Assessing urban development trajectories using landscape expansion metrics and multivariate statistical approaches: evidences from rohtak city, NCR, India

1 Introduction

Urban growth is one of the most radical anthropogenic processes of the twenty-first century, which radically changes ecological systems, socioeconomic systems, and aspects of human wellbeing at unprecedented levels. At the global level, the amount of land covered with urban development is expected to triple over the next 50 years, with a rate that is more than 50 percent higher than the rate of population growth (Seto et al., 2012), a trend that has serious consequences on the loss of biodiversity, carbon emissions, and resource security. Indeed, 90 percent of future urbanization will occur in developing regions (United Nations Human Settlement Programme UN-Habitat, 2022), where the typical trend is usually low-density sprawling development that takes over agricultural and ecological land and exacerbates infrastructure gaps and climate vulnerabilities. The spatial and temporal dynamics of such development are poorly measured, especially in secondary cities that have undergone a rapid shift in administration. A vivid example is the Rohtak city in India, which increased by approximately four times, i.e., the area has grown to 6,686.36 ha in 2021 compared to 1,640.79 ha in 1991 (Sharma and Kumar, 2022).

The current urbanisation being witnessed in the national context has a very strong representation in Rohtak, a significant metropolitan city in Haryana. The city is located just 70 km away from the national capital Delhi, which has made its geographical location strategically important and a major center in the local governance. Rohtak was initially granted a municipal status in 1867 and since then it has grown in terms of its strategic location and the economic significance that the state government has given it. A major constitutional change in 2010 extended the municipal sphere by 240 percent, which demonstrates the substantial contribution of the deliberate governmental action to the land-use transformation that otherwise would not have been triggered by demographic or economic processes (Department of Urban Local Bodies and Haryana, 2025). Earlier research using remote sensing and geographical information systems has recorded the urban development pathway of Rohtak by plotting the development of built-up areas, the absorption of rural settlements, and the calibration of built-form to the prevailing transport routes. The case of Rohtak changing its status as a Municipal committee to a Municipal Corporation was specifically analysed by Singh and Kumar (2012) and they noted that this transformation has been supported by outward extension of ring-roads, concentrated growth along national highways and development of new residential and industrial areas. These previous findings are further supported by the latest geospatial study of Rohtak (Sharma and Kumar, 2022) that demonstrates that the development of the city has taken place mainly along arterial and ring roads, with the main focus on Delhi, resulting in sprawling suburbanisation instead of densification. The factors that have contributed to this development as noted by this study are the expansion of municipal borders, the annexation of neighboring villages, intense real-estate marketing operations, and the development of new transport infrastructure that strengthens the ties with the national capital. Taken together, these contributions outline Rohtak as a case of interest in examining the interaction between governance systems and territorial choices and demographic, economic and environmental parameters that influence metropolitan form.

Although spatial analysis has been developing recently, there is a significant gap in the accurate use of landscape expansion indices, which include Landscape Expansion Index (LEI), to measure and classify the urban expansion of Rohtak. Most of the existing literature employs simple area statistics or general land-use change analysis, thus, generating a narrow conceptualisation of the modes, patterns, and drivers that define urban landscape transformation like Singh and Kumar (2012) and Punia et al. (2017). To fill this gap, advanced landscape metrics are needed to shed light on not only scale but also typology and spatial organisation of the urbanisation in Rohtak. The implementation of the Landscape Expansion Index (LEI), which allow a more detailed understanding of the development of urban growth patterns in a series of years by quantifying and classifying them, is more explanatory than the classic metrics used at a single point in time (Tian et al., 2022). Moreover, the hierarchical patch dynamics frameworks integration allows studying growth on various levels, which allows discovering micro (patch-level) and macro (city-level) growth patterns. Lastly, it is suggested to use new metrics that can be used to analyse both expansion and redevelopment paths at the same time and reflect the complexity of the urban landscape change, as well as provide detailed information that is impossible to achieve with the traditional methods (Xia et al., 2020).

The study adds a unique analytic perspective to the study of urban growth, which is unique in the existing literature because it takes into account not only the distance but also the direction. The investigative tool is a refined Landscape Expansion Index (LEI), which allows a subtle mapping of the stages of urban development and the forces driving changes with the trajectories of such indices during the period 2000–2020. The combination of spatial measures with direction-sensitive analysis methodologically provides a full understanding of the dynamics of urban growth, which is still poorly studied in the literature. The main objectives of the research are to define the spatio-temporal dynamics of urban growth in the study area in the period between 2000 and 2020 using the Landscape Expansion Index (LEI), and to determine the typology, distance to the central city, and directional trends of growth in this period and investigate the stages and trajectories of such urban development in NCR region, India.

Despite this progress, three gaps remain unresolved. First, existing assessments of Rohtak and comparable Indian secondary cities rely largely on aggregate area statistics or single-date land-use change and therefore cannot separate the mode of expansion (infilling, edge-expansion or leapfrog) from its mere magnitude. Second, the joint dependence of the expansion mode on both distance from the core and cardinal direction has rarely been quantified within a single, internally consistent framework. Third, the temporal ordering of expansion, whether a city moves from fragmentation toward coalescence, has seldom been characterised with an explicit and reproducible trajectory metric. The scientific contribution of this study is therefore methodological as well as empirical: it integrates a Landscape Expansion Index (LEI) classification with a distance–direction stratification and a Principal Component Analysis (PCA)-based trajectory metric to produce a spatially differentiated and reproducible account of how, and not only how much, a rapidly urbanising secondary city grows. This integrated distance–direction–trajectory framework is transferable to other rapidly urbanising regions and constitutes the principal advance offered here over prior local applications of established methods.

