The study, led by Abhisek Santra of Adamas University together with Shreyashi S. Mitra of Techno India University, Akhilesh Kumar of the University of New South Wales, and Shidharth Routh of Haldia Institute of Technology, set out to answer questions that earlier work on Kolkata had left unresolved: how urban expansion has maintained its dynamics over the last fifty years, and what the micro-level spatial character of future growth will look like. Rather than treating the metropolis as a single undifferentiated unit, the researchers divided the KMA into eight cardinal directions and ten concentric buffer zones at 5-kilometre intervals, producing an unusually fine-grained picture of where fragmentation, consolidation, and sprawl are unfolding. The metropolitan area, which spans roughly 1,887 square kilometres across four districts of West Bengal and houses nearly 14 million people, comprises four municipal corporations—Kolkata, Howrah, Bidhannagar, and Chandannagar—and 37 municipalities.

The analytical backbone of the study is a time series of Landsat imagery stretching from 1975 to 2025. Landsat MSS data provided the earliest baseline, while the team relied on the Thematic Mapper sensors of Landsat 4–5 for the period from 1980 to 2005, Enhanced Thematic Mapper Plus imagery for 2010, and the Operational Land Imager instruments aboard Landsat 8 and 9 for 2015 through 2025. All images were co-registered to the WGS 84-based UTM Zone 45 coordinate system and radiometrically corrected using the ATCOR 2 module, which is based on the MODTRAN 4 radiative transfer code. From these images, the researchers generated land use and land cover maps classifying the landscape into five categories: built-up, vegetation, agriculture, water, and barren land. Classification was performed with a machine learning Support Vector Machine classifier, and accuracy was assessed using 500 systematically random reference points allocated through an area-stratified sampling design. Producer and user accuracies both exceeded 0.9, with kappa values ranging from 0.893 in 1975 to 0.93 in 1995—figures the authors describe as satisfactory for the analyses that followed.

To project the future, the team turned to the Cellular Automata–Markov chain model, a framework that couples the temporal transition probabilities of the Markov process with the spatial neighbourhood rules of cellular automata. Crucially, the model was guided by sixteen driver variables—eleven factors and five constraints—selected for their influence on urban growth. The factors included elevation, slope, groundwater depth, and distances from the central business districts, schools, higher education institutions, hospitals, roads, railway stations, and existing built-up areas, grouped into physical and cultural or infrastructural drivers. The constraints, which restrict expansion, comprised distance from the main river, distance from wetlands, restricted areas, distance from railway lines, and existing water bodies. Each variable was tested for multicollinearity before entering the model; pairwise correlations never exceeded 0.5 and variance inflation factors stayed well below the conventional threshold of 3, ranging from 1.01 to 2.55 for factors and peaking at 1.68 for constraints. Fuzzy standardization and the Analytical Hierarchy Process were then used to weight and integrate the variables into a suitability surface, from which transition potential maps and ultimately predicted land use maps for 2030 through 2070 were produced.

Validation of the model was rigorous. A simulated 2025 map was compared against the classified 2025 map using three complementary diagnostics: the Figure of Merit, which measures the overlap between observed and predicted change; Quantity Disagreement, which captures errors in class proportions; and Allocation Disagreement, which captures errors in spatial placement. The model achieved a Figure of Merit of 81.58%, indicating strong overlap between predicted and actual built-up expansion, a very low Quantity Disagreement of just 0.35%, and an Allocation Disagreement of 7.14%, showing that nearly all residual error stemmed from misplaced pixels rather than wrong class totals. The authors caution, however, that the projections should be read as scenario-based representations of potential futures under current growth tendencies—not as deterministic forecasts, since the model cannot capture policy shifts, economic transitions, or climate-driven migration.

The numbers charting the historical transformation are stark. Urban land in the KMA grew from just over 89 square kilometres in 1975 to approximately 219 square kilometres by 1980—nearly a two-and-a-half-fold increase in five years. The expansion continued steadily: 21% of the total land area by 1990, 25% by 1995, 30% by 2000, 32% by 2005, 35% by 2010, 37% by 2015, 42% by 2020, and 48% by 2025. Projections suggest 54% by 2040, followed by 58%, 62%, and finally 67% by 2070. While agricultural land has remained comparatively resilient—declining from 45% in 1975 to 41.52% by 2020, and projected to fall to 24% by 2070—vegetation has collapsed far more rapidly. Green cover, which accounted for 40 to 45% of the landscape until 1980, dropped to 20% by 2000, 15% by 2010, and just over 10% by 2020, with the model anticipating a mere 4.08% remaining by 2070. Wetlands in the southeast of the metropolitan area, including the East Kolkata Wetlands, a Ramsar-listed conservation site, have been progressively fragmented and converted, a trend the authors single out as particularly alarming.

