"Urban sprawl" refers to a type of spatial growth distinguished by its low population density, scattered and discontinuous expansion that skips over areas, and the separation of different land uses (Manesha et al., 2021; Patra et al., 2022a). The expansion of urban sprawl has a direct consequence on altering the land use and land cover (LULC) of the region by accele-rating the growth of developed and impermeable areas (Antalyn & Weerasinghe, 2020; Sudhira & Ramacha-ndra, 2007). This has raised significant concerns about the potential ecological risks posed by urban encroach-ment to the fundamental pillars of rural livelihoods, including forests, agriculture, and related sectors (Antalyn & Weerasinghe, 2020; Sudhira & Ramachan-dra, 2007). It encompasses key attributes such as development with a singular purpose, fragmentation, irregular shapes, low concentration or inequality, and the linear expansion (Aguilera et al., 2011; Antalyn and Weerasinghe, 2020; Keita et al., 2021; Liu and Meng, 2020; Manesha et al., 2021; Mosammam et al., 2017; Sudhira and Ramachandra, 2007; Verbeek et al.,  2014; Wei and Ewing, 2018). Therefore, urban sprawl has played a significant role in transforming rural land use patterns into urban ones, reducing the availability of rural land (Manesha et al., 2021; Nejadi et al., 2011). When discussing sprawl, the opposite concept is compact urban development, and sprawl is primarily characterized by the worry of a citys expansion occur-ring in an unplanned and unregulated manner (Mane-sha et al., 2021). Urban sprawl poses significant chall-enges that have a detrimental impact on the prospects of achieving sustainable urban development (Páez & Scott, 2004). Effective management of urban develop-ment plays a crucial role in ensuring sustain-able urban development (Aguilera et al., 2011; Wei and Ewing, 2018). This information significantly benefits urban planners and other professionals in related fields, helping them comprehend suitable methods for evaluating urban sprawl (Milad et al., 2017). At present, planners and policy makers extensively employ contemporary methods like Geographic Information Systems (GIS) and Remote Sensing (RS) to characterize spatial phenomena (Liu & Meng, 2020). GIS and RS are employed to address the spatio-temporal aspect, enabling the monitoring, regulation, analysis, assessment, and the measurement of urban growth patterns and alterations in land use (Rama-chandra et al., 2013). As a result, various statistical scales and parameters have been created to gauge urban sprawl by integrating these GIS and RS methods (Páez & Scott, 2004). Among these options, the utilization of Shannons entropy approach and the Urban Expansion Intensity Index stands out as potent quantitative methods for assessing urban growth (Al-sharif et al., 2016; Boori et al., 2015; Manesha et al., 2021; Milad et al., 2017; Mosammam et al., 2017; Patra et al., 2022a; Sridhar et al., 2020). These indices hold importance for various reasons, including their ability to determine the pace of urban expansion, assess urban development patterns, and evaluate and track urban phenomena over different time intervals (Ramachandra et al., 2013; Alom MJ., 2024). Conver-sely, landscape metrics are employed to evaluate the spatiotemporal characteristics of urban sprawl, encom-passing attributes like disorder, aggregation, intricacy, and the degree of dispersion among urban land classes within the landscape of the study area (Manesha et al., 2021; Taubenböck et al., 2009).  

Over the past two decades in Afghanistan, urban expansion especially in major cities, has led to the emergence of densely populated slums and extensive settlements on the outskirts of cities. This rapid urban-ization has resulted in cities consuming large tracts of land to accommodate new developments. In certain areas, the rate of urban growth has outpaced the growth of the urban population, leading to less con-centrated, poorly organized and inefficient land-use arrangements. The urban population in Afghanistan is continuously growing, leading to uncontrolled and swift urban development (Kristy, 2018a). Projections indicate that Afghan cities are expected to experience a doubling of their population in the next 15 years (UN-Habitat, 2015). By 2060, it is estimated that one out of every Afghan will be living in urban areas (UN-Habitat, 2015). To manage this transformation effec-tively and harness it for economic and social progress, accurate data and information are crucial (UN-Habitat, 2015). 