2 Materials and methods

Rohtak is a city in the Indian state of Haryana, which is located in the National Capital Region (NCR) with approximate coordinates of 28°54′N and 76°34′E (Figure 1). It is located about 70 km northwest of Delhi and its strategic geographic location has made it a major regional hub, with the advantage of having close proximity to the national capital, and also major transportation corridors. The city is located on an area of about 115 km² and is surrounded by agricultural fields and peri-urban settlements which have continuously been integrated into an ever-growing urban fabric in the last 20 years. Rohtak is topographically located on the Indo-Gangetic alluvial plains, which are flat with smooth slopes, which is very favorable in terms of construction and urbanization. The urban core has little vegetation and is mainly ornamental trees and green belts, and the urban fringe still has some cropland and grassland. The rapid changes in land use have been made possible by infrastructure developments, especially the Delhi Rohtak rail and highway links, producing marked urban sprawl, infill and conversion of agricultural land to residential, commercial and institutional purposes. Its spatial growth has also been boosted by historic policy measures such as the incorporation of Rohtak into the NCR Planning Board structure and the development of local master plans. The current paper explores Rohtak between 2000 and 2020 to study the trends of urban growth because the city represents the case of a mid-sized Indian city that has been transformed due to regional integration, infrastructural investment, and demographic change. Its strong spatial development, the presence of multi-temporal data, and characteristic urbanization processes make it a perfect example to study the causes and trends of urban sprawl.

The research used multi-temporal satellite images obtained through the United States Geological Survey (USGS) Earth Explorer portal in 2000, 2005, 2010, 2015 and 2020 of the month of October-November for least cloud cover at the ground. The imagery was Landsat 5 TM and Landsat 8 OLI/TIRS collection 2, level2 dataset for the surface reflectance, these are atmospherically calibrated by the atmospheric model and ready to application (U.S. Geological Survey, 2023).

2.1 Land use and land cover classification and identification of urban expansion

The study area Land Use/Land Cover (LULC) classification was performed with a supervised classification workflow within QGIS. All available Landsat 5 Thematic Mapper (TM) scenes during the post-monsoon period were used in the analysis, thus reducing the possible atmospheric and phenological variation (Rahman et al., 2025). Before classification, a pre-processing chain of atmospheric correction and layer stacking was used to ensure radiometric consistency. High-resolution Google Earth imagery, field observations, and previous knowledge of the study area were used to compile training samples representing the key land-use and land-cover (LULC) classes built-up, cropland, vegetation, water bodies, and fallow land. To reduce the within-class spectral heterogeneity, at least 50–100 pixels were kept per class, according to the recommendations given by Congalton and Green (2019). Minimum Distance classifier was used because of its computational efficiency and insensitivity to overfitting in cases where the means of the spectra are well-separated (Richards and Jia, 2006). The classification was performed in the Semi-Automatic Classification Plugin (SCP) of QGIS, which allows user-friendly management of training data, extraction of spectral signatures, and the use of the classifier. The post-classification processing involved elimination of isolated pixels by using a majority filter and merging of spectrally similar classes where the merging increased the thematic coherence. After the classification, the data regarding the built-up areas per calendar year was obtained by means of raster-to-vector conversion. The polygons obtained were then examined to determine the spatial extension in the north, north-east, east, south-east, south, south-west, west and north-west directions at 2, 4, 6, 8 and 10 km away the city centre. This geographical study explains the rate of urbanisation in certain directions and to the different degrees at different times.

2.2 Accuracy assessment

An accuracy assessment is an important step to validate the LULC classification from the satellite imagery using the ground truth data using confusion matrix (Avcı et al., 2023). The study considered Google earth data and field based surveys for accuracy assessment. A total of 200 sample points (40 samples from each class) were considered using stratified random sampling method for accuracy assessment through overall accuracy and kappa statistics. Both statistics are very useful for assessment at holistic level.

2.3 Trend analysis

The temporal trend of urbanisation was analysed through Mann-Kendall (M-K) and Sen (S) slope estimator (Equations 1–3). M-K test is a common non-parametric method of identifying monotonic increasing or decreasing trends in time series data. Its principal advantages are that it can be used with minimal distributional assumptions and it is robust against outliers (Hamed and Rao, 1998). For a time series x₁, x₂,…, x_n each data point x_j (where j > i) is compared to every previous data point xi. Calculated as follow;where,

S = ∑ i = 1 n − 1 ∑ j = i + 1 n s g n x j − x i (1)

• s g n θ = 1 if θ > 0
• 0 if θ = 0
• − 1 if θ < 0

Then calculate the variance by the following equation;

For series with no ties

V a r S = n n − 1 2 n + 5 18 (2)

For series with ties, adjust using the number and size of tied groups (Wang et al., 2020).

After the Mann-Kendall test, the Sen Slope Estimator is used to measure the strength of the trend identified in a time series (Sudarsan and Lasitha, 2023). A slope is computed between each of the pairs of data values using the following formula:where, i = 1, 2, 3, ……, N and j > i, on the other hand x₁, x₂, x₃, ……, x_n are the data values and the median of N values of d k series can be obtained as Sen’s slope estimator.

d k = x j − x i j − i (3)

2.4 Landscape expansion index

The Landscape Expansion Index (LEI) framework was applied to provide a rigorous quantification of the spatial patterns and dynamics of urban expansion, supplemented by a set of landscape metrics that were calculated using classified LULC maps of 2000, 2005, 2010, 2015, and 2020. LecoS (QGIS Plugin) was used to compute these metrics at the class and landscape levels to provide complementary information on spatial configuration and fragmentation. The measures used were (Demirdağ and Cubukcu, 2025): Edge Length (EL) total length of patch boundaries (meters), a measure of the amount of urban edges; Edge Density (ED) edge length per unit area (m/ha), a normalization of edge length by landscape size; Number of Patches (NP) total count of discrete urban patches; Patch Density (PD) number of patches per 100 ha, a size independent measure of fragmentation. Reductions in NoP/PD promote the unification of patches into fewer, bigger patches.; Mean Patch Area (MPA) - average area of individual urban patches (km²); Largest Patch Index (LPI) - percentage of the total landscape area covered by the largest patch, indicating dominance of the primary urban core; Larger MPA/LPI indicates dominance, contiguous urban growth (e.g., infill or edge-expansion); Landscape Division Index (DIVISION) - Trajectory Analysis: probability that two randomly selected pixels are in different patches, higher values reflect greater fragmentation; Splitting Index (SPLIT) - measure of how the landscape is subdivided into disconnected units; the lower the values, the less fragmented the built-up mosaic (e.g., aggregated growth).

