Predicting and Analyzing Urban Growth in a Developing Capital, Trends, Drivers, and Future Directions : Case of Antananarivo Agglomeration, Madagascar (1995~2045)

2.1. Related Previous Research

Previous studies has demonstrated the effectiveness of remote sensing in detecting urban sprawl and analyzing land-use transformations across various geographic contexts. For instance, [7] employed Landsat imagery and change detection techniques to examine urban sprawl in Tshwane, South Africa, revealing a 109% increase in built-up areas over three decades. [13] used GIS and Shannon entropy to investigate the rapid urbanization of Kabul, highlighting a significant reduction in vegetation cover resulting from urban expansion. In African cities such as Bamako, Nairobi, and Cairo, [14] draw attention to the role of remote sensing in tracking green space loss associated with urbanization.

Over the years, various analytical tools and indices have been developed to enhance the understanding of urban sprawl’s characteristics and magnitude [15]. Two commonly used indices for evaluating urban sprawl include the Urban Expansion Intensity Index (UEII) and Shannon’s Entropy Model (SEM). The UEII measures the proportion of recently developed urban land proportionate to the total area, allowing to understand the speed and potential of urban sprawl, while SEM assesses the degree of sprawl by analyzing how urbanized areas are distributed and concentrated spatially, making it a worthwile tool for detecting patterns of urban spread [15~17]. [18] employed Shannon’s entropy alongside GIS to analyze urban sprawl in the Pearl River Delta, effectively capturing dispersed growth patterns. More recently, [19] utilized this approach to assess urban expansion in Semarang, Indonesia, emphasizing the influence of diverse land use on spatial growth. Furthermore, [20] combined Shannon’s entropy with UEII to study urban growth in Jalpaiguri, India, revealing significant shifts in spatial development over time. These studies reinforce the utility of entropy-based indices as reliable tools for quantifying and understanding the complexities of urban sprawl.

In addition to these indices, modeling techniques have proven essential for predicting future urban expansion. The Markov Cellular Automata (CA) approach is frequently utilized to simulate potential future land cover changes. Advancements in predictive modeling, particularly using tools such as the MOLUSCE plugin and Cellular Automata-Artificial Neural Network (CA-ANN), have significantly enhanced researchers’ ability to forecast urban sprawl. For example, [21] used the CA-ANN modeling within QGIS to predict urban expansion, finding continuous increases in impervious surfaces alongside declining green areas projected through 2050. In a similar effort, [22] applied machine learning models, including CA-ANN, to anticipate urban growth in Nasiriyah, Iraq, revealing considerable unplanned expansion by 2052. Additionally, [23] used CA-Markov and ANN models in India to forecast substantial urban growth and associated agricultural land loss by mid-century. Various techniques have been employed to estimate LULC, and one noteworthy approach is MOLUSCE (Modules for Land Use Change Evaluation), a QGIS plugin that combines Markov chain analysis and cellular automata (CA), to analyze land use dynamics. Its applications are diverse, including assessing temporal LULC changes, predicting future land use scenarios, modeling transitions in land and forest cover, and identifying areas at risk of deforestation [23]. These tools and methodologies will significantly enhance our knowledge of urban sprawl and will support urban planning strategies.

As urban sprawl emerges as a global issue, particularly in terms of its sustainability impacts, its underlying causes have also drawn significant attention from researchers. After analyzing urban sprawl in Ajmer city, India, [24] tried to determine the correlation between urban sprawl and its influencing factors. Their findings highlighted that population growth and density play a major role in driving sprawl. They predicted that, under existing trends, the urban sprawl rate could be twice as much the pace of population growth by the year 2051. Similarly, [25], through a global analysis of urban growth patterns, affirmed that sprawl tends to occur when land is developed at a speed greater than the rate at which the population expands. Another research by [26] on urban sprawl in Chile argued that while urban sprawl is often linked to inadequate planning and liberal real estate policies, the government itself has played a role in its expansion. By passing legislation that encourages land market freedom, especially in areas beyond formal urban boundaries, the state has indirectly supported the continued spread of urban sprawl. The causes of urban sprawl tend to change according to local context. For instance, in the United States, suburban growth supported by automobile usage is identified as a major contributor to sprawl [26] while in developing countries urban sprawl are more linked to congested urban centers and insufficient urban planning. Still, a literature review conducted by [27] on the driving forces behind urban sprawl found that two key factors are most frequently cited: firstly, the influence of spatial or land use policies, and secondly, population growth.

