## 2 Materials and Methods
### Step IV: Urban Growth Simulation  
Simulation models tracking urban growth have been widely employed over the past two decades, and the predictions derived from these models are utilized to mitigate potential environmental degradation in urban areas during land use planning processes [22; 23]. Cellular automata (CA) models, originating from the 1940s work of physicist [PERSON] and further explored by [PERSON], offer a powerful tool for deriving urban growth models. They integrate spatial and temporal inputs, allowing for simulation based on predefined rules [41; 42]. Furthermore, Markov chain models have also been used to predict LULC changes based on transition probabilities, but sudden changes between LULC states can impact simulation accuracy [43]. Moreover, the SLEUTH model, an open-source urban simulation application developed by [PERSON] [21], has been widely used and offers scalability and flexibility, but lacks socio-economic data integration [44]. Machine learning (ML) methods have also been leveraged for LULC change analysis and urban growth simulation. Compared to traditional models, ML algorithms offer advantages in handling complex and non-linear relationships in urban dynamics [45]. Among the most commonly used ML methods are logistic regression (LR), support vector machines (SVM) [46], and artificial neural networks (ANN) [47]. LR models, for instance, can express LULC changes mathematically and predict future LULC states based on multiple dependent variables, making them suitable for binary classification problems [48; 49]. While each ML method has its strengths and weaknesses, LR was chosen as the primary method for urban growth simulation in this study due to its suitability for binary classification problems and its ability to predict the presence or absence of urban growth based on a set of independent variables. LR assumes that the probability of a cell transitioning to urban use follows a logistic function, with LR coefficients being used to estimate the probability ratios for each independent variable in the model [44]. By representing urban growth outcomes as binary values (Yes or No), LR provides a useful tool for analyzing and predicting urban growth patterns. The probability calculation involves determining how much Y will turn into 1, as shown in Equation (8). \[P(Y=1|X_{1},X_{2},\ \ldots,X_{n})=\frac{1}{1+e^{\alpha+\sum_{i=1}^{n}\beta_{i}X _{i}}} \tag{8}\]  
Here, \(P(Y=1|X_{1},X_{2},\ \ldots,X_{n})\) is the probability of Y given the values of \(X_{i}(i=1,2,\ldots,n)\). In other words, it is the transformation of non-urban pixel to urban pixel. Additionally, \(1-P\) represents the probability of non-existence of urban growth. The regression model is obtained through logistic transformation (Equation (9)). \[\ln\left(\frac{p}{1-p}\right)=\alpha+\beta_{1}X_{1}+\beta_{2}X_{2}+\cdots+ \beta_{n}X_{n} \tag{9}\]  
The coefficients of the independent variables here can be interpreted as factors influencing urban growth, and the probability of urban growth for the entire study area can be calculated iteratively [48]. For the creation of urban growth simulation, past data on LULC classes is required. The input data for urban growth simulation consists of LULC maps from the years 2007,2012, 2017, and 2022, along with road network data. The road network map, converted from vector to raster format with a 30 m resolution, was compatible with the LULC maps. The reason for using only the road network during simulation is that the analysis of built-up area changes over the years in Mersin indicated that the road network was the most significant factor influencing urbanization. Urban growth simulations were generated for the year 2017 based on the LULC maps from 2007-2012, for 2022 based on the maps from 2012-2017, and for 2027 based on the maps from 2017-2022. The simulation process is illustrated step by step in Figure 9.  
The MOLUSCE package was utilized to generate urban growth simulations.