To classify the mode of urban expansion, and not merely its configuration, the Landscape Expansion Index (LEI) was computed for between the year (e.g., between 2000–2005) (Equation 4). The Landscape Expansion Index (LEI), proposed by Liu et al. (2010), quantifies the spatial relationship between newly grown urban patches and pre-existing urban land to classify expansion types. It is implemented in ArcMap through a dedicated LEI toolbox (available from the original developers) or equivalent standard ArcGIS tools combined with field calculations. For each newly grown urban patch, a buffer zone is generated around it. LEI is then calculated as:where, A 0 = area of the intersection between the buffer zone of the new patch and the pre-existing (occupied) urban land, A v = area of the intersection between the buffer zone and the vacant (non-urban) land. The buffer distance is conventionally set to 1 m (as recommended by Liu et al. for stability and minimal sensitivity to patch shape). LEI values range from 0 to 100. Following the established thresholds, patches were classified as infilling (LEI > 50), edge-expansion (0 < LEI ≤ 50) or leapfrog (LEI = 0). The area and proportion of each expansion type were then summarised by distance ring (2–10 km) and by direction. The class- and landscape-level metrics listed above (EL, ED, NP, PD, MPA, LPI, DIVISION and SPLIT) are reported as complementary configuration indicators that corroborate, but do not replace, this LEI classification.

L E I = 100 × A 0 A 0 + A v (4)

Three related but non-interchangeable concepts are distinguished in this study. Landscape pattern refers to the composition and configuration of patches (captured here by NP, PD, MPA, LPI, DIVISION and SPLIT) and describes how fragmented or aggregated the built-up mosaic is at a given time. Landscape expansion, captured by the LEI, describes the mode by which new built-up patches are added relative to existing ones (infilling, edge-expansion or leapfrog). Morphological contiguity, by contrast, describes the functional or structural linkage of habitat or green patches and must be derived from explicit network methods such as morphological spatial-pattern analysis and minimum-cumulative-resistance modelling (Wang et al., 2023); morphological contiguity can itself be reshaped through policy-oriented land-use simulation and optimisation (Wang et al., 2026a). Accordingly, the reductions in DIVISION and SPLIT reported below are interpreted only as decreasing fragmentation and increasing contiguity of the built-up class, and are not treated as evidence of ecological connectivity.

For the trajectories analysis, Principal Component Analysis (PCA) was applied to identify the dominant dimensions of urban landscape structure and to construct a common metric space for tracing urban development trajectories. PCA is particularly suitable for this purpose because commonly used landscape metrics, such as Edge density, Patch density, DIVISION, SPLIT, Largest patch Index (LPI) and Mean Patch Area, or often highly interconnected. PCA reduces this multicollinear set of variables into a smaller number of orthogonal components while retaining the major independent dimensions of landscape structure (Riitters et al., 1995). Prior to PCA, all landscape metrics were standardized to eliminate the influence of difference in measurement scale. The standardized metrics were considered across both distance and directional strata. Principal component scores were subsequently calculated for each observation point for each year, distance and direction. For example, the score corresponding to the 2000 observation at a distance of 2 km in the eastern direction represents its position within the PCA-derived metric space. By projecting successive yearly observations onto the two-dimensional space defined by the retained principal components, a common references framework was established for tracing and comparing urban development trajectories across different distance and directional strata. Thus, changes in component scores between successive years represent shifts in the underlying configuration and composition of the urban landscape, allowing the direction and magnitude of urban development to be assessed consistently across space and time. The principal components were retained according to the Kaiser criterion, with components having eigenvalues greater than 1 considered significant (Kaiser, 1960). This approach ensured that the retained components represented meaningful dimensions of variation while avoiding unnecessary components with limited explanatory power. The retained principal component scores were then used to derive the following trajectory-based metrics for characterizing the magnitude, direction, persistence and spatial difference in urban development using Equations 5–10, Step length between consecutive years:

d = P C 1 t + 1 − P C 1 t 2 + P C 2 t + 1 − P C 2 t 2 (5)

Total length (L):

L = ∑ t = 1 T − 1 d (6)

Net displacement (D):

D = P C 1 T − P C 1 1 2 + P C 2 T − P C 2 1 2 (7)

Straightness (S):(0 < S ≤ 1; S = 1 mean perfectly straight)

S = D L (8)

Mean step length = L T − 1 (9)

Direction angle = θ = atan ⁡ 2 P C 2 T − P C 2 1 , P C 1 T − P C 1 1 (10)

3 Results

3.1 LULC configuration (2000–2020)

Through the use of various statistical tests, the paper outlines substantial spatio-temporal variability in land-use/land-cover (LULC) change between 2000 and 2020 (Figure 2). The spatial patterns show significant differences in distance and direction: the first one is reflected in gradients of land-use classes, the later in individual land-use classes trajectories.

The patterns are observed in the spatial distribution of LULC classes over the study area with urban/built-up being dominant in the central region and croplands being dominant in peripheral regions. This pattern is very stable between the 2000 baseline and 2020, and it represents a typical rural-urban continuum.

The urban growth limited croplands throughout the research period, but the growth began spreading westward and later moved eastward. Annual Land Use Land Cover (LULC) data show unique spatial patterns in each of the distance rings, especially in the northwest-southeast axis (see Supplementary Table S1). The strongest growth of urban areas was in the NW and W directions, such as a 69.60 percent increase in built-up area at 6 km NW (from 3.03 km² in 2000 to 5.14 km² in 2020), accompanied by a corresponding decline of cropland within the same wedge.

An equally impressive trend was noted at 4 km N where urban area increased by 410 percent to 3.32 km² out of 0.65 km² indicating faster urbanization in these corridors. It was found that, in the 4 km radius around city nodes, the urban growth led to significant crop-land loss: 65.90% of the total was lost at 4 km E (1.35 km²–0.46 km²), and 70.30% was lost at 4 km NE (2.56 km²–0.76 km²). The rates of cropland loss were exponentially decreasing with distance, though; at 10 km E, the LULC change was only 3.20% (12.60 km²–12.20 km²). There was a strong bifurcation pattern of vegetation: near the city core the extent of vegetation decreased rapidly, e.g., 2 km S had a decrease of 77.80% (0.36 km²–0.08 km²), whereas after 4 km it increased significantly, especially in the northeast quadrant, e.g., 6 km E had an increase of +194% (0.18 km² to 0.53 km²). Water bodies also showed insignificant changes with little growth in some areas (6 km NE: 0.00 km²–0.24 km²) and little change in general, e.g., 6 km SE showed little growth (0.01 km²–0.02 km²). All these results indicate a spatial pattern in LULC trajectories: urban sprawl occurs mainly in NW/W/N directions at the shortest distances, cropland conversion is most intense within 6 km, and vegetation regrowth takes place in the intermediate distances. These findings support the need to consider subtle policy actions that can reconcile developmental ambitions and environmental sustainability.

