# Urbanization Trends Analysis Using Hybrid Modeling of Fuzzy Analytical Hierarchical Process-Cellular Automata-Markov Chain and Investigating Its Impact on Land Surface Temperature over Gharbia City, Egypt

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The population density was estimated in 2018 as almost 5,066,000 persons, whereas it was hardly 4,011,320 and 3,790,670 in 2006 and 2001, respectively. Our study focused on such areas suffering from accelerating urban sprawl on agricultural lands, resulting in food security challenges and LST increase.

#### 2.2. Data Collection and Processing

#### 2.3. LULC Classification

#### 2.4. LULC Change Modeling

- (1)
- Model Calibration

- (2)
- LULC Simulation and Model Validation

- (3)
- Model Projection

#### 2.4.1. CA-Markov Chain Model

_{n+1}and X

_{n}are two successive state vectors of a Markov chain with transition matrix T, then

#### 2.4.2. FAHP-CA-Markov Chain Hybrid Model

- a.
- Driving factors

- b.
- Steps of applying the FAHP model [64] based on the aforementioned criteria:

_{ij}is the element of the FPCM of n: no. of criteria.

#### 2.5. Estimation of Land Surface Temperature

#### 2.5.1. LST Estimation from Landsat Imageries

- L = spectral radiance at the sensor’s aperture (Watts m
^{−2}sr^{−1}μm^{−1}); - Qcal = the quantized calibrated pixel value in DN;
- LMIN
_{λ}= the spectral radiance scaled to QCALMIN in (Watts m^{−2}sr^{−1}μm^{−1}); - LMAX
_{λ}= the spectral radiance scaled to QCALMAX in (Watts m^{−2}sr^{−1}μm^{−1}); - Qcalmin = the minimum quantized calibrated pixel value (corresponding to LMIN) in DN;
- Qcalmax = the maximum quantized calibrated pixel value (corresponding to LMAX) in DN.

- T
_{B}—is the satellite brightness temperature in degrees Kelvin; - K
_{1}_constant_band_6 of TM 5 = 607.76; - K
_{2}_constant_band_6 of TM 5 = 1260.56; - K
_{1}_constant_band_10 of TIRS 8 = 774.8853; - K
_{2}_constant_band_10 of TIRS 8 = 1321.0789; - L
_{λ}—is TOA spectral radiance.

- S
_{t}—is the emissivity-corrected land surface temperature in degrees Kelvin; - T
_{B}—is the satellite brightness temperature in degrees Kelvin recaptured earlier; - λ = 11.457 µm;
- $\mathsf{\rho}=\frac{\mathrm{h}\times \mathrm{c}}{\mathsf{\delta}}$ = 1.438 × 10
^{−2}m k= 1.438 × 10^{4}µm k; - h—is Planck’s constant = 6.626 × 10
^{−34}J s^{−1}; - c is velocity of light = 2.998 × 108 m s
^{−1}; - δ is Boltzmann’s constant = 1.38 × 10
^{−23}J k^{−1}.

#### 2.5.2. Computation of LSE ε

^{THM}) was adopted. NDVI

^{THM}, which was first introduced by Sobrino and Raissouni [74], uses specific NDVI values (thresholds) to discriminate between soil pixels (NDVI < NDVI

_{S}) and fully vegetated pixels (NDVI > NDVI

_{V}). For those pixels composed of soil and vegetation (mixed pixels; NDVI

_{S}≤ NDVI ≤ NDVI

_{V}), the method uses the simplified Equation (13):

_{S}and ε

_{V}are the soil and vegetation emissivities, respectively, PV is the portion of vegetation (also referred to as fractional vegetation cover, FVC); the soil influence is lower with increasing PV, and C is a term that takes into account the cavity effect owing to surface roughness (C = 0 for flat surfaces, as in our case).

