Monitoring and Prediction Functional Change of Land Uses Toward Urban Sustainability

The Markov model is a method of analyzing the current behavior of a specific variable, to predict the state of the phenomenon in the future [1]. This model was discovered by Andrey Andreyevich Markov, a Russian mathematician.

Markov chains are one of the "dynamic programming" and "Probability Models" in Operations Research. The Markov model is interested in the decision-making process, it deals with the probability of a specific event in the future [2]. Markov models are commonly used in planning to model and analyze systems. These models allow planners to analyze the behavior of a system over time, based on the probabilities of different events occurring. Planning using Markov models involves analyzing the transition matrix to determine the long-term behavior of the system.

There are other definitions of this pattern, which is a random process that speculates on the future without needing to know the past [3].

Markov models are commonly used to study how land use in urban areas changes over time. It is a statistical tool that predicts the probability of a future state based on the current state and the probabilities of transition between different states, there are two different forms of Markov chains:

"Discrete-time Markov chains" and "continuous-time Markov chains". This indicates that there are two cases: one in which the changes are limited to certain states, and the other in which the changes are ongoing. For this, on discrete-time Markov chains, we shall concentrate [4]. Markov operations depend on imposing the stability of the possibilities of transformation of the state from one period of time to another period and the existence of equal periods, the transformation between them and the number of transformation cases can be limited, which is known as "a finite Markov chain" [4]. The logical steps of applying mathematics should be portrayed as in the ensuing math calculations [3].

$S(t+1)=B i j \times S(t)$                 (1)

where, S(t+1)=status of the phenomenon at t or t+1; Bij=a state's "transition probability matrix," which is shown below:

$\begin{gathered}{\left[\begin{array}{llll}B_{11} & B_{12} & \ldots & B_{1 n} \\ B_{21} & B_{22} & \ldots & B_{2 n} \\ B_{n 1} & B_{n 2} & \ldots & B_{n n}\end{array}\right]} \\ \left(0<1 \text { and } \leq B_{i j} \sum_{j=1}^N B_{i j}=1,(i, j=1,2, \ldots \ldots, n)\right) \\ or  \\ \begin{align*}& \begin{array}{ccccccccc}& 0~~~~~~ & 1~~~~~ & 2~~~~& 3~~~~& 4~~~~~& 5& ~~~\cdot & \cdot \\\end{array} \\ & \begin{array}{}0 \\ 1 \\ 2 \\3 \\4\\5\\ \cdot\\\cdot\\\end{array}\left[\begin{array}{cccccccc} B_{00} & B_{01} & B_{02} & B_{03} & B_{04} & B_{05} & \cdot & \cdot\\ B_{10} & B_{11} & B_{12} & B_{13} & B_{14} & B_{15} & \cdot & \cdot\\ B_{20} & B_{21} & B_{22} & B_{23} & B_{24} & B_{25} & \cdot & \cdot\\ B_{30} & B_{31} & B_{32} & B_{33} & B_{34} & B_{35} & \cdot & \cdot\\ B_{40} & B_{41} & B_{42} & B_{43} & B_{44} & B_{45} & \cdot & \cdot\\ B_{50} & B_{51} & B_{52} & B_{43} & B_{54} & B_{55} & \cdot & \cdot\\ \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\end{array} \right] \\ \end{align*}\\\end{gathered}$

According to the following equation, the outcome of the forecast is dependent on the phenomenon's existing circumstances, i.e., the current change in the research area's urban land use functions [3].

$S(t, t+1)=\int(S(t), N)$                   (3)

Probability assumptions in statistics are based on the assumption that all probability values between zero and one, when multiplied multiple times or multiplied by themselves, will either lead to stability or be based on a specific value. This is a feature of problem-able values. For instance, when it rains, what is the weather forecast for the next two months? There should be ways to indicate this by weather variations over the past period and probabilities to determine if it is raining or sunny. The anticipated value, whether or not it will rain after this time (For instance, two months), demonstrates weather stability and reveals weather tendency, i.e., no matter if it's sunny or raining. The stabilization of the possibility of the likelihood of Markov adjustments represented by Markov chains is what is referred to as the steady state of Markov chains.

To understand the logical steps of applying Markov, see Figure 1.

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Figure 1. A flowchart of the research methodology

The article will use information provided by the local urban management in Karbala and satellite imagery processed by GIS software to determine the extent of changes in urban land use. The Markov chain method will then be used to forecast future changes in the city's spatial functions over the next 50 years.

