Analyzing Vegetation Heterogeneity Trends in an Urban-Agricultural Landscape in Iran Using Continuous Metrics and NDVI

Abstract

Understanding vegetation heterogeneity dynamics is crucial for assessing ecosystem resilience, biodiversity patterns, and the impacts of environmental changes on landscape functions. While previous studies primarily focused on NDVI pixel trends, shifts in landscape heterogeneity have often been overlooked. To address this gap, our study evaluated the effectiveness of continuous metrics in capturing vegetation dynamics over time, emphasizing their utility in short-term trend analysis. The study area, located in Iran, encompasses a mix of urban and agricultural landscapes dominated by farming-related vegetation. Using 11 Landsat 8 OLI images from 2013 to 2023, we calculated NDVI to analyze vegetation trends and heterogeneity dynamics. We applied three categories of continuous metrics: texture-based metrics (dissimilarity, entropy, and homogeneity), spatial autocorrelation indices (Getis and Moran), and surface metrics (Sa, Sku, and Ssk) to assess vegetation heterogeneity. By generating slope maps through linear regression, we identified significant trends in NDVI and correlated them with the slope maps of the continuous metrics to determine their effectiveness in capturing vegetation dynamics. Our findings revealed that Moran’s Index exhibited the highest positive correlation (0.63) with NDVI trends, followed by Getis (0.49), indicating strong spatial clustering in areas with increasing NDVI. Texture-based metrics, particularly dissimilarity (0.45) and entropy (0.28), also correlated positively with NDVI dynamics, reflecting increased variability and heterogeneity in vegetation composition. In contrast, negative correlations were observed with metrics such as homogeneity (−0.41), Sku (−0.12), and Ssk (−0.24), indicating that increasing NDVI trends were associated with reduced uniformity and surface dominance. Our analysis underscores the complementary roles of these metrics, with spatial autocorrelation metrics excelling in capturing clustering patterns and texture-based metrics highlighting value variability within clusters. By demonstrating the utility of spatial autocorrelation and texture-based metrics in capturing heterogeneity trends, our findings offer valuable tools for land management and conservation planning.

1. Introduction

Landscape heterogeneity, defined as the degree of variation among different elements within a landscape [1,2], is a focal point of landscape ecology. This field investigates the factors contributing to such variation, including the impacts of natural events and human activities [3], and examines how this diversity influences ecological dynamics and interactions across the landscape [4]. Assessing spatial heterogeneity at an appropriate scale and resolution for the species or processes under investigation is a critical challenge in landscape studies [5,6]. Accurate estimation of relationships between landscape patterns and ecological processes relies on identifying heterogeneity in ways that align with the target organism or phenomenon. To address this, landscape ecologists often adopt a discrete framework, viewing landscapes as collections of distinct patches [7]. The patch-corridor-matrix (PCM) model, introduced in the 1980s, conceptualizes landscape structure as a mosaic of homogeneous areas represented in discrete units. This approach necessitates a thematic resolution suitable for classifying the landscape into distinct categories, enabling effective quantification of heterogeneity [1].

In recent years, landscape metrics [8] and land use maps have been widely used to explore relationships between landscape heterogeneity and ecological patterns. While discrete models effectively measure landscape structure in various studies [9], many metrics often exhibit high correlations [10], and their comparability across scales remains a challenge. Additionally, the sensitivity of these metrics to spatial and temporal resolution has emerged as a critical issue in landscape ecology [11,12]. Selecting appropriate metrics that accurately reflect landscape characteristics is particularly complex for urban areas, where mixed land cover types pose classification difficulties [13].

To address these limitations, continuous methods have been proposed as alternatives to traditional discrete models [14]. Texture-based metrics [15,16,17,18,19], for instance, leverage remote sensing data, such as the Normalized Difference Vegetation Index (NDVI), to capture landscape heterogeneity directly, offering a more detailed and realistic representation of landscapes. Other continuous approaches, including fuzzy set theory [20], spectral unmixing [21], surface metrics [22,23], spatial autocorrelation indices [24,25,26], and Fourier analysis, have also proven valuable for detecting landscape changes, such as fragmentation [27,28]. These methods provide a nuanced view of urban and non-urban landscapes, enabling improved analysis of heterogeneity and ecological processes.