Referring to the 2015 report by (UN-Habitat, 2015), it is evident that Afghan cities hold significant impor-tance in fostering social and economic development, state-building, and peace-building efforts. Nonethe-less, their complete potential has been limited by the lack of appropriate urban regulations and policies, inadequate and disjointed investments, and insufficient municipal governance and land management (UN-Habitat, 2015). For this study, Herat City has been chosen as the designated research area. Herat stands out as one of the rapidly expanding urban centers in western Afghanistan (UN-Habitat, 2015). In 2021, the urban population of Herat City reached 636,000, indicating a growth rate of 4.95% compared to the previous year, 2020 (UN-Habitat, 2015). A clear correlation exists between population size and the progress of urban development (Bhatta 2009; Patra et al., 2022b). The combination of unregulated urban expansion and population growth has driven the process of urbanization in Herat City (UN-Habitat, 2015). Numerous investigations have been conducted in Herat city regarding the topic of urban development (Ali Mahaqi et al., 2020; Kristy, 2018b). 

The conducted studies predominantly concentrated on the ramifications of urban development on cultural heritage, and also, they examined various facets linked to the environmental hydro-geochemical attributes, controlling variables, and the assessment of ground-water quality within Herat City. As a result, a quanti-tative investigation of the urban sprawl utilizing Shannons entropy approach and the Urban Expansion Intensity Index in Herat City is currently lacking. Upon reviewing the pertinent literature, it is evident that there has been no prior research conducted in Herat City, Afghanistan, that specifically addresses the measurement of urban growth using the Shannons entropy approach and the Urban Expansion Intensity Index, and this study will mark the inaugural research endeavor in this geographical region. The research methodologies and microscale approach employed in this study will offer utility to quantify urban expansion using Shannons entropy approach and the Urban Expansion Intensity Index in cities of varying sizes, including small, medium, and large urban areas. As a result, this research seeks to assess the rate of urban expansion and urban development in Herat City by employing Shannons entropy approach and the Urban Expansion Intensity Index through the utilization of optical remote sensing data. The outputs of this rese-arch will serve as valuable tools for policymakers at the Ministry of Urban Development and Land of Afghanistan, the Herat Municipality, the National Environmental Protection Agency (NEPA) of Afgha-nistan, and various other domestic and the inter national organizations involved. They will help these stakeholders comprehend the trajectory of urban exp-ansion and formulate appropriate strategies and the policies to promote sustainable development in Afghanistans major cities.

Fig. 1: The geographic location of the study area. 

Study area 

Herat province is located in the western part of Afghanistan, positioned at a latitude of 34°20′31′′ North and a longitude of 62°12′11′′ East (Fig. 1). To the east, it shares its border with Iran at the Islam Qala crossing, and to the north, it borders Turkmenistan at the Torghundi crossing. In Afghanistan, Herat pro-vince shares its boundaries with Badghis, Ghor, and Farah provinces (Nasery et al., 2021a).  

Herat city, situated in western Afghanistan, serves as the capital of the Herat province, and has gained recognition for its rapid development. Its history as a settlement trace back to ancient periods, including the Iron Age. Even in pre-Islamic epochs, especially during the reign of Alexander the Great, the city held a prominent and well-established position (Kristy, 2018b). In the past, Herat city faced destruction as a result of historical conflicts, including invasions by both Genghis Khan and Timur. However, during the reign of Sharooz, a leader from the Timurid dynasty, significant initiatives were launched to rebuild and develop the city, with a particular emphasis on expanding and beautifying it (Urban Development Threatens the Old City of Herat | UNAMA, n.d.). During July, Herat typically sees an average high temperature of 30°C, whereas in January, the minimum temperature decreases to 4°C (Nasery et al., 2021b). Over the past 21 years, Herat city has wit-nessed a considerable influx of immigrants and rapid population growth. Unfortunately, this has resulted in significant degradation of the natural land cover, causing the once-pristine scenery and landscapes to disappear. Therefore, urban development has exp-anded rapidly within the city. To comprehensively assess the extent of urbanization, including impervious surfaces and other spatial characteristics, Herat city was chosen as the primary focal point for this research.

This study utilized multispectral data, namely Landsat 7 and Landsat 8 for the years 2000, 2013, and 2021 to create land use land cover within Herat city with higher accuracy (Table 1).  In this study we employed the Cloud Computing Platform of Google Earth Engine (GEE), to classify the study area. The atmos-pherically corrected surface reflectance from the Land-sat 7 and Landsat 8 dataset are used.  This study utili-zed three machine learning algorithms: SVM, RF, and CART, to categorize the study area. The accuracy of each algorithm was evaluated for each study period. 

Following the assessment, the RF algorithm classified the study area with higher accuracy and was chosen as the classification method. The study area was classi-fied using the GEE cloud platform, and thematic layers were generated within the GIS environment. To identify and quantify urban patterns such as built-up areas as spatial phenomena, both the Urbanization Intensity Index and Shannons entropy were computed. The following techniques are discussed below.