The spatial metrics analysis reveals a fascinating shift in the morphology of growth. Before 2015, urbanization in the KMA was dominated by fragmentation: new, isolated patches were proliferating across the landscape, pushing the number of patches ever upward. After 2015, the pattern inverted. Patch numbers began to decline while the Largest Patch Index, a measure of the dominance of the biggest contiguous urban patch, rose steadily—evidence that scattered developments are now merging into consolidated urban masses. The CLUMPY index, which ranges from -1 for complete disaggregation to +1 for maximum aggregation, dipped marginally until 2000 and then climbed continuously, while the contagion and cohesion indices traced similar consolidation trajectories. Growth initially followed the Hooghly River, producing an elongated urban spine, and later fanned out northward and along major transport corridors as central areas saturated.

The direction- and distance-wise breakdown adds critical nuance. Urban expansion now reaches up to 50 kilometres from the centre in the north-northeast direction, 45 kilometres in the north-northwest, and 35 kilometres in the south-southeast and west-southwest. The number of urban patches peaks first near the city centre and progressively later at greater buffer distances, indicating that central zones saturate sooner while peripheral zones continue generating new developments. In the north-northeast corridor—home to municipalities such as Barrackpore, Titagarh, Barasat, Madhyamgram, Kalyani, and Naihati—the analysis detected a distinctive two-peak fragmentation pattern, while the southwest fringe around Uluberia and the southeast around Rajpur-Sonarpur and Baruipur show their own fragmented growth signatures. Fragmentation was most intense in the 20 to 30 kilometre buffers, where split values in some directions were nearly 4,000 times greater than in the inner 5-kilometre ring. Shannon’s Entropy, used as an indicator of sprawl with values above 0.5 signalling dispersed growth, remained highest in the north-northeast and north-northwest directions and in the mid-peripheral buffers between 20 and 40 kilometres, confirming that sprawl is now essentially a peripheral phenomenon.

The policy implications are unambiguous. The authors argue that Kolkata’s trajectory illustrates the classic dynamics of unregulated sprawl: cheap fringe land, improved transport links encouraging long-distance commuting, rising living standards, and weak planning controls feeding a self-reinforcing loop of outward expansion. Their recommendations centre on compact development models—so-called new urbanism—in which housing, commerce, and public amenities are concentrated in walkable, human-scaled districts, supplemented by zoning, building permits, urban growth boundaries, tax incentives for cluster housing, and the redirection of public investment away from ecologically sensitive zones. The findings are explicitly tied to United Nations Sustainable Development Goal 11, on sustainable cities and communities, and the authors suggest that coupling the CA-Markov framework with agent-based or system dynamics models could better capture the socio-economic and institutional decision-making processes that ultimately shape urban form. They also acknowledge that future work should pay particular attention to the East Kolkata Wetlands, which merit a dedicated assessment given their ecological status. For planners across rapidly urbanizing Asia and Africa, the study offers both a methodological template and a sobering glimpse of what the coming half-century may hold if compact, sustainable growth fails to replace the sprawling pattern now etched into Kolkata’s landscape.

The eikonal equation, a hallmark of wave propagation theory, typically describes how wavefronts evolve over time and space. Traditionally applied in fields like optics and acoustics, the researchers have ingeniously repurposed this mathematical framework to address the intricate challenges posed by urban boundary changes. Cities are in constant flux, shaped by various factors such as population density, infrastructure development, and geographical constraints. Understanding and modeling these changes is crucial for effective urban planning.

Central to the study is Huygens’ principle, which asserts that every point on a wavefront serves as a source of secondary wavelets. This principle lends itself beautifully to the modeling of urban growth patterns. By adopting Huygens’ principle, the researchers are able to simulate urban boundary evolution as a series of propagating wavefronts. This perspective provides new avenues for exploring the interactions between different urban infrastructures and their environments.

Moreover, the integration of machine learning into this model represents a significant leap forward. Machine learning algorithms, known for their ability to glean patterns from vast datasets, enhance the researchers’ capacity to predict future urban dynamics. By training their model on existing urban data, Kachroo and colleagues can identify correlations between urban expansion and specific socio-economic factors. This symbiotic relationship between mathematical modeling and machine learning allows for a more nuanced understanding of urban evolution.

