3.1. SPMOR Model
The SPMOR framework consists of five layers: State, Pressure, Modelling, Optimization, and Response (
Figure 3). Indicator assignment was based on the primary ecological diagnostic function of each variable, following the conceptual logic of the PSR framework and its extended applications in ecological security assessment [
28].
The State layer describes the current ecological condition and ecosystem service capacity, including land surface temperature, evapotranspiration, landscape pattern metrics, and ecosystem service value.
The Pressure layer reflects external disturbances and human activity intensity through indicators such as population density, steep-slope cultivated land, regional development intensity, land-use intensity, and distance to construction land.
The Response layer reflects the capacity of socio-ecological systems to cope with pressures and support ecological recovery [
28,
29]. Based on this interpretation, GDP per unit area, ecosystem resilience, and distance to the core ecological zone were selected to characterize socio-economic support capacity, natural recovery potential, and the spatial governance context, respectively.
The Modelling layer is interpreted as a modelling-oriented diagnostic component that integrates indicators derived from ecological assessment models and temporal change analyses to characterize ecological vulnerability, sensitivity, and historical ecosystem dynamics, rather than to simulate or predict future conditions. Specifically, the slope–FVC vulnerability index represents ecological vulnerability associated with terrain and vegetation conditions, while NDVI change trends and land-use change frequency characterize vegetation dynamics and land-use transitions over time.
The Optimization layer evaluates the potential for ecological restoration and land-use regulation. Ecological land allocation rationality reflects the adequacy of ecological land within each grid, whereas high-intensity land-use pressure identifies areas requiring stricter development control or ecological restoration.
All indicators were standardized and assigned to a single SPMOR layer (
Table 2). A consistent sign convention was adopted, where “+” indicates a positive contribution to ecological security, and “−“ indicates a negative contribution.
(1) State: This layer characterizes baseline ecosystem condition—structural integrity, functional stability, and service capacity—via landscape configuration and composition metrics and service valuation. X1 Land Surface Temperature (LST, −) captures thermal stress and surface energy balance as a first-order proxy of ecosystem condition. X2 Evapotranspiration (ET, −) reflects land–atmosphere water exchange through soil evaporation and vegetation transpiration. In this study, higher ET indicates greater water consumption and potential water loss, which may reduce soil moisture and available water resources. Therefore, from the perspective of water conservation and ecological security, ET was treated as a negative indicator in the ESI calculation [
30,
31]. Landscape structure is then characterized by X3 Patch Density (PD, −) and X4 Patch Cohesion Index (COHESION, +) following FRAGSTATS conventions: PD quantifies fragmentation intensity (Equation (1)), while COHESION measures physical connectedness of class
i (Equation (2)) [
32]. Compositional heterogeneity is captured by X5 Shannon Diversity Index (SHDI, +) and X6 Shannon Evenness Index (SHEI, +), computed by Equations (3) and (4), which diagnose richness and balance of land-cover types at the landscape scale. Finally, service provision capacity is monetized by X7 Ecosystem Service Value (ESV, +) using the equivalent-factor method localized for Fanjingshan (Equation (5)); this approach is widely adopted in regional studies because it is transparent and requires relatively few input parameters [
33]. The local standard equivalent value was then multiplied by the ecosystem service equivalent coefficients assigned to each land-use category and converted to yuan/km
2. The resulting category-specific ESV coefficients are reported in
Table 3.
where
is the total patch count,
the landscape area (
),
and
the perimeter and area of the
-th patch of class
, and
the landscape area in cell units.
with
being the area share of class
and
the number of classes.
where
(yuan
) is the unit-area value coefficient of service
for land-use type
, and
is the corresponding area.
(2) Pressure: This layer identifies external stressors with emphasis on human-activity intensity and land-use disturbance. X8 Population Density (−) represents human activity intensity and background anthropogenic pressure [
34]. X9 Percentage of cultivated area on steep slopes (−) flags erosion-prone farming where slope > 15°, computed by Equation (6), consistent with soil-loss/erosion standards (RUSLE/CSLE) [
35]. X10 Regional Development Index, RDI (−), aggregates cropland and construction-land shares via Equation (7) to provide a compact proxy of urbanization intensity and the human footprint [
36]. X11 Land-Use Intensity (−) was calculated as the area-weighted sum of land-use intensity grades across land-use classes (Equation (8)), reflecting the overall intensity of human land utilization within each grid [
37]. X12 Distance to Construction Land (+)—the Euclidean distance to the nearest built-up pixel—captures edge-driven disturbance and encroachment pressure recognized in landscape ecology edge-effect theory.
where
is the cropland area,
is the construction-land area, and TA is the cell area.
where
is the land-use intensity grade of land-use class
, and
is the area proportion of land-use class (
i) within the grid.