Table 1: Description of satellites Landsat 8 OLI/TIRS and Landsat 7.

Quantification of urban sprawl

Urban Expansion Intensity Index

The Urban Expansion Intensity Index, abbreviated as UEII, can be employed to quantitatively assess the variations in urban spatial expansion. Furthermore, 

UEII can be utilized to identify urban growth patterns and to compare the rate or speed of changes in urban land use within a specific timeframe. Formula (1) illustrates the equation used for calculating UEII.

In this equation,  〖UEII〗_it  represents the annual aver-age urban expansion intensity index for the (ith) zone during time period (t). 〖ULA〗_(i,a) and 〖ULA〗_(i,b) denote the built-up area quantities at time periods a and b in the (ith) spatial zone, respectively. 〖TLA〗_i stands for the total area of the (ith) spatial zone(Al-sharif et al., 2016; Manesha et al., 2021; Milad et al., 2017). The UEII has been categorized into various groups, as depicted in Table 2.

Table 2: The division standard of Urban Expansion Intensity Index (UEII).

Shannons Entropy Model

Shannons entropy is a widely recognized approach for evaluating patterns of urban expansion (Antalyn & Weerasinghe, 2020; Bhatta et al., 2010a; Manesha et al., 2021). Shannons entropy can be applied to gauge the level of spatial clustering or dispersion of a geographic variable (xi) across n zones (Yang, 2018). Shannons urban entropy quantifies the degree of spatial density and dispersion of built-up land cover across various time intervals (Abubakr et al., 2015; Rahman et al., 2011; Verma et al., 2017). The equation below is employed for computing Shannons entropy (Jat et al., 2008b):

To scale up the entropy values from 0 to 1, relative Shannons entropy will be used. The following equation is used to estimate relative entropy (Thomas, 1981).

Where Pi stands for the probability or proportion of the variable (in this case, the built-up area) occurring in the ith zone, Xi represents the estimated value of the variable in the ith zone, and n is the total number of zones. Shannons entropy values fall within the range of 0 to log(n). When the value is closer to zero, it signifies concentrated urban growth, while a value closer to log(n) indicates a more dispersed pattern in the built-up environment (Yeh & Li, 2001).  The rate of change in urban sprawl is computed using the following equation.

Where, H_n (t_1 )represents the relative entropy at time (t_1 ), while H_n (t_2 ) signifies the relative entropy at time (t_2 ). The alteration in entropy can be employed to determine whether land development adheres to a more scattered (sprawled) or concentrated pattern of urban expansion. When the relative Shannons entr-opy value exceeds 0.5 (the threshold), it indicates urban sprawl in the area. Conversely, if the result falls below 0.5, it suggests a densely developed built-up area. The study area has been divided into distinct zones to investigate the expansion of urban sprawl. (Bhatta et al., 2010a) partitioned the research area into eight pie sections to evaluate urban sprawl. (Sudhira et al., 2004b) highlighted significant factors in urban growth such as roads and city centers. They esta-blished buffer zones around these factors to quantify urban expansion (Sabet et al., 2011) established a concentric circular zone around the center of the research area to evaluate its growth. In our current research, despite having access to well-defined admin-istrative and ward boundaries in the study area, we opted not to utilize them.  This decision was based on the fact that these wards experience alterations in both their geographical size and number over time, with the aim of enhancing administrative efficiency and effec-tiveness. In this study, we divided the research region starting from Herat Government Office, which is located in the center of Herat city. Here, we employed relative Shannons entropy, which is not constrained by the number of divisions and remains unaffected by the manner in which we segment the study area (Bhatta et al., 2010b; Patra et al., 2022a). Therefore, we divide the study area into eight pie sections starting from the Herat Government Office. The study area encompasses eight primary compass directions, which include East (E), Northwest (NW), North (N), West (W), Southwest (SW), South (S), and South-east (SE). Each of these zones is further divided into a concentric circle arrangement with a radius of 3 kilometers, aiming to examine urban sprawl comprehensively across every nook and cranny of Herat City. In total, 27 vector maps of the research area have been gene-rated and are employed to delineate 27 zones within which the raster image is extracted Fig. 2.

Fig. 2: Zone division of study area.