In Antananarivo, Madagascar, remote sensing has emerged as a valuable tool for analyzing land use land cover changes and addressing associated challenges. [11] employed spatiotemporal analysis using GIS to investigate the relationship between urban growth and flood risks, revealing that by 2017, nearly a quarter of the city’s buildings were situated in flood-prone areas. Similarly, [28] utilized remote sensing to explore urban agriculture, emphasizing its role in enhancing food security and reducing flood risks. Complementing these findings, [29] conducted a multi-temporal analysis to identify high-risk zones for landslides within the city. Despite the ongoing pressures of urban expansion, [30] underscored the persistence and importance of urban agriculture in the region. Collectively, these studies highlight the diverse applications of remote sensing in addressing Antananarivo’s urban development challenges.

2.2. Research Question and Hypothesis

Previous research demonstrated the effectiveness of remote sensing and statistical model analysis like Shannon’s entropy and UEII to monitor and evaluate urban sprawl. Predictive modeling like MOLUSCE has also proved its effectiveness in forecasting future urban growth.While several studies have applied remote sensing to various aspects of urban development in Madagascar’s capital, a comprehensive analysis focusing specifically on urban growth patterns and its possible causative factors remains unexplored. Given the critical need for effective urban planning, understanding the spatial and temporal growth patterns of Antananarivo is essential for informing decision-making processes. Despite being the most densely populated city in the country, a systematic assessment of current and future urban sprawl trends within the agglomeration has yet to be conducted. To address this gap in literature, our study aims to answer the following research questions:

1-How has urban expansion and urban sprawl evolved in Antananarivo in the last 20 years (from 1995 to 2024)?

2-What are the potential future growth patterns of the city in the next 20 years (2025 to 2045) if the current state of growth continues?

3-What area the possible urban sprawl inhibitors relevant to the case of the Agglomeration of Antananarivo based on previous research?

While our research questions 1 and 3 are addressed through hypothesis-driven analysis, question 2 is exploratory and aims to project potential future growth trends using geospatial modeling techniques. As such, it is not accompanied by a formal hypothesis. Our hypothesis on Question 1 and 2 are then as follows:

1-H1: Based on previous studies conducted in Sub-Saharan African Countries like Tswane in South Africa (3.52%), Bamako (5.57%), Nairobi (4.99%) and Cairo (2.79%), this study hypothesizes that Antananarivo also has experienced a comparable rapid increase of built up area per years of more than 3% as observed through the remote sensing data result.

1-H2: In line with the findings of [20] on urban expansion in medium-and small-sized cities, which showed that a rapid increase in built-up areas was accompanied by a compact inner center and more sprawled dispersed development on the outskirts, it is expected that Antananarivo has followed a similar pattern—characterized by compact infill growth in the city center and sprawling on the periphery, as demonstrated by the Urban Expansion Intensity Index (UEII) and Shannon’s Entropy values.

3-H1: A study analyzing urban sprawl in Ajmer city, India by [24] highlighted that population increase and density are significant factors contributing to the expansion of urban sprawl. [25], through a global examination of urban development trends, affirmed that sprawl tends to occur when land is developed at a speed greater than the rate at which the population expands. In Antananarivo Madagascar, the drivers of urban sprawl are expected to be directly related to population growth, similarly due to urbanization rate surpassing the population growth rate.

3-H2: A research by [26], on urban sprawl in Chile argued that the government played a role in urban sprawl by passing legislation that encourages land market freedom. Our hypothesis is that similarly, in Antananarivo, land use regulations passed by the Government contributed significantly to urban sprawl in the Agglomeration of Antananarivo.