3.2 Accuracy assessment

The accuracy of the classified images was calculated by selecting a total of 200 random sample points, considering 40 sampling points from each class. The overall accuracy of the images was 85.63% (2000), 86.34% (2005), 87.89% (2010), 90.35% (2015) and 92.38% (2020) respectively, and the kappa statistics 0.85, 0.86, 0.88, 0.90 and 0.92 respectively (Table 1). The results showed a gradual improvement of classification for sensor upgrade features during this period, especially for radiometric resolution and spectral range.

TABLE 1. Accuracy assessment.

3.3 Urban expansion

The spatial-temporal trend of urbanization of the Rohtak city as represented by the case study shows a systematic invasion of the neighbouring land area thus demoting other natural and cropland (Figure 3). The spatial-temporal trajectories are clear as the analysis was carried out using concentric distance buffers and directional wedges that radiate out of the city centre. The west-southwest areas showed the greatest and fastest spatial growth; growth was weaker along the south and northwest axes. The first urbanization was recorded in 2000 within a radius of 2-km. In later years, the radius of urban expansion was gradually growing beyond 6 km, and there was a period of 2005–2020 when there was a strong outward migration in several directions. Empirical results indicate that built-up area increased by 365% in the southwest (SW) area at 8 km, which is the greatest regional increase recorded during the entire study period. At the same time, the highest growth rate of 1 decade was registered at 6 km, and it was 26.90% in the period between 2015 and 2020. The spatial patterns also show fringe growth in the northwest (NW) at 6 km where the built-up area expanded by 69.60% (3.03–5.14 km²) between 2000 and 2020. The lowest growth rate on the other hand was recorded in the east (E) at 2 km at only 1.30%. The NW peaked at 6 km with a surge in 2010–2015. The analysis of the longitudinal expansion patterns indicates that the peaks of the trajectories can be distinguished clearly: in 2000, the maximum extent of the built-up area was at 4 km in NW (4.29 km²) and the minimum at 10 km in NE (0.17 km²). A strong spatial heterogeneity of spatial change rates became evident in the city between the years 2000 and 2005. Northeast Quadrant recorded the highest rate of growth of 4.23 km², and the south expanded so marginally at 2.00 km². The rate of growth was increased by 42.3% (0.65–0.93 km²) at 4 km in the north and was significantly lower at 2 km in the east by 1.3% (1.55–1.57 km²). During the next decade, the growth patterns changed significantly. There was increased growth at 6 km in the north-west sector by 4.07 km² and growth was still small at 10 km in the north-east by 0.36 km². The 2005–2010 showed a strong directional bias (westward) in urban extension, the rate of spatial growth increased by 6 km in NW (6.00%; 3.84–4.07 km²), but there was no growth in NE (3.50%; 0.35–0.36 km²). The growth in 2015 was toward saturation, with the highest urbanization area at 6 km in the west (5.78 km²), as opposed to a more limited one at 2 km in the east (1.57 km²). The greatest dispersion was at 6 km in W (10.60%; 5.23 to km²), as compared to 2 km SE (0.50%; 1.53–1.54 km²) where the growth rate was nearly at its limit. By 2020, a leading band appeared at 6 km in NW (5.14 km²) and W (5.99 km²) and growth had ceased at 2 km in the east, indicating saturation in the urban core and outward expansion to the west. There was no remarkable change in 6 km in N (0.3%; 3.33–3.36 km²) or in E (1.0%; 3.64–3.65 km²) but in 10 km NW (4.1%; 1.97–2.2 km²) and 10 km SW (3.1%; 11.97–12.0 km²) there was remarkable growth. The growth in East at 2 km was steady (0.5%; 1.52–1.56 km²). Within the 2015–2020 period, significant strengthening was observed at 6 km in NW (11.5%; 4.60–5.14 km²) and W (10.60%; 5.23–5.78 km²) and convergence towards stabilization at 2 km in the east.

3.4 Trend of urban expansion in different distance and direction

The non-parametric Mann–Kendall test combined with Sen’s slope estimator was applied to time-series data of areal extent (km²) within successive concentric distance bands (2, 4, 6, 8 and 10 km) and eight cardinal/inter-cardinal sectors. The test evaluates the presence of a monotonic trend; a positive Sen’s slope quantifies the median rate of areal increase (km² yr^-1), while the 95% confidence interval and p-value (α = 0.05) establish statistical significance and uncertainty (Table 2).

TABLE 2. Trends of urbanization in different distance and direction.

At the innermost 2 km radius the signal is spatially heterogeneous. Significant increasing trends (p ≤ 0.043) appear in the NE, N, NW, SW, S and SE sectors, with the steepest rates recorded northward (Sen’s slope = 0.034 km² yr^-1) and southward (0.025 km² yr^-1). The pure east and west sectors remain non-significant (p = 0.096 and 0.289), indicating that near-field change is directionally selective rather than isotropic. From 4 km outward the pattern becomes uniformly significant. Every sector at 4, 6, 8 and 10 km exhibits a statistically significant increasing trend (p = 0.0275 or 0.043). Magnitude of change peaks at intermediate distances, the highest single slope occurs in the northern sector at 4 km (0.127 km² yr^-1), followed by the eastern sector at 6 km (0.135 km² yr^-1). Beyond 6 km the rates generally moderate, yet remain positive and significant, implying that the process of areal expansion continues, albeit at a slower absolute rate, into the outer annuli.

Northern and north-eastern sectors display the most upward and often the strongest positive trends across all distances, consistent with preferential growth along these axes. Eastern and south-eastern sectors show pronounced mid-range acceleration (especially 4–8 km), while western and south-western sectors exhibit comparatively modest but still significant slopes that become relatively more important only at the outermost (10 km) band. The pure west sector is the only direction that fails to reach significance at 2 km and yields the smallest slope at 4 km, suggesting a residual constraint on westward expansion in the immediate vicinity of the origin.

3.5 Nature of urban expansion in different direction at different distance

The temporal trajectories of eight class- and landscape-level metrics like edge length, edge density, number of patches, patch density, mean patch area, largest-patch index (LPI), landscape division and splitting index were quantified for eight directional sectors over the period 2000–2020 (Figure 4). These metrics collectively diagnose the spatial organisation of built-up land and discriminate among infill, edge-expansion and leap-frog modes of growth.