Land-use/Cover Classification 

The Google Earth Engine (GEE) JavaScript API Code Editor was utilized to access information from satellite images. GEE provides access to a wide range of publicly available image data and offers an API for performing analysis and creating visualizations with this data (Sahak et al., 2023). Data on surface reflec-tance from Landsat 7 and 8 were gathered using the USGS Landsat surface reflectance tier 1 dataset avail-able through Google Earth Engine. Surface reflectance was computed by utilizing data from Landsat (TM, OLI/TIRS) sensors that have undergone orthorectifi-cation and atmospheric correction. For this analysis, bands one through seven were employed, and the resulting spatial resolution was set at 30 meters. Tem-poral aggregation was employed in conjunction with filters for geographical boundaries, dates, and cloud cover. This process also included the computation of both the mean and median values when selecting bands of reflectance values from all available images for each specific study period. Consequently, for every study timeframe and aggregation method, a solitary image with seven bands was created. In this study, three supervised algorithms were employed: SVM, RF, and CART.  In this research, 80 percent of the data were utilized for training purposes, while 20 percent were reserved for testing, for each of the algorithms. The accuracy of each algorithm was ass-essed. Based on the results, the RF supervised algo-rithm consistently provided higher classification accuracy for each study period. Therefore, the RF algorithm was chosen as the classification method. For each time interval, the study area has been categorized into four groups: Built-Up, Vegetation, Water, and Barren Land, and the outputs are demonstrated in Fig. 3.

Fig. 3: Spatial dynamics of LU/LC in Herat City; (a) 2000, (b) 2013, and (c) 2021.

As stated above, in this study, three supervised machine learning algorithms were employed: SVM, RF, and CART.  In this research, 20 percent of the data were utilized for testing purposes, while 80 percent were reserved for training, for each of the algorithms. The accuracy of each algorithm for every study period was assessed respectively. The outputs of the assessment are demonstrated in Table 3.  Based on Table 3, the results indicate that in the year 2000, the overall accuracy for SVM, RF, and CART algorithms was 94%, 98%, and 97%, respectively, with corres-ponding Kappa coefficients of 0.81, 0.93, and 0.91, respectively. In 2013, the overall accuracy for SVM, RF, and CART algorithms changed to 88%, 92%, and 88%, while the Kappa coefficients for each algorithm were estimated at 0.82, 0.88, and 0.81, respectively. Consequently, in 2021, the outputs demonstrate that the overall accuracy for each algorithm is as follows: 84%, 88%, and 84%, with corresponding Kappa co-efficients of 0.74, 0.81, and 0.76, respectively. Based on the overall evaluation, the RF supervised algorithm consistently provided higher classification accuracy for each study period. Therefore, the RF algorithm was chosen as the classification method. The findings indicated that various land cover tegories, including built-up areas, water bodies, vegetation, and barren land, were accurately recognized.

Table 3: Accuracy assessment of LU/LC classification in 2000, 2013, and 2021.

Assessment of changes in land use and land cover (LU/LC)

As previously stated, the study area in this research was divided into four distinct categories (Built-Up, Vegetation, Water, and Bare Land) utilizing the random forest supervised classification algorithm. This classification was employed to assess the changes in land use and land cover (LU/LC) for the years 2000, 2013, and 2021. The classified map results are depicted in Fig. 3. Table 4 presents the summary statistics for the estimated areas and percentages of each LU/LC type, while Table 5 provides summary statistics for the various changes in land use and land cover (LU/LC) observed over Herat city. In Table 5, a negative sign indicates a decrease in a particular land use/land cover (LU/LC) type, whereas a positive sign signifies an increase in that specific LU/LC type during the previous study period. Based on the data provided in Table 4 and Table 5, there was a significant increase in the Built-up area from 26.41 km² in 2000 to 68.75 km² in 2013, signifying an expansion of 42.34 km², which corresponds to a growth of 22.77%. Conversely, the Vegetation, Water, and Bare land regions decreased from 59.05 km², 2.71 km², and 97.77 km² in 2000 to 50.00 km², 1.03 km², and 66.16 km² in 2013, resulting in a reduction of 9.05 km² (4.87%), 1.68 km² (0.90%), and 31.61 km² (17.00%), respectively.  Furthermore, from 2013 to 2021, there was an increase in the built-up area, which expanded from 68.75 km² to 82.30 km², representing a growth of 13.55 km² (7.29%). In contrast, the Vege-tation, Water, and Bare land regions decreased from 50.00 km², 1.03 km², and 66.16 km² to 43.21 km² (3.65% decrease), 0.84 km² (0.1% decrease), and 59.59 km² (3.53% decrease), respectively. Consequently, between 2000 and 2021, the built-up area exhibited substantial growth, increasing from 26.41 km² to 82.30 km², which represents a significant expansion of 55.89 km² (30.06%). Conversely, the Vegetation, Water, and Bare land regions decreased from their respective sizes of 59.05 km², 2.71 km², and 97.77 km² in 2000 to 43.21 km², 0.84 km², and 59.59 km² in 2021, resulting in a reduction of 15.83 km² (8.51%), 1.88 km² (1.01%), and 38.18 km² (20.53%), respectively. The overall evaluation demonstrates that the built-up areas have increased by 30.06%, indicating a high rate of urban development in Herat City over the course of 21 years. 