3.1. Study Area

The Municipality of Antananarivo, located in Analamanga Region, capital of Madagascar, is the fastest developing area of the country. Antananarivo agglomeration or Greater Antananarivo (Grand Tàna) is composed of 38 municipalities including the Urban Municipality of Antananarivo (Commune Urbaine d’Antananarivo) in the center, part of the district Antananarivo Avaradrano in the North and Southeast, Antananarivo Atsimondrano in the West and Southwest, and Ambohidratrimo in the North part (Fig. 1.). According to [31], in 2024 the city’s population was counted at 4,048,670 in 2024 with a growth rate of 4,5 %, the city is one of those that notice the fastest urbanization growth.

Fig. 1.

Study area map

3.2. Data Acquisition and Pre-Processing

To assess the extent of urban expansion in the study region, four satellite images were obtained from the United States Geological Survey (USGS) platform, covering path 159 and row 73. Only images with cloud cover below 5% were chosen to improve the precision of classification and reduce the likelihood of analytical errors. Two image correction were processed, Radiometric calibration and Quick Atmospheric Correction (QUAC). As the original satellite images covered a wider region than the specific area of interest, they were cropped to isolate only the intended study zone. This pre-processing step was conducted using ENVI 64-bit software, ensuring that only relevant portions of the images were included in the analysis. These processed and refined images were subsequently used to analyze shifts in Land Use and Land Cover (LULC) and to examine trends in urban sprawl across the selected time frames.

3.3. Image Classification and Accuracy Assessment

Prior to classification, all images were georeferenced to the WGS 84 UTM Zone 38S coordinate system. Once corrected, the images were classified into five land cover categories: built-up areas, plains, vegetation, bare land (including dry agricultural areas), and water bodies. This classification process was carried out using the support vector machine (SVM) supervised classification technique within the ENVI 5.3 software. An accuracy assessment was conducted as part of the study to evaluate the reliability of the classified maps and to determine the performance of the classification algorithm. According to [32], the values of Kappa that are defined between 0.81~1.0 is a nearly perfect connection. This study utilized the Kappa coefficient to measure the accuracy of the land use and land cover (LULC) classifications. The assessment was based on more than 400 reference points identified across the classified maps. The kappa values are 0.83, 0.81, 0.85, 0.89 for the years 1995, 2005, 2015 and 2024, respectively, which are measurably nearly perfect agreement indication of classification accuracy.

3.4. MOLUSCE

As more people around the world migrate to urban areas, managing this growth while ensuring both social stability and environmental balance remains a key area of research. To address this challenge, researchers have developed models to predict land use and land cover (LULC) changes over time. One approach involves using the MOLUSCE (Modules for Land-Use Change Simulation) plugin in QGIS, a tool that enables to model spatial transitions and predict future urban expansion scenarios [21]. The MOLUSCE plugin,developed by Asia Air Survey for QGIS version 2.0 and onward, is an open-source tool for analyzing and simulating land use and land cover (LULC) changes. It combines multiple modeling approaches, including artificial neural networks (ANNs), multi-criteria evaluation (MCE), weights of evidence (WoE), logistic regression (LR), and Monte Carlo-based cellular automata (CA). The CA-ANN model in the MOLUSCE plugin for QGIS 2.xx has been a trusted and reliable tool among researchers for predicting future LULC, making it highly useful for land use planning and management [33~36]. Originally developed for QGIS 2.xx, the MOLUSCE plugin became incompatible with QGIS 3.xx after it transitioned to Python 3 in 2018. As a result, researchers relied on QGIS 2.14 to access its features until the software developers updated the plugin. Compatibility was restored with the release of MOLUSCE 4.0.0 in August 2024, so this research utilizes the updated version of MOLUSCE 4.0.0 in QGIS 3.40.

3.5. Urban Expansion Intensity Index (UEII)

By highlighting areas of concentrated urban development and offering insights into likely directions and intensity of future growth, the Urban Expansion Intensity Index (UEII) delivers a quantitative measure of spatial urban growth, showing the proportion of urban area increase within spatial unit i relative to the total area of that unit [15,37]. UEII is calculated using the following equation (1):

where UEII_i stand for UEII of spatial unit i and $$ UL{A}_i^{t^2}$$ and $$ UL{A}_i^{t^1}$$are the urbanized area at times t2 and t1, respectively. TLA_i is the total area of the spatial unit i, and Δt is the duration of the study period. For reference UEII value ranging from 0–0.28 is slow development, 0.28-0.59 low-speed development, 0.59-1.05 medium-speed development, 1.05-1.92 high-speed development, and ≥1.92 very high-speed development [38].

