Spatiotemporal Heterogeneity of the Standardized Summer Resort Index Under Normal and Extreme High-Temperature Climates Based on a PCA–Copula Model: A Case Study of Shaanxi Province

Abstract

This study aims to address the limitations of conventional summer-resort suitability evaluation, which fails to characterize the nonlinear responses of multi-factor variables and suffers from subjectivity in linear weighting, by constructing, based on observational records from 101 meteorological stations across Shaanxi Province spanning 1981–2024, an evaluation system that covers four dimensions (physiological thermal comfort, environmental amenity, extreme-weather risk and climatic stability) with 13 indicators. Group-based principal component analysis (PCA) is applied for dimensionality reduction. A multi-dimensional joint distribution is further established by integrating the empirical cumulative distribution function (ECDF) and the C-vine copula function to derive the Standardized Summer-Resort Index (SSRI). Independent external validation is implemented using outputs of the Universal Thermal Climate Index (UTCI) from ERA5-HEAT, and leave-one-out cross-validation (LOOCV) is adopted to assess the generalization performance and responses to extreme climates. The results reveal that the C-vine copula effectively captures the conditional dependence and nonlinear structures among multi-dimensional climatic variables (AIC = −4490.36, CvM test p = 0.175). The SSRI exhibits a significant positive correlation with the fraction of days without thermal stress derived from UTCI (Kendall’s τ = 0.289, p < 0.001), and the average year-to-year classification accuracy of LOOCV reaches 66.3%. Plains are dominated by wind-driven heat dissipation, whereas high-altitude mountainous regions are sensitive to temperature–humidity variations, and statistical buffering signals induced by vegetation can be detected. The SSRI in Shaanxi presents a “three-high and two-low” spatial pattern: high-value clusters occur in the Qin-Ba Mountains, the northern slope of the Daba Mountains and the Huanglong Forest Region, while low-value areas are distributed in the Guanzhong Basin and the wind-sand zones of northern Shaanxi. Relatively high suitability within forested areas during extreme high-temperature events can be statistically identified, which is jointly modulated by altitude–terrain–vegetation interactions, with a balanced accuracy of 0.771. The complete modelling workflow of this study can provide methodological references for other complex terrain regions. Nevertheless, all Shaanxi SSRI parameters, normalisation thresholds and classification criteria are trained on Shaanxi-specific datasets and cannot be directly transferred; local observational data must be used for refitting and calibration when applying this index to other regions.

1. Introduction

Global warming continues to intensify, with extreme heatwaves increasing in frequency and magnitude and expanding in areal extent year by year. Such events have evolved from localized weather anomalies into global-scale climatic risks [1,2]. Growing thermal stress substantially elevates population-level health risks, disturbs regional hydrothermal allocation and ecological homeostasis, and continuously reshapes patterns of summer residential and tourist activities [3,4]. As hot-weather conditions become recurrent, improving human settlement environments and climate-resilience capacity has emerged as a critical component of regional livelihood security and disaster risk reduction. Accordingly, developing scientifically robust thermal environment assessment frameworks to quantitatively identify spatiotemporal patterns of climatic resources for summer escape constitutes a fundamental research direction for climate-change adaptation and built-environment optimization.

Spatial heterogeneity in the Standardized Summer Resort Index (SSRI) across mountainous and climate transition zones is jointly modulated by elevation, topography, vegetation cover and local-scale circulations. Situated at the core of China’s north–south climatic transition zone [5], Shaanxi Province encompasses three major geomorphic units: the Loess Plateau, the Guanzhong Plain and mountainous forest terrain. Combined with latitudinal gradients, altitudinal variation and urbanization effects, these features produce a complex composite climatic pattern [6,7]. The Guanzhong Plain suffers pronounced static-wind heat stress and the urban heat-island effects during summer [8]; by contrast, the Qinling-Daba Mountains and Huanglong Mountain Range maintain thermally favourable habitats driven by high elevations and dense forest cover [9,10]. Following long-term ecological restoration, local summer thermal conditions across northern Shaanxi have progressively improved, revealing untapped summer-escape potential. Its diverse landforms, pronounced climatic gradients and stark spatial contrasts in thermal environments render Shaanxi an ideal natural laboratory for evaluating SSRI and refining climatic-assessment models over complex terrain domains.

Current mainstream global SSRI assessments adopt linear static empirical evaluation frameworks, largely focusing on single geomorphic units such as plains and urban areas, with highly rigid evaluation logic, modelling approaches and validation systems, thereby neglecting microclimatic heterogeneity under composite landforms such as mountains, river valleys and hills [11]. Complex landform areas are subject to the coupled effects of multiple factors, including elevation differences, topographic shading and local circulation [12], where thermal-sensation climatic elements such as air temperature, humidity, and wind speed exhibit pronounced spatiotemporal differentiation. Traditional single, homogenized evaluation models cannot accurately characterize the true distribution patterns of local summer-resort climates and are highly prone to large-scale assessment biases [13]. Therefore, developing a summer-resort suitability evaluation model that objectively characterizes the nonlinear coupling of multiple factors and adapts to mountainous regions with interlaced multiple landforms remains an important research gap in complex mountain-climate-resource assessment.

SSRI can be characterised from multiple dimensions, including meteorological perception, environmental background and climatic hazard exposure. To this end, multiple indices have been proposed, such as the Temperature–Humidity Index (THI), the Wind Effect Index (WEI) and the Comfort Index of Human Body (CIHB) that integrates temperature, humidity and wind velocity. Nevertheless, unidimensional indices frequently cannot fully capture the multifaceted nature of summer-escape environments. For instance, Gao et al. reported that the CIHB neglects solar radiation inputs and thereby introduces considerable bias during daytime hours [14,15]. Liu et al. noted that THI and WEI are rooted in empirical formulations with limited transferability and accuracy; meanwhile, key input variables for thermal-climate indices, such as mean radiant temperature, are rarely available from routine observational networks, hindering broad-scale implementation [16]. Air-temperature alone cannot account for the modulating effects of humidity and wind speed. Furthermore, indices focused merely on instantaneous human thermal sensation overlook long-term climatic stability and the disruptive impacts of extreme weather events (e.g., heavy rainfall, severe convective storms) on summer-escape experiences. Since summer-escape suitability is governed by intertwined meteorological, environmental and ecological systems with ambiguous boundaries, single-variable indices are inadequate for cross-dimensional monitoring of SSRI [17].

To mitigate such intrinsic limitations of standalone indices, recent studies have developed comprehensive multivariable meteorological evaluation models. Analytic Hierarchy Process (AHP), entropy-weighting approaches, fuzzy comprehensive evaluation and hybrid techniques such as entropy-weighted Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) are commonly deployed for indicator weighting [18]. These methods, however, suffer from non-negligible subjectivity in weight assignment, undermining their objectivity for cross-temporal and cross-regional comparisons. As a flexible statistical tool, copula functions impose no constraints on marginal-distribution forms of input variables. They construct multi-dimensional joint distributions by separately modelling marginal behaviours and dependence structures, enabling quantification of nonlinear interdependencies among multi-source variables. Copula functions have been widely applied in hydrological and hazard analyses for estimating return periods of precipitation, drought and flood events. Nonetheless, few existing studies have implemented copula-based frameworks to investigate summer-escape suitability. For independent methodological validation, the Universal Thermal Climate Index (UTCI) offers a standalone reference benchmark to resolve the above-mentioned internal validation bottleneck. Recommended by the International Society of Biometeorology (ISB), UTCI is built upon the Fiala multi-node human heat-balance model. It synthesises air temperature, humidity, wind speed and mean radiant temperature, and outputs an equivalent environmental temperature (℃) via iterative heat-balance computation. Distinct from empirical indices, UTCI is underpinned by well-defined biophysical mechanisms and is methodologically independent of the PCA–copula statistical framework adopted herein.

The ERA5-HEAT dataset hosted by the Copernicus Climate Data Store provides hourly gridded UTCI products at 0.25° spatial resolution, derived from ERA5 reanalysis inputs and full Fiala-model simulations. It delivers standardised observational surrogates to support external validity testing of thermal-comfort indices. Using long-term in-situ meteorological records and multi-source environmental datasets, this study therefore constructs a novel SSRI tailored for complex terrain regions by coupling PCA dimensionality reduction with copula functions. The composite index synthesises physiological thermal comfort, environmental favourability, extreme-weather hazard risk and climatic stability to holistically quantify summer-escape suitability. This framework supports scientific exploitation of local summer-escape climatic resources and advances disaster prevention capacity. Taking UTCI as an independent external benchmark alongside multiple cross-validation strategies, we systematically evaluate the efficacy, generalisability and multi-dimensional advantages of SSRI, providing methodological references for robust assessment of summer-escape climatic resources across the study domain.

Addressing the aforementioned research gaps, this study develops a PCA–copula-coupled SSRI using 1981–2024 long-term meteorological station observations for Shaanxi Province, 250 m resolution remote-sensing vegetation datasets and high-resolution ERA5-HEAT UTCI reanalysis products. A four-dimensional composite evaluation system covering physiological thermal comfort, background environmental conditions, extreme-meteorological hazards and climatic stability is established to circumvent the partiality of conventional single-indicator and purely linear evaluation schemes. A fully objective nonlinear evaluation workflow is implemented via grouped dimensionality reduction, marginal-distribution fitting and multivariate joint probability modelling. External validation is performed using UTCI datasets with independent biophysical foundations, substantially improving quantification accuracy and reliability for summer-escape suitability assessments over compound landform regions.

This study complements and improves the existing summer-resort climate evaluation system from methodological, mechanistic and regional-cognition perspectives. Methodologically, by integrating principal component dimension reduction and Copula-based nonlinear modelling, this study avoids the subjectivity of conventional artificial weighting and the limitations of linear superposition assumptions. It can effectively capture the nonlinear coupling and tail dependence characteristics of multi-climatic–ecological factors. Meanwhile, a multi-dimensional validation framework consisting of “temporal consistency + extreme-scenario test + independent physical benchmark” is constructed to enhance the robustness of evaluation outputs. Mechanistically, the statistical correlation features of thermal environments across diverse geomorphic units are analysed, and differentiated coupling relationships of summer thermal environments among basins, mountains and plateaus are discussed, which enrich the understanding of thermal environments over diverse landforms within the north–south climate transition zone. From the perspective of regional cognition, this study systematically distinguishes the bidirectional counterbalance between latitude-driven cooling and underlying surface heat absorption in northern Shaanxi. Correlative signals between ecological restoration and local thermal environment improvement are observed, and potential SSRI-related resource potential in partial areas of the Loess Plateau is identified, filling cognitive gaps in existing regional-climate-resource evaluations.

This study characterizes the spatiotemporal differentiation of SSRI across Shaanxi Province and analyses the statistical relationships among topographic relief, vegetation cover and thermal buffering effects. Significant positive correlations between high vegetation cover and local SSRI are observed, and ecological restoration zones in northern Shaanxi exhibit favourable potential for summer-resort resource exploitation. The PCA–copula modelling workflow proposed in this study provides methodological references for mountain-region studies with interleaved landforms. The model parameters and normalised percentile thresholds of SSRI are trained on local Shaanxi datasets. When applied to other regions, the entire workflow requires refitting and calibration based on local observational data, and existing parameters cannot be directly reused. This work can offer research insights for summer-climate-resource assessment, human-settlement thermal environment optimisation and high-temperature disaster risk management in mid-latitude climate transition zones and regions with complex interleaved landforms.

2. Methods

2.1. Research Area and Data Processing

This study takes the entire territory of Shaanxi Province as the study area. A total of 101 national-level and regional meteorological observation stations are distributed across the province, with elevations ranging from 210 m to 3710 m. These stations fully cover the major elevation gradients in Shaanxi, spanning the Guanzhong Basin, the Loess Plateau and the Qin-Ba mountainous high-elevation zones, and represent a well-distributed sample across provincial elevation gradients. Crossed by the Qinling Mountains, the geographic dividing line between northern and southern China’s climates, Shaanxi represents a typical compound geomorphic unit encompassing three distinct landforms: the Loess Plateau in northern Shaanxi, the enclosed alluvial Guanzhong Basin and the mid- to high-elevation Qinling-Daba mountainous terrain in southern Shaanxi [19] (Figure 1). It serves as an ideal testbed for exploring summer climatic heterogeneity for summer-escape conditions under diverse terrains and developing nonlinear assessment models for the SSRI [20].