Assessing the extent of overall urban growth

The UEII, defined as the average yearly expansion area relative to the total geographical unit area, demonstrates the potential for urban growth (Norouzi, 2023). The outcome of the overall UEII metric within the study area is displayed in Table 6 and Fig. 4.  Based on Table 6 and Fig. 4, the results indicate that Herat city underwent high-speed development between 2000 and 2013, while experiencing medium speed development between 2013 and 2021. Moreover, the data reveals that between 2000 and 2013, the built-up area increased from 26.42 km² to 68.13 km². Furthermore, between 2013 and 2021, it expanded from 68.13 km² to 82.30 km².

Fig. 4: The overall built-up area expansion from 2000 to 2021 in Herat city.

Table 4: Land-use/land-cover areas and percentage over Herat city in 2000, 2013, and 2021.

Table 5: Summary Statistics of Land-use/land cover variations over Herat city in 2000, 2013, and 2021.

Table 6: Overall Urban Expansion Intensity Index (UEII) between 2000-2013, and 2013-2021 within Herat City.

Quantification of urban expansion intensity in different cardinal direction and buffer zones 

As previously mentioned, we divided the study area into eight directional sections, 27 directional zones, and five buffer ring zones with 3km radius from the Herat Government Office which is situated in the center of the Herat City. The study area comprises eight primary compass directions, 27 directional zones, which are as follows:

• East (E) (zones 14, 15, 16, 17, and 18)

• Northeast (NE) (zones 26 and 27)

• Northwest (NW) (zones 19, 20, 21, 22, and 23)

• North (N) (zones 24 and 25)

• West (W) (zones 10, 11, 12, and 13)

• Southwest (SW) (zones 1, 2, and 3)

• South (S) (zones 4 and 5)

• Southeast (SE) (zones 6, 7, 8, and 9).

This visualization aims to depict the speed and scale of urban expansion in each direction (see Fig. 5), and also in this study the speed and scale of urban expansion evaluated in in each 3km ring buffer zones.  These buffer zones are viewed as fundamental spatial units used to describe the spatiotemporal pattern of urban development over specific distances. Table 7 and Fig. 6 present the summary statistics for the estimated area of urban area and urbanization intensity 

index in each direction and directional zones. Based on the data presented in Table 7 and Fig. 6, the findings indicate that between 2000 and 2013, the built-up area increased from 4.321 km², 4.038 km², 5.443 km², and 5.928 km² to 17.886 km², 14.219 km², 11.374 km², and 9.989 km², representing expansions of 13.57 km², 10.18 km², 5.93 km², and 4.06 km² in the NW (zones 19, 20, 21, 22, and 23), E (zones 14, 15, 16, 17, and 18), W (zones 10, 11, 12, and 13), and SW (zones 1, 2, and 3) directions and respective zones. Meanwhile, in the S (zones 4 and 5), SE (zones 6, 7, 8, and 9), N (zones 24 and 25), and NE (zones 26 and 27) directions, the built-up area changed from 2.492 km², 2.877 km², 0.514 km², and 0.798 km² to 9.984 km², 5.621 km², 1.514 km², and 3.226 km², indicating expansions of 1.81 km², 2.74 km², 1 km², and 2.43 km², respectively.  Between 2013 and 2021, the data reveals that the built-up area increased from 9.984 km², 4.305 km², 5.621 km², 11.734 km², 14.219 km², 17.886 km², 1.514 km², and 3.226 km², to 10.557 km², 4.940 km², 6.996 km², 13.168 km², 18.953 km², 22.355 km², 1.968 km², and 3.377 km²  indicating expansions of 0.573 km², 0.635 km², 1.375 km², 1.794 km², 4.734 km², 4.469 km²,0.454 km²,  and 0.151 km² in the SW (zones 1, 2, and 3), S (zones 4 and 5), SE (zones 6, 7, 8, and 9), W (zones 10, 11, 12, and 13), E (zones 14, 15, 16, 17, and 18), NW (zones 19, 20, 21, 22, and 23), N (zones 24 and 25), and NE (zones 26 and 27) directions and respective zones.