_{V}and NDVI

_{S}values (NDVI for vegetated and soil pixels, respectively) can be extracted from the NDVI histogram. Values of NDVI

_{V}= 0.5 and NDVI

_{S}= 0.2 were confirmed by Sobrino and Raissouni [74] to apply this method in global conditions. In order to gain harmonic values of PV, it must be set to zero for pixels with NDVI < NDVI

_{S}and set to one for pixels with NDVI > NDVI

_{V}. When NDVI > NDVI

_{V}, the pixel is considered fully vegetated and has been granted a constant value of εV = 0.99. NDVI

^{THM}estimates the surface emissivity for pixels of bare soil whose PV = 0 (NDVI < NDVI

_{S}) as a function of the sensor red band reflectivity (ρred). The relationship between emissivity and red reflectivity is assumed to be linear, and the coefficients are obtained from laboratory spectra of soils and statistical fits. The reasonable formulae for estimating soil emissivity are shown in Equations (15) and (16) for Landsat 5 and Landsat 8 images, respectively:

^{THM}can be applied as follows:

#### 2.6. Regression Analysis

## 3. Results

#### 3.1. Accuracy of LULC Maps

#### 3.2. Spatiotemporal Analysis of LULCC

^{2}(91.2%) and diminished to 1674 km

^{2}(83.7%) in 2018. Otherwise, the class of water represents the least area (1%) and almost no change through the study period. For the built-up land use, the statistical analysis for the year 2003 exhibited that the built-up area has increased in contrast to the decrease in agricultural land. This expansion through the period of 1991–2003 is not disturbing as it is only about 2%. However, urban augmentation was driven to significant growth (almost 5.5%) in the period of 2003–2018 due to urbanization desire. The built-up class occupied 7.8%, 9.7%, and 15.2% in 1991, 2003, and 2018, respectively, which means that the built-up area almost doubled during the study period.

^{2}and 110.38 km

^{2}within the 1991–2003 and 2003–2018 time periods, respectively. The percentage of built-up land use has increased from 7.8% to 15.2% (nearly doubled) throughout the whole study period (27 years). The agricultural land revealed a similar (but reverse) trend from 1991 to 2018, since the urban growth was extended over the agricultural land.

#### 3.3. LULCC Modeling, Simulation, and Projection

#### 3.3.1. Analysis of the CA-Markov Chain Model

#### 3.3.2. Analysis of FAHP-CA-Markov Chain Model

^{2}and 514 km

^{2}by 2033 and 2048, respectively. It means that the built-up cover will occupy more than one-fifth of the area by 2033 and more than a quarter of the area by 2048. The area of built-up is almost doubled by 2048 with respect to 2018. On the other hand, the area of agricultural activity will decrease owing to the increase in the urban area. It means that the agricultural land will be diminished by the same amount of built-up increase (160.4 km

^{2}and 259.5 km

^{2}by 2033 and 2048, respectively).

#### 3.4. Analysis of LST

#### 3.5. Analysis of the UHI

#### 3.6. Relationship between LULC and LST

## 4. Discussion

#### 4.1. Current Study Compared to Previous LULC and Corresponding LST Studies

^{2}through a 19-year study period.

#### 4.2. Current and Possible Future Alternative Land-Use Strategies

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The study area of Gharbia governorate, Egypt [35].

**Figure 2.**The conceptual flowchart of the adopted methodology. (

**a**) Supervised classification of the processed images for obtaining LULC maps; (

**b**) simulating the LULCC using CA-Markov chain model and the integrated model of CA-Markov chain with FAHP; and (

**c**) estimation of LST and investigating the impact of LULCC on LST based on regression analysis; and (

**d**) conducting regression analysis to obtain the relationship between LULC and the corresponding LST.

**Figure 3.**Spatial distribution of LULC over the study area during the study period: (

**a**) LULC map in 1991; (

**b**) LULC map in 2003; and (

**c**) LULC map in 2018.

**Figure 7.**Spatial distribution of daytime land surface temperature (LST) over the study area during the study period in June 1991, 2003, and 2018, all at around 8:00 am.

**Figure 8.**Land surface temperature maps illustrating UHI intensity and UHI zones. The white color represents non-UHI zones, and UHI intensity is mentioned for each image.

**Figure 9.**Regression analysis to retrieve the relationship between the LST and LULC over Gharbia in (

**a**) 1991, (

**b**) 2003, and (

**c**) 2018.

Data Type | Capture Date | Resolution | Source | Output |
---|---|---|---|---|

Landsat 1991™ | 27 June 1991 | 30 m | USGS | LULC map |

Landsat 2003™ | 28 June 2003 | 30 m | USGS | LULC map |

Landsat 2018^{OLI-TIRS} | 21 June 2018 | 30 m | USGS | LULC map |

Google Earth historical images | June 1991, 2003, 2018 | Google Earth Pro | Training/validation | |