Edge length rose steadily in seven of the eight sectors, with the largest absolute gains recorded in the northern (+0.43 × 10⁵) and eastern (+0.46 × 10⁵) corridors. Concurrently, LPI increased or remained near saturation (>90%) in the northern, north-eastern, eastern and south-eastern sectors, indicating progressive dominance by a single contiguous urban core. Mean patch area exhibited a pronounced post-2010 acceleration, most markedly in the south-eastern (from 2.5 × 10⁵ to 7.0 × 10⁵) and eastern (from 1.8 × 10⁵ to 5.3 × 10⁵) sectors, consistent with coalescence of previously discrete patches. In parallel, both edge density and patch density declined across all directions. The steepest reductions occurred in the southern sector (edge density from 1.75 × 10⁻² to 1.30 × 10⁻²; patch density from 1.15 × 10⁻⁵ to 0.50 × 10⁻⁵). Number of patches fell correspondingly; the most rapid loss being observed in the south-east (from 40 to 14). Landscape division and splitting index likewise decreased monotonically; by 2020 both metrics had fallen below 0.2 and 1.5, respectively, in the majority of sectors, signalling a measurable reduction in fragmentation and a corresponding rise in morphological contiguity. Directional differentiation is evident. In the eastern and northern corridors, the combination of rising LPI (N: 60%–95%; E: 80%–90%), falling landscape division (<0.2) and declining patch density points to consolidated growth driven by the absorption of satellite patches into the main urban continuum.

The north-western and western sectors maintained low patch densities (<4 × 10⁻⁶) together with significant high LPI (>80%) and landscape-division values < 0.3, a configuration compatible with either continuous edge accretion or limited leap-frog development. In the south-east the simultaneous sharp rise in mean patch area and LPI, coupled with a pronounced drop in patch density, is diagnostic of edge expansion outward from an already continuous core. The southern sector, by contrast, retained the highest residual landscape division (0.3) and splitting index (2.5) in 2020, indicating slower consolidation and residual fragmentation. The north-eastern quadrant displayed near-stable, near-maximum LPI (95%) throughout the period, while edge length continued to increase and patch density declined modestly, patterns consistent with limited edge expansion accompanied by internal infilling.

The distance-dependent trajectories of the eight landscape metrics (Figure 5) demonstrate a strongly urban-centric pattern of growth throughout 2000–2020. At the innermost 2 km radius the urban fabric is already highly consolidated. Number of patches remains minimal (5–10), mean patch area rises sharply after 2010 (from 2.5 × 10⁵ to 12 × 10⁵), and the largest-patch index (LPI) stays saturated near 95%–100%.

Landscape division and splitting index are effectively zero after 2010, confirming that a single, continuous built-up core dominates the central zone and that further internal fragmentation is negligible. At 4 km the metrics record a clear transition from moderate fragmentation to progressive agglomeration. Between 2000 and 2005 the sector contained 39–47 patches, mean patch areas remained modest, and LPI hovered around 85%. After 2010 the number of patches and patch density decline steeply (to 15 patches and near-zero density), mean patch area increases, and LPI approaches 96%–100%. Concurrently, landscape division collapses from 0.55 to 0 and the splitting index falls to unity. These changes indicate that the expanding urban core has absorbed most satellite patches, producing a nearly continuous built-up ring with only residual peripheral fragments. Beyond 6 km the landscape remains markedly fragmented. At 6 km LPI stabilises near 60%, landscape division stays elevated (0.65), and both the number of patches (100) and splitting index remain comparatively high. At 8 km and 10 km fragmentation intensifies further: patch counts stay high and even increase slightly (96–113), LPI remains low (13%–30% at 8 km; <15% at 10 km), and landscape division and splitting indices persist at high levels (division 0.9–0.95; splitting index 5–16). Mean patch areas are correspondingly small. These outer annuli therefore continue to exhibit a dispersed, multi-patch morphology with no dominant core and no evidence of large-scale coalescence.

The tabulated LEI values and corresponding expansion modes reveal a clear distance-dependent and temporally progressive shift in the dominant growth process (Supplementary Table S2). At distance 2, expansion was classified as Infilling in nearly all directions and periods from 2000 to 2020, with LEI values ranging from 46.17 to 99.80 and generally remaining high or increasing over successive intervals. At distance 4, results were mixed: Infilling predominated in the NW and W directions (LEI 64.95–99.40), while E, N, NE, S, SE and SW were mostly Edge expansion (LEI 10.41–64.15), with some directional shifts toward Infilling in later periods. At distances 6, 8 and 10, expansion was classified as Edge expansion in every direction and period, with LEI values ranging from 0.87 to 44.57 and generally declining with greater distance while remaining comparatively low and stable across the four time intervals.

Infilling is strongly concentrated in the innermost ring (Distance 2), accounting for 12.93%–15.44% of total expansion and essentially all growth in that zone after 2005 (Edge Expansion drops to 0%). Distance 4 is transitional, with Infilling (12.39%–15.01%) and Edge Expansion (14.09%–17.91%) contributing roughly comparable shares. Beyond Distance 4, Infilling disappears completely; all expansion at Distances 6, 8 and 10 is Edge Expansion, with Distance 6 consistently contributing the largest single share (23.74%–25.29%) (Table 3). This produces a clear concentric gradient: densifying, gap-filling growth near the core and continuous outward edge accretion at the periphery.

TABLE 3. Nature of Urbanisation according to distance with area in percentage.

Area in percentage to total area in sector.

Infilling is markedly anisotropic. The western (W) and north western (NW) sectors consistently record the highest Infilling percentages (W: 6.29%–8.88%; NW: 6.24%–8.52%), while northern (N) and southern (S) sectors remain low (≤1.64%). Edge Expansion dominates in every direction, yet the absolute largest Edge Expansion shares also occur in the W sector (12.91%–14.39%). Eastern (E) Infilling shows a progressive rise over time (2.22%–5.48%) (Table 4), indicating a directional shift toward more compact growth on the eastern flank.

TABLE 4. Nature of Urbanisation according to distance with area in percentage.

Area in percentage to total area in sector.