The overall assessment indicates that between 2000 and 2013, the largest expansion of the built-up area occurred in the NW (zones 19, 20, 21, 22, and 23), E (zones 14, 15, 16, 17, and 18), W (zones 10, 11, 12, and 13), and SW (zones 1, 2, and 3) directions and zones. Meanwhile, from 2013 to 2021, the greatest expansion of the built-up area was observed in the E (zones 14, 15, 16, 17, and 18) and NW (zones 19, 20, 21, 22, and 23) directions and zones. Once again, based on the data from Table 7, between 2000 and 2013, the highest urban expansion intensity occurred in the N (zones 24 and 25), NE (zones 26 and 27), S (zones 4 and 5), and NW (zones 19, 20, 21, 22, and 23) directions and their corresponding zones, with intensity values of 0.028%, 0.030%, 0.023%, and 0.025%, respectively. However, between 2013 and 2021, the data indicates that the maximum urban intensity was observed in the N (zones 24 and 25), NW (zones 19, 20, 21, 22, and 23), E (zones 14, 15, 16, 17, and 18), S (zones 4 and 5), and W (zones 10, 11, 12, and 13) directions and their associated zones, with intensity values of 0.016%, 0.012%, 0.011%, and 0.01%, respectively. The summary statistics for the estimated area of built-up areas and the urbanization intensity index in each buffer rings are presented in Table 8 and Fig. 7. 

The findings reveal that between 2000 and 2013, the built-up areas expanded from 13.254 km2, 8.0403 km2, 3.09 km2, 1.296 km2, and 0.401 km2 to 22.231 km2, 26.571 km2, 11.003 km2, 5.151 km2, and 3.203 km2, respectively. This indicates an expansion of 8.98 km2, 18.17 km2, 7.91 km2, 3.85 km2, and 2.80 km2, with urban expansion intensities of 0.025%, 0.027%, 0.013%, 0.007%, and 0.014% in the 3km, 6km, 9km, 12km, and 15km buffer zones, respectively. Further-more, the results indicate that between 2013 and 2021, the built-up areas increased from 22.231 km2, 26.571 km2, 11.003 km2, 5.151 km2, and 3.203 km2 to 22.795 km2, 31.07 km2, 12.628 km2, 9.50 km2, and 6.34 km2, respectively. This represents expansions of 1.57 km2, 4.5 km2, 1.63 km2, 4.35 km2, and 3.14 km2, with urban expansion intensities of 0.007%, 0.01%, 0.005%, 0.013%, and 0.023% in the 3km, 6km, 9km, 12km, and 15km buffer zones, respectively. The overall assessment indicates that the maximum urban expan-sion and urban expansion intensity occurred between 2000 and 2013 in each buffer zone, respectively. Based on data from the United Nations (UN) and the International Committee of the Red Cross (ICRC), approximately 730,000 individuals have been forced to leave their homes in Afghanistan due to conflict since 2006, leading to an average of 400 people being internally displaced every day  (APPRO, 2012). The drought in 2006, along with subsequent food shortages and a harsh winter in 2007 and 2008, coupled with the global rise in the costs of essential food items in 2008, resulted in the emergence of numerous newly dis-placed and resettled populations (APPRO, 2012). In 2011, UNHCR estimated that there were 447,547 internally displaced persons (IDPs) in Afghanistan, with 43 percent of them being a result of conflict (APPRO, 2012). As a result, conflicts, insufficient employment opportunities, and limited living ameni-ties in rural regions served as the primary factors driving internal migration towards major cities, ulti-mately contributing to the urban development in Afghanistan.

Table 7: Urban Expansion Intensity Index (UEII) in each direction and directional zone between 2000, 2013, and 2021in Herat.

Table 8: Urban Expansion Intensity Index (UEII) in each 3km buffer zone between 2000, 2013, and 2021.

Relative Shannons Entropy for the Urban Sprawl Analysis

Shannons entropy quantifies the degree of spatial compactness or dispersion of a geophysical parameter within a set of n zones (Al-sharif et al., 2016; Jat et al., 2008a). In this study, the built-up area is regarded as a geophysical factor, and it is employed to examine urban growth (including overall expansion, expansion in each cardinal direction, and expansion in each of the 27 zones) across the entire time frame within the study area. The entropy  and relative entropy values over the 

years in the overall study area, each cardinal direction, and across 27 distinct zones are displayed in Table 9, Table 10 and Table 11. The relative Shannons ent-ropy scale ranges from 0 to 1. A value closer to 0 signifies a tightly packed or concentrated distribution of urban areas, while a value closer to 1 indicates urban sprawl in a more scattered fashion. Therefore, increased entropy corresponds to a greater extent of urban sprawl (Al-sharif et al., 2016; Jat et al., 2008a). The critical threshold for relative Shannons entropy is set at 0.5. If the value is below 0.5, it signifies a con-centrated urban area distribution, whereas a value above 0.5 indicates urban sprawl. The overall relative Shannons entropy of Herat City is demonstrated in Table 9.

