automated cell model
Entropy model
By using this model, we can understand the equilibrium rate of space for population clearance and the number of cities at the urban, state, regional, and country level. The whole structure of model is: In the entropy model, trending to zero, will means the increase of centralization or more centralization or unbalance in population distribution between cities, and movement toward one or higher than shows unbalance distribution in area level (Hekmatnia and Mousavi 2006). Definition of centralization degree or geographical phenomenon has been accomplished by this index (Wilson 1996).
Shannon entropy model
In the above formula:
H = Shannon entropy value; Pi = ratio of built area (total residential density) i = area to the total built area; N = total areas. The value of the entropy from zero to Ln, (n) represents a sprawl urban development. When the value of entropy is greater than in (n), urban sprawl growth has occurred (Hekmatnia and Mousavi 2006).
Holdern entropy model
Holdern is one of the basic methods for determining uneven urban growth. It is possible to determine the amount of city growth based on population growth and the amount of uneven urban growth with this method. This model first was applied to calculate the ratio population to any other source by Holdern in 1991. According to Beck et al. (2003).
Kappa coefficient analysis
Calculating the kappa coefficient
Kappa considers all the cells of an error matrix and thus incorporates more information (Rosenfield and FitzpatrickLins 1986; Fung and LeDrew 1988; Dicks and Lo 1990; Janssen and Vanderwel 1994);
Kappa is suitable for comparison between different error matrices because it removes chance agreement (Congalton et al. 1983; Congalton 1991).

C: is the number of categories in the error matrix

P_{ii} is the number of cells in row i and column i

P_{IT} is the total number of cells in row i (shown as the row total in the matrix)

P_{TI} is the total number of cells in column i (shown as the column total in the matrix)

Where P_{a} is the percent correct for model output, and P_{E} is the expected percent correct due merely to chance.
Research methodology
The research method of this article is practical which its theoretical bases are collected by documentary method and quantitative and comparative methods have been used for its analysis. In this study, first, the automated cell model is checked and then the effective factors on urban growth are determined by using resource review and aerial photography of the study area at different time intervals. Subsequently, analytical maps related to the effective factors on urban growth in GIS software are produced and the weights obtained through the hierarchical analysis process of comparing the development stimuli relative to each other in the applied layers and overlapping the different layers and Considering the limitations of developing land suitability map as inputs for the automated cell model is produced. Finally, the model is conceptually designed and integrated with the hierarchical analysis process which using the model definition of the automated cell model. Then the conceptual model has been converted into software codes and used to predict city growth in the surrounding lands.
Recognition of the studied area
Data and preparation of them
Specifications satellite images of Qazvin city (http://glovis.usgs.gov)
Satellite  Sensor type  Spatial resolution  Base level 

Terra  ASTER  30  WGS84 
Imaging date  Type of satellite  Sensor type  Spatial resolution  Baselevel  Image system 

19961127  Landsat  ETM  30  WGS84  UTM, Zone 39 N 
20160807  Landsat  ETM  28.5  WGS84  UTM, Zone 39 N 
Sprawl study in Qazvin city
Entropy model
Investigation of urban sprawl growth in Qazvin using the holdern model (for the years 1956–2016)
Calculation of Shannon entropy for the year 1996 in Qazvin
(Source: Calculations of Writers)
Region  The built area (hectare)  Pi  (Ln)Pi  Pi*Ln(Pi) 

1  587  0.4054  0.9028  0.3660 
2  716  0.4954  0.7024  0.3480 
3  145  0.1001  2.3016  0.2303 
Total  1448  \( \sum {Pi = 1} \)  \( \sum {Pi*Ln(Pi)} \)  0.9443 
Calculation of Shannon entropy for the year 2016 in Qazvin
(Source: Calculations of Writers)
Region  The built area (hectare)  Pi  (Ln)Pi  Pi*Ln(Pi) 

1  1328  0.3204  1.1382  0.3647 
2  1136  0.4040  0.9063  0.3661 
3  933  0.2756  1.2888  0.3551 
Total  2297  \( \sum {Pi = 1} \)  \( \sum {Pi*Ln(Pi)} \)  1.0859 
The investigation of sprawl growth of Qazvin using Holdern model
(Source: Calculations of Writers)
Years 1996–2016  Years 1976–1996  Years 1956–1976 

r = 1.52 + (− 0.52) 100% due to population growth 0% due to per capita growth  r = 0.511 + 0.49 49% due to per capita growth 51% due to population growth  Due to population growth 
According to the result of two Shannon and Holdern Modern, it is observed that Qazvin has grown physically increasingly due to over concentration on population and activity.
Findings from the studying of Qazvin’s documents and reports, natural and artificial factors affecting the physical development of Qazvin
Obstacles, directions and reasons for lack of physical development in Qazvin
(Source: Calculations of Writers)
Reasons  Directions  Obstacles  Factors 