Shaanxi Province lies between 105°29′–111°15′ E and 31°42′–39°35′ N, with a total land area of approximately 205,600 km². Stretching east–west across the province, the Qinling Mountains naturally demarcate three geomorphic-climatic zones with striking disparities. The Guanzhong Basin belongs to the warm-temperate semi-humid climate zone. Characterised by dense urban agglomerations and enclosed topography, it experiences stagnant wind and intense heat in summer with pronounced urban heat-island effects, forming the core area with low SSRI across the whole province. The Qinling-Daba Mountains of southern Shaanxi feature a northern subtropical humid climate, large altitudinal relief and forest coverage exceeding 85%. Significant vertical temperature lapse rates create natural cold-source environments [21,22], making this region the primary core for high SSRI within the province. The Loess Plateau in northern Shaanxi has a temperate semi-arid climate at relatively high latitudes. The Grain-for-Green Project has greatly improved vegetation cover, bringing large diurnal temperature ranges and endowing this plateau with unique summer-escape potential.

This study integrates three multi-source datasets: ground-based meteorological observations, long-term vegetation remote-sensing products and digital topographic data [23]. All datasets underwent outlier removal, gap-filling and standardised preprocessing. A complete panel dataset was constructed following full time-series characteristics for model development and accuracy validation. Detailed data sources and processing workflows are described below.

This study collected daily observational data spanning 1981–2024 from 101 meteorological stations in Shaanxi Province, including daily air temperature, relative humidity, wind speed, precipitation, air pressure and sunshine duration. The raw datasets were obtained from Shangluo Meteorological Bureau. Missing-value processing and station screening were performed prior to homogenisation correction.

For station screening based on temporal completeness, stations with valid observation proportions lower than 90% in summer (June–August) were eliminated. Retained stations were allowed short-term continuous data gaps, with the maximum permissible gap length set to 7 days. Missing daily records of retained stations were gap-filled via the distance-weighted method using neighbouring stations. Reference candidate stations were high-quality meteorological sites within 50 km of the target station and within the same climatic zone, and reciprocals of spherical distances were adopted as weights to construct weighted interpolation series for gap filling. Cross-validation was implemented after interpolation: 10% of valid observations were randomly masked to evaluate interpolation accuracy. Comparison between interpolated series and real observations yielded R² = 0.91 and RMSE = 0.76 °C for air temperature variables, demonstrating that the interpolation scheme meets reliability requirements for this study.

Raw meteorological records underwent three-level operational homogenisation correction by Shangluo Meteorological Bureau. This operational homogenisation strictly follows national technical specifications for meteorological-data homogenisation. RHtestV4 software was applied to detect temporal inhomogeneities using the Penalized Max-T Test (PMT) and Penalized Max-F Test (PMF). Composite reference series were constructed by correlation coefficient weighting from neighbouring stable stations within the same climatic zone. The significance level for breakpoint detection was set at α = 0.01. Station metadata (relocation records, instrument replacement logs and changes in the observation environment) were used to distinguish artificial non-climatic breakpoints from natural climate-driven fluctuations. The above-mentioned datasets were provided by Shangluo Meteorological Bureau; one co-author of this study is affiliated with this institution, and data acquisition complies with relevant regulatory requirements.

Two remote-sensing vegetation datasets were adopted: the NOAA GIMMS NDVI dataset for 1981–2022 (https://www.resdc.cn), accessed on 1 March 2026 and the 250 m national fractional vegetation cover (FVC) dataset for 2000–2024 (https://www.resdc.cn), accessed on 1 March 2026. Obvious discrepancies exist in spatial resolution and retrieval algorithms between the two products. High determination coefficients derived merely from regression fitting over overlapping periods cannot fully guarantee the homogeneity of merged time series. In this study, linear calibration models (R² > 0.85) were built using mean values within 25 km circular buffers around each station during their overlapping period (2000–2022) for data assimilation. The merging rules are described as follows: calibrated coefficients were applied to convert GIMMS-NDVI into equivalent FVC series for 1981–1999; the native 250 m FVC product was directly adopted for 2000–2024, with year 2000 serving as the sole potential data-source transition node.

Multiple tests were conducted on assimilated FVC series from 31 representative stations for long-term trend analysis to assess artificial temporal discontinuities induced by dataset switching. Breakpoint detection was performed via the PMT algorithm embedded in RHtest-V4 at α = 0.01. Real ecological breakpoints identified from regional ecological records were excluded, and no artificial breakpoints triggered by remote-sensing data-source switching were detected. Residual analysis over the overlapping period yielded an overall mean residual of 0.012 and standard deviation of 0.041 across all stations; 92% of stations presented absolute residuals below 0.05, indicating no systematic step-shift at the merging node. A paired-sample t-test was further carried out for two decades before and after the merging node (1990–1999 versus 2000–2009), producing p = 0.113 > 0.05, suggesting no statistically significant stepwise difference in statistical distributions across the transition. Input-sensitivity tests were further performed: SSRI was calculated, respectively, using the fully assimilated FVC time series and the native 2000–2024 FVC subset. Consistent robustness was observed for SSRI spatial patterns, inter-annual Mann–Kendall trends, and identification performance for the 1997 extreme-high-temperature scenario. Station-scale fractional vegetation cover was represented by the mean value within a 25 km circular buffer surrounding each meteorological station.

UTCI validation datasets were retrieved from the ERA5-HEAT dataset (derived-utci-historical, version 1.1, product type = consolidated dataset) hosted by the Copernicus Climate Data Store. This dataset provides hourly UTCI outputs calculated by the full Fiala thermal-balance model from ERA5 reanalysis at a 0.25° horizontal resolution. The nearest ERA5 grid cell was extracted for each of the 101 stations (mean distance = 0.095° and standard deviation = 0.038°). Daily UTCI values were defined as the average of five daytime UTC timestamps (00:00, 03:00, 06:00, 09:00, 12:00 UTC; corresponding to 08:00–20:00 Beijing Time). Summer comfortable days were counted as days with UTCI ranging from 9 °C to 26 °C (non-heat-stress conditions).

Elevation data were obtained from the Digital Elevation Model (DEM), with consistent resolution, downloaded from the Geospatial Data Cloud platform of the Chinese Academy of Sciences (https://www.gscloud.cn/search), accessed on 1 March 2026, to characterize topographic constraints. Data preprocessing, grouped-PCA dimension reduction, multi-distribution fitting, copula coupling modelling and spatiotemporal statistical tests were all implemented in MATLAB version 2023b (https://matlab.mathworks.com). Study area spatial zoning, grid interpolation and spatial mapping visualisation were completed in ArcGIS version 10.8 (https://www.arcgis.com).

Outlier quality control was applied to raw daily observations. The 3-σ criterion was used for preliminary outlier screening. Samples exceeding the 3σ threshold were not automatically discarded; all candidates underwent manual review. Sample properties were assessed against local meteorological bulletins and historical disaster records. Abnormal values supported by documented extreme-weather events (extreme heat, gales, heavy rainfall, etc.) were regarded as genuine extreme observations and retained. Records without corresponding extreme-event evidence but accompanied by metadata records of instrument failure or station relocation were treated as erroneous observations and subjected to flagging, checking, correction or elimination. Subject to internal meteorological-data confidentiality regulations, exact counts of flagged, corrected and eliminated records per individual station cannot be released. Overall statistics for all 101 stations show that flagged samples account for 2.14% of total raw observations, of which manually corrected samples account for 0.82%, eliminated invalid and erroneous observations account for 0.47% and the remaining flagged samples correspond to real extreme meteorological observations and were kept. The complete workflow for anomaly identification and authenticity discrimination is documented in the manuscript to ensure reproducibility of preprocessing procedures.

This study established a three-level evaluation system comprising 13 indicators under four dimensions: physiological thermal comfort, environmental suitability, extreme-weather risk and climate stability. To verify the scientific validity and regional adaptability of all indicators, 80 experts with in-depth research experience in Qin-Ba Mountains meteorology, high-temperature disasters, summer-resort cultural tourism and mountain ecology were invited to score indicator importance on a 1–10 scale (0 = totally unimportant, 10 = extremely important) (Figure 2). Questionnaires were distributed and collected anonymously, and no multi-round Delphi feedback was performed for expert scoring. It should be specifically noted that the expert evaluation results only served as auxiliary references for indicator screening and were not incorporated into the numerical weighting procedure of the subsequent PCA–copula model; indicator weights were objectively determined via principal component analysis.

Consistency tests for expert scoring yielded an overall score of 7.32 ± 1.35 (mean ± standard deviation) for the 13 indicators from 80 experts. The two-way random-effects intraclass correlation coefficient (ICC) was adopted to assess inter-rater consistency. The single-measure ICC (2,1) = 0.641 and the average-measure ICC (2,k) = 0.993 for the 80 experts indicated moderate-to-good consistency for aggregated expert ratings. The coefficient of variation (CV) of scores for each indicator ranged from 5.32% to 17.79%. Core indicators including days with favourable temperature–humidity index (CV = 5.32%), days with minimum temperature < 22 °C (CV = 5.43%) and days of hot-windless weather (CV = 6.35%) achieved high expert consensus, whereas indicators such as gale days (CV = 17.79%) and sunny days (CV = 15.80%) showed relatively high divergence in expert opinions. Ranked by mean expert scores, high-temperature days (9.16), hot-windless weather days (8.94), and days with favourable temperature–humidity index (8.28) ranked as the top three, which is consistent with theoretical expectations for summer-resort climate evaluation.

Uniform criteria were applied for expert selection: participants held associate-senior professional titles or doctoral degrees and had more than 8 years of research or practical experience related to Shaanxi regional climate. Experts were recruited from local meteorological authorities, geography and tourism disciplines in universities and ecological-planning institutions. Such multidisciplinary backgrounds guaranteed balanced and comprehensive scoring perspectives.

This expert-scoring exercise was only a pre-validation step for constructing the indicator system and was not involved in any modelling calculation for SSRI. First, it verified that the 13 pre-selected three-level indicators were not subjectively chosen; collective judgements from multidisciplinary experts supported the suitability of these indicators for summer-resort evaluation across diverse landforms in Shaanxi. Second, it indirectly justified the disciplinary rationality of the four-dimensional framework (physiological thermal comfort, environmental suitability, extreme-weather risk and climate stability), confirming that the four dimensions are widely recognised core components for summer-resort assessment. Third, scoring results were plotted as a heatmap to intuitively visualise discrepancies in industry-level recognition among indicators, which merely acts as visual supporting evidence.

2.2. Research Methodology

This study aims to develop an SSRI that comprehensively reflects human thermal perception, environmental comfort, hazard risk and climatic stability [24,25]. Given the large number of involved variables and complex nonlinear dependencies among them (e.g., positive correlation between high temperature and intense solar radiation and a negative correlation between heavy precipitation and air temperature), conventional linear-weighting approaches cannot achieve objective weight assignment. Copula functions impose no constraints on the marginal distributions of individual variables. They can objectively capture situations in which multiple common indices fall below given thresholds and construct joint distributions for multivariate meteorological variables with heterogeneous marginal distributions [25,26,27]. Accordingly, this study proposes a coupled evaluation model based on the PCA–copula function. The detailed construction workflow is presented below.

Following the principles of scientific validity, systematicness and data availability, a summer-escape suitability evaluation system comprising four secondary indicators and thirteen tertiary indicators was established in this study (

Table 1. SSRI evaluation system.

Secondary Indicators	Tertiary Indicators	Formula/Definition	Direction
Physiological thermal comfort	Number of THI-suitable days	THI = T − 0.55 × (1 − RH) × (T − 14.5); count of days with THI within [17, 25.4]	Positive
	Number of WEI-suitable days	$\mathrm{W}\mathrm{E}\mathrm{I}=-\left(10\sqrt{\mathrm{V}}+10.45-\mathrm{V}\right)\left(33-\mathrm{T}\right)+8.55\mathrm{S}$ count of days with WEI within [−299, −100]	Positive
	Number of days with daily minimum temperature < 22 °C	Count of days when daily minimum air temperature is below 22 °C	Positive
	Number of days with diurnal temperature range ≥ 8 °C	Count of days where (daily maximum temperature − daily minimum temperature) ≥ 8 °C	Positive
	Number of sultry, calm-wind days	Count of days with daily mean RH > 70% and daily mean wind speed < 2 m/s	Negative
Environmental suitability	Number of clear-sky days	Count of days with sunshine duration > 0 h and no precipitation	Positive
	Fractional vegetation cover (FVC)	Annual mean value of FVC/NDVI within the 25 km circular buffer (after calibration and fusion)	Positive
Extreme-weather hazard	Number of heavy rain days	Count of days with daily precipitation ≥ 25 mm (heavy-rain grade)	Negative
	Number of heatwave days	Count of days with daily maximum air temperature ≥ 35 °C	Negative
	Number of gale days	Count of days with daily mean wind speed ≥ 10.8 m/s (Beaufort Scale 6)	Negative
	Number of long-sunshine days	Count of days with sunshine duration > 10 h	Negative
Climatic stability	Inter-daily variability of mean air temperature	Standard deviation of daily mean air temperature during June–August	Negative
	Inter-daily variability of maximum air temperature	Standard deviation of daily maximum air temperature during June–August	Negative

):

Prior to calculation, all third-level indicators were normalised to a unified interval using the range-standardisation method (Equation (1)) to eliminate dimensional heterogeneity. This transformation ensures that higher normalised values correspond to greater summer-resort suitability and avoids ambiguous loading signs in subsequent principal component analysis (PCA) arising from inconsistent directionalities of the original reverse indicators.

$$x_{\mathit{ij}}^{\prime }=\left\{\begin{array}{c}{\displaystyle \frac{x_{\mathit{ij}}-\min \left(x_j\right)}{\max \left(x_j\right)-\min \left(x_j\right)}}, (\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{w}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s})\\ {\displaystyle \frac{\max \left(x_j\right)-x_{\mathit{ij}}}{\max \left(x_j\right)-\min \left(x_j\right)}}, (\mathrm{R}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s})\end{array}\right.$$

(1)

where x_ij denotes the raw value of the j-th indicator in the i-th year, and x_ij is its normalised value.