Fig. 5: Built-Up Area expansion in each direction and directional zone within Herat City; (a) 2000, (b) 2013, and (c) 2021.

According to Table 9, the data reveals that in 2000, the overall relative Shannons entropy value was 0.696. In 2013, it reached 0.795, and in 2021, it reached 0.791. Therefore, the overall relative Shannons entropy value exceeded the threshold of 0.5, indicating the expansion of Herat City in a sprawling manner throughout the study period. Furthermore, the outputs indicate that the highest relative Shannons entropy value occurred in 2013, while the lowest value was recorded in 2000. Table 10, Table 11, and Table 12 display the relative Shannons entropy values for each cardinal direction and zones. Based on the data, in 2000 the highest relative Shannons entropy values are observed in the SW directions (zones 1, 2, and 3), S direction (zones 4 and 5), and W direction (zones 10, 11, 12, and 13), as well as in the respective zones. Conversely, the lowest values are recorded in the SE directions (zones 6, 7, 8, and 9), E direction (zones 14, 15, 16, 17, and 18), and NW direction (zones 19, 20, 21, 22, and 23), along with the corresponding zones. Furthermore, in 2013, the highest relative Shannons entropy values are found in the NE direction (zones 26 and 27), N direction (zones 24 and 25), NW direction (zones 19, 20, 21, 22, and 23), E direction (zones 14, 15, 16, 17, and 18), and W direction (zones 10, 11, 12, and 13) along with their respective zones. The lowest value is measured in the S direction (zones 4 and 5) and their corresponding zones. Moreover, in 2021, the highest relative Shan-nons entropy value is estimated in the NE direction (zones 26 and 27), E direction (zones 14, 15, 16, 17, and 18), NW direction (zones 19, 20, 21, 22, and 23), N direction (zones 24 and 25), and SE directions (zones 6, 7, 8, and 9) and their corresponding zones.  Table 13 demonstrates the rate of change in urban sprawl rate between 2000, 2013, and 2021. Based on the outcomes, between 2000 and 2013 the maximum rate of change in urban sprawl is estimated in E (zones14, 15, 16, 17, and 18), NW (zones 19, 20, 21, 22, and 23), SE (zones 6, 7, 8, and 9), and NE (zones 26 and 27) directions and zones, while the minimum rate of change in urban sprawl is observed in S (zones 4 and 5), SW (zones1, 2, and 3), W (zones 10, 11, 12, and 13), and N (zones 24 and 25) directions and zones. Moreover, between 2013 and 2021, the outputs reveal that the maximum rate of change in urban sprawl is estimated in E (zones 14, 15, 16, 17, and 18), SE (zones 6, 7, 8, and 9), S (zones 4 and 5), and SE (zones 6, 7, 8, and 9) directions and zones respectively, whereas the minimum values are estimated in NW (zones19, 20, 21, 22, and 23), and W (zones 10, 11, 12, and 13), and SW (zones 1, 2, and 3) directions and zones. Furthermore, between 2000 and 2021 the maximum rate of change in urban sprawl is estimated in S (zones 4 and 5), W (zones 10, 11, 12, and 13), and SW (zones 1, 2, and 3) directions and zones, while the minimum values are measured in E (zones 14, 15, 16, 17, and 18), NW (zones 19, 20, 21, 22, and 23), NE (zones 26 and 27), and SW (zones 1, 2, and 3) directions and zones.

Table 14 indicates the statistics of the relative Shannons entropy within each of the five buffer rings with a 3km radius from the Herat Government Office. Based on the outputs in Table 14, in 2000, the maxi-mum relative Shannons entropy values are measured in the 3km, 6km, and 9km buffer rings, respectively, while the minimum values are recorded in the 12km and 15km buffer zones.

Fig. 6: Statistics of Built-Up area expansion and changes in each direction and directional zone; (a), (b), and (c) Built-Up area expansion, and (d), (e), and (f) Built-Up area changes.

Table 9: Overall relative Shannons entropy of Herat city (2000 - 2021).

Table 10: Summary statistics of Shannons Entropy values in 2000 for each direction and directional zone.

Table 11: Summary statistics of Shannons Entropy values in 2013 for each direction and directional zone.