In practice, the implications of their research extend beyond theoretical exploration. By creating accurate models of urban boundary evolution, city planners can better assess the impact of new developments, changes in policy, or shifts in demographic patterns. This capability empowers stakeholders to make more informed decisions, optimizing resource allocation and enhancing community engagement in the urban planning process.

Furthermore, this research underscores the pressing need for interdisciplinary collaboration. The fusion of physics, urban studies, and machine learning exemplifies how multifaceted challenges in contemporary society require diverse expertise. By breaking down traditional academic silos, researchers can forge new pathways that foster innovation and practical solutions to real-world problems.

As urban areas continue to burgeon globally, understanding the mechanisms driving boundary evolution becomes ever more critical. The methodologies developed in this study may offer valuable insights into managing urban sprawl, addressing sustainability concerns, and mitigating the adverse effects of rapid urbanization. For cities grappling with issues such as traffic congestion, pollution, and inadequate infrastructure, these models could pave the way for more sustainable urban environments.

The researchers also highlight the potential of their findings in the context of climate change. Urban areas are particularly susceptible to the impacts of climate variability, and understanding boundary dynamics can play a pivotal role in developing resilience strategies. By predicting how urban boundaries may shift in response to changing environmental conditions, planners can implement proactive measures to safeguard communities.

In addition, Kachroo and his colleagues’ work offers a glimpse into the future of artificial intelligence in urban planning. The ability to harness machine learning algorithms for predictive modeling represents a colossal shift in how cities could be designed and managed. This transformative approach not only aims to enhance efficiency but also aspires to create more livable spaces that prioritize human well-being.

The implications of this research stretch into multiple domains, including transportation, housing, and public policy. As cities worldwide explore innovative solutions to common challenges, modeling urban boundary evolution becomes an indispensable tool for fostering intelligent urban development. The researchers are optimistic that their findings will inspire further exploration and application of similar methodologies across various contexts.

By positioning their work at the intersection of traditional urban studies and modern computational techniques, Kachroo, Bhatia, and Patil are setting a precedent for future research. The eikonal equation, combined with Huygens’ principle and machine learning, could potentially revolutionize the way we understand urban environments. It challenges existing paradigms and invites a reimagining of how cities can grow in harmony with their inhabitants and the environment.

As the need for more resilient, adaptive urban environments becomes increasingly clear, the contributions of scholars like Kachroo, Bhatia, and Patil cannot be overstated. Their research underscores the power of interdisciplinary approaches in addressing complex challenges. With the continued evolution of urban landscapes, it is crucial for researchers and practitioners to stay ahead of the curve, leveraging innovative models and technologies to create better cities for the future.

In conclusion, the study by Kachroo and his colleagues emphasizes the importance of harnessing mathematical and computational tools to address the pressing challenges of urbanization. With their unique approach, they contribute significantly to the discourse on sustainable development, urban resilience, and smart city innovation. As cities continue to expand and evolve, ongoing research in this area will be critical to fostering environments that are not only functional but also enriching and sustainable for future generations.

Subject of Research: Urban boundary evolution modeling using mathematical and machine learning methods.

Article Title: Eikonal equation for modelling urban boundary evolution using Huygens principle and machine learning.

Article References: Kachroo, P., Bhatia, S.Y. & Patil, G.R. Eikonal equation for modelling urban boundary evolution using Huygens principle and machine learning. Discov Cities 2, 123 (2025). https://doi.org/10.1007/s44327-025-00168-x

Image Credits: AI Generated

DOI: https://doi.org/10.1007/s44327-025-00168-x

Keywords: Urban development, Eikonal equation, Machine learning, Urban planning, Huygens principle, Boundary evolution.

Flooded with data, urban sprawl studies often rely on a mix of traditional methods and innovative techniques. Nagasa’s work ambitiously seeks to bridge this gap by utilizing CA-Markov Modeling, a spatially explicit approach that captures the dynamics of land use changes over time. By examining the historical land use patterns in Naqamte, the model predicts future growth and helps identify areas at risk of unsustainable development. This modeling technique allows researchers and urban planners to visualize potential scenarios and plan interventions accordingly.

Nagasa’s research does not stop at mere predictions. It further incorporates machine learning classifiers, including Decision Trees, Random Forests, and Support Vector Machines. These classifiers enhance the predictive power of the CA-Markov model by processing large datasets and recognizing complex relationships among variables such as socio-economic factors, land topography, and proximity to essential services. The integration of machine learning enables more accurate projections of urban growth and helps guide policy decisions more effectively.