2.3. PCA-Based Indicator Dimensionality Reduction

Considerable multicollinearity is present among the third-level indicators. For example, high-temperature days exhibit a strong positive correlation with strong radiation days (Pearson r > 0.7). Direct input of the 13 raw indicators into the copula joint-distribution model would generate redundant information and distort the weight assignments across dimensions. Therefore, separate principal component analysis (PCA) was implemented for subsets of third-level indicators grouped under the four second-level indicators to achieve dimensionality reduction.

This study adopted the dual criteria of the Kaiser criterion and cumulative variance contribution rate to determine the number of retained principal components for each grouped dimension: ① Kaiser criterion: principal components with eigenvalue λ > 1 were retained; ② cumulative variance contribution criterion: priority was given to ensuring the cumulative explained variance ≥ 60%. When conflicts occurred between the two criteria, the Kaiser criterion was prioritized, while model complexity was also considered to avoid introducing noise-dominated principal components. According to these decision rules, only the first principal component with an eigenvalue greater than 1 was retained for physiological thermal comfort, environmental suitability and climate stability. For the extreme-weather dimension, two principal components had eigenvalues greater than 1, yielding a cumulative explained variance of 70.8%; hence, both PC1 and PC2 were retained for this dimension.

After grouped principal component dimensionality reduction, a total of five valid variables were input for subsequent copula modelling: physiological thermal comfort PC1, environmental-suitability PC1, extreme-weather PC1, extreme-weather PC2 and climate-stability PC1. It should be specifically noted that although the evaluation system contains four secondary dimensions, the extreme-weather dimension produced two principal components, resulting in a five-dimensional input for the final model. Extreme-weather PC1 characterizes high-temperature and strong radiation features, whereas PC2 represents gale-related extreme events. Together, these two principal components carry all indicator information of the extreme-weather dimension. Neither can be arbitrarily discarded; otherwise, gale-related extreme meteorological information would be lost and the output of the SSRI would be altered.

The retention of principal components was jointly governed by the Kaiser criterion and cumulative variance contribution rate. The detailed retention scheme is as follows: the first principal component was retained for the physiological thermal-comfort dimension; the first principal component was retained for the environmental-suitability dimension; the first two principal components were retained for the extreme-weather dimension; the first principal component was retained for the climate-stability dimension. Since the extreme-weather dimension generates two principal components, the copula-model input has five dimensions rather than a one-to-one correspondence with the four secondary evaluation dimensions. Among them, extreme-weather PC2 specifically encodes information on extreme gale events and constitutes an indispensable input variable for the model. In total, five principal components (thermal PC1, env PC1, extreme PC1, extreme PC2, stability PC1) were fed into the subsequent copula modelling.

The Kaiser–Meyer–Olkin (KMO) sampling adequacy test and Bartlett’s test of sphericity were performed for each dimension to statistically assess the validity of PCA-based dimensionality reduction. The physiological thermal-comfort dimension returned a KMO value of 0.750, whereas the extreme-weather dimension produced an acceptable KMO value of 0.559. Bartlett’s test of sphericity was significant at p < 0.001 across all four dimensions, confirming adequate internal collinear structures within each dimension to justify dimensionality reduction procedures. A summary of PCA diagnostic outputs is provided in

Table 2. A summary of PCA diagnostic outputs.

Dimension	Number of Indicators	Retained PCs	PC λ	Cumulative Variance (%)	KMO	Bartlett’s χ2	Bartlett’s p
Physiological thermal comfort	5	PC1	2.911	58.2	0.75	7762.72	<0.001
Environmental suitability	2	PC1	1.405	70.3	0.5	631.54	<0.001
Extreme weather	4	PC1	1.839	70.8	0.559	2299.5	<0.001
		PC2	0.995
Climate stability	2	PC1	1.262	63.1	0.5	249.39	<0.001

.

The loading matrix reveals the climatic characteristics represented by each principal component. PC1 of the thermal-comfort dimension accounts for 58.2% of the total variance, with positive loadings for all five indicators. Days with minimum temperature below 22 °C (+0.526), THI-comfortable days (+0.487) and WEI-comfortable days (+0.489) make substantial contributions, whereas days with diurnal temperature range ≥ 8 °C exhibit a relatively low loading (+0.180). Accordingly, thermal-comfort PC1 mainly reflects the comprehensive summer thermal-comfort level, namely the covariation pattern of multiple comfort-related indicators. Higher PC1 values generally correspond to more thermally comfortable days and favourable nocturnal cooling conditions, while the diurnal-range indicator contributes comparatively little to this principal component.

PC1 of the extreme-weather dimension explains 46.0% of the variance, with high loadings for high-temperature days (+0.615) and strong radiation days (+0.653). This indicates that this principal component primarily captures the covariation of elevated summer temperature and intensified radiation and can be interpreted as a high-temperature–strong-radiation characteristic axis. Extreme-weather PC2 further accounts for 24.9% of the variance. It features a large positive loading for gale days (+0.936) and a negative loading for heavy-precipitation days (−0.346), suggesting that this principal component predominantly conveys variation associated with gale events and serves as a complement to the high-temperature–radiation axis.

PC1 of the environmental-suitability dimension explains 70.3% of the variance. Vegetation coverage and clear-sky days show loadings of identical magnitude but opposite signs (±0.707), implying that this principal component reflects the inverse covariation structure between the two environmental factors. It should be noted that the sign of principal component scores is arbitrary; this relationship therefore describes the relative variation pattern among indicators rather than absolute positive or negative effects. PC1 of the climate-stability dimension accounts for 63.1% of the variance. Both mean diurnal temperature variation and maximum-temperature diurnal variation yield identical loadings (+0.707), jointly characterizing the magnitude of summer temperature fluctuations.

It is worth emphasizing that retaining only PC1 for the thermal-comfort dimension incorporates 58.2% of the total shared variance among indicators into the subsequent model. The remaining 41.8% unexplained variance largely corresponds to local variation features of individual indicators. Specifically, PC2 (λ = 1.018, explaining 20.3% of variance) is dominated by days with diurnal temperature range ≥ 8 °C (loading = +0.924), representing an independent information dimension of diurnal temperature range variability. PC3-PC5 (cumulatively 21.5% of the variance) further describe local variations in THI, WEI and sultry, calm-wind conditions. Since this study focuses on regional-scale evaluation of overall summer comfort rather than the variation mechanisms of individual climatic factors, adopting PC1 as the representative of the thermal-comfort dimension effectively reduces model complexity while preserving dominant climatic information.

Furthermore, results from subsequent copula joint-distribution fitting and goodness-of-fit tests demonstrate that adding extra principal components from the thermal-comfort dimension does not markedly improve model performance under the available sample size. Consequently, retaining thermal-comfort PC1 as the synthetic proxy for this dimension achieves effective dimensionality reduction of the indicator system while guaranteeing model stability.

2.4. Marginal Distribution Functions

To accurately characterize the probabilistic distribution features of each evaluation dimension and construct the joint distribution for multi-dimensional variables, it is first necessary to determine the optimal marginal distribution form for each principal component variable.

Given the diverse distribution patterns of meteorological and environmental data (e.g., skewness, leptokurtosis or heavy-tail behaviours), ten continuous probability distribution models covering symmetric, skewed and extreme-value features were selected as the candidate set. These include the normal distribution (Norm), log-normal distribution (LogNorm), gamma distribution (gamma), beta distribution (Beta), Weibull distribution (Weib), exponential Weibull distribution (EWeib) and generalized extreme value distribution (GEV).

Three goodness-of-fit tests, namely the Kolmogorov–Smirnov (K-S) test, Anderson–Darling (A–D) test and Cramér–von Mises (CvM) test, were implemented, with AIC and BIC adopted as auxiliary criteria. Marginal-distribution fitting diagnostics reveal the limitations of parametric distributions. Taking physiological thermal-comfort PC1 as an example, the Kolmogorov–Smirnov test rejects all ten candidate parametric distributions. Although the Exponential Weibull distribution yields the best fit (AIC = 12,448.2), its K-S test p = 1.14 × 10⁻⁵ still indicates statistically significant rejection.

The above-mentioned multi-parameter distribution fitting, AIC and K-S test serve only as diagnostic screening tools for variable distribution patterns. Although some parametric distributions yield lower AIC values relative to alternative candidate models, none of these candidate parametric distributions pass the goodness-of-fit test. Therefore, no analytical parametric distributions are adopted as marginal inputs for formal copula modelling in this study. The empirical cumulative distribution function (ECDF) is uniformly used to implement the probability integral transform (PIT).

Non-parametric probability integral transformation was performed through ECDF to convert each principal component variable into pseudo-observations defined over the domain (0,1). The ECDF avoids systematic biases induced by parametric misspecification, preserves the empirical distribution shape of raw samples and effectively mitigates systematic errors arising from mis-specified parametric distributions.

2.5. Construction of Copula Joint Distribution Functions

Copula functions have diverse construction forms, and different families exhibit distinct advantages in characterizing dependence structures among variables, such as symmetry and tail dependence. The elliptical copula family includes Gaussian and t copulas, both of which feature concise structures and wide applicability. Among them, the t copula can capture symmetric tail dependence characteristics between variables well. The Archimedean copula family contains Clayton, Gumbel, Joe and other types. Equipped with explicit generators, they can flexibly describe asymmetric tail dependence structures: for instance, Clayton is sensitive to lower tails, while Gumbel is sensitive to upper tails. In addition, a vine copula decomposes high-dimensional joint distributions into a series of bivariate copulas, granting it unique flexibility for addressing complex high-dimensional dependence relationships. Considering the necessity to accurately capture potential nonlinear and tail dependence structures among the five modelling dimensions (derived from four secondary evaluation dimensions, with two principal components output from the extreme-weather dimension), nine functions, namely the independence copula, Gaussian, Student’s t, Clayton, Gumbel, Frank, Joe, R-vine and C-vine, were selected to form the candidate model set in this study.

All models were estimated via canonical maximum likelihood estimation (CMLE) based on pseudo-observations. Specifically, pseudo-observations U were first derived from ECDF-based probability integral transformation; copula parameters for each candidate model were then estimated by maximum-likelihood methods using these pseudo-observations. Model selection was primarily based on the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) and Akaike weights were computed to quantify model-selection uncertainty. ΔAIC < 2 indicates negligible differences between competing models; 2 < ΔAIC < 7 suggests moderate supporting evidence; and ΔAIC >10 corresponds to strong evidence in favour of the superior model. It should be noted that most of the nine candidate models are non-nested (e.g., Clayton versus Gaussian, C-vine versus Gumbel), where the χ² asymptotic distribution is invalid for conventional likelihood ratio tests (LRTs). Therefore, LRTs were not employed to draw firm conclusions for these non-nested comparisons.

The model-comparison results (

Table 3. Model selection for copula-based joint-distribution functions.

Copula Model	LRT	AIC	BIC	ΔAIC	Akaike Weight
C-vine	2256.18	−4490.36	−4422.51	0	0.9973
R-vine	2251.26	−4478.52	−4404.51	11.84	0.0027
Student’s t	2081.53	−4123.06	−3999.70	367.30	≈0
Gumbel	1921.66	−3823.33	−3761.65	667.03	≈0
Clayton	1881.73	−3743.47	−3681.79	746.89	≈0
Joe	1699.29	−3378.57	−3316.89	1111.79	≈0
Gaussian	1626.40	−3232.80	−3171.12	1257.56	≈0
Frank	879.64	−1743.27	−1693.93	2747.09	0
Independence	0	0	0	4490.36	0

) summarize the full performance of all nine candidates. The C-vine copula with automatic structure selection achieved the optimal performance, with AIC = −4490.36 and BIC = −4422.51, and an Akaike weight as high as 0.9973. The R-vine copula ranked second (ΔAIC = 11.84, weight = 0.0027). The univariate parameter Archimedean family (Clayton, Gumbel, Frank and Joe) and the Gaussian elliptical copula showed substantially higher AIC values than vine copulas, implying that their fitting capacity cannot match that of vine copulas after accounting for model complexity. An AIC value of zero for the independence model arises by definition: both the penalty term (2k = 0) and likelihood term (−2 × 0 = 0) equal zero for this zero-parameter model. Its extremely large ΔAIC of 4490 provides clear evidence of pronounced dependence among variables within the dataset.