3.6. Shannon’s Entropy

In the context of urban studies, Shannon’s entropy model has become a widely applied technique for assessing the degree of urban sprawl and understanding patterns of spatial diffusion or compactness within urban areas. By utilizing Remote Sensing (RS) and Geographic Information Systems (GIS), researchers can effectively measure the distribution of urban growth across a region and evaluate whether the expansion is occurring in a more dispersed or compact manner [20,39]. The model’s structure can be calculated by applying equation (2) below:

where, Hn is Shannon’s entropy calculated for each study period, P_i is the proportion of variable in the i-th zone relative to the entire area. m is the total number of zones. Values approaching 0 suggest compact urban development, whereas values nearing log m indicate more dispersed growth, characteristic of urban sprawl.

4.1. Spatiotemporal Analysis

As the dominant land use within the municipality of Antananarivo, built-up areas have expanded rapidly over the past few decades, particularly within the central district of Antananarivo Renivohitra (AR). Monitoring built-up patterns plays a critical role in identifying urban sprawl, which is the focus of this study for the years 1995, 2005, 2015, and 2024 (Fig. 2.). In the first year, the built-up area covered approximately 82.44km² of the study area across all districts and has steadily increased over the years (Table 1.). In Antananarivo Renivohitra (AR), urbanized areas went from 28% in 1995 to more than 56% of the total area within two decades. Meanwhile, surrounding areas like AAT that were once predominantly rural, with urbanization rates below 10%, have been gradually transitioning toward more urbanized landscapes. Table 1 presents data demonstrating consistent and gradual growth of built-up areas throughout the study period. As the center municipality became very saturated, urban sprawl intensified in surrounding cities especially since 2005, as we can see based on these built-up maps (Fig. 2.).

Fig. 2.

Land Use Land Cover Map (LULC) 1995~2024

Table 1.

Urbanized area extracted from LULC map

4.2. Urban Growth Forecasting with MOLUSCE

In predicting future changes using MOLUSCE, researchers prioritize physical and socioeconomic factors when selecting variables, as these have been shown to have a more significant influence on the dynamics of land use and land cover (LULC) changes [21]. For this study, to predict LULC for 2025, 2035, and 2045, we used the MOLUSCE CA-ANN method with remotely sensed data from 1995 to 2024 at 10 years intervals, incorporating spatial factors as digital elevation models (DEM), slope, aspect, proximity to rivers and roads, and population density. Initially, we utilized LULC data from 1995 to 2005, combined with spatial variables, to simulate the LULC distribution for the year 2015. The transition potential model generated a validation Kappa coefficient of 0.62. Following the projection, the simulated 2015 map was compared with the observed LULC map for the same year and obtained a percentage of correctness of 74.73% and an overall kappa value of 0.60 (Fig. 3.). In prediction modeling, a Kappa value exceeding 0.5 can be considered satisfactory [40]. Recent research on prediction modeling using MOLUSCE considered an overall kappa value greater than 0.60 as satisfactory [21,23,41]. Following successful model validation, we projected land use and land cover (LULC) for the years 2025, 2035, and 2045. This prediction used temporal LULC data from 1995 and 2005, along with spatial variables such as DEM, slope, aspect, distances to rivers and roads, population density, and the transition probability matrix. Fig. 4. shows the projected map for 2025, 2035 and 2045.

Fig. 3.

Actual vs predicted LULC map (2015)

Fig. 4.

Predicted LULC map (2025, 2035, 2045)