In 2013, the maximum relative Shannons entropy values are estimated in the 6km, 9km, and 15km buf-fer zones, whereas the minimum values are measured in the 3km and 12km buffer rings. Moreover, in 2021, the maximum relative Shannons entropy values are measured in the 15km, 9km, 6km, 12km buffer zones. 

Table 12: Summary statistics of Shannons Entropy values in 2021 for each direction and directional zone.

Table 13: Summary statistics rate of change in urban sprawl in (2000 - 2021) for each direction and directional zone in Herat city.

Table 14: Summary statistics of Shannons Entropy values from 2000 to 2021 within each 3km buffer ring over Herat City.

Fig. 7: Built-up area changes in each buffer ring (1, 2, 3, 4, and 5).

While the minimum value is recorded in the 3km buffer zone. Again, according to the results in Table 14, the most significant increase in the change of urban sprawl rate between 2000 and 2013 is observed in the 15km and 9km buffer zones, with urban sprawl rates of 0.1444 and 0.1, respectively. Conversely, the lowest urban sprawl rate is recorded in the 3km buffer zone, indicating a decrease of -0.118 between 2000 and 2013. Furthermore, between 2013 and 2021, the maximum change in urban sprawl rate is estimated in the 12km and 15km buffer zones, with urban sprawl rates of 0.059 and 0.031, respectively, while the minimum change in urban sprawl rate is recorded in the 3km and 6km buffer zones, with a change in urban sprawl rate of -0.014 and 0.008, respectively.

Furthermore, the overall assessment of the change in urban sprawl rate between 2000 and 2021 indicates that the highest change in urban sprawl rate is estimated in the 15km, 12km, and 9km buffer zones, with change in urban sprawl rates of 0.169, 0.152, and 0.117, respectively, while the minimum change in urban sprawl rate is estimated in the 3km and 6km buffer zones, with a change in urban sprawl rate of -0.112 and 0.038, respectively. Consequently, as stated above internal migration to major cities in Afghanistan was predominantly motivated by conflicts, a lack of employment opportunities, and limited access to essential amenities in rural areas. This migration has played a significant role in the change in urban sprawl rates over the study period in Herat City.

To attain sustainable development and foster a policy of continuous urban growth, uncontrolled urban development stands as a possible risk. The current study aims to evaluate the trends and progression of urban expansion within Herat City. The objective is to provide urban planners with insights to enhance and implement more effective and sustainable urban development strategies. Temporal satellite imagery was employed in urban growth modeling to classify and analyze changes in land use and land cover characteristics over the study period. In this research, three different machine learning algorithms are used to classify the study area: 

Support Vector Machine (SVM), Smile Random Forest (SRF), and Classification and Regression Trees (CART). The accuracy of each algorithm was eva-luated for different study periods. After evaluating their performance, the Random Forest (RF) algorithm was found to have the highest accuracy and was chosen as the classification method. The classification of the study area was carried out using the Google Earth Engine cloud platform, and thematic layers were created within a Geographic Information System (GIS) environment. The study area was divided into eight directional sections, 27 directional zones, and five ring buffer zones with 3km radius from the center of the city. The Urban Expansion Intensity Index was used to measure the urban expansion speed from 2000 to 2021. From 2000 to 2013, Herat City saw an overall high-speed urban expansion; while from 2013 to 2021, the citys urban expansion occurred at a medium speed. This suggests that during this period, there was rapid development, significant population growth, and an increase in infrastructure and construction activities in the city. The Relative Shannons entropy statistical algorithm was used to analyze the pace of transform-ation in urban sprawl, compactness, and the dispersed pattern of the built-up environment in various cardinal directions, directional zones, buffer rings, and across the entire research area. The overall Relative Shan-nons entropy values changed from 0.696 to 0.0.795 and 0.791 from 2000, 2013 and 2021 within Herat City respectively. These values suggest that Herat City experienced a trend of increasingly scattered urban expansion throughout the entire study period. In general, the analysis shows that Herat City experienced a transition from a less dispersed urban sprawl pattern in 2000 to a more dispersed by 2013, and this trend continued to 2021. The practical study of built-up density patterns within urban areas, as outlined in this paper, provides a new perspective on how policy ad-justments can impact spatial arrangements. This analysis has the capacity to assist urban planners and policymakers in assessing the effectiveness of policies aimed at urban consolidation or developing compact cities.

I would like to thank our colleagues for their assistance and guidance in helping us successfully complete this work. 

The authors declare that there is no conflict of interest to publish it.