The optimal variable sequence obtained from the automatic C-vine structure search is [1,2,3,4,5], with physiological thermal-comfort PC1 (variable 1) serving as the root node. The first tree layer connects thermal-comfort PC1 with climate-stability PC1 (variable 4) and environmental-suitability PC1 (variable 5). The second tree layer further characterizes the conditional dependence of extreme-weather PC2 (variable 3) and extreme-weather PC1 (variable 2), conditional on thermal-comfort conditions. This configuration highlights that thermal-comfort PC1 exerts strong overall associations within the multi-dimensional climate-evaluation system and is accordingly identified as the central variable in the dependence network. Even after conditioning on thermal-comfort levels, conditional dependence persists among climate-stability, environmental-suitability and extreme-weather dimensions, demonstrating intricate nonlinear dependence structures across diverse climatic factors.

The actual calculation of the SSRI in this study is based on the above-mentioned five-dimensional C-vine copula model. In Section 3.3 below, exploratory dependence-structure analysis is performed using a four-dimensional setup (only PC1 of each dimension, discarding extreme-weather PC2), in which the Clayton copula is adopted. This four-dimensional model is not applied for SSRI calculation and serves merely for mechanistic interpretation; it should not be confused with the formal modelling workflow.

2.6. Goodness-of-Fit Test for Copula Models

Although AIC and BIC enable relative comparison among competing models, they cannot verify whether the selected model adequately captures the dependence structure embedded in observational data. Therefore, the Cramér–von Mises (CvM) test based on the Kendall distribution transform was adopted in this study to evaluate the goodness-of-fit of the copula model. The underlying principle is as follows: if the copula model is correctly specified, the newly derived variable V obtained via the Kendall probability transform should approximately follow the uniform distribution Uniform (0,1). The CvM distance between the empirical cumulative distribution function of V and the theoretical uniform distribution was computed. A Monte Carlo simulation scheme (M = 10,000) replications) based on the fitted copula model was implemented to obtain the null-hypothesis distribution of the test statistic and corresponding p-value. A Monte Carlo-calibrated (p > 0.05) indicates insufficient evidence to reject the copula model at the 5% significance level. The test results are presented in

Table 4. Goodness-of-fit test results for copula models.

Model	CvM Statistic	Monte Carlo-Calibrated p	Conclusion
C-vine	0.00168	0.175	Fail to reject H0
R-vine	0.00185	0.088	Fail to reject H0
Student’s t	0.00147	0.25	Fail to reject H0
Gumbel	0.00199	0	Reject H0
Clayton	0.00354	0.213	Fail to reject H0
Joe	0.00416	0.013	Reject H0
Gaussian	0.00206	0.45	Fail to reject H0
Frank	0.04794	0	Reject H0
Independence	0.18373	0	Reject H0

.

The test results reveal the following findings: (1) The Monte Carlo-calibrated p-values for C-vine (p = 0.175), R-vine (p = 0.088) and Student’s t copula (p = 0.250) are all greater than 0.05, indicating no statistically significant lack-of-fit at the 5% significance level. Among these candidates, the C-vine copula yields the lowest AIC and BIC values together with acceptable goodness-of-fit performance and is therefore selected as the final joint-distribution model. (2) The null hypotheses for Gumbel, Joe and Frank copulas are statistically rejected. This suggests that these fixed-form dependence structures alone are insufficient to adequately capture the complex nonlinear associations among the multi-dimensional climatic indicators in this study. (3) The independence copula is strongly rejected by the goodness-of-fit (GOF) test. Combined with its extremely large ΔAIC value, this result further confirms pronounced non-independent dependence among the five principal components. Although the Gaussian copula passes the GOF test, it produces substantially higher AIC values relative to the vine-based models. This implies that the Gaussian copula can represent part of the overall dependence patterns yet fails to fully characterize the intricate conditional-dependence structures across variables.

2.7. SSRI

After constructing the five-dimensional joint-distribution function with physiological thermal comfort, environmental suitability, extreme weather and climate stability as input variables, its output corresponds to a joint cumulative-probability value that integrates thermal comfort, environmental suitability, extreme-weather conditions and climate stability. Nevertheless, this cumulative probability follows the specific distribution induced by the C-vine copula. For observations from different sites or years, its value is constrained by respective marginal distributions and dependence structures and thus cannot be directly applied for cross-site or inter-annual comparisons of summer-resort suitability. The detailed procedures for deriving a generalized standardised index are described below:

Step 1: Calculate the joint cumulative probability $= C\left(u_{i1},u_{i2},\dots ,u_{i5}\right)$ under the C-vine copula for each observational sample. The output represents the cumulative-probability position of each sample within the five-dimensional joint distribution.

Step 2: Estimate the Kendall distribution function $K_c\left(t\right) = P\left(C\left(U_1,\cdots ,U_5\right)\le t\right)$, i.e., the distribution of copula-probability variables obtained by simulating samples from the fitted C-vine joint distribution. Since Kc for the C-vine has no closed-form analytical solution, Monte Carlo simulation (M = 10,000 replications) based on the calibrated C-vine copula parameters is adopted. Synthetic samples are generated from the fitted joint distribution, and the corresponding joint-CDF values are computed to estimate the Kendall-distribution function as $k_i ={ K}_c\left(t_i\right)$.

Step 3: Two-step normalisation to obtain the standard normal-transformed Z_SSRI. First, an empirical-CDF transformation $U_{K_c,i} = {F_{\mathit{emp},K_c}(k}_i)$ is applied to the $K_c\left(t\right)$ values across all samples to correct discretization errors in the empirical Kendall distribution originating from the finite size of Monte Carlo simulated samples. Subsequently, $K_c\left(t\right)$ is mapped onto the standard normal scale via the inverse standard normal CDF: $Z_{\mathit{SSRI}} ={ \mathsf{\Phi }}^{-1}\left(U_{K_c,i}\right)$. This two-step normalisation guarantees that $Z_{\mathit{SSRI}}$ approximately follows a standard normal distribution within the reference sample set. Step 4: Percentile mapping to the 0–100 range: $\mathit{SSRI} = F_{\mathit{emp}}\left(Z_{\mathit{SSRI}}\right) \times 100$, where $F_{\mathit{emp}}$ denotes the empirical CDF of $Z_{\mathit{SSRI}}$ over all reference samples. This mapping grants the SSRI an intuitive percentile interpretation; for instance, SSRI = 70 indicates that the site-year observation lies at the 70th percentile among all samples. The comprehensive summer-resort suitability index is defined as:

$$\mathit{SSRI} = F_{\mathit{emp}}\left(Z_{\mathit{SSRI}}\right)\times 100$$

(2)

where $F_{\mathit{emp}}\left(·\right)$ represents the empirical cumulative-distribution function of $Z_{\mathit{SSRI}}$ for the reference samples. The distributional properties of $Z_{\mathit{SSRI}}$ support its normal approximation: mean = 0.000, standard deviation = 1.000, skewness = 0.001, kurtosis = −0.01. The Kolmogorov–Smirnov normality test yields p ≈ 1.000, the Jarque–Bera test gives p = 0.645, and the D’Agostino normality test returns p = 0.660. Theoretically, $Z_{\mathit{SSRI}}$ should follow a standard normal distribution owing to the probability integral transform. Empirical sample statistics show that its mean, standard deviation, skewness and kurtosis are close to theoretical values, and normality tests detect no substantial departures from normality. Such normality provides the statistical foundation for the subsequent five-level classification scheme based on thresholds of ±0.5σ and ±1.5σ (

Table 5. SSRI classification standard based on statistical distribution characteristics.

Level	SSRI Value Range	Cumulative Probability (%)
Extremely suitable	$78.0 \le \mathrm{SSRI}$	6.7
Suitable	$61.7 \le \mathrm{SSRI} < 78.0$	24.2
Moderate	$45.4 \le \mathrm{SSRI} < 61.7$	38.3
Marginally unsuitable	$29.1 \le \mathrm{SSRI} < 45.4$	24.2
Unsuitable	$\mathrm{SSRI} < 29.1$	6.7

).

The above-mentioned normality tests were performed on the intermediate latent variables, which approximately follow the standard normal distribution (mean = 0.000, standard deviation = 1.000, skewness = 0.001, kurtosis = −0.01; K-S normality test (p ≈ 1.000), Jarque–Bera test (p = 0.645). It should be noted that the final output SSRI is a bounded index ranging from 0 to 100 obtained via empirical percentile mapping, and the SSRI itself does not strictly follow a normal distribution. The five-level classification thresholds in this study are derived by mapping the latent-variable thresholds of 0.5σ and μ ± 1.5σ onto the SSRI value range. The classification is based on the statistical characteristics of the latent variable rather than direct normal-based segmentation of the SSRI samples.

2.8. Sensitivity Analysis for Temporal-Spatial Dependence of Copula-Fitting Samples

All station-year pooled samples were adopted for constructing the C-vine copula in this study. Meteorological observations exhibit both intra-station temporal autocorrelation and inter-station spatial autocorrelation, so the samples do not fully satisfy the independent and identically distributed assumption. To evaluate disturbances induced by such dependence on copula parameter estimation and model-selection outcomes, two resampling-based sensitivity tests were designed.

Scheme A: Group-leave resampling at the station level (to eliminate the spatial clustering effect). In each trial, 70% of stations were randomly sampled with all annual observations retained for selected stations, while all records from the remaining stations were discarded. Resampling was repeated 50 times. ECDF marginal fitting and C-vine copula parameter estimation were reperformed in each iteration, and the AIC values, core dependence parameters of C-vine, and p-values of the CvM goodness-of-fit test were recorded.

Scheme B: Annual-block resampling (to mitigate temporal autocorrelation within individual station time series). A block bootstrap was applied to the time series of each station with a block length of 5 years to preserve intra-block inter-annual dependence structures. Fifty resampled datasets were generated, and the C-vine copula was fitted for each dataset.

Sensitivity-test results: For Scheme A (station-based resampling), the C-vine AIC across 50 repetitions ranged from −4611.72 to −4357.18. The C-vine remained the optimal model according to AIC in all replicates, with Akaike weights consistently above 0.97. The coefficient of variation (CV) of key dependence parameters was lower than 7.2%, and all CvM test p-values exceeded 0.05, indicating no model rejection. For Scheme B (temporal-block bootstrap), the C-vine maintained optimal performance; the CV of model parameters was below 5.8%, and CvM p-values ranged from 0.121 to 0.238, close to the original full-sample p-value of 0.175.

The two sets of sensitivity tests demonstrate that the C-vine copula remains the optimal joint-distribution model with no substantial shifts in dependence parameters or goodness-of-fit, even when temporal and spatial dependence within station-year samples is taken into account. Although the original pooled samples present partial non-independence, such an effect exerts limited disturbance on the major modelling conclusions of this study. Nevertheless, sample dependence may underestimate standard errors to some extent, and uncertainties still exist for parameter confidence intervals.

3. Results

3.1. External Validation and Mechanistic Analysis of the SSRI Based on UTCI

To examine the consistency between the SSRI and an independent physical benchmark, the Universal Thermal Climate Index (UTCI) was adopted for external validation in this study. Based on the Fiala multi-node human thermoregulation model, the UTCI characterizes human thermal-stress conditions by integrating environmental factors including air temperature, humidity, wind speed and mean radiant temperature. It outputs a UTCI equivalent temperature classified into ten thermal-stress grades, among which the range of 9–26 °C corresponds to the “no thermal stress” interval. The UTCI and SSRI are fully independent in terms of indicator construction and statistical-modelling workflows: the former represents a deterministic biophysical model, whereas the latter is established within a statistical joint-distribution framework. Accordingly, UTCI serves as an external reference independent of SSRI model development to test the external validity of the SSRI.

Hourly UTCI reanalysis datasets from ERA5-HEAT with a spatial resolution of 0.25° × 0.25° were employed for validation. For each meteorological station across Shaanxi Province, the nearest ERA5-HEAT grid cell was extracted as the corresponding UTCI data source. For each summer day, the daily mean UTCI value was first calculated from the 24-h hourly UTCI records within the target grid cell.

$$\overline{{\mathit{UTCI}}_d}={\displaystyle \frac{1}{24}}{\displaystyle \sum _{\mathrm{h}=1}^{24}}{\mathit{UTCI}}_{d,\mathrm{h}}$$

(3)

Subsequently, a given day is defined as a UTCI no-thermal-stress day when the daily-mean UTCI satisfies 9 ≤ $\overline{{\mathit{UTCI}}_d}$ ≤ 26 °C. The proportion of UTCI no-thermal-stress days relative to all valid summer days (June–August) was calculated for each station in each year, which is defined as the UTCI-derived fraction of no-thermal-stress days:

$${\mathit{UTCI}-\mathit{CDP}}_{s,y} = {\displaystyle \frac{{\sum }_{d=1}^{D}I\left(9 \le \overline{{ \mathit{UTCI}}_{s,y,d}} \le 26\right)}{D}}\times 100\%$$

(4)

where s denotes the station, y denotes the year, and D represents the number of valid summer days in that specific year.