4.3. Urban Expansion Intensity Index (UEII)

The analysis of the Urban Expansion Intensity Index (UEII) reveals significant trends in urban sprawl in each different district across different timelines. Initially, the AR district was rapidly expanding from 1995~2005 but then saw a significant decline in urban expansion in the following years. Predicted future values suggest continued decline, approaching very slow development. As for AAV district, it started with moderate medium-speed expansion, with a dip in 2005~2015 but a slight increase again in 2015~2025. Future projections indicate fluctuations but an overall slow-to-moderate expansion rate. AAT was Initially a slow-developing area, but as the city center began to get saturated, the area gradually noticed an increase in 2015 which suggests an urban expansion phase and slow sprawling. As for AMB, the area had relatively steady UEII values in the early periods. A slight negative value in predicted growth from 2015 to 2025 suggests a possible contraction in urban growth. However, the projections for 2025-2045 show a strong increase in UEII, indicating future rapid expansion. Overall, the observed data from 1995 to 2024 indicates that urban expansion in the Great Antananarivo has slowed down over time in the city center while neighboring district notice increasing expansion (Fig. 5.). The predicted 2025~2045 UEII trends suggest a continuation of the slowdown in the city center with lower expansion while in the other district, expansion will continue to increase until 2035 and begin to stabilize onward (Fig. 5.).

Fig. 5.

Comparison of UEII value from real (1995~2024) vs predicted (2025~2045) map

4.4. Shannon’s Entropy

Shannon’s Entropy was utilized to quantify urban sprawl both over time and across different zones within the agglomeration. Urban areas extracted from land use maps were analyzed temporally and divided into eight directional zones for zone-specific evaluation: North-Northeast (NNE), North-Northwest (NNW), East-Northeast (ENE), East-Southeast (ESE), South-Southeast (SSE), South-Southwest (SSW), West-Southwest (WSW), and West-Northwest (WNW). Two types of Entropy calculations were done, General Entropy for the whole study area and Entropy per direction. Urban growth doesn’t usually happen evenly in all directions. Some parts of a city tend to grow faster or more chaotically than others. By dividing the city into directional zones, we could better observe where land use is changing the most and where development is more disorganized. This approach helps highlight specific areas, or “hotspots,” where urban sprawl is more intense or unpredictable. Analyzing entropy in this way makes it easier to spot trends, anticipate where future expansion might occur, and identify zones that may require more focused planning or regulation. As a result, urban forecasting and planning efforts can be more precise and effective. For reference, entropy values near 0 indicate compact urban development, whereas values approaching log (n) signify urban sprawl. A value at half of log (n) is used as the threshold between these two growth patterns. Results of the Entropy value calculations revealed that, first for the study area in general, urban sprawl in the study area has been steadily increasing over time, as reflected in the rising entropy values from 1995 to 2024 (Fig. 6.). The sharpest rise was noticed during 1995 and 2005 period. After 2005, the growth rate of entropy slowed down, but sprawl continued, suggesting that urban development is spreading more randomly than being compact. The entropy obtained from projected data from 2025 onwards indicates a slowdown in sprawl growth (Fig. 6.). If we look at sprawl across directions, certain areas experience more rapid expansion than others. The ENE, ESE, and WSW directions exhibit the highest entropy values, indicating that urban expansion is most prominent in these directions (Fig. 7.). Those areas experience more dispersed development compared to other directions. If we compare Entropy from the existent data (1995~2024) and the predicted data (2025~2045), the entropy from existent data consistently shows increasing entropy, reflecting the continuous and unchecked urban sprawl caused by rapid urbanization. However, the predicted data (2025~2045) suggests a slowdown in entropy growth, and in some cases, even a decline in entropy values (Fig. 7.). This could indicate a natural limitation to sprawl, as urban areas become congested or land becomes less available for expansion. Additionally, some areas that have already seen high entropy values (such as WSW and ESE) may continue sprawling even in the predicted period.

Fig. 6.

General entropy value from real (1995~2024) and predicted (2025~2045) map data

Fig. 7.