High elevation of the area between 1700 and 2400 m Lack of soil formation High slope of the region so as the 60° slope is observed  North  Altitudes  Natural 
Food value Economic development of area Groundwater penetration and nutrition of its aquifers Problems of infrastructures due to the alluvial nature of the land Having Privacy  South, East, West  Agricultural lands  
Employment Economic development of the region Environmental pollution Finding Proper location in terms of climate  Southeast  Industrial towns  Manmade 
Lack of land Appropriate location Appropriate distance from the city Dependent use  Southeast  Cemetery  
Very large area Military significance  Different parts of city  Garrisons 
Studies factors in Qazvin city
Allow construction, and vision and perspective.
Distance from the river, distance from fault, contour line, type of soil, accessibility to urban roads and land prices.
The quantitative results of Kappa
(Source: Calculations of Writers)
2016  1996  

Urban  Nonurban  Total 1996  
Urban  1920.81  0  1920.81 
Nonurban  1781.14  6358.39  8139.53 
Total 2016  3701.95  6358.39  10060.34 
Results of kappa
The quantitative results of the model are illustrated Table 10.
How to implement AHP and cellular automate models in Qazvin
First step: At this step, first, layers associated with the effective factors on urban growth are prepared and after repackaging each layer, the weights calculated by the hierarchical analysis process are applied to the layers and overlapped. At this step, the probability of each cell’s status being transformed into a celldependent status is rely on the effective factors on urban growth and the effect of each factor on the weight of each cell is considered as weight shape.
This probability is calculated by the following relation where P_{AHF} is Probability of cell change indicates the ‘ in this equation \( s_{n} \) is equaled to \( w_{1} \times s_{1} + w_{2} \times s_{2} + \cdots + w_{n} \times s_{n} \) and \( \sum\nolimits_{1}^{n} {w_{n} s_{n} } \) growth factor is the ‘ value of the class in which the intended cell is growth to the growth factors and \( w_{n} \).
Second step: At this step, according to the components, the automated cells are divided into four main parts, the cell, the cell status, the neighborhood, the transfer rules and the subpart of time and at this step the automated cell model is defined as its components.
Third step: This will be calculated by checking the population and the number of cells which built in previous years. Because of using of this limiting factor, this type of automated cells is called as autorestricted cells.
Data preparation
Then, after calculating the weight of each of the effective factors in urban growth, using the hierarchical process and preparation of layers associated with the factors of growth of layers’ overlap by applying the weight of each layer. Then the weighted probability of transforming the cell status is calculated. The results are prepared in the form of land suitability map and as input to the model. In order to calculate the land conversion rate, population and cell number of the state constructed in different periods, the correlation coefficient value was calculated by deviating from the mean for two population variables and the number of land pixels constructed.
In order to calculate the land conversion rate, population and cell number, the status has been determining at different time periods and then the Pearson correlation coefficient has been calculated by the way of deviating from the mean for the two population variables X and the number of land pixels Y calculated. The calculated value of Pearson’s correlation coefficient was 8.83 which indicating a strong correlation between the two variables. After determining the existence of a direct and strong correlation between the two variables x and y, linear Regression method has been used to predict the number of convertible pixels in different time periods and predicted year.
At the end, the model becomes software codes. Due to the high volume of data and computations in the model designed according to the time and data flow in the model, the formulas and the model work, the computer has been used to implement it. In order to implement the model in the computer, each supply step and model components are separately converted into software codes and then linked together for initial testing and final output. The computer codes of this program are written in MATLAB programming language.
Then the validation and model results are performed. In order to evaluate the validity of the designed model, first the land growth map in 2016 is modeled by using data available in 1996 and to evaluate the degree of agreement of a model with reality, the Kappa coefficient reality, visual matching overlap and observation are used. The calculated kappa coefficient is 0.95.
This value represents a 92% compliance with the modeled reality map which is based on the provided standard by the United States Geological Survey institute that considers the minimum acceptable value for the Kappa coefficient to be 85%. It can be said that the designed model has sufficient reliability and validity to modeling the urban growth in the surrounding lands. According to the acceptable results of the model, it has been used to predict the urban growth in the surrounding lands. Then, all the happened steps in the data of 2016 are implemented as input data and the growth simulation of Qazvin city up to 2026 is performed which the results are presented in map 10.
Conclusion
Nowadays, cities are experiencing rapid urban growth that destroys farmland, the formation of private housing, and the irregular expansion of the city. Expanding cities always changes the use of different lands to urban use. Due to the inevitable changes, awareness of this trend is important for its guidance towards the desired direction. Therefore, there is a fundamental need to realistically predict cities growth in the future, to determine the impact of various planning scenarios on the urban growth process and to answer the questions ((what if) any) questions. Due to the inevitable changes, awareness of this trend is important for its guidance towards the desired direction. For this reason, so far, many models have been created and used to simulate the development of the city and to expand the use of urban lands. In this research, the automated cellular model.
This model uses a suitable method for searching and selecting land for development. The implemented model was applied using data for 2016 to predict the development of 2026 year.
Notes
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