Road network layer | OSM | Distance to nearest road |

Criteria | LULC | Dist. to Persist. Built-Up | Dist. to Urban Centers | Dist. to Railway Stations | Dist. to Near Road | Neighbor. Effect | Population Density | Local Develop. | Employment |
---|---|---|---|---|---|---|---|---|---|

LULC | (1,1,1) | $\left(\frac{1}{9},\frac{1}{8},\frac{1}{7}\right)$ | $\left(\frac{1}{9},\frac{1}{8},\frac{1}{7}\right)$ | $\left(\frac{1}{8},\frac{1}{7},\frac{1}{6}\right)$ | $\left(\frac{1}{9},\frac{1}{8},\frac{1}{7}\right)$ | $\left(\frac{1}{8},\frac{1}{7},\frac{1}{6}\right)$ | $\left(\frac{1}{6},\frac{1}{5},\frac{1}{4}\right)$ | $\left(\frac{1}{6},\frac{1}{5},\frac{1}{4}\right)$ | $\left(\frac{1}{8},\frac{1}{7},\frac{1}{6}\right)$ |

Dist. to persist. built-up | (7,8,9) | (1,1,1) | (1,1,1) | (4,5,6) | (2,3,4) | (1,1,1) | (2,3,4) | (2,3,4) | (2,3,4) |

Dist. to urban centers | (7,8,9) | (1,1,1) | (1,1,1) | (2,3,4) | (1,2,3) | (1,1,1) | (2,3,4) | (3,4,5) | (2,3,4) |

Dist. to railway stations | (6,7,8) | $\left(\frac{1}{6},\frac{1}{5},\frac{1}{4}\right)$ | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | (1,1,1) | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | $\left(\frac{1}{6},\frac{1}{5},\frac{1}{4}\right)$ | (1,1,1) | (2,3,4) | (1,1,1) |

Dist. to nearest road | (7,8,9) | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | $\left(\frac{1}{3},\frac{1}{2},1\right)$ | (2,3,4) | (1,1,1) | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | (2,3,4) | (3,4,5) | (2,3,4) |

Neighborhood effect | (6,7,8) | (1,1,1) | (1,1,1) | (4,5,6) | (2,3,4) | (1,1,1) | (1,1,1) | (2,3,4) | (2,3,4) |

Population density | (4,5,6) | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | (1,1,1) | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | (1,1,1) | (1,1,1) | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | (1,1,1) |

Local development | (4,5,6) | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | $\left(\frac{1}{5},\frac{1}{4},\frac{1}{3}\right)$ | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | $\left(\frac{1}{5},\frac{1}{4},\frac{1}{3}\right)$ | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | (2,3,4) | (1,1,1) | $\left(\frac{1}{3},\frac{1}{2},1\right)$ |

Employment | (6,7,8) | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | (1,1,1) | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | $\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$ | (1,1,1) | (1,2,3) | (1,1,1) |