3.6 Trajectories matrix of urban development

The trajectories matrix quantifies the nature of urbanisation in different direction and distance based on the LEI using PCA. The results of the PCA shown in Table 5. The two PCA explained 86.01 and 92.35 percent in case of direction and distance respectively of the total variance. In case of direction wise trajectories of urban development mainly controlled by the all features without no. Of patches and mean patch area. However, except mean patch area, all the features had significant controlled in case of distance wise urban development.

TABLE 5. Direction and distance wise PCA results.

The trajectories in PC1–PC2 space over 2000–2020 reveal Distance-dependent multivariate change, with the largest total path lengths occurring at Distance 2 (L = 2.26) and Distance 8 (L = 2.13), indicating the greatest cumulative shifts, while the smallest path lengths at Distance 4 (L = 0.94) and Distance 6 (L = 0.91) reflect relative temporal stability and Distance 10 occupies an intermediate position (L = 0.98); net displacement follows the same ranking, confirming that these differences are not artefacts of path tortuosity (Table 6). All trajectories are strongly directional, with straightness indices ranging from 0.74 to 0.99. Distance 8 nearly linear (S = 0.99), Distance 4 the most meandering (S = 0.74), and Distances 2, 6 and 10 highly directed (S = 0.97), demonstrating that change was dominated by a consistent, influential driver rather than random or oscillatory fluctuations and that the underlying process operated coherently across the two decades. Step lengths were temporally uneven. Distance 2 showed little early change, followed by a marked increase in 2010–2015 (step = 1.70) and relatively limited change thereafter. Distance 4 recorded its largest step during 2005–2010, while Distance 6 increased progressively and reached its maximum in 2010–2015. Distance 8 exhibited consistently large step lengths, with the highest value also occurring in 2010–2015, whereas Distance 10 showed an increasing pattern and recorded its largest step during 2015–2020. The frequent occurrence of the single largest displacement within the 2010–2015 window therefore marks a period of accelerated multivariate change affecting most Distance classes. Net movement vectors further differentiated the classes like Distance 2 advanced strongly toward negative PC2 and modestly negative PC1 (angle = −67.41°), Distance 4 moved predominantly toward negative PC1 (angle = −160.91°), and Distances 6, 8 and 10 progressed toward negative PC1 and positive PC2 (angle = 126°–151°), revealing a shared directional component along the negative PC1 axis across most classes while the PC2 component reversed sign between the lowest Distance and the higher Distances, consistent with a gradient-dependent response to the same external driver.

TABLE 6. Trajectories matrix (distance wise urban development).

Northern, eastern and south-eastern sectors exhibit the longest total path lengths (L = 3.30–4.10 km) and largest net displacements, accompanied by relatively high straightness indices (S = 0.72–0.86) (Table 7). These trajectories indicate rapid, significantly outward-directed edge expansion, with the strongest pulses occurring early (N, 2000–2005) or mid-period (E and SE, 2010–2015). In contrast, the north-eastern, western, south-western and north-western sectors display short total lengths (L = 1.71–1.78 km), low net displacements and the lowest straightness values (S = 0.43–0.55) except north-eastern. Their growth paths are therefore short-range and highly tortuous, consistent with local densification and limited net radial advance. Mean step lengths mirror the same contrast: large, episodic steps on the N–E–SE flanks versus uniformly small steps on the western side.

TABLE 7. Trajectories matrix (direction wise urban development).

4 Discussion

A part of the National Capital Region (NCR) of India, Rohtak has undergone pronounced spatial transformation over the past four decades, with the acceleration of built-up area, population and urban footprint becoming most conspicuous after 2000 and intensifying following its elevation to Municipal Corporation status in 2010 (Singh and Kumar, 2012). This growth has proceeded through the outward absorption of neighbouring villages and cropland, primarily along major highways and trunk roads. Rather than describing this expansion in isolation, the present findings are best interpreted through the diffusion–coalescence framework of urban growth (Dietzel et al., 2005), which conceptualises urbanisation as an oscillation between a diffusion phase, when dispersed and often disconnected patches emerge, and a coalescence phase, when infilling and edge accretion knit these patches into a compact fabric. Read through this lens, the three empirical signatures recovered for Rohtak like anisotropic outward growth concentrated to the north, west and north-west; saturation and congestion of the inner core; and a comparatively inert eastern corridor, are not three separate observations but coupled expressions of a single, spatially differentiated diffusion–coalescence cycle.

4.1 Directional bias in urban sprawl

The empirical results identify the north-western and western sectors as the most aggressive fronts of built-up growth, the north-west recording the largest cumulative gain (a 69.6% increase at 6 km, from 3.03 to 5.14 km²) and reaching peak acceleration in 2010–2015, while the west peaked slightly later in 2015–2020. This directionality is closely coupled to Rohtak’s role as an education city, anchored by Maharshi Dayananda University (MDU), the Indian Institute of Management Rohtak (IIM Rohtak) and the Pt. B.D. Sharma University of Health Sciences (Singh, 2012), which generate sustained demand for housing, retail and ancillary services and thereby act as durable growth engines. The catalytic role of higher-education campuses in reorienting urban growth is well documented internationally, for instance around Kyushu University in Ito, Japan (Mohammed et al., 2022), and, more recently, in the peri-urban expansion of Malang, Indonesia, where growth clustered around higher-education institutions and shifted from edge-expansion toward infilling over two decades (Hafiz et al., 2025). Industrial and infrastructural forces reinforce the westward and south-westward bias, the Industrial Model Township (IMT) developed by HSIIDC along NH-9, together with radial National Highway connectivity to Delhi, concentrates labour, commerce and supporting settlement along these axes (Kasraian et al., 2019). Critically, because Rohtak sits on the flat Indo-Gangetic alluvial plain, this anisotropy cannot be attributed to topographic constraint. This distinguishes the case sharply from terrain-constrained valley cities in western China, where rugged relief and river segmentation force corridor-oriented and leapfrog forms and where growth is channelled by the availability of buildable low-slope land. On relatively homogeneous plains growth tends to default to broadly concentric expansion (Yin et al., 2025; Sun et al., 2026); the strong directional signal observed here is therefore endogenously generated by the uneven spatial distribution of institutional and industrial anchors and by radial transport, rather than exogenously imposed by physical geography. In this respect Rohtak parallels the policy- and nuclei-driven directional bias (toward the SSW and WSW) reported for the purpose-built Federal District of Brazil (Li et al., 2022), underscoring that the directional geometry of diffusion–coalescence can be reproduced on unconstrained terrain purely through the placement of economic pull-factors. The direction-wise trajectory metrics (Figure 6) sharpen this interpretation and, importantly, reveal a pattern that raw area statistics conceal. The northern, eastern and south-eastern sectors trace the longest, most displaced paths in PC1–PC2 space, indicating that these directions underwent the largest transformation in landscape configuration, that is, the most complete transition from fragmented to coalesced form. By contrast, the western, south-western and north-western sectors follow short, tortuous, low-straightness paths, signalling that their considerable built-up gain was achieved largely through in-place densification and infilling rather than radial advance—consistent with the west’s significantly high infilling share in the LEI results.