3.1 Study area and data required for analysis

Karbala is a city located in central Iraq, about 100 kilometers southwest of Baghdad. It is one of the holiest cities for Shia Muslims and is home to the shrine of Imam Hussein, the grandson of Prophet Muhammad, who was martyred in Karbala in 680 CE. Millions of pilgrims visit Karbala every year during the annual Shia Muslim commemoration of Ashura, which marks the martyrdom of Imam Hussein. The city has a rich history.

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Figure 2. The location of the study area for Karbala Governorate and for Iraq

Source: Using the ARC GIS 10.8 software

The Iraqi city of Karbala, which is located within the location coordinates (latitude: 32°36′57″ N Longitude: 44°01′29″ E Elevation above sea level: 32 m, see Figure 2. It was distinguished by an important position that made its importance, because of its land originated and formed the oldest human civilizations Which supplied the world with various sciences, which were an extension of the civilization of Babylon, and thus increased its importance and became populated with residents and housing units, especially for Muslims.

3.2 The functional change of urban land uses passed through two important stages

First: the stage growth and expansion for the period (1972/1922):

This stage is one of the important urban stages that the study area went through during its history, the city expanded from the year (1870 AD), And depending on A group of factors these data growth population Whether this data (natural or human) and extended towards the south After it collapsed and demolished its wall on the side of the Bab al-Najaf district, it led to the construction of the new locality, which was known as al-Abbasiya, which extended and expanded and was divided into two localities with (Al-Abbasiya, its western and eastern branches), So he lost this expansion and development came in response to the growth of the number of population and their development, Including (City planning), In addition to the city’s inadequacy of the functional and service requirements and conditions for them, the expansion was represented by the development of a new locality through the sorting and division of lands and the provision of services.

Table 1. The change in the land uses from 1922-1972 (H.C)

Source: Karbala Department of Municipality/ Department of City Planning/ data of secretarial maps. Unpublished data, 2021.

Karbala Department of Physical Planning. Karbala city master plans. Unpublished data, 2021

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Figure 3. The change in land uses from 1922-1972

Source: Table 1

It is also clear that the city always seeks to provide several necessary facilities for its residents to ensure the social life of the recipient, as it appears at the beginning of this stage that there were no clear effects on the construction and engineering of the city, which made urban and architectural planning limited to the presence of administrative and military buildings. In the year (1922 AD) the city of Karbala began the twenties of the last century to take a privileged position, due to the political position of Karbala as well as its religious location. Ali (peace be upon him), which works to connect the north of the city with its south, and also Imam Ali al-Akbar Street (peace be upon him), which connects the two shrines, which was built using an iron. As for the year (1948 AD), Al-Muheet Street was opened in the shrine of Imam Abi Abdullah (peace be upon him), which is considered a method of isolating the honorable shrine from the urban fabric, and (Bab Al-Qibla) Street came in the year (1949 AD) whose purpose was to confirm the Western style, while in the year (1950 AD) The Iraqi government began to deal with foreign companies in development projects and the construction of cities. Table 1 and Figure 3 show details of the areas of land use during this stage.

During this stage, the local administration, in cooperation with the Greek company Doxiadis (Greek Docksides Company) in Iraq, specifically in the forties of the last century, by building and constructing some residential neighborhoods represented by (Al-Iskan neighborhood), which was established during the time of Abdul Karim Qasim Which is 6.2 km away from the old city center and has a population of (8850 people), which was intended for state employees and in terms of its location, it is located to the southwest of the central commercial area. As for the year (1958 AD), the government worked to implement (Al-Hussein neighborhood), in addition to other neighborhoods Such as (Al-Hurr, Al-Naqeeb, Al-Baladiya, Al-Muallimeen) respectively for each of them. Else for the city, which was a compliment and modification of the plan of the Doxiadis Company with the addition of other new areas, it established neighborhoods, including (Al-Islah Al-Zaraiyyah, Al-Abbas, Al-Ulama, Al-Ansar) (Figure 4), and other residential neighborhoods, and at present, the number of neighborhoods in the city is (65 residential neighborhoods). In addition, the city at this stage lacks a basic plan that regulates the uses of some uses administration in addition to some other uses, including commercial use, which is relatively superior to the previous stage.