(3) Modelling: This layer expresses temporal evolution to anticipate system trajectories. X13 Slope–FVC Vulnerability Index (−) (Equation (9)) couples topographic sensitivity with vegetation stability, following ecological vulnerability assessment practice in erosion-prone regions [
38]. A higher value indicates a greater risk of degradation under disturbance. The X14 NDVI Change Trend Index (+) (Equation (10)) is calculated separately for each assessment interval (e.g., 2000–2005, 2005–2010, etc.) by performing a pixel-wise linear regression of annual NDVI values within that interval, and the resulting slope is used to represent the direction and magnitude of vegetation change during that specific period, which is widely used to indicate vegetation degradation or recovery in remote-sensing ecology [
39]. X15 Land-Use Change Frequency (−) (Equation (11)) is also computed for each assessment interval by counting the number of land-use type transitions for each pixel between consecutive land-cover maps within that interval (e.g., changes from 2000 to 2005, 2005 to 2010, etc.), thereby quantifying the frequency of land-use conversions during that period as a proxy for disturbance intensity and spatial instability in land-system science [
40].
where
is the normalized slope, and
is the normalized fractional vegetation cover (FVC).
where
is the regression slope of the NDVI time series for each pixel within the corresponding assessment interval.
where
is the land-use change frequency within assessment interval
,
is the land-use class at time
within interval
,
is the number of land-use observations in that interval, and
I(·) equals 1 when a land-use transition occurs and 0 otherwise.
(4) Optimization: This layer is operationalized as an optimization-oriented diagnostic component that evaluates the rationality of ecological land allocation and high-intensity land-use pressure. X16 Ecological Land Allocation Rationality (ELAR, +) (Equation (12)) measures the proportion of ecological land (forest, grassland, and water bodies) within each grid cell, reflecting the adequacy and spatial support capacity of ecological land in maintaining ecosystem stability [
15]. A higher RELA indicates a more favorable ecological land structure, consistent with conservation-planning theory emphasizing connectivity [
41]. X17 Proportion of High-Intensity Land Use (PHILU, −) (Equation (13)) quantifies the share of impervious or construction land, capturing the encroachment effect of intensive human activities and serving as a negative optimization indicator [
42].
where
, and
are the areas of forest, grassland, and water bodies within the grid cell, and
is the total cell area.
where
is the area of high-intensity land use (impervious/construction land) within the grid cell, and
is the total cell area.
(5) Response: This layer evaluates the management capacity and societal response to ecological risks, serving as the institutional guarantee for ecological restoration and sustainable management. X18 GDP per unit area (+) was used to represent regional socio-economic support capacity within the Response layer. Therefore, GDP per unit area was treated as a positive indicator in the ESI calculation, while development-related pressures were represented separately by indicators such as regional development intensity, land-use intensity, and high-intensity land-use pressure [
43]. X19 Ecosystem Resilience (NPP, +) measures the capacity of ecosystems to maintain and recover functions after disturbance, with net primary productivity widely recognized as a robust proxy for resilience [
44]. X20 Distance to Core Ecological Zone (+) captures the spatial proximity to strictly protected areas, reflecting the effectiveness of zoning policies in mitigating human disturbance and providing refuge for biodiversity [
45].
3.2. CRITIC Objective Weight Analysis
To ensure the comparability of indicators with different units and magnitudes, all raw data were first normalized using the range standardization method. For positive indicators, where larger values indicate higher ecological security, normalization follows Equation (14). For negative indicators, where larger values denote stronger stress or lower security, normalization follows Equation (15). This step eliminates the influence of scale heterogeneity and enables the integration of diverse ecological, environmental, and socioeconomic variables into a unified evaluation framework [
46].
where
is the raw value of indicator
for grid cell
,
is the normalized value, and
and
are the maximum and minimum values of indicator
across all grid cells, respectively.
Following normalization, the CRITIC method (Criteria Importance Through Intercriteria Correlation) was applied to determine indicator weights objectively. Unlike subjective weighting approaches such as AHP, CRITIC accounts for both the contrast intensity of each indicator (standard deviation) and its conflict with others (correlation), thereby providing a robust and data-driven weighting scheme [
47]. Specifically, the information content of indicator
j is calculated as in Equation (16).
where
is the standard deviation of indicator
, and
is the Pearson correlation coefficient between indicators
and
. The normalized weight is then given by Equation (17).
To assess the robustness of the ESI results to the weighting scheme, a sensitivity analysis was performed by perturbing the CRITIC-derived weights. For each year, weights were randomly varied within ±10% and then normalized to sum to 1. This process was repeated 1000 times, with ESI recalculated each time. Robustness was evaluated using the mean ESI, standard deviation, coefficient of variation, and Spearman’s rank correlation with the baseline results.