4.2 Distance gradient

Movement outward from the core reveals a clear distance-decay structure. The innermost 2 km ring records minimal net change (<5% over 20 years), whereas pronounced growth concentrates at intermediate radii and moderate but positive increases extend to the 10 km periphery, most notably in the south-east. The exceptional rates at specific radii are diagnostic of a transition from edge-expansion to leapfrog development. The intense hotspot at 4 km north corresponds to the immediate periphery of the major university campuses, an effect closely paralleling the institutional-cluster–driven peri-urban growth reported for Lucknow (Dutta, 2012), a zone close enough to the institutions to be highly convenient yet far enough from the saturated core to retain developable land. A second hotspot at 8 km south-west aligns with the Industrial Model Township.

The elevated growth around the Industrial Model Township reflects the development not merely of industrial plots but of an accompanying ecosystem of worker housing, supply-chain firms and commercial services; comparable mid-distance intensification (5–8 km) has been documented for Jaipur (Jat et al., 2008), and slower core-proximal change relative to faster mid-distance growth for peripheral Bhubaneswar (Chettry, 2022). The saturation of the 2 km core, where infilling dominates and little vacant land remains, mirrors the core-area consolidation reported for Kolkata (Bhatta, 2010) and central Bengaluru (Ramachandra et al., 2012), and results from intense competition for a limited land supply that drives up prices and forecloses large-scale new construction. Interpreted through diffusion–coalescence theory (Dietzel et al., 2005), this concentric structure is essentially a spatial snapshot of the temporal cycle: the core has already completed coalescence, the 4–6 km belt is actively coalescing, and the 6–10 km fringe remains in the diffusion phase. The same ring-differentiated signature underlies the megacity growth pathways synthesised by Chakraborty et al. (2022), in which cities oscillate between diffusion and densification; what distinguishes Rohtak is that, as a secondary city, this full sequence is compressed into roughly two decades rather than unfolding over the multi-decadal cycles typical of megacities. The distance-wise trajectories (Figure 7) corroborate this reading: the largest multivariate displacement occurs in the innermost ring (reflecting terminal infilling of the core) and in the 8 km ring (reflecting active fringe coalescence), whereas the 4–6 km rings show comparatively short paths indicative of a more stable, mid-transition configuration.

Taken together, these directional and distance signatures show that urbanisation in Rohtak is neither uniform nor simply monotonic with distance; it proceeds as a set of multi-directional, radius-dependent processes, simultaneous fragmentation, clustering, sprawl and densification whose relative dominance shifts systematically with position. This distance-decay behaviour, with densification and infilling at the core and sprawl at the periphery, is consistent with earlier characterisations of Indian and other rapidly urbanising cities (Taubenböck et al., 2009; Herold et al., 2003), but the present analysis adds the directional dimension that those aggregate treatments omit.

4.3 Saturation and infill vs. sprawl

The stability of built-up area at 2 km across all directions—less than 2% change between 2015 and 2020—confirms infill saturation of the core, while the 365% surge at 8 km in the south-west over 2000–2020, steepest in 2015–2020, exemplifies leapfrog development at the fringe. This coexistence of a saturated, infilling core and a leapfrogging periphery reproduces, within a single city and a single snapshot, the alternation of infilling and spontaneous outlying growth that Bag et al. (2024) and others report as a temporal sequence, reinforcing the reading of concentric structure as a spatialised cycle. Two processes are thereby underscored: a proximity-driven transition, in which near-core zones (≤4 km) stabilised early (<10% change before 2010) while mid-distance zones (6–8 km) grew by more than 50% over two decades, in line with urban-gradient theory; and anisotropic expansion, in which the NW/W bias (e.g., +69.6% at 6 km NW) reflects infrastructure and industrial investment while the NE/E sectors stagnate. The muted eastern growth is most plausibly attributable to a comparative absence of development drivers rather than to a physical barrier: whereas other directions host major universities, industrial estates and arterial highways, the eastern corridor lacks equivalent pull-factors and may additionally have been zoned under the Rohtak Master Plan for agriculture, green belts or future-use reserves. The documented proposal for a new eastern industrial township suggests this corridor is earmarked for later-phase growth, which would explain its current quiescence—an interpretable, driver-based asymmetry rather than noise.

At the landscape level, expansion is dominated by edge-expansion and infilling with monotonically declining fragmentation, the eastern and northern sectors showing the most dynamic consolidation and the western sectors remaining comparatively stable and contiguous; early phases of higher fragmentation give way to dominant, contiguous urban forms by 2020. The progression of the active growth front from within the core in 2000 to beyond 6 km by 2020 is a direct consequence of core saturation under sustained demographic and economic pressure, a ripple effect amplified by transport investment, as rising land prices in the developed 2–4 km belt push developers and households progressively outward. The 2000–2020 window of economic liberalisation and infrastructure spending would have intensified this outward propagation. Such ripple dynamics are widely observed across Indian metropolitan systems, for example, the emergence of Whitefield, Electronic City and the Marathahalli–Sarjapur belt beyond Bengaluru’s outer ring road (Aithal et al., 2013) and within the NCR itself, the expressway-led transformation of Gurugram and Noida from agrarian peripheries into corporate and IT hubs dependent on new transport links to the wider region (Bansal, 2025; Mookherjee and Geyer, 2011). Rohtak’s trajectory indicates that the same corridor-based, ripple-effect logic that reshaped the NCR’s first-tier satellites now operates at the scale of its secondary cities.