To address these challenges, we carefully selected more efficient and robust metrics that balance methodological complexity with practical applicability. Our approach emphasizes indicators capable of addressing spatial heterogeneity while accommodating non-stationary patterns within the study area. This allowed us to capture meaningful ecological insights without the restrictive assumptions required by some geostatistical or spectral analysis methods. By focusing on metrics that align closely with the objectives of our analysis, we ensured the reliability and relevance of our findings in quantifying and interpreting vegetation heterogeneity.

Surface metrics, as elucidated by McGarigal, et al. [21], exhibit unique attributes and demonstrate a robust capacity to elucidate the correlation between landscape patterns and underlying processes. A recent investigation by Kedron, et al. [10 evaluated the effectiveness and suitability of surface metrics in characterizing diverse forest landscapes. The results indicated that surface metrics vary in their suitability for landscape analysis. Local spatial autocorrelation indices, including local Moran’s Index and local Getis-Ord (Gi), present an alternative method for evaluating landscape heterogeneity. Fan, et al. [24] employed Gi statistics to assess urban landscape heterogeneity and compared their performance with traditional landscape metrics, highlighting their effectiveness in capturing landscape heterogeneity. Texture-based measures, akin to local spatial autocorrelation indices, directly utilize remote sensing data to capture landscape heterogeneity [19]. These measures quantify spatial properties of landscapes using gray-level co-occurrence matrix (GLCM) indices, which emphasize texture properties, such as smoothness or coarseness. These properties reflect the uniformity or variability of image color or tone [16,29].

In a recent study, Rahimi, et al. [23] compared landscape metrics [30] derived from the discrete model with alternative continuous metrics, which included spatial autocorrelation indices, Fourier transforms [27], and surface metrics. To achieve this objective, two subsets were utilized, differing in terms of urban and agricultural changes, and temporal changes were measured across two subsets between 2013 and 2020 in Iran. The findings revealed that the percentage of landscape (PLAND) exhibited a strong statistical relationship with the Getis of NDVI (R² = 95.9%). Moreover, the study underscored certain limitations of landscape metrics in assessing landscape patterns, some of which might be mitigated by the utilization of continuous metrics.

The choice between discrete and continuous approaches depends on factors such as study scale, available resources, target ecological processes, and the landscape’s degree of heterogeneity [31]. Continuous metrics are particularly advantageous due to their sensitivity to subtle changes, making them more effective than traditional landscape metrics for detecting minor shifts [23]. These metrics are also time-efficient as they rely on easily calculable vegetation indices. They are recommended for rapid assessments of large landscapes, particularly when monitoring temporal changes or dealing with highly heterogeneous spatial arrangements.

Therefore, vegetation heterogeneity analysis can be approached using two general methods [14,23]. The initial method entails land use and land cover classification using satellite images obtained over different years, commonly referred to as the discrete approach [7]. In this approach, landscapes are perceived as a compilation of discrete patches, with each patch representing a unique land cover type or land use category. In contrast, the second method employs continuous metrics within a continuous approach framework. Unlike the discrete approach, continuous methods directly utilize remotely sensed data, such as NDVI, to measure changes in landscape patterns, providing a more detailed and precise comprehension of ecosystem dynamics [32].

Analyzing vegetation patterns is imperative for several reasons. Primarily, these trends serve as pivotal indicators of environmental changes over time, facilitating the assessment of ecosystem vitality, degradation, or enhancement, and identifying regions susceptible to issues like desertification or deforestation [33,34]. Furthermore, they provide insights into the responses of ecosystems to climate change, including shifts in vegetation types, phenology, and productivity. This contribution enhances climate change research by elucidating the dynamic interactions between ecosystems and changing environmental conditions [35,36,37]. Additionally, changes in vegetation cover and composition directly affect biodiversity, making it crucial to monitor these trends. By identifying habitat loss or fragmentation and invasion by alien species, such monitoring guides conservation initiatives aimed at preserving biodiversity [38,39].

NDVI is a widely used indicator of vegetation health and vitality [40,41], providing critical insights into changes in vegetation coverage, density, and productivity. By quantifying the difference between near-infrared and visible light reflected by vegetation [42], NDVI serves as a cornerstone for analyzing vegetation trends and understanding terrestrial ecosystem dynamics [23]. Its application has grown significantly, with research papers indexed in the Web of Science Core Collection rising from 795 in the 1990s to 12,618 in the 2010s, reflecting its pivotal role in vegetation studies [43]. Numerous studies have investigated vegetation trend analysis, resulting in the characterization of positive, negative, or neutral trends for individual pixels across NDVI maps [44,45,46,47,48,49].