Directional entropy value from 1995 to 2045

4.5. Urban Sprawl Drivers

A review of literature on urban sprawl drivers identifies land use policies and population growth as the most influencing factors [27]. Researches conducted in Antananarivo, Madagascar echoed that result, urban sprawl has also been attributed to same drivers. From 1993 to 2018, Antananarivo’s annual population growth was approximately 3.8%, with the metropolitan area reaching nearly 3 million residents in 2018 [11]. This growth was driven by both natural increase and rural-to-urban migration, particularly among individuals seeking improved economic opportunities, education, and services. Due to limited availability and high costs of land within the urban core, many migrants have settled in peripheral zones, where land is more affordable and less regulated. These peri-urban areas have experienced growth rates exceeding 5% annually, far outpacing those of the central urban commune [11]. Since 2018, the annual growth rate of population has been decreasing although it still stays above 3% yearly and the population in the agglomeration is now a bit more than 4 million [31]. However, this rapid demographic expansion has not been matched by infrastructural development. The resulting housing shortages and insufficient urban planning have contributed to the proliferation of informal settlements, especially in flood-prone lowlands where land remains inexpensive and unregulated. From 1968 to 2004, the city lacked an updated urban master plan, which led to a near-total absence of formal land use regulation [11]. Although a new plan was adopted in 2004, its implementation has been partial and inconsistently enforced. As a result, land conversion and illegal settlements have proliferated. Moreover, land speculation and real estate development have intensified pressure on peri-urban and agricultural areas. Developers have increasingly targeted lowland flood zones, traditionally used for rice cultivation and urban agriculture, for residential and commercial development [11]. These agricultural lands are often viewed as land reserves rather than spaces for food production, further accelerating their conversion into urban land uses [42].

To evaluate if population growth could be counted as sprawl drivers, we did a comparison between population growth and urban growth. Urban Growth was calculated based on the data from the LULC while population growth was calculated following the equation (3):

Where P₁ is the population at a time t1 and P₀ the population at a time t0 while n is the period interval between t0 and t1, here 9 intervals between 10 years period. Comparison between urban growth rate (Built-up area growth) and population growth rate in our study area shows that urban development did not keep pace with the population increase for the past 20 years especially since 2005. In the second period 2005 to 2015, population growth rate surpassed the 5% while urban growth rate was only about 1.84%. And finally, for the past 10 years (2015 to 2024), we can notice a bit of a balance between population growth which was 3.16% and urban growth of 2.78% yearly (Fig. 8.). The imbalance between rapid population growth and slower urbanization is a key condition for urban sprawl. When formal urban planning and infrastructure cannot accommodate growing populations, new residents often settle in informal or peripheral areas where regulation and services are limited. What makes this observation particularly noteworthy is that in contrast with findings from [25], who reported that urban sprawl typically happens when land development outpaces population growth.. Our case suggests a different dynamic starting from the year 2005, especially in developing countries, where land development struggles to keep up with fast-rising populations. This perspective adds nuance to how we understand the causes of urban sprawl in contexts with limited planning capacity and resource constraints.

Fig. 8.

Average yearly growth rate in the study area, comparison between population and urban growth

4.6. Hypothesis Validation

Our first and second hypothesis aimed to answer the question of how urban expansion and urban sprawl have evolved in Antananarivo over the last 20 years (from 1995 to 2024). The first hypothesis was that similar to other Sub-Saharian African countries, urban expansion in Antananarivo has occurred at a fast rate, with annual growth exceeding 3%. Based on the analysis results, this hypothesis was confirmed, as the average urban growth rate in Antananarivo from 1995 to 2024 was calculated at 3.17% per year. The second hypothesis was that in line with past findings on urban growth in medium-and small-sized cities, a rapid increase in built-up area would be accompanied by compact development in the city center and more dispersed, sprawling growth in the outskirts. The hypothesis was also confirmed the UEII and Shannon’s Entropy values trend in Antananarivo shows a saturation of the city center AR and dispersed urban growth toward the neighboring districts.

As for our second and third hypotheses, they aimed to address the third research question regarding the possible cause of urban sprawl relevant to the case of the Agglomeration of Antananarivo, based on previous research. The third hypothesis was based on a study analyzing urban growth pattern by [25] affirming that urban sprawl tends to occur when land development outpaces population growth. However, in Antananarivo Madagascar, the hypothesis was proven to be false. In our case the results showed that from 1995 to 2024, the average annual urbanization rate was 3.17%, while the population growth rate was 3.97%, meaning that urban expansion did not exceed population growth. Lastly, the final hypothesis proposed that government land use policies have been a key factor affecting uncontrolled development in the Antananarivo agglomeration. This hypothesis is partially verified because from 1968 to 2004, the absence of formal land use regulation may have caused the proliferation of uncontrolled urban growth of the city [11]. However from 2004, even if a new urban plan was adopted, the detail, implementation and enforcement remain inconsistent limiting its effectiveness in managing urban growth.

Table 2.

Hypothesis validation