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Figure 4. The first phase of the growth and expansion of the study area

Source: Using the ARC GIS 10.8 software

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Figure 5. The second phase of the growth and expansion of the study area

Source: Using the ARC GIS 10.8 software

Second: the stage of maturation and completion (the contemporary stage) (1972-2022M)

At this stage, the city was distinguished by features and characteristics that exceeded the previous urban stages, represented by an urban and population structure, as well as urban integration, through which it was crystallized. The most developed urban functions and religious services formed a significant part of the urban land uses, and it seems clear that the composition of the population in the city was constantly increasing, as the estimates indicated the current population with a population increase of about (1,550,552 people). As they are distributed over three residential sectors, namely (the old city, al-Haidariyya, and al-Jazeera) with (65) residential neighborhoods (Figure 5). In this phase has become a crucial period in the city's development due to its integration into the urban structure. As a result, the study area has entered a new phase of growth and development, marked by a significant increase in population due to migration for work and settlement. Additionally, there has been a considerable expansion in residential and commercial areas, driven by the city's economic growth and development focused on tourism and commercial activities, which are directly linked to its religious function. Despite its vast size and diverse population, the city remains a focal point for religious rituals, attracting visitors from various regions of the country and beyond.

This is in addition to increasing the areas allocated for religious uses. Table 2 and Figure 6 show details of land use during this stage.

Table 2. The change in the land uses from 1972-2022 (HC)

Source: Karbala Department of Municipality/ Department of City Planning/ data of secretarial maps. Unpublished data, 2021.

Karbala Department of Physical Planning. Karbala city master plans. Unpublished data, 2021 [9, 10].

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Figure 6. The change in the land uses from 1972-2022

Source: Table 2

It is clear that some land uses are still growing despite the spatial expansion that occurred in the city in recent times, thus making most of them dominate and strongly over the rest of the other types of uses, and this stems from the expansion of urbanization, while we see some land uses have diminished as a result of their competition with urban land use else.

The reasons are due to Population growth, Economic development, Technological advancements, Environmental factors and Government policies such as zoning regulations, land use planning, and urban renewal policies.

Table 3. Functional change data in Karbala for 1972-2022 (HC)

Table 4. Markov transition probability matrix

Source: The Authors by using SPSS

Table 5. Functional change matrix for first round

Table 6. Functional change matrix for second round

Table 7. Functional change matrix for third round

Table 8. Functional change matrix for final round (Absorbing states)

Source: The Authors by using SPSS

The Markov chains model is one of the most important models that are commonly used for the prediction of spatial phenomena. Changes in the functions of urban land use over the past period (the past 50 years) were relied upon to extract the prediction transition matrix. The city of Karbala witnessed functional changes in urban land uses during the period The reasons are due to the importance of the city being an important religious tourism center at the regional and international levels, as well as population growth, immigration, and rapid urbanization.

That some urban land uses are still growing and changing, and there are some land uses that have declined as a result of their competition with other urban land use, and the strength of spatial competition affected that change rapidly and remarkably outside the standards of local urban planning.

The functional change of land uses was significantly associated with the areas of urban events and activities, and this was shown through the results of applying the linear regression model using the program (SPSS). It was clear from the statistical results that the functional change of land uses is directly proportional to the area of use, the greater the area, the greater the possibility of functional change and vice versa, assuming the stability of the rest of the factors been extracted (Markov Transition Probability Matrix) Which is (a diagonal matrix) And it was relied upon to do the math rounds (Round States) It took four rounds to get there (Absorbing states) It is the case that assumes the stability of the values of change in the transition matrix for future prediction. We found a decline in agricultural and green lands estimated at more than a third (agricultural lands) current. And that the city will suffer from an increase in residential slums, which will negatively affect the overall urban environment. Commercial functions will change during the coming period by more than half of the current space allocated for commercial use, as well as for industrial functions in a similar way. Transport functions will change to occupy more than a third of the space currently allocated for functions Transport. And it will increase religious functions, administrative functions, cemetery areas, administrative, educational and health functions significantly increased, as shown by the results of the study.

The findings of this study can be used as a basis for an urban observatory, which is crucial for the development of future urban policies that address changes in spatial functions and control of factors that affect these changes. These results will inform the development of housing policies, urban plans, regional development plans, urban land management policies, and spatial organization. The transition matrix is advantageous because it can be used for future predictions if different data is entered for a different time period.

1. The research recommends adopting (Markov Transition Probability Matrix) extracted to diagnose future functional change when studying urban functions independently.

2. Activating the urban observatory to control the change in land use functions and enabling local administrations to monitor changes and address them immediately to prevent their aggravation.

3. Building digital databases for urban land use in the city to facilitate electronic transactions and electronic management of urban functions data.

4. The possibility of simulating the results extracted in this research on other cities, since the approach is useful for city planners and urban administrations.

5. Reconsidering the current master plan for the city by drawing up a long-term development plan that takes into account the development of effective solutions to the effects of unplanned change in urban functions.