The majority of existing studies have primarily focused on identifying changes in individual NDVI pixels over time, often overlooking the critical aspect of landscape heterogeneity dynamics. Understanding whether a landscape has become more fragmented or aggregated over time is essential for making a comprehensive assessment of vegetation trends. Despite this importance, continuous metrics have not been widely utilized in time series analysis and have received relatively little attention in vegetation trend studies. To address this gap, this study aims to explore vegetation heterogeneity trends alongside the positive and negative changes in NDVI by using three categories of continuous metrics: surface metrics, local spatial autocorrelation indices, and texture-based metrics. These metrics allow for both the detection of pixel-level trends and the assessment of fragmentation dynamics over time. The novelty of this study lies in its application of continuous metrics to analyze vegetation heterogeneity trends over time, a dimension that has not been thoroughly examined in previous research.

2. Materials and Methods

2.1. Study Area

The study area for this research encompasses the western regions of Isfahan city, including cities such as Najaf Abad, Qahdrijan, and Flowerjan, located in central Iran. Geographically, this region lies approximately between 32.5° N to 32.8° N latitude and 51.3° E to 51.5° E longitude. The area experiences a semi-arid climate with hot, dry summers and cold winters. The average annual precipitation is approximately 125–150 mm, primarily occurring during the winter and early spring months, while the average annual temperature ranges between 15 °C and 18 °C. Vegetation in the region is dominated by hand-planted species, primarily including drought-resistant trees such as Ailanthus altissima and Robinia pseudoacacia, alongside crops like wheat and barley [50,51]. The region’s rapid urbanization and its dependence on managed vegetation make it an ideal setting for assessing vegetation heterogeneity dynamics. Significant changes in vegetation cover and fragmentation are anticipated over the study’s ten-year timeline, making it crucial to evaluate continuous indicators for capturing these trends effectively (Figure 1).

2.2. Spatial Data

The data utilized in this study comprises 11 satellite images obtained from the Landsat 8 OLI satellite (

Table 1. Details of satellite data used in this study.

Date	Path	Row	Satellite	Sensor	Resolution
30 July 2013	164	37	Landsat 8	OLI	30 m
22 August 2014	164	37	Landsat 8	OLI	30 m
5 August 2015	164	37	Landsat 8	OLI	30 m
7 August 2016	164	37	Landsat 8	OLI	30 m
10 August 2017	164	37	Landsat 8	OLI	30 m
13 August 2018	164	37	Landsat 8	OLI	30 m
16 August 2019	164	37	Landsat 8	OLI	30 m
18 August 2020	164	37	Landsat 8	OLI	30 m
18 June 2021	164	37	Landsat 8	OLI	30 m
8 August 2022	164	37	Landsat 8	OLI	30 m
11 August 2023	164	37	Landsat 8	OLI	30 m

). These Landsat 8 OLI images offer a spatial resolution of 30 m and possess a 16-bit radiometric precision. The majority of these images were captured in August, coinciding with the vegetation growing seasons. They were acquired from the Landsat archive maintained by the United States Geological Survey (USGS) and are freely accessible at http://glovis.usgs.gov (accessed on 1 April 2024). Specifically, we downloaded Landsat Collection 2 level 2 data for our analysis. These products were generated by applying atmospheric correction to Level-1 Systematic Terrain (Corrected) (L1GT) or Level-1 Precision Terrain (Corrected) (L1TP) products [52]. Notably, the image data within the Level-2 Surface Product (L2SP) underwent atmospheric correction [52]. Subsequently, for each path and row per year, a visual inspection was conducted on the list of available images. All data were employed for NDVI extraction in a change detection manner spanning a period of 10 years (2013–2023).

2.3. Vegetation Heterogeneity Analysis

Landscape ecologists are constrained in the selection of continuous metrics due to the specific requirements and assumptions inherent to these approaches, such as stationarity and spatial autocorrelation [53]. However, their application demands a consistent spatial covariance structure across the study area, which is not always feasible in heterogeneous landscapes. Bolliger, et al. [54] extensively reviewed the available metrics for continuous measurement in landscape patterns, providing a foundational understanding of their applicability. Since then, newer metrics, such as texture-based methods, have been introduced, expanding the range of tools available for analyzing landscape heterogeneity. Despite this progress, it is important to note that not all metrics are suitable for measuring landscape patterns [28]. As highlighted by Rahimi, et al. [23], certain methods may lack compatibility with the spatial and ecological complexities inherent to landscape studies, limiting their utility in specific contexts.