To enrich the predictive model, spatial metrics are employed to quantify urban form and structure. Metrics such as patch density, land use diversity, and fragmentation rate provide insights into the environmental impacts of urban expansion. By applying these metrics to the data processed by the CA-Markov model, Nagasa’s analysis reveals the underlying patterns of sprawl in Naqamte City, allowing for a comprehensive overview of spatial dynamics. Such detailed spatial analysis is critical for identifying areas of concern and prioritizing strategic urban planning efforts.

Incorporating these sophisticated tools and methodologies presents a significant advantage in tackling urban sprawl. Nagasa’s research highlights that traditional methods alone are often inadequate for grasping the complexities of modern urban development. By using a multi-faceted approach, the study emphasizes the importance of robust data analysis frameworks in urban policy formulation. Predictive modeling technologies offer diverse stakeholders insights into land use planning, resource allocation, and environmental conservation objectives.

Additionally, Nagasa emphasizes the need for continuous data monitoring and updating within urban planning. The landscape of urbanization is continually evolving, influenced by political, economic, and social changes. Thus, the development of real-time data integration systems can ensure that city planners remain adaptable and can anticipate future challenges. This proactive approach can mitigate the adverse effects of unregulated urban growth, promoting more sustainable urban environments.

The broader implications of Nagasa’s findings extend beyond Naqamte City. The methodologies developed can be adapted and applied to other rapidly urbanizing regions in Ethiopia and beyond. As cities worldwide grapple with the consequences of urban sprawl, replicating such integrative research can catalyze improved urban governance and sustainable development practices, marking a significant step towards resilient urban ecosystems.

A salient aspect of the study is its commitment to interdisciplinary collaboration. Through partnerships among urban planners, environmental scientists, and data analysts, Nagasa’s approach fosters a comprehensive understanding of urban issues. Engaging various experts not only amplifies the knowledge base but also encourages diverse perspectives in addressing urbanization challenges, intertwining technological advancement with grounded community experiences.

Public engagement also plays a vital role in the research. By including community feedback in planning processes, urban stakeholders can ensure that developments reflect the needs and aspirations of local populations. Nagasa’s research advocates for participatory planning as a critical element in managing urban expansion while preserving the rich cultural heritage and social fabrics of cities like Naqamte.

As populations continue to rise and urban centers grow, the challenge of urban sprawl will only intensify. The methodologies described in Nagasa’s work signify a leap forward in analytical capabilities, equipping urban planners with vital tools to navigate this intricate landscape. The potential for real-time analysis and responsive planning offers a ray of hope for urban sustainability, ensuring that as cities evolve, they do so in harmony with the environment and community well-being.

In summary, Nagasa’s pioneering research effectively merges CA-Markov modeling, advanced machine learning techniques, and spatial analytics to dissect urban sprawl in Naqamte City, Ethiopia. This innovative approach not only enhances our understanding of urban dynamics but also paves the way for more effective and sustainable urban planning strategies. As cities face the challenge of accommodating growing populations, studies like this offer invaluable frameworks for fostering resilient urban futures.

This research underscores the importance of a tailored, multifaceted approach in urban studies, ensuring that predictive techniques can evolve alongside changing urban landscapes. By highlighting the interconnectedness of social, economic, and environmental factors in urban planning, Nagasa’s work sets a precedent for future research initiatives aimed at tackling the global issue of urban sprawl. As our understanding deepens, so too does our ability to forge sustainable pathways forward for cities around the world.

In conclusion, the research by M.D. Nagasa represents a significant step forward in the quest to understand and manage urban sprawl effectively. By integrating advanced modeling techniques with machine learning and spatial metrics, it offers a compelling blueprint for future studies and interventions in urban planning. This approach promises to yield fruitful insights into sustainable urban development, geography, and the overall quality of life within rapidly growing cities.

Subject of Research: Urban sprawl analysis in Naqamte City, Ethiopia.

Article Title: Integrating CA-Markov Modeling, machine learning classifiers, and spatial metrics for urban sprawl analysis in Naqamte City, Ethiopia.

Article References:

Nagasa, M.D. Integrating CA-Markov Modeling, machine learning classifiers, and spatial metrics for urban sprawl analysis in Naqamte City, Ethiopia.
Discov Cities 2, 114 (2025). https://doi.org/10.1007/s44327-025-00147-2

Image Credits: AI Generated

DOI: https://doi.org/10.1007/s44327-025-00147-2

Keywords: Urban sprawl, CA-Markov modeling, machine learning, spatial metrics, sustainable urban planning, Naqamte City.