This metric quantifies the fraction of summer days with daily-mean thermal conditions falling within the UTCI no-thermal-stress range, rather than the fraction of comfortable hourly periods. Such a definition emphasizes overall summer thermal-exposure conditions instead of intra-diurnal extreme thermal-stress episodes.

Within the pooled sample comprising all site-year observations, the Kendall rank-correlation coefficient and Spearman rank-correlation coefficient were computed between the SSRI and the UTCI-derived fraction of no-thermal-stress days to evaluate their consistency at the aggregate scale. Meanwhile, Kendall τ was calculated separately for each station using its inter-annual time series to examine consistency in temporal variations between the SSRI and UTCI. This approach mitigates the confounding effects of long-term climatic background differences across stations on overall correlation estimates.

For the full pooled dataset, the SSRI shows statistically significant positive rank-correlations with the UTCI-derived fraction of no-thermal-stress days (Kendall’s τ = 0.289, p < 0.001; Spearman’s ρ = 0.440). This reveals a marked positive association at the aggregate scale, even though UTCI was not incorporated into SSRI construction. Further station-specific analyses yield a mean Kendall τ of 0.171 and a median of 0.135 across the 101 stations, with values ranging from −0.24 to 0.63. Approximately 81% of stations yield positive τ values, and 35% attain statistical significance at the α = 0.05 level.

This indicates that the positive association between the SSRI and the independent UTCI reference is not entirely driven by spatial disparities at a small subset of stations; positive trends are instead observed across most stations.

Correlation strengths show evident spatial heterogeneity among stations. For example, Mizhi (τ = 0.319, p = 0.010) and Wuqi (τ = 0.266, p = 0.024) yield significant positive correlations, while several stations exhibit only non-significant positive correlations or weak negative correlations. These discrepancies do not necessarily indicate that the SSRI malfunctions in some regions. Rather, they may reflect that different climatic dimensions embedded in the SSRI possess distinct relative contributions across geographical locations. At certain stations, physiological thermal comfort acts as the dominant constraint on summer-resort suitability. Inter-annual fluctuations of SSRI are largely modulated by thermal environment metrics including THI and WEI, which produce relatively consistent variation patterns with UTCI. By contrast, some stations experience little fluctuation in physiological thermal-comfort conditions. Their SSRI variations originate mainly from vegetation cover, extreme-weather risk and climate stability, leading to limited consistency with single thermophysiological indicators. Such spatial heterogeneity is consistent with the design rationale of the SSRI as a multi-dimensional composite index.

It should be noted that a spatial-representativeness mismatch exists between the 0.25° × 0.25° grid-scale ERA5-HEAT product and point-scale meteorological-station observations. Over complex terrain zones such as the Qinling Mountains, a single grid cell may encompass substantial elevation and topographic gradients. Consequently, the scale mismatch between gridded UTCI and real local thermal conditions at station locations can introduce representativeness errors and degrade the estimation precision of station-level correlation coefficients.

Furthermore, the SSRI integrates multi-dimensional information including physiological thermal comfort, environmental suitability, extreme-weather hazards and climate-stability metrics. Hence it cannot perfectly align with any single thermal-physiological indicator, suggesting that conventional temperature–humidity comfort metrics are insufficient to fully capture the comprehensive climatic suitability characterized by the SSRI. Combined with the UTCI external-validation outcomes, these results confirm that the SSRI possesses a solid physiological-thermal-response basis, yet its variability cannot be fully explained by standalone thermal-comfort indices.

3.2. Cross-Validation and Generalization-Performance Evaluation

As a multi-dimensional composite index, the validation of the SSRI requires not only consistency checks against external physical benchmarks but also assessments of its inter-annual stability. In this section, the fraction of combined comfortable days derived from THI and WEI (CP), defined as the proportion of summer days satisfying both THI ∈ [17, 25.4] and WEI ∈ [−300, −100], is adopted as the conventional thermal-comfort reference indicator. Sharing the same meteorological data sources with the SSRI, this reference indicator is calculated by raw counting rather than PCA–copula modelling. It is employed to compare the similarities and discrepancies between the SSRI and traditional thermal-comfort indices and to identify the incremental information embedded in SSRI.

First, linear regression was performed to quantify the explanatory power of traditional temperature–humidity metrics for SSRI variability. The results indicate that the combined THI-WEI metric explains only 18.3% of the SSRI variance (R² = 0.183, n = 3527). This means approximately 81.7% of SSRI variation cannot be accounted for by simple temperature–humidity indicators, demonstrating that SSRI incorporates non-thermal environment signals and the integrated effects of multi-dimensional climatic factors. Further analysis reveals a significant correlation between SSRI regression residuals and vegetation coverage (r = 0.567, p < 0.001), suggesting that non-thermal factors such as vegetation provide supplementary explanatory information beyond thermal indices.

Leave-one-year-out cross-validation (LOOCV) was implemented to test the inter-annual stability of the SSRI. In each iteration, one year was reserved as the test set, and data from the remaining years served as the training set. The median values of the SSRI and CP derived from the training dataset were separately used as thresholds for high- versus low-suitability classification. Across LOOCV runs covering 1981–2024, the mean classification accuracy reached 66.3% ± 10.2%, with no declining trend over time. This demonstrates that SSRI classification outputs possess favourable stability under long-term climatic variability.

It should be emphasized that CP only characterizes the thermal-comfort dimension, whereas SSRI synthesizes thermal comfort, environmental suitability, extreme-weather hazards and climate stability simultaneously. Some degree of discrepancy between the two metrics is thus an inherent consequence of the multi-dimensional index design. The LOOCV results indicate that SSRI shows partial response consistency with conventional thermal-comfort indicators, while reflecting multi-dimensional climatic information that cannot be captured by traditional indices.

3.3. Evolution, Nonlinear Dependence and Spatiotemporal Differentiation Characteristics of the Four Key Indicators and SSRI

This study integrates observational records from 101 meteorological stations across Shaanxi Province. Nevertheless, the observational periods vary substantially among individual stations, and the annual number of valid samples fluctuates drastically. Direct application of full-station time-series data may produce spurious significant trends driven by unbalanced sample sizes. To eliminate statistical biases originating from sample-size heterogeneity and ensure the reliability of long-term change analysis, a subset of 31 stations with complete observations for both 1981–1990 and 2011–2020 was selected for inter-annual trend analysis. When performing long-term trend analysis spanning 1981–2024, dynamic shifts in time-series composition caused by station construction, decommissioning and relocation may introduce statistical artifacts. Spurious trend signals can arise when the number of stations involved in the calculation changes over time. Accordingly, 31 representative stations were filtered from the original 101-station dataset for temporal-evolution analysis. The selection criterion required continuous and complete observational records for both the 1981–1990 and 2011–2020 characteristic decades. This guarantees consistent sample bases for the key early and late phases of the study period and yields robust, stable and credible inter-annual trend statistics. The selected 31 time-series stations provide balanced coverage of major climate-geomorphic units in Shaanxi Province, including the Northern Shaanxi Loess Plateau, Guanzhong Plain and Qin-Ba Mountains, in terms of geographical distribution, elevation gradients and geomorphic types (see Appendix A). These stations can represent the temporal-evolution characteristics of major climate types across the province, and no systematic bias of climatic signals is introduced by this reduced-sample subset.

The dataset of all 101 stations is used for static spatial pattern mapping. The application scenarios of these two types of datasets are distinguished from each other to avoid statistical confusion. Based on the annual panel data from 31 complete meteorological stations from 1981 to 2024, the standardised PC1 (Z-score) is used to represent the four-dimensional comprehensive levels of physiological thermal comfort (TC), environmental suitability (ES), extreme weather suitability (EW), and climate stability (CS). Combined with the annual average spline smoothing curve, the 5-year moving average, the 25–75% and 10–90% sample set shadow intervals and the decadal anomaly colour bands, the Mann–Kendall (MK) non-parametric test is used to quantify the long-term change amplitude and significance of each dimension.

The annual change slope of physiological thermal comfort is −0.0087/year, with MK Z = −1.596 and p = 0.220. It only shows a slight oscillatory downward trend, and there is no continuous and widespread decline in thermal comfort across the province. The environmental suitability shows a weak positive fluctuation, with an annual slope of +0.0031/year. The p-value of the MK test is 0.357, indicating no statistically significant change. This is mainly attributed to the slight increase in vegetation cover brought about by the continuous implementation of the Grain-for-Green Project in the province, resulting in a weak environmental gain. The extreme weather dimension is the only indicator that has significantly deteriorated during the study period. After positive standardisation in this dimension (lower values represent higher frequencies and intensities of extreme events such as high temperatures, strong sunshine and heavy rainfall), the annual change slope is −0.0208/year, with MK Z = −2.715 and p = 0.007 (p < 0.01), indicating that extreme climates continue to intensify against the background of global warming, which is the main factor eroding the summer-resort resources over the past 40 years. The annual change slope of climate stability is only +0.0005/year, with MK p = 0.861. The inter-annual oscillation amplitude has remained stable for a long time, with no systematic one-way deviation, as shown in Figure 3.

Based on the comprehensive time-series test results, it can be seen that the long-term downward pressure on the summer-resort background in Shaanxi Province from 1981 to 2020 entirely comes from the frequent occurrence of extreme climate events. There is no systematic decline in the three dimensions of human perception, ecological foundation, and climate fluctuation. At the same time, this study adopts a hierarchical time-scale design, covering the annual continuous sequence, the 5-year window and the difference between the beginning and the end of the 40-year period simultaneously. By comparing multi-layer time-series dimensions, it conducts a comprehensive time-series analysis and avoids one-sided conclusions caused by a single time scale.

As shown in Figure 4, physiological thermal comfort exhibits the strongest positive correlation with extreme weather (ρ = 0.444). Hot and stuffy physical sensations occur simultaneously with heatwaves and persistent strong sunshine, and the compound heat stress is synergistically amplified. Physiological thermal comfort is significantly negatively correlated with environmental suitability (ρ = −0.315). The transpiration cooling and shading effects of vegetation in high-altitude and dense forest areas significantly reduce the stuffy feeling in summer. Environmental suitability has a moderate positive correlation with extreme weather (ρ = 0.309). The probability of extreme meteorological events is higher in areas with lower vegetation coverage. The overall correlation between climate stability and the other three dimensions is relatively weak (ρ ranges from 0.077 to 0.214), and the coupling degree among inter-annual temperature fluctuations, human physical sensations and ecological conditions is low. Candidate parametric distribution fitting-screening was performed for PC1 of the four secondary dimensions, and the results are shown in

Table 6. Optimal results of marginal distribution model fitting.

Variable	Optimal Distribution	AIC Value	p-Value
Thermal comfort	Beta	12,182	0.06
Environmental Suitability	Weib	11,550	0.10
Extreme weather	EWeib	12,080	0.09
Climatic stability	EWeib	10,807	0.21

. Comparison of AIC values reveals that Beta, Weibull and Exponential Weibull outperform other alternative parametric distributions. Nevertheless, none of these parametric models pass rigorous goodness-of-fit tests. Neither the five-dimensional C-vine copula adopted for SSRI construction nor the four-dimensional exploratory-dependence analysis in this section employs these analytical parametric distributions as marginal inputs. The empirical cumulative distribution function (ECDF) is uniformly applied for the probability integral transformation across all analyses. Table 6 is only used to diagnose the distribution-pattern characteristics of each variable.

The formal modelling for the SSRI described above adopts five-dimensional principal components (including extreme-weather PC1 and PC2; PC2 carries information on gale-related extreme events and constitutes an indispensable model input that cannot be omitted) together with the C-vine copula. To further interpret the nonlinear-dependence mechanisms among the integrated levels of the four secondary dimensions, only the first principal components of each dimension are taken as representative variables in this section, while the second principal component of the extreme-weather dimension is discarded for exploratory joint-distribution analysis of four-dimensional variables.

An essential distinction should be emphasized: this four-dimensional copula serves only for mechanistic exploration and is not the official model for SSRI calculation. The formal SSRI model is the five-dimensional C-vine copula. Omission of extreme-weather PC2 will lead to the loss of gale-extreme-event information and directly alter the SSRI values, spatial patterns and identification performance under extreme high-temperature scenarios. This four-dimensional exploratory analysis merely reveals the statistical-coupling characteristics among thermal comfort, environmental suitability, extreme-weather risk and climate stability, and is not involved in SSRI calculation and generation.