Figure 2 presents the methodology flowchart for comparing continuous metrics in vegetation heterogeneity analysis. According to the outlined methodology, Landsat 8 images from 2013 to 2023 were collected to calculate NDVI values. Efforts were made to standardize the temporal selection of these images, with most being chosen from August each year within the specified time frame. After computing NDVI for each year, the resulting rasters were overlaid to create a composite map, where each cell contained 11 NDVI values corresponding to the 11 years. A similar approach was applied to generate continuous metrics from the NDVI maps, which were subsequently analyzed for vegetation heterogeneity changes. This analysis utilized surface metrics, local spatial autocorrelation indices, and texture-based metrics to quantify spatial and temporal variability.

Linear regression analysis was utilized to evaluate the direction and statistical significance of vegetation changes across the study area. One of the key outputs of this analysis was the slope map, which illustrates both positive and negative trends in NDVI values at the cell level for the entire study area. To identify the most effective indicators for detecting vegetation heterogeneity, we calculated the correlations between the NDVI slope map and the slope maps of various continuous metrics. The metric showing the highest correlation with the NDVI slope map was considered the most reliable for assessing vegetation heterogeneity trends or clustering patterns of NDVI values in this study. This approach allowed us to determine the best metric for monitoring vegetation dynamics and spatial clustering trends across the landscape.

2.4. NDVI Calculation

We selected the Normalized Difference Vegetation Index (NDVI) as an indicator of landscape attributes due to its proven effectiveness in measuring green vegetation biomass. NDVI is calculated using the strong absorption of red light (Band 3) and high reflectance in the near-infrared band (Band 4), making it a reliable proxy for vegetation health and density [24]. Its extensive use across various applications, from vegetation monitoring to urban sprawl analysis, demonstrates its robustness and adaptability. Given its widespread acceptance and suitability for analyzing vegetation dynamics, NDVI was deemed the most appropriate choice for our objectives [46,55,56].

$$\mathrm{N}\mathrm{D}\mathrm{V}\mathrm{I}={\displaystyle \frac{\mathrm{N}\mathrm{I}\mathrm{R}-\mathrm{R}\mathrm{E}\mathrm{D}}{\mathrm{N}\mathrm{I}\mathrm{R}+\mathrm{R}\mathrm{E}\mathrm{D}}}$$

(1)

where Red and NIR stand for the spectral reflectance measurements acquired in the red (visible) and near-infrared regions, respectively.

2.5. Local Spatial Autocorrelation Indices

Local indicators of spatial autocorrelation facilitate the detection of clustered pixels by evaluating the consistency of features within a predetermined neighborhood. In our investigation, we utilized the Getis–Ord Local Gi statistic [57], which contrasts the values of pixels at a specific location with those of pixels situated at a defined lag distance, d, from the original pixel at location i. The formula established by Getis and Ord (1992) [57] is represented by the following equation:

$${\mathrm{G}}_{\mathrm{i}}(\mathrm{d})={\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}\mathrm{j}}\left(\mathrm{d}\right){\mathrm{x}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{i}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}\mathrm{j}}\left(\mathrm{d}\right)}{{\mathrm{S}}_{\left(\mathrm{i}\right)}\sqrt{\left[(\mathrm{N}-1)\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}\mathrm{j}}\left(\mathrm{d}\right)-{\left(\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}\mathrm{j}}\left(\mathrm{d}\right)\right)}^2\right]/\mathrm{N}-2}}}$$

(2)

where N is the total pixel number, i stands for pixel i, x_i and x_j are intensities in points i and j (with i ≠ j), value, and w_ij (d) represents a weight matrix which varies according to distance, S_i= $\sum _{\mathrm{j}=1}^{\mathrm{N}}{{\mathrm{w}}_{\mathrm{i}\mathrm{j}}}^2$.