Phases of development: The metrics resolve three developmental phases. In the initial stage (2000–2010), expansion is dispersed and fragmented, numerous small patches, high edge and patch densities are reflecting opportunistic development on land assembled piecemeal by many small builders and individual owners as surrounding villages were gradually engulfed, before peripheral-growth controls matured (Barman et al., 2024; Manna et al., 2024). In the transitional stage (2010–2015), patches begin to merge as mean patch area and the largest-patch index rise and fragmentation indices fall, marking a shift from opportunistic to structured, consolidated expansion supported by improving infrastructure and formal planning (Permanasari et al., 2024; Zhang et al., 2025). In the consolidation stage (2015–2020), contiguous large patches dominate and edge and patch densities fall, producing a classic coalescence pattern as integration with national highways such as NH-9 and the guidance of the Rohtak Master Plan 2031 promote contiguous development (Nagpal, 2017). This ordered fragmentation-to-coalescence sequence is precisely what diffusion–coalescence theory predicts (Dietzel et al., 2005) and what has been observed empirically from Brasília (Li et al., 2022) to peri-urban Malang (Hafiz et al., 2025), confirming that the theory holds for a mid-sized NCR city. The trajectory analysis, however, adds a mechanistic nuance seldom highlighted in the largely market-driven Chinese and Brazilian literature: the single largest multivariate jump clusters in the 2010–2015 window, coincident with Rohtak’s 2010 elevation to Municipal Corporation status and the attendant 240% enlargement of the municipal boundary. This suggests that a discrete administrative–institutional shock may be temporally associated with an accelerated transition from diffusion toward greater morphological contiguity, complementing the incremental, market-led drivers emphasised elsewhere. These associations are consistent with known drivers but cannot be interpreted as causal effects given the observational design.

Broader significance and transferability of the framework: Beyond the specific case, these results carry a wider methodological and conceptual contribution. By integrating LEI-based mode classification (infilling, edge-expansion and leapfrog) with an explicit distance–direction stratification and a PCA-derived trajectory metric, the framework moves the analysis of urban growth beyond the question of how much a city expands to how, where and in what temporal order it does so. In doing so it reconciles two views usually reported separately, the magnitude view (area gain) and the configuration view (landscape pattern) and demonstrates that they can diverge: the western sectors of Rohtak record large area gains yet short configurational trajectories because their growth is infill-dominated, a divergence invisible to area statistics alone. The framework thereby operationalises the diffusion–coalescence cycle (Dietzel et al., 2005) as a measurable, reproducible trajectory rather than a qualitative narrative, and shows that its directional geometry can be endogenously generated on flat, unconstrained terrain by the spatial arrangement of institutional and industrial anchors, a finding that extends a theory largely developed on Chinese, North American and terrain-constrained cases to the driver-rich, policy-shaped context of Indian secondary cities.

The framework is readily transferable to other rapidly urbanising regions. Its only essential inputs are multi-date classified built-up layers and a defined urban core, data now freely available anywhere Landsat and Sentinel archives reach, so the same distance–direction–trajectory protocol can be applied across the secondary cities of South and Southeast Asia, Sub-Saharan Africa and Latin America, where an estimated 90% of future urban growth will occur and where planning still relies heavily on aggregate-area assessments. Applied comparatively, the directional and radial trajectory signatures could support a much-needed empirical typology of secondary-city growth and enable early identification of nascent leapfrog corridors for pre-emptive infrastructure and green-space planning, complementing the megacity-focused syntheses that currently dominate the global literature.

5 Limitation

Several limitations affect interpretation and generalisability. First, only five observation years (2000, 2005, 2010, 2015, 2020) were available; denser temporal sampling would improve detection of short-term fluctuations and the precise timing of phase transitions. Second, Landsat imagery at 30 m resolution cannot capture fine-grained intra-urban changes or very small patches; classification error therefore propagates into small-change estimates and patch metrics. Historical accuracy assessment relies partly on Google Earth imagery whose own temporal and spatial limitations introduce uncertainty. Third, landscape metrics are sensitive to the spatial grain of analysis, the majority-filter post-processing step and the precise delineation of distance and directional boundaries; alternative filtering or boundary definitions could alter absolute values, although relative trends are expected to be robust. Fourth, Principal Component Analysis performed on a very small temporal sample (five time points) yields trajectories whose statistical stability is limited; the reported percentages of variance explained should be interpreted with caution. Fifth, the observational design cannot establish causal effects of universities, industrial estates, transport infrastructure or specific policy instruments; the associations described are consistent with known drivers but remain correlational. Finally, because the manuscript links urban development to environmental sustainability and ecosystem-service implications, it must be stated that the present data support conclusions only about morphological configuration of built-up land; formal morphological contiguity, biodiversity or ecosystem-service assessments would require additional data and methods (e.g., graph-theoretic or circuit-theoretic connectivity analysis). A broader synthesis of the evolution of ecosystem-services research is provided by Wang et al. (2026b).

6 Conclusion

The study quantifies the spatiotemporal nature of urban expansion in Rohtak (National Capital Region) from 2000 to 2020 through landscape ecological metrics stratified by distance and direction from the city centre, revealing a clear transition from fragmented, dispersed growth to progressive consolidation and coalescence. Expansion preferentially followed major roads and corridors of higher social-economic connectivity, with rapid patch growth and consolidation concentrated in the north, west and related sectors, while the south, south-east and north-east exhibited slower, more constrained transitions attributable to geographical and infrastructural factors. Core zones (2–4 km) rapidly shifted toward single-patch dominance, intermediate rings displayed gradual coalescence, and the rural fringe (≈10 km) remained fragmented, producing an overall gradient from monocentric compactness at the centre to polycentric and incomplete consolidation outward. These patterns align with classic urban expansion theory, wherein initial scattered development evolves through edge expansion and infill into more connected forms, as evidenced by statistically significant declines in division and splitting indices. By integrating multi-temporal landscape metrics with trajectory analysis, the research provides a replicable, empirically grounded framework for characterising directional and distance-dependent urbanisation processes in mid-sized NCR cities, thereby advancing landscape-ecological understanding of urban form evolution in rapidly transforming Metropolitan contexts.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/frsen.2026.1912607/full#supplementary-material

Supplementary material Supplementary material at the source

Footnotes

Edited by: Shengbiao Wu, The University of Hong Kong, Hong Kong SAR, China

Reviewed by: Zechen Wang, Beijing Normal University, China

I. Gede Wyana Lokantara, State University of Medan, Indonesia