To further uncover the statistical coupling features among the first principal components of the four secondary dimensions, PC2 of the extreme-weather dimension, which characterizes gale events, is excluded in this section. Only four-dimensional variables are employed for exploratory joint-distribution analysis (this four-dimensional model is not used for SSRI generation). According to the AIC, BIC and log-likelihood results listed in

Table 7. Optimal selection of copula function joint distribution model fitting (top three).

Copula Model	AIC	BIC	LRT
Clayton	−32,538.9	−32,532.7	16,270.45
Gumbel	−25,308.4	−25,302.2	12,655.19
Gaussian	−2183.56	−2146.55	1097.78

, the Clayton model from the Archimedean copula family yields the best-fitting performance for this four-dimensional exploratory analysis. It can capture lower-tail dependence associated with the simultaneous deterioration of multiple four-dimensional variables, which helps explain the intrinsic mechanism of compound extreme thermal stress that conventional linear evaluation models cannot identify.

It should be stressed once more that the formal SSRI calculation uses the five-dimensional C-vine copula including extreme-weather PC2, instead of this four-dimensional Clayton copula. A full standardised statistical pipeline was implemented in the modelling stage, encompassing the fitting of ten distribution types, the K-S goodness-of-fit test and maximum-likelihood estimation (MLE). All fitted parameters are quantitatively reported, and the data-processing workflow is fully reproducible.

The model-selection results are presented in Figure 4. This four-dimensional-variable corner joint-distribution plot is constructed based on 3527 station-year observations. The diagonal panels display kernel-density marginal distribution curves for each dimension. The lower-triangle panels show bivariate hexbin sample-count density, while the upper-triangle panels illustrate empirical joint cumulative-probability contours of the optimal Clayton copula. Spearman’s rank-correlation coefficients are annotated for each variable pair to intuitively characterize the upper-tail and lower-tail nonlinear coupling features among multiple meteorological factors. This plot originates from exploratory dependence analysis using PC1 of the four secondary dimensions. The actual SSRI modelling employs the five-dimensional principal-component C-vine copula. This four-dimensional Clayton copula serves only for mechanistic exploration and is not used for SSRI calculation; the SSRI is generated by the five-dimensional C-vine copula model. The diagonal panels show empirical kernel-density visualisations of samples rather than theoretical probability densities of the parametric distributions in Table 6. ECDF is also adopted as the marginal input for this four-dimensional exploratory analysis.

A spatiotemporal heat matrix was constructed based on the long-term SSRI time series (1981–2020) from the 31 complete-record stations. The Ward hierarchical clustering algorithm was applied to classify four temporal clusters using two metrics: annual mean level of the index and magnitude of inter-annual fluctuation. The results are shown in Figure 5. The clustering outcomes do not fully match the geographical divisions of Northern Shaanxi, Guanzhong and Southern Shaanxi or conventional perceptions. This demonstrates that variations in local topography and vegetation cover are strongly associated with the long-term evolution of summer-resort suitability. Compared with latitudinal differentiation, the effects of local factors are more pronounced.

The stations of Ankang, Qindu and Pucheng persistently exhibit low SSRI values, corresponding to the urban heat-island zones in river-valley areas of the Guanzhong and southern Shaanxi regions. Sustained high temperatures under summer calm-wind conditions continuously suppress summer-resort suitability. Huashan and northern Shaanxi stations show moderate SSRI suitability with prominent diurnal temperature range advantages; nevertheless, heterogeneous vegetation coverage across this region leads to considerable temporal variability. Valleys within the Qinling-Daba Mountains in southern Shaanxi maintain moderately high suitability due to balanced hydrothermal conditions. A core high-suitability cluster consisting of 16 stations distributed on both northern and southern sides of the Qinling Mountains is dominated by mid-to-high-elevation mountainous forests, with the SSRI stably above 60 over the study period.

Clustering was implemented for temporal pattern classification. Stations were grouped according to the multi-year mean SSRI, inter-annual fluctuation and response characteristics to extreme events. The clustering outcomes do not strictly follow the conventional geographic division of northern Shaanxi, Guanzhong and southern Shaanxi. Terrain and vegetation modulate not only the spatial mean level of the SSRI but also exhibit significant coupling with temporal-series properties. Enclosed basins and river valleys lack topographic barriers, which tend to amplify extreme-heat stress. Such sites feature low baseline suitability and pronounced SSRI declines during heatwave years. By contrast, mountainous terrain mitigates advective heat stress via topographic shielding and effectively reduces the inter-annual amplitude of the index. Vegetation exerts dynamic buffering effects: stations with dense forest cover attain higher average suitability and experience smaller SSRI drops under extreme climatic events, and forested sites generally display decadal increasing trends in the SSRI. Even under relatively favourable latitudinal backgrounds, regions with fragile vegetation still suffer strong inter-annual index fluctuations. Within a single conventional geographic unit, stations can be assigned to distinct temporal clusters driven by local combinations of terrain and vegetation. This pattern implies that terrain-vegetation coupling acts as a key potential driver of SSRI temporal differentiation, whereas latitude serves primarily as a background modulating factor. The province-wide averaged SSRI time series presents distinct troughs in 1997, 2006 and 2014, consistent with historical province-wide extreme heat and drought episodes, which directly reflect the pervasive suppressing impacts of extreme climate on summer-resort resources across Shaanxi. The right-hand bar plot quantifies suitability hierarchies among four clusters and enables intuitive visual comparison of temporal classifications. Sample sizes, clustering rules and statistical auxiliary lines are uniformly annotated in the figure, yielding self-contained caption information that supports independent interpretation without reference to the main text.

The period from 1981 to 2020 is divided into four decadal sub-periods: 1981–1990, 1991–2000, 2001–2010 and 2011–2020. The spatial scatter plots of the station-level mean SSRI values are drawn for each decade, and the index difference ΔSSRI between the first and the last decades is calculated and interpolated into a spatial differentiation map (Figure 6). The average SSRI of the whole region in the four decades are 58.1, 55.4, 55.6 and 55.2, respectively, showing a slight overall downward trend. The average ΔSSRI of all 31 stations in the whole region is −2.92. The single-sample t-test shows that t = −1.83 and p = 0.077. The overall downward trend over 40 years does not pass the significance test at the 0.05 level, indicating that there is no significant and unified attenuation pattern in the whole region.

SSRI trends across individual stations exhibit pronounced spatial heterogeneity. Among the 31 analysed stations, 18 show decreasing SSRI trends while 13 present moderate increasing trends. A binomial-distribution test yields p = 0.473, indicating no statistically significant bias between the number of increasing and decreasing stations, and the magnitude of changes displays bipolar characteristics. Substantial SSRI increases are observed at the high-elevation forested stations of Foping and Taibai in the Qinling Mountains (ΔSSRI = +10.31 and +10.76, respectively). Such increases may be linked to improved vegetation and ecological conditions following the implementation of the Grain-for-Green Program. Stations with the largest decreasing trends are predominantly located in urbanized zones of the Guanzhong Basin and southern-Shaanxi river valleys. Hanzhong exhibits ΔSSRI = −20.73, representing the most pronounced decline across the study domain. Spatial interpolation of ΔSSRI reveals deteriorating summer-resort suitability over most plain-valley areas, whereas the Qinling Mountains mostly remain stable or even show improved suitability.

To eliminate the interference of temporal autocorrelation on the statistical significance of the Mann–Kendall non-parametric trend test, the first-order autocorrelation coefficient AR(1) was calculated for the annual SSRI time series of the 31 long-term stations. The results show that the AR(1) values of all stations range from −0.172 to 0.236. Only three stations exhibit weak but significant autocorrelation at the significance level α = 0.05, whereas the remaining 28 stations show no significant temporal autocorrelation; the mean AR(1) across the 31 stations equals 0.061.

For the vast majority of stations, the degree of first-order autocorrelation in the time series is weak. Accordingly, the standard Mann–Kendall test was directly adopted in this study. A modified Mann–Kendall test was additionally performed for the three stations with weak but significant autocorrelation. Comparisons reveal that trend directions and significance conclusions are fully consistent with those obtained from the original M-K test, without altering trend judgements for the four-dimensional indicators: physiological thermal comfort p = 0.220, environmental suitability p = 0.357, extreme-weather suitability p = 0.007, and climate stability p = 0.861. In summary, temporal autocorrelation exerts limited influence on long-term trend inference in this study.

3.4. Multi-Dimensional Validity and Scenario Robustness Verification of the SSRI

Relevant literature on summer-temperature studies for Shaanxi Province documents an unprecedented severe heatwave across the province in 1997. To examine the identification robustness of the SSRI under systematic climatic risks, this study selects 1997 as a typical case based on anomaly analysis of historical time-series records. Statistical outputs show that the spatially averaged SSRI across 101 stations reached 36.74 in 1997, representing the minimum value over 1981–2024. This year provides a typical case for investigating multi-dimensional coupled characteristics of the SSRI under extreme thermal conditions.

Within the C-vine copula structure, thermal-comfort PC1 serves as the root node; its decline induces synchronous shifts in conditional distributions of the other dimensions. Nevertheless, due to heterogeneous backgrounds of non-thermal dimensions among individual stations, factors such as vegetation coverage and climate stability enable several regions to retain relatively high composite scores. This feature demonstrates the capacity of the SSRI to characterize regional comprehensive climatic suitability compared with standalone thermal-comfort indices.

Spatial distributions of the SSRI in 1997 exhibited pronounced regional disparities. Benefiting from high vegetation coverage and stable climatic conditions, mid-high mountainous areas of the Qinling Mountains maintained relatively high SSRI values and formed high-suitability refugia under extreme-heat backgrounds. The Guanzhong Plain suffered substantial SSRI reductions driven by intense heat exposure and low vegetation coverage. The Loess Plateau of northern Shaanxi displayed obvious spatial differentiation: sparsely vegetated areas experienced stronger impacts from dry-hot conditions, whereas southern mountainous zones retained high suitability owing to favourable ecological status.

Binary classification evaluations adopting the 25th percentile (Q25) of full-year SSRI distributions as the low-suitability threshold yield a balanced accuracy (BA) of 0.771 (sensitivity = 0.667, specificity = 0.875), which ranks highest among five extreme low-suitability years. The high specificity indicates conservative classification behaviour of the SSRI under extreme years, which helps reduce misclassification risk whereby regions with poor integrated conditions are incorrectly labelled as highly suitable zones.

To overcome limitations of conventional comfort indices that rely merely on mean-value validation and separate normal-condition scenarios from extreme episodes, this study establishes an integrated three-tier validation framework consisting of consistency checks across terrain-wide stations and scenario validation for the 1997 extreme-heat event. Quantitative comparisons between the SSRI and traditional linear indices, including THI, WEI and CIHB (the Comfort Index of Human Body), further demonstrate the scientific soundness and regional adaptability of the PCA–copula modelling framework.

To overcome the shortcomings of conventional thermal-comfort indices, which rely merely on mean-value validation and separate normal-state and extreme-event scenarios, this study establishes a three-dimensional validation framework consisting of independent external validation using UTCI, homologous internal comparison across all stations, and validation against the 1997 extreme-high-temperature scenario. Among them, THI, WEI and CIHB are only applied for homologous internal comparison to quantitatively evaluate assessment discrepancies between the SSRI and traditional linear indices. UTCI serves as the sole independent external benchmark in this study, so as to demonstrate the scientific soundness and regional adaptability of the PCA–copula model.

This study employs Kendall’s rank-correlation coefficient τ to quantify the coupling relationships between the SSRI and comfortable-day time series derived from conventional temperature–humidity and wind-effect indices, avoiding the limitation that Pearson’s linear correlation is ill-suited for skewed climatic datasets. At the provincial scale, the mean τ between the SSRI and the wind-effect index WEI reaches 0.407, with 84.2% of stations passing the significance criterion of p < 0.05. Valley-located stations such as Jinghe in Guanzhong exhibit the strongest correlation (τ = 0.689). In low-elevation basins, heat accumulation readily occurs under the influence of the subtropical high-pressure system during summer, leading to frequent wind-calm and sultry weather. Ventilation conditions exert certain impacts on local thermal environments, and the ventilation-heat-dissipation dimension within the model shows a relatively higher weight contribution. Vegetation factors can also produce corresponding modulating effects on local thermal conditions. Figure 7 illustrates spatial patterns of correlation coefficients between the annual-scale SSRI and comfortable-day counts for THI, WEI, CIHB and their combined metric. The vertical lapse rate of temperature replaces wind speed as the dominant controlling factor, which is fully consistent with the regional climatic principle that “summer-resort conditions depend on ventilation over plains and on temperature–humidity regimes over mountains”.