A high value of the Getis index denotes a positive correlation for high values of intensity, implying the clustering of high-intensity values. Conversely, a low value of the index indicates a positive correlation for low values of intensity, suggesting the clustering of low-intensity values [26]. The primary difference between the local Moran’s Index and the Getis statistic lies in their computation of covariance rather than sums [58]. The local Moran’s Index is mathematically expressed as follows:

$${\mathrm{I}}_{\mathrm{i}}={\displaystyle \frac{({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{X}})}{{{\mathrm{S}}_{\mathrm{x}}}^2}}\sum _{\mathrm{i}=1}^{\mathrm{N}}\left({\mathrm{w}}_{\mathrm{i}\mathrm{j}}\right({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{X}}\left)\right)$$

(3)

where, ${\mathrm{X}}_{\mathrm{i}}$ denotes the variable value in the location I and $\overline{\mathrm{X}}$ represents the average value of all pixels in the study area. We used ENVI5.3 software for calculating the local spatial autocorrelation index. The local spatial autocorrelation indices were computed within a 5 × 5 window around each NDVI pixel, resulting in a 330 m window size (300 m + 30 m-pixel size), as each pixel corresponds to a 30 m spatial resolution. This window size allows for the capture of local vegetation variations while maintaining a balance between detail and computational efficiency. Previous studies have used similar window sizes to analyze landscape heterogeneity, ensuring meaningful results without excessive computational demand [10,23,24].

2.6. Surface Metrics

In this analysis, we used three surface metrics (

Table 2. Descriptions of the selected surface metrics.

Metric	Name	Equation
Ssk	Surface Skewness	${\displaystyle \frac{1}{{MNSq}^3}}{\displaystyle \sum _{k=0}^{M-1}}{\displaystyle \sum _{l=1}^{N-1}}{\left[z\left(x_k,y_l\right)-\mu \right]}^3$
Sku	Surface Kurtosis	${\displaystyle \frac{1}{{MNSq}^4}}{\displaystyle \sum _{k=0}^{M-1}}{\displaystyle \sum _{l=1}^{N-1}}{\left[z\left(x_k,y_l\right)-\mu \right]}^4$
Sa	Average Roughness	${\displaystyle \frac{1}{MN}}\underset{k=0}{\overset{M-1}{\int }}{\int }_{l=0}^{N-1}\left|z\left(x_{k,}{y}_l\right)-\mu \right|$

Where μ = the mean height of NDVI, M = raster rows, N = raster columns, Sq = the root mean square.

) computed with the geodiv R package [59]: surface skewness (Ssk), kurtosis (Sku), and average roughness (Sa). Ssk measures the asymmetry in the NDVI distribution, with negative values indicating a predominance of high NDVI peaks (dense vegetation) and positive values reflecting low NDVI valleys (sparse vegetation). Sku measures deviation from the mean, with values above 3 indicating significant deviation. Sa reflects landscape diversity by calculating the average NDVI height deviation [22]. We applied a 5 × 5 window size for calculating the indices to align with other metrics and ensure consistency in the analysis.

2.7. Texture-Based Measures

We applied three second-order texture measures to NDVI, as detailed in

Table 3. Texture metrics considered as measures of spatial landscape heterogeneity.

Metric	Measure	Value Range	Expected Relationship *	Equation
Dissimilarity	Inversely related to homogeneity.	≥0	H~X	${\displaystyle \sum _i^{N_g}}{\displaystyle \sum _j^{N_g}}p\left(i,j\right)\left|i-j\right|$
Entropy	Shannon-diversity. High when the pixel values of the GLCM have varying values.	≥0	H~X	$-{\displaystyle \sum _i^{N_g}}{\displaystyle \sum _j^{N_g}}p\left(i,j\right)log\left[p\left(i,j\right)\right]$
Homogeneity	A measure of homogenous pixel values across an image.	≥0; ≤1	H~−X	${\displaystyle \sum _i^{N_g}}{\displaystyle \sum _j^{N_g}}{\displaystyle \frac{1}{1+{\left(i-j\right)}^2}}{p}_d\left(i,j\right)$

* H~X, larger values indicate greater heterogeneity; H~–X, lower values indicate greater heterogeneity.

. These measures are based on the probability of observing value pairs at specified inter-pixel distances and orientations. Specifically, we utilized entropy, homogeneity, and dissimilarity metrics [15]. Larger values of dissimilarity and entropy signify increased heterogeneity, while higher values of homogeneity indicate the opposite trend. Texture-based metrics were also computed within a 5 × 5 window around each NDVI pixel.

2.8. Linear Regression

Simple linear regression models the relationship between two variables: a dependent variable (Y) and an independent variable (X). It assumes a linear connection, where changes in X lead to changes in Y. The slope indicates the rate of change in Y for a one-unit change in X, with a positive slope suggesting a direct relationship and a negative slope indicating an inverse relationship. The formula for simple linear regression is:

Y = β0 + β1X + ε

where:

-

Y is the dependent variable (response variable),

-

X is the independent variable (predictor variable),

-

β is the intercept of the regression line,

-

β1 is the slope of the regression line,

-

ε represents the error term, which captures the difference between the observed values of Y and the values predicted by the regression line.