The study focuses on “gers,” the traditional Mongolian ger dwellings that proliferate on the urban outskirts of Ulaanbaatar, the capital city. Gers symbolize more than housing; they reflect cultural heritage intertwined with the challenges posed by rapid urbanization and climate extremes. Amidst the pandemic, the expansion and improvement of these informal settlements have been notably slowed, a phenomenon meticulously quantified through advanced AI-driven image recognition technologies.

Leveraging satellite imagery and machine learning algorithms, the researchers developed an AI-based ger detection model capable of identifying informal housing clusters with remarkable precision. This technology harnessed multispectral satellite data combined with high-resolution optical images, allowing the differentiation of ger tents from other urban features with unprecedented accuracy. Such technical innovation marks a milestone in remote sensing applications for urban planning and socio-economic research.

The AI system utilized convolutional neural networks (CNN), a class of deep learning architectures particularly adept at image classification and object detection tasks. Through training on vast datasets labeled with ground-truthed locations of gers, the model learned to recognize subtle textural and spectral signatures unique to these informal dwellings. This methodological transparency and rigor in AI training ensured robustness against environmental variabilities like seasonal snow cover and atmospheric interference.

Post-pandemic lockdowns and economic downturns have constrained governmental and non-governmental organizations’ capacity to provide services and infrastructure upgrades in ger areas. The study’s longitudinal analysis covering pre-pandemic to current conditions reveals striking deceleration in housing upgrades and new construction within these communities. These delays compound longstanding issues such as inadequate sanitation, energy scarcity, and vulnerability to harsh winters that disproportionately affect residents.

From an urban sustainability perspective, Mongolia’s situation is a poignant case study of resilience and fragility co-existing. The ger districts, housing nearly 60% of Ulaanbaatar’s population, existed in a state of dynamic flux even before the pandemic. The AI-driven insights illuminate the pandemic’s disruptive role as a stressor exacerbating existing inequalities, impeding urban integration efforts, and threatening public health improvements.

Importantly, the research transcends conventional census and survey methodologies that often miss transient and informal settlements. The scalability and temporal frequency of satellite data allow near-real-time monitoring, empowering policymakers with actionable intelligence. This capability could transform urban governance by enabling targeted interventions and resource allocation even under crisis scenarios.

Furthermore, the technical sophistication of the study showcases interdisciplinary collaboration, melding computer science, urban studies, and social geography. It underscores a paradigm shift where AI tools not only analyze big data but also interpret socio-cultural phenomena grounded in place-based realities. Such integrative approaches are critical for addressing complex urban sustainability challenges in the Anthropocene.

While this AI application is technical, it carries profound humanitarian implications. The capacity to rapidly track informal housing dynamics can support emergency response, inform housing policies tailored to vulnerable populations, and promote inclusive urban development. In Mongolia’s ger districts, this means mitigating health risks amplified by overcrowded living and low access to public services, thereby fostering equitable growth.

Moreover, the study sets a precedent for similar analyses in other global cities grappling with informal settlements, from Asia to Latin America and Africa. The AI model’s adaptability to diverse environmental and urban contexts promises to democratize spatial intelligence, enabling more inclusive and informed urban planning worldwide.

Technological advancement in remote sensing combined with AI also opens pathways for longitudinal studies monitoring environmental impacts, such as urban heat island effects or pollution exposure in ger areas. Such data are vital for designing climate-resilient infrastructure and social programs, especially under rising global temperatures and more frequent extreme weather events.

The pandemic-induced delay documented in Mongolia’s informal housing progress serves as a cautionary tale about the vulnerability of marginalized urban communities to global crises. It reinforces the urgency for resilient, flexible urban systems buttressed by technological innovation and inclusive governance frameworks.

In conclusion, this pioneering research contribution pushes the frontier of urban sustainability studies by applying state-of-the-art AI technology to real-world social challenges. It offers a powerful lens into Mongolia’s ger settlements while setting a roadmap for harnessing AI in transformative urban policy and development. As the world recovers and rebuilds from the pandemic, tools like these are indispensable for creating cities that are not only smarter but fairer and more humane.

Subject of Research: The study investigates the impact of the COVID-19 pandemic on informal housing progress, specifically focusing on ger settlements in Mongolia using AI-based detection methods.

Article Title: AI-based Ger detection reveals post-pandemic delay in informal housing progress in Mongolia.

Article References:
Yang, J., Lee, S., Park, S. et al. AI-based Ger detection reveals post-pandemic delay in informal housing progress in Mongolia. npj Urban Sustain 5, 78 (2025). https://doi.org/10.1038/s42949-025-00273-1

Image Credits: AI Generated