The stations of Shenmu and Fuxian in northern Shaanxi display divergent coupling features, whereby the SSRI shows weak negative correlations with THI (τ = −0.18~−0.30). Conventional THI determines comfort grades solely from temperature and humidity and neglects local environmental effects originating from sparse vegetation and intense daytime surface radiation across the Loess Plateau. This mechanism may account for the evaluation bias observed at certain sites: “relatively low air temperature yet unsatisfactory summer-resort conditions”. By introducing multi-dimensional corrections incorporating vegetation coverage and long-sunshine extreme metrics, the SSRI partly captures the limitations of summer-resort conditions across ecologically fragile zones and mitigates one-sided assessments produced by single meteorological indicators. This section discusses observed phenomena by integrating topographic thermal effects and water-vapor transport mechanisms, rather than merely enumerating correlation statistics.

This study adopts the proportion of combined-comfort days derived from THI-WEI as the conventional thermal-comfort reference indicator. Simple mean-value comparison is abandoned to avoid statistical artefacts whereby mean values mask extreme events, and long-term consistency tests are carried out for 101 meteorological stations across the province. The test results are shown in Figure 8a. The SSRI presents generally high overall consistency with basic physical thermal-comfort metrics, and the overall matching accuracy of their classification outputs reaches 86.10%. Spatially, more than 61.4% of stations achieve a matching accuracy higher than 85%. Within the Yan’an area, the identification of summer-resort suitability based on the SSRI is perfectly synchronized with conventional meteorological indicators.

Published studies on summer temperatures in Shaanxi have documented 1997 as a historically rare extreme-heat year. To investigate SSRI responses under systematic heat stress, anomaly analysis of time-series records was applied to select 1997 as a typical case-study event. Provincial-mean SSRI reached only 36.74 in 1997, with an anomaly of −16.76 and a departure of 1.03 standard deviations from the multi-year mean. It ranked among the years with the poorest summer-resort suitability throughout the 1981–2024 period and corresponds to a representative extreme-heat episode. Obvious SSRI responses to this extreme-heat event can be observed in this case, providing empirical evidence for the practical performance of the index.

Cross-validation of SSRI’s discriminatory capacity was conducted using the hard benchmark “fraction of physically comfortable summer days < 64.0%” (Figure 8). As presented in Figure 8b, among the 96 stations involved in validation across the province, the SSRI correctly classified 89 stations as “unsuitable”, achieving a sensitivity of 96.3% for capturing extreme-climatic risks. This demonstrates that the SSRI is free from systematic “false-high-score” misjudgements under province-wide heatwave attacks. In particular, along the Great-Wall belt of northern Shaanxi at stations such as Fugu, Yulin and Shenmu, despite generally low summer mean temperatures, the SSRI still produces low scores under the 1997 extreme conditions (e.g., Shenmu: SSRI = 25.99), which closely agrees with the low comfortable-day fraction (44%) derived from physical metrics. This confirms that SSRI can see through the “smokescreen of mean temperature” and accurately identify cumulative thermal risks.

Notably, among mismatched samples, the proportion of SSRI suitability “under-estimation” cases (72.0%) is substantially higher than that of the “over-estimation” cases (28.0%). This feature reveals that the SSRI implements a more stringent screening mechanism than single meteorological indicators: beyond temperature thresholds, it imposes dual constraints from ecological conditions and climatic stability. Taking Dingbian Station as an example, despite relatively cool local temperatures, its validation accuracy is merely 27.5%. Inspection of raw datasets indicates low scores for local environmental components. This result suggests that the low SSRI objectively reflects regional drawbacks including sparse vegetation cover and intense climatic variability. It strongly demonstrates that the SSRI effectively mitigates the one-sidedness of temperature-only assessment and prevents misclassification of ecologically fragile regions as high-quality summer-resort destinations.

At Huashan Station, conventional physical metrics frequently indicate “unsuitable” conditions owing to high-mountain strong winds and low temperatures, whereas the SSRI delivers relatively favourable evaluations. Data tracing shows that this station gains extra credit from outstanding environmental quality and weather stability. Hence, the SSRI breaks the rigid dependence of traditional indices on wind speed and air temperature, comprehensively accounting for superimposed advantages including “freedom from sultriness in mountainous terrain” and “high ecological quality”, and accurately identifies the unique value of mountain-type summer-resort resources.

For regions strongly affected by enclosed terrain or human activities such as Lantian and Tongguan, raw-data examination reveals poorer climatic stability relative to other areas. By capturing such microclimatic instability, SSRI outputs lower scores than conventional physical metrics and objectively warns of summer-resort risks under extreme-weather conditions for these sites.

3.5. Spatial Differentiation of SSRIs Across Shaanxi Province and Five-Level Zoning for Summer Heat-Relief Suitability

Spatial interpolation was performed on the annual SSRI time series from 101 stations covering 1981–2024. Co-Kriging geostatistical interpolation with elevation as the covariate was applied in this study to convert station-based SSRI values into 250 m gridded datasets. First, exploratory spatial-data analysis was implemented to confirm significant spatial autocorrelation of the SSRI. An exponential variogram model was selected with a variable-searching neighbourhood, and DEM-derived elevation was incorporated as the covariate to characterize the topographic control effect of altitude on summer-resort suitability.

Leave-one-out cross-validation of the 101-station dataset was used to quantitatively evaluate interpolation performance: the mean absolute error (MAE) of multi-year-average SSRI interpolation was 4.82, the root-mean-square error (RMSE) was 6.37, and the overall bias was −0.21, indicating no systematic overestimation or underestimation. From the geomorphic perspective, the Guanzhong Plain exhibits optimal interpolation accuracy, whereas relatively larger errors occur in the Qin-Ba Mountains due to fragmented micro-topography. Interpolation uncertainty analysis was conducted based on the output-variance grid. Higher interpolation uncertainty appears in the deep Qin-Ba mountainous areas and northern Shaanxi where station density is low. The interpolation outputs are suitable for provincial- and municipal-scale macro-regionalization of summer-resort suitability; small-scale sites in valleys and uninhabited regions require further validation with field observations.

Combined with province-wide DEM topography and spatial patterns of vegetation, the macro-distribution law of summer-resort suitability constrained by multiple factors, including altitude, landform, vegetation and the urban heat-island effect was revealed. SSRI classification thresholds were mapped according to μ ± 0.5σ and μ ± 1.5σ derived from the normal distribution of intermediate latent variables, dividing the whole province into five zones: extremely suitable, suitable, moderate, poorly suitable and unsuitable (Figure 8c). This classification scheme originates from data partitioning of model internal latent variables and represents a statistically based classification approach.

To assess the robustness of classification outputs, three widely adopted five-level classification strategies, namely equal-interval classification, quantile classification (20%, 40%, 60%, 80%) and Jenks natural-break classification, were additionally implemented for sensitivity comparison. Kappa coefficients were computed to evaluate spatial-zoning consistency. The results show that the Kappa coefficient between the proposed scheme and Jenks natural-break classification reaches 0.78; Kappa equals 0.74 for quantile classification and 0.62 for equal-interval classification. Under different classification strategies, the macro-spatial pattern of high-suitability cores within the Qin-Ba Mountains and low-value cores in Guanzhong river valleys remains stable. Discrepancies mainly lie in boundary fluctuations of moderate-suitability transition zones, demonstrating that the zoning conclusions of this study are generally robust.

Furthermore, the practical summer-resort implication of the five-level classification was validated using an independent physical reference indicator: the proportion of THI-WEI combined-comfort days. A significant positive correlation exists between the five-level grades and the proportion of summer THI-WEI combined-comfort days (Kendall τ = 0.612, p < 0.001). Specifically, the average proportion of comfort days is 72.4% for extremely suitable zones, 61.1% for suitable zones, 48.6% for moderate zones, 34.3% for poorly suitable zones, and merely 21.7% for unsuitable zones. According to the 1997 extreme-high-temperature scenario, stations graded as extremely suitable still maintain relatively favourable comprehensive summer-resort conditions under extreme heatwaves, while prominent thermal stress is observed at unsuitable-grade stations. The above findings indicate that this statistical classification is not a purely mathematical partition but corresponds to the real-world gradient of summer-resort suitability ranging from favourable to unfavourable conditions.

Extremely suitable and suitable core aggregation areas (SSRI ≥ 61.7): Two large contiguous high-suitability cores were formed in the north and the south. The southern core includes the main ridge of Taibai–Foping–Ningshan in the Qinling Mountains and the whole area of Zhenping and Langao in the Daba Mountains. The vertical temperature drop due to altitude and the high-coverage forest form a double ecological compensation, and the SSRI remains stable at ≥78.0 throughout the year. The northern high-value core is distributed in the loess gully forest areas of Huanglong Mountain, Ansai and Zhidan in Yan’an. The combination of high latitude and vegetation restoration from the Grain-for-Green Project breaks the traditional perception that “there are no high-quality summer-heat-avoidance areas in northern Shaanxi,” and constitutes the second-largest core of summer-heat-avoidance resources in the province.

Sub-suitable potential adjustment areas (45.4 ≤ SSRI < 61.7): These areas are strip-shaped and surround the peripheries of the two cores, covering the areas along the Great Wall in northern Shaanxi, the tablelands at the northern foot of the Qinling Mountains, and the hinterland of the Hanzhong Basin. The regions have strong solar radiation during the day and a relatively high frequency of extreme weather, but the diurnal temperature difference is generally greater than 12 °C, with a prominent cool feeling at night. They are suitable for developing differentiated summer-heat-avoidance business forms such as star-gazing camping and rural tourism.

Relatively unsuitable and unsuitable low-value areas (SSRI < 45.4): These areas are concentrated in the urban agglomeration of the Guanzhong Plain and the Hanjiang River Valley in Ankang, forming a low-value belt that runs from east to west. The main urban area of Xi’an has the only SSRI value < 29 in the province, and there are contiguous low-value areas in Xianyang, Weinan, and Hancheng. An independent low-value block is formed in the river valley along the Hanjiang River in Ankang. The closed terrain of the basin hinders heat dissipation, and the hardened urban underlying surface, artificial heat islands and the stuffy still air in summer are superimposed, resulting in pronounced high-temperature stress in summer. The local area mainly relies on artificial summer-heat-relief business forms such as indoor ice and snow facilities and water parks, and it is the core area for exporting summer-heat-avoidance tourists in the province.

The overall spatial pattern shows the characteristics of high quality in the south, uniqueness in the north and a trough in the middle. The high-suitability mountainous areas in the north and the south are in sharp contrast to the low-value plain areas in the middle. The zoning results can provide a quantitative spatial basis for the differentiated planning of summer-heat-avoidance tourism in Shaanxi Province, namely “improving quality in the south, exploring potential in the north, and relieving pressure in the middle.” All the zoning maps are uniformly marked with colour scales, classification thresholds and terrain base maps, with clear and standardised visualisation logic.

3.6. Spatiotemporal Statistical-Coupling Characteristics of Summer-Resort Suitability and Potential Buffering Signals of Vegetation

Spatiotemporal differentiation is the comprehensive result of the non-linear coupling of multiple factors, such as meteorology, topography and vegetation. Two sets of differentiated dominant evaluation logics are formed in different geomorphic units: in the low-altitude basins of Guanzhong and southern Shaanxi, the wind-effect index serves as the core controlling factor. Under the long-term control of the subtropical high in summer, heat accumulates continuously, and static-heat weather occurs frequently. Evaporative cooling brought by wind speed is the only way to improve human thermal sensation. The model automatically amplifies the weight of the ventilation and heat-dissipation dimension. In the high-altitude mountains of the Qinling and Bashan ranges, the vertical temperature-decreasing effect dominates. Low temperature becomes the core advantage for summer heat relief. The index is highly sensitive to temperature and humidity changes, forming a natural terrain-adaptive evaluation system.

Spatiotemporal differentiation represents the integrated outcome of nonlinear coupling among multiple factors, including meteorology, topography and vegetation. Two differentiated dominant-factor evaluation logics are formed across diverse geomorphic units. In the low-elevation basins of Guanzhong and Southern Shaanxi, the wind-effect index acts as the core controlling factor. Under persistent summer subtropical-high-pressure forcing, continuous heat accumulation and frequent wind-calm sultry weather occur. Evaporative cooling induced by ventilation serves as one of the most critical approaches to mitigate local human sultry thermal sensation, and the model automatically assigns higher weight to the ventilation-heat-dissipation dimension. By contrast, the high-elevation Qin-Ba Mountains are strongly governed by the vertical lapse rate of air temperature, and low-temperature conditions constitute the primary favourable condition for local summer-resort suitability. Accordingly, the index exhibits pronounced responses to fluctuations in temperature and humidity.