In this study, we treated the period from 2013 to 2023 as the independent variable, while NDVI and other continuous metric values served as the dependent variables. Subsequently, we generated two trend maps indicating pixels with negative (decreasing) and positive (increasing) slopes. Additionally, a significance map was created, displaying the p-value of the regression slope to delineate significant changes exclusively. Finally, for every metric, the significant pixels of the NDVI map (p-value ≥ 0.05) were overlapped with the trend map of each continuous metric to identify the positive or negative trends concerning these pixels. This approach enables the assessment of changes in the heterogeneity of vegetation patterns, as each metric captures a distinct aspect of the heterogeneity.

3. Results

Our study area consisted of 327,104 pixels, for which we calculated 8 metrics on 11 NDVI maps spanning from 2013 to 2023. As a result, for each pixel, we obtained 11 values on which we applied linear regression, calculating the p-value, R-squared, and slope for each pixel. This process yielded 3 maps for each metric, totaling 24 raster maps. Additionally, we calculated three similar maps for NDVI, bringing the total to 27 images. However, we decided that presenting all the maps was unnecessary and selected a subset of them for presentation.

Figure 3 displays (a) the slope coefficient, (b) the p-value, (c) the negative and positive trend, and (d) significant p-values of NDVI pixels spanning from 2013 to 2023. The trend map illustrates all pixels manifesting either positive or negative trends, though not all represent significant changes. Conversely, the significance map highlights only a subset of pixels that have undergone notable alterations during the specified timeframe. In Figure 4, a slope coefficient map is presented for dissimilarity (a) and homogeneity (b) of NDVI values, along with Sa and Moran metrics. Dissimilarity and homogeneity of NDVI exhibit an inverse correlation, showcasing contrasting high values for landscape heterogeneity. The Sa metric map displays similar patterns to the dissimilarity of NDVI, while Moran of NDVI demonstrates different landscape patterns. Higher values of spatial autocorrelation indices indicate clustered NDVI patterns, while lower values signify landscape heterogeneity. Surface metrics like Sa provide insights into whether NDVI values have increased or decreased, indicating dominance in the landscape. However, continuous metrics reveal diverse NDVI patterns. For a more comprehensive comparison, it is crucial to distinguish the positive and negative trends of significant pixels exclusively. This approach facilitates determining the proportion of significant pixels displaying positive or negative trends, enabling a more nuanced interpretation of the results.

Figure 5 illustrates the trends and significance of various NDVI-based metrics: (a) dissimilarity, (b) entropy, (c) homogeneity, (d) Getis, (e) Moran, (f) Sa, (g) Sku, and (h) Ssk. For each metric, two maps are presented: one showing the positive and negative heterogeneity trends across all pixels and another highlighting only the statistically significant pixels based on linear regression. The map showing positive and negative trends includes all pixels exhibiting a trend, regardless of statistical significance. The interpretation of each map depends on the definition and nature of the corresponding metric.

For instance, local spatial autocorrelation metrics such as Getis and Moran of NDVI capture clustering patterns. Positive trends indicate that NDVI pixels have become more clustered over time, whereas negative trends suggest increasing heterogeneity. In contrast, surface metrics like Sa, Sku, and Ssk do not address clustering, but rather analyze the valleys (pixels with low NDVI values) and peaks (pixels with high NDVI values representing denser vegetation) in the NDVI maps. For example, the Sa metric, analogous to the “Number of Patches” (NP) in landscape metrics, reflects the abundance of vegetated pixels over time. A positive trend in Sa suggests an increase in the presence of vegetated pixels, while a negative trend indicates a decline. Each metric provides unique insights into vegetation heterogeneity and landscape dynamics, emphasizing the need to interpret the results in the context of their specific characteristics.

Statistical Comparison

Figure 6 displays the correlation values between the slope of NDVI and the slopes of other continuous metrics across the study area (n = 327,104 pixels). The correlations range from positive to negative, indicating varying relationships between NDVI changes and other metrics. Among the metrics, Moran exhibits the highest positive correlation with NDVI (0.63), suggesting a strong spatial autocorrelation between NDVI changes and neighboring areas’ trends. Similarly, Getis (0.49) and dissimilarity (0.45) also show moderate positive correlations, indicating some alignment between NDVI trends and these spatial heterogeneity metrics. On the other hand, homogeneity demonstrates the most pronounced negative correlation (−0.41), implying that areas with declining NDVI trends tend to become less homogeneous in terms of vegetation distribution. Weak negative correlations are observed for Sku (−0.12) and Ssk (−0.24), suggesting a minimal relationship between NDVI trends and surface metrics like skewness and asymmetry, respectively. Entropy and Sa show weaker positive correlations (0.28 and 0.37, respectively), indicating a slight association between NDVI trends and these metrics.

4. Discussion

In this study, we evaluated the relationships between NDVI trends and other continuous metrics across the study area to assess vegetation heterogeneity and clustering patterns over time. Using linear regression, we generated slope maps for each metric, representing pixel-level trends, and correlated these with the NDVI slope map to identify metrics most strongly associated with vegetation dynamics. Our results revealed that Moran’s Index showed the highest positive correlation (0.63) with NDVI trends, indicating that areas with increasing NDVI tend to exhibit stronger spatial clustering. Other metrics, such as Getis (0.49), dissimilarity (0.45), and Sa (0.37), also demonstrated positive correlations, suggesting that they are useful indicators of vegetation dynamics. In contrast, homogeneity (−0.41), Sku (−0.12), and Ssk (−0.24) exhibited negative correlations, indicating that increasing NDVI trends are associated with reduced uniformity and surface dominance.

The interpretation of these correlations highlights important aspects of landscape changes. Positive correlations between NDVI and dissimilarity or entropy suggest that areas with increasing vegetation cover often show higher variability and heterogeneity in vegetation composition. Similarly, the strong positive correlation with Moran’s Index reflects that higher NDVI trends align with a more clustered spatial arrangement, where similar NDVI values are concentrated in specific regions. These findings do not indicate inconsistency, but rather emphasize the complementary nature of these metrics. While Moran’s Index and Getis reveal patterns of clustering (spatial autocorrelation), dissimilarity and entropy focus on value variability, which can exist within those clusters.

While the efficacy of continuous metrics has been explored in various studies [19,23,24,29,60], their applicability in trend analysis remains underexamined. In this study, spatial autocorrelation metrics, such as Moran of NDVI and Getis of NDVI, exhibited the strongest correlations with NDVI trends across the study area. This indicates that similar NDVI values tend to cluster, leading to an increase in spatial autocorrelation over time. These metrics effectively captured the clustered spatial patterns of vegetation and other land cover types within the landscape. Previous research has extensively demonstrated the effectiveness of spatial autocorrelation metrics in characterizing landscape heterogeneity. For example, Fan and Myint (2014) [24] established a robust relationship between Getis of NDVI and key landscape metrics, achieving high R² values of 95% and 82% for PLAND (percentage of landscape) and LPI (largest patch index), respectively. Similarly, Rahimi et al. (2022) [23] reported strong correlations between Getis of NDVI and PLAND and LPI metrics, with R² values of 95% and 92%. These studies underscore the utility of spatial autocorrelation metrics, particularly in detecting subtle land-use changes and rapidly assessing landscape patterns using NDVI imagery. The findings of our study align with these observations, highlighting the reliability of these metrics in analyzing temporal trends and landscape dynamics.

Texture-based indices, particularly the dissimilarity of NDVI, showed the highest correlation with the slope of NDVI trends in this study, followed by homogeneity and other texture-based metrics, like entropy. These results highlight the utility of texture-based indicators in capturing changes in vegetation dynamics over time. Other research has similarly validated the effectiveness of these texture-based metrics when compared to traditional landscape metrics, which typically rely on classified satellite imagery and discrete land-use maps as inputs. For instance, Rahimi, et al. [19] examined the relationship between land surface temperature (LST) and vegetation cover in Tehran using texture-based metrics. Their study found that the entropy of NDVI could explain nearly 50% of the variation in LST values (R² = 49.5%), whereas no traditional landscape metric accounted for more than 22.7% of the variation. The findings demonstrated that in urban environments with heterogeneous vegetation patterns, increased heterogeneity correlates with higher LST values. Texture-based indicators generally fall into two categories based on their ability to measure landscape heterogeneity: (1) metrics where higher values indicate greater heterogeneity, such as mean, variance, contrast, dissimilarity, and entropy, and (2) metrics where lower values correspond to higher heterogeneity, including homogeneity, correlation, and energy [15,61,62]. These indicators provide a more nuanced understanding of landscape heterogeneity, making them particularly effective for analyzing dynamic environments and vegetation patterns.

This study also incorporated three surface metrics to assess landscape heterogeneity, although these metrics exhibited the lowest correlation with the NDVI slope map, indicating limited alignment with NDVI dynamics over the study period. Among these, positive values of surface skewness (Ssk) suggest a higher prevalence of bare soil and built-up areas relative to vegetation cover, aligning with the observed decline in vegetation over the study period. Conversely, surface kurtosis (Sku) reflects the dominance of a specific cover type, showing minimal change in cover dominance between 2013 and 2023. For a more comprehensive understanding, Sku should be interpreted alongside Ssk. Similarly, the average roughness (Sa) metric, which does not differentiate between cover types, suggests an increase in patch richness within the study area, likely due to a rise in non-vegetated pixels, as inferred from the other metrics.

While surface metrics are recognized for their sensitivity to subtle land-use changes and their suitability for analyzing long-term landscape alterations [23], they do have limitations. For instance, their estimates of landscape dominance are highly sensitive to input data, leading to variability in results [21]. Additionally, their interpretation can be complex, and unlike landscape metrics, surface metrics do not quantify changes in area units. Despite these challenges, prior studies have demonstrated their effectiveness in quantifying landscape heterogeneity [10,60]. Surface metrics remain valuable tools for capturing nuanced changes in land-use patterns, offering insights into long-term trends and subtle variations in landscape composition.

In this study, local spatial autocorrelation metrics proved to be more effective in capturing vegetation heterogeneity compared to other metrics as they demonstrated a strong alignment with NDVI trends. This alignment highlights their capacity to reflect finer spatial variations in vegetation patterns, which is critical for accurately assessing heterogeneity. While this does not universally establish these metrics as superior, their ability to closely match NDVI trends makes them particularly well-suited for detecting vegetation dynamics, especially within the specific context of clustering NDVI changes over time or trend analysis.

The strong correspondence between the slope of Moran’s NDVI and NDVI trends underscores the sensitivity of spatial autocorrelation metrics to vegetation dynamics. These metrics excel in capturing subtle spatial variations, allowing them to identify nuanced changes in vegetation patterns that other metrics, such as surface metrics or texture-based indices, may miss. By focusing on vegetation heterogeneity, this study demonstrates the utility of autocorrelation metrics in providing a more comprehensive and detailed understanding of how vegetation patterns are spatially distributed. Their alignment with NDVI trends reinforces their value as powerful tools for analyzing changes and heterogeneity in vegetation over time.

5. Conclusions

This study provides a comprehensive evaluation of NDVI trends from 2013 to 2023 in a study area in Iran, emphasizing the importance of analyzing landscape heterogeneity alongside NDVI dynamics. By correlating the slope of NDVI with various continuous metrics, this research identifies the most effective indicators of vegetation heterogeneity and clustering patterns over time. Moran’s Index demonstrated the highest positive correlation (0.63) with NDVI trends, indicating strong spatial clustering in areas with increasing NDVI. Metrics like Getis (0.49) and dissimilarity (0.45) also showed notable positive correlations, underscoring their utility in assessing vegetation dynamics. Conversely, metrics such as homogeneity (−0.41), Sku (−0.12), and Ssk (−0.24) exhibited negative correlations, reflecting reduced uniformity and surface dominance in areas with increasing NDVI.

Spatial autocorrelation metrics emerged as the most effective tools for capturing vegetation heterogeneity, aligning closely with NDVI trends and providing insights into clustered spatial patterns. These metrics excelled in detecting subtle changes in vegetation dynamics that other approaches, such as surface or texture-based metrics, might overlook. Texture-based metrics like dissimilarity and entropy were also effective in capturing changes in vegetation heterogeneity, complementing spatial autocorrelation metrics by highlighting value variability within clusters. Surface metrics, although less aligned with NDVI dynamics, provided additional insights into landscape composition, such as the prevalence of bare soil and built-up areas.

This study demonstrates the importance of integrating diverse metrics to achieve a nuanced understanding of vegetation heterogeneity and spatial clustering over time. The findings highlight the utility of spatial autocorrelation metrics in detecting vegetation dynamics and their potential for analyzing long-term trends. These results reinforce the need for robust methodologies that incorporate complementary metrics to capture the complexity of landscape changes, offering valuable tools for monitoring and managing vegetation in dynamic environments.