Accuracy | LULC Class | 1991 | 2003 | 2018 |
---|---|---|---|---|

User’s accuracy (%) | Built-up | 80.7 | 85.7 | 91.8 |

Water | 82.1 | 82.6 | 94.7 | |

Agricultural land | 97.0 | 96.4 | 95.1 | |

Producer’s accuracy (%) | Built-up | 80.0 | 80.9 | 81.3 |

Water | 82.1 | 86.4 | 85.7 | |

Agricultural land | 97.1 | 97.2 | 98.1 | |

Overall accuracy (%) | 94.9 | 94.7 | 94.6 | |

Kappa coefficient | 0.78 | 0.81 | 0.84 |

LULC | 1991 | 2003 | 2018 | |||
---|---|---|---|---|---|---|

Area (km^{2}) | % | Area (km^{2}) | % | Area (km^{2}) | % | |

Built-up | 156.75 | 7.8 | 193.37 | 9.7 | 303.75 | 15.2 |

Water | 19.57 | 1.0 | 24.48 | 1.2 | 21.56 | 1.1 |

Agricultural land | 1832.01 | 91.2 | 1781.48 | 89.1 | 1674.02 | 83.7 |

Total | 1999.33 | 100 | 1999.33 | 100 | 1999.33 | 100 |

Model Criteria | AHP | FAHP |
---|---|---|

LULC | 0.017 | 0 |

Dist. to persistent built-up area | 0.202 | 0.260 |

Dist. to urban centers | 0.185 | 0.238 |

Dist. to railway stations | 0.07 | 0.040 |

Dist. to nearest road | 0.134 | 0.206 |

Neighborhood effect | 0.186 | 0.226 |

Population density | 0.071 | 0 |

Local development | 0.065 | 0 |

Employment | 0.07 | 0.030 |

LULC | 2018 | 2033 | 2048 | RD% 2018–2033 | RD% 2018–2033 | |||
---|---|---|---|---|---|---|---|---|

Area (km^{2}) | % | Area (km^{2}) | % | Area (km^{2}) | % | |||

Built-up | 251.62 | 12.6 | 414.90 | 20.7 | 514.00 | 25.7 | 64.9 | 104.3 |

Water | 24.48 | 1.2 | 21.56 | 1.1 | 21.56 | 1.1 | −11.9 | −11.9 |

Agricultural land | 1723.23 | 86.2 | 1562.87 | 78.2 | 1463.77 | 73.2 | −9.3 | −15.1 |

Total | 1999.33 | 100 | 1999.33 | 100 | 1999.33 | 100 |

**Table 7.**Calculation of urban heat island intensity from land surface temperature (LST) based on Landsat images.

Image Acquisition Date | Mean Urban LST (°C) | Mean Rural LST (°C) | UHI (°C) |
---|---|---|---|

1991 | 32.48 | 29.23 | 3.25 |

2003 | 37.29 | 32.57 | 4.72 |

2018 | 41.50 | 37.46 | 4.04 |

**Table 8.**Calculation of UHI intensities from land surface temperature (LST) based on Landsat images.

Urban LST (°C) | Rural LST (°C) | UHI (°C) | |||||||
---|---|---|---|---|---|---|---|---|---|

Districts | Mean Temperature (μ) 1991 | Mean Temperature (μ) 2003 | Mean Temperature (μ) 2018 | Mean Temperature (μ) 1991 | Mean Temperature (μ) 2003 | Mean Temperature (μ) 2018 | 1991 | 2003 | 2018 |

Mahalla Kubra | 32.16 | 36.62 | 40.63 | 28.65 | 31.09 | 36.26 | 3.51 | 5.53 | 4.37 |

Tanta | 32.87 | 37.95 | 41.29 | 29.77 | 33.30 | 37.38 | 3.10 | 4.65 | 3.91 |

Basyun | 32.80 | 36.77 | 40.42 | 29.89 | 32.44 | 38.19 | 2.91 | 4.33 | 2.23 |

Zefta | 32.32 | 37.84 | 41.50 | 29.29 | 33.86 | 38.26 | 3.03 | 3.98 | 3.24 |

Santah | 32.41 | 37.65 | 41.02 | 29.32 | 33.31 | 37.44 | 3.09 | 4.34 | 3.58 |

Kafr Elzayat | 32.74 | 38.03 | 41.40 | 29.43 | 34.44 | 39.48 | 3.31 | 3.59 | 1.92 |

Samanod | 31.72 | 36.53 | 40.53 | 28.52 | 31.92 | 36.58 | 3.2 | 4.61 | 3.95 |

Qotur | 32.74 | 36.70 | 41.04 | 29.45 | 31.76 | 37.77 | 3.29 | 4.94 | 3.27 |

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## Share and Cite

**MDPI and ACS Style**

Mostafa, E.; Li, X.; Sadek, M.
Urbanization Trends Analysis Using Hybrid Modeling of Fuzzy Analytical Hierarchical Process-Cellular Automata-Markov Chain and Investigating Its Impact on Land Surface Temperature over Gharbia City, Egypt. *Remote Sens.* **2023**, *15*, 843.
https://doi.org/10.3390/rs15030843

**AMA Style**

Mostafa E, Li X, Sadek M.
Urbanization Trends Analysis Using Hybrid Modeling of Fuzzy Analytical Hierarchical Process-Cellular Automata-Markov Chain and Investigating Its Impact on Land Surface Temperature over Gharbia City, Egypt. *Remote Sensing*. 2023; 15(3):843.
https://doi.org/10.3390/rs15030843

**Chicago/Turabian Style**

Mostafa, Eman, Xuxiang Li, and Mohammed Sadek.
2023. "Urbanization Trends Analysis Using Hybrid Modeling of Fuzzy Analytical Hierarchical Process-Cellular Automata-Markov Chain and Investigating Its Impact on Land Surface Temperature over Gharbia City, Egypt" *Remote Sensing* 15, no. 3: 843.
https://doi.org/10.3390/rs15030843