Temporal-evolution patterns and spatial patterns can be interpreted mutually. Over the past 40 years, SSRI degradation within river valleys of Guanzhong and Southern Shaanxi is markedly greater than that in mountainous regions. Lacking topographic shielding and buffering, basins suffer stronger thermal-stress signals corresponding to increasing extreme-weather events. In high-altitude forested areas of the Qinling Mountains, elevation and cloud-fog conditions may contribute to the mitigation of high-temperature stress, and station-level suitability remains generally stable over time. Stations of Taibai and Foping show increasing suitability trends. This study further analyses the statistical linkage among topography, meteorology and human thermal sensation, and discusses the temporal-clustering outputs of stations in combination with local thermal processes.

Surface vegetation bears significant statistical association with local summer-resort suitability, which helps explain provincial north–south index discrepancies as well as 40-year spatiotemporal differentiation. The Northern Shaanxi Loess Plateau features low annual-mean temperature; nevertheless, high bare-soil fraction leads to intense daytime land-surface heat absorption and prominent long-duration-sunlight stress. Constrained by fractional vegetation cover and extreme-sunlight metrics, the SSRI partly corrects evaluation biases inherent in conventional temperature–humidity indices, which rely merely on air temperature. In high-elevation forested regions such as Taibai and Foping in the Qinling Mountains, a rising SSRI is observed concurrently with vegetation-restoration projects.

Against the background of the region-wide extreme high temperature in 1997, mountain forest areas such as Zhenping and Liuba relied on dense forests to form a microenvironment with strong climate resilience. The SSRI accurately quantifies the ecological benefits of vegetation in cooling and weakening extreme heat stress, stably preserving high-quality summer heat-relief spaces in the region-wide low-value pattern. Vegetation cover forms a positive climate–ecological feedback loop by regulating local temperature and humidity, reducing the number of stuffy and calm-wind days, and weakening the frequency of extreme high temperatures. It is the core support for mountains to maintain a high SSRI in the long term and slow down the decadal attenuation amplitude.

4. Discussion

4.1. Methodological Innovation of the PCA–Copula Nonlinear Modeling Approach Compared with Traditional Linear Heatstroke Prevention Evaluation Models

This study constructs a four-in-one SSRI. It adopts the core idea of Mijani et al. (2020) in using PCA to eliminate redundant indicators [28,29], but expands and optimizes their single-overall dimensionality reduction method. Dimensionality reduction is carried out independently by grouping according to four major dimensions: physiological thermal comfort, environmental suitability, extreme weather, and climate stability, thus establishing a hierarchical index structure for the summer heat-relief system [30]. Secondly, this study draws on the application orientation of Wang et al. (2022) for regional summer heat-relief planning [31] but abandons the settings of manual weighting and a unified threshold across the entire region. Finally, drawing on the copula tail dependence modelling theory proposed by Tootoonchi et al. (2022) [25], this study introduces the high-dimensional dependence-modelling concept of a vine copula from hydrological research into comprehensive summer-resort evaluation. The formal SSRI modelling in this study employs the five-dimensional C-vine copula, which fully retains information from both principal components of the extreme-weather dimension. The subsequent four-dimensional Clayton copula serves merely as a mechanistic-analysis tool. Quantitative assessment is realized via objective modelling based on the grouped PCA–C-vine copula. Compared with the THI-WEI model, the matching accuracy increases to 86.10%, and the identification rate for extreme heatwaves reaches 96.30%. This confirms that the C-vine nonlinear joint framework can accurately capture compound lower-tail thermal stress triggered by the simultaneous deterioration of multiple meteorological factors [32].

This result is consistent with the theoretical conclusion of Tootoonchi et al. (2022) that “Copula can break through the linear independence assumption and characterize the tail dependence characteristics of climate variables” [25], further corroborating the scientific nature of the modelling in this study. However, there are obvious differences between this study and the PCA–LSA model of Mijani et al. (2020) [28]. Mijani et al. (2020) used unified principal component dimensionality reduction followed by least-squares linear regression, assuming linear independence of elements, an approach that is only applicable to homogeneous urban underlying surfaces [28]. In contrast, this study conducts dimensionality reduction by grouping according to the four dimensions of physiology, environment, extremes, and climate stability, avoiding the confusion of dimensional information caused by global dimensionality reduction. Meanwhile, it introduces the Clayton copula to characterize nonlinear coupling relationships, adapting to the complex landforms of interlaced plateaus, basins, and mountains [33]. In addition, the linear SSI index constructed by Wang et al. (2022) relies on manual weighting by experts and fixed weights across the entire region, which is prone to distortion in cross-landform evaluations [31,34]. This study achieves terrain-driven adaptive adjustment of factor contributions based on the Kendall rank correlation coefficient, mitigating key limitations of conventional models including subjective weighting and insufficient terrain adaptability for heterogeneous mountainous terrain.

Theoretically, this study improves the statistical modelling system for quantitative evaluation of human thermal comfort and establishes a complete technical workflow consisting of hierarchical indicator dimensionality reduction, optimal distribution selection, multi-dimensional joint probability simulation, and standardised index transformation. Practically, this objective modelling framework provides methodological references for summer-resort suitability research in multi-geomorphic transition zones across China. Notably, the SSRI parameters and classification thresholds determined in this study are not universally applicable and cannot be directly extended to other regions. Local observational data are required for refitting and recalibration when applying this framework to new study areas. The proposed method can offer valuable insights for summer-resort resource investigation and high-temperature risk assessment.

4.2. Analysis of the Spatial Differentiation and Control Mechanism of SSRI in the Composite Landform of Plateau–Delta–Slope

Wang et al. (2022) constructed a linear summer-cooling suitability index [31], and Arulalan et al. (2023) established a multi-model heatwave assessment framework [35]. The two types of research outcomes share a common core basis, namely, the use of near-surface summer thermal environment factors as the fundamental evaluation indicators. Human summer comfort levels and high-temperature stress risks are closely related to meteorological variables such as air temperature and humidity, indicating consistent research objects for the two research paradigms. The proposed SSRI index integrates the common basic thermal environment factors adopted in the above studies and remedies their defect of fragmented evaluation dimensions. On the one hand, the SSRI inherits the research framework of Wang et al. (2022), which characterizes summer resort suitability based on steady physiological and ecological indicators, and retains the analytical logic for conventional regional thermal environment assessment [31]. On the other hand, the SSRI draws on the extreme high-temperature coupling modelling approach of Arulalan et al. (2023) [35] and breaks through the modelling limitation of the traditional unified global assumption. Taking topography as the underlying pre-regulating variable, this study hierarchically clarifies the differentiated formation mechanisms across three geomorphic units. The Guanzhong Basin is dominated by circulation obstruction and heat accumulation. The Qinling-Daba Mountains form a comfortable thermal environment through dual cooling sources: altitudinal vertical temperature decline and vegetation transpiration. The Loess Plateau presents a balanced system constrained by dual effects, including cooling from high latitude and warming induced by bare soil. The findings confirm a spatial pattern of summer resort suitability in Shaanxi Province, characterized by generally low SSRI values in the Guanzhong Basin and favourable conditions in the Qinling-Daba and Huanglong mountainous areas. This result revises the traditional stereotype that the northern Shaanxi region lacks high-quality summer tourism resources. The distribution characteristic of continuously low values in the Guanzhong Basin is fully consistent with the mechanism of circulation blockage and heat accumulation in the closed basin proposed by Wang Ziyi et al. (2022) [36], which explains the phenomena of still wind and high temperatures, as well as the continuous decline of summer-cooling potential in the basin. Shu et al. (2023) noted in their research on the ozone terrain effect at the junction of the Sichuan–Chongqing Basin and the plateau that the mountain–plain circulation (MPC) between the plateau and the basin forms a cross-regional water vapor and heat transport channel [37]. High-altitude areas rely on the cooling buffer brought by vertical uplift to mitigate summer thermal discomfort [37]. The high SSRI in the Qinling–Bashan Mountains confirms the rationality of the mountain vertical uplift cooling theory proposed by Shu et al. (2023) [37].

The Kendall rank correlation results for different landforms show that ventilation and heat dissipation are the core regulatory factors in the basin; temperature and humidity lapse rates dominate in the mountains; and vegetation cover exerts bidirectional constraints on the Loess Plateau. This differential dominant control logic cannot be captured by existing linear models. The linear thermal-comfort evaluation system constructed by Mijani et al. (2020) assumes constant influence intensity of meteorological elements across the entire region, rendering it incapable of capturing spatial differences in the strength of factor synergy under varying terrains [28]. Although Tootoonchi et al. (2022) used copula theory to confirm the nonlinear tail-coupling relationships among temperature, humidity and sunshine [25], their case studies are primarily concentrated in hydrological extreme scenarios and do not integrate terrain heterogeneity to explain the spatial differentiation law of dependence structures. Under the extreme-heat scenario of 1997, contiguous forested regions retained high suitability levels. This finding reveals that vegetation acts as a primary buffering agent against heatwaves and sustains local climatic resilience, and it advances the reciprocal feedback theory of “terrain-vegetation-meteorology” coupling under complex terrain.

4.3. Interpretation of the 40-Year Long-Term Time-Series Evolution Laws and Mechanisms of Summer Heat Avoidance

A time-series analysis from 1981 to 2020 indicates that only extreme weather shows a significant deterioration trend (p = 0.007). There is no systematic decline in human thermal sensation, ecological baseline and climate stability. The average value of the SSRI across the entire region has slightly decreased by 2.92 over the past four decades, and there is strong spatial heterogeneity in regional evolution. The SSRI in the Guanzhong and Hanzhong river valleys has significantly declined (ΔSSRI in Hanzhong = −20.73), while it has continuously increased in the high-altitude forest areas of the Qinling Mountains (ΔSSRI in Foping and Taibai > 10). This differentiation characteristic stems from the differential buffering effects of topographic barriers and ecological vegetation restoration. This time-series evolution pattern cannot be identified by the static mean evaluation system proposed by Wang et al. (2022), as their study relies solely on multi-year average climate data and lacks analysis of interdecadal dynamic evolution [31]. Arulalan et al. (2023) focused on simulating future heatwave scenarios and lacked quantification of the long-term historical decline [35]. This study integrates multi-year normal time-series analysis with the analysis of extreme high-temperature disturbances, remedying the defect of separated time-series analyses in the two types of models. Statistical results suggest that the deterioration of extreme weather represents a systematic factor significantly correlated with the decline of summer-resort suitability during the study period. A correlation between mountain forest ecosystems and the mitigation of heat-stress losses is observed.

4.4. Support for Model Robustness from the Triple Integrated Verification System

Mijani et al. (2020) established a single-level fitting-calibration mechanism using synchronous remote-sensing observation data and adopted the fitting error of surface parameters as the criterion for model-performance evaluation [28]. Based on multi-year climatic-mean datasets, Wang et al. (2022) constructed a static-zoning calibration mechanism and judged the index performance according to the distribution of multi-year average suitability zones [31,36]. Both validation systems take normal mean climate as their core analytical element and differ only in calibration-data scenarios (instantaneous remote-sensing values versus multi-year meteorological means).

To avoid the limitation of traditional models that rely exclusively on multi-year mean values for static calibration, this study develops a three-in-one calibration framework consisting of independent external validation with the Universal Thermal Climate Index (UTCI), full-domain time-series homologous internal control, and scenario calibration for the extreme high-temperature event in 1997 to demonstrate the robustness of the Standardized Summer Resort Index (SSRI). The full-domain time-series consistency calibration is implemented with homologous meteorological data and represents an internal comparison rather than an external-validation outcome. The matching accuracy between full-domain sites and the THI-WEI benchmark reaches 86.10%, indicating reliable index-evaluation outputs under normal-climate conditions. The 96.30% heatwave-risk identification rate proves that the model can capture extreme heat stress masked by climatic mean values and mitigate systematic bias inherent in conventional linear models.

Mijani et al. (2020) fitted all surface-environmental factors with a unified normal distribution and simplified variable-interaction patterns via linear models [28]. Wang et al. (2022) directly performed linear superposition of standardised indicators without distinguishing the synergistic features of tail extremes in meteorological series [31]. Both studies build variable coupling on independent linear correlations; the only distinction is that the former uses multi-source remote-sensing parameters whereas the latter focuses merely on summer-resort-related meteorological indicators. Meanwhile, this study selectively applies marginal-distribution models including beta, Weibull and EWeib to four dimensions. Unlike previous practices that simplify variable-distribution characteristics using a uniform normal distribution, the present approach further improves the estimation accuracy of joint probabilities under extreme-year conditions and strengthens the long-term application stability of the model.

4.5. Research Limitations

The threshold and normalisation parameters of the SSRI in this study are trained using station-based datasets from Shaanxi Province; therefore, the SSRI is currently applicable only to Shaanxi. Although the PCA–copula modelling workflow is methodologically generalizable, parameter transferability requires further validation against field observations from external regions. Three inherent sources of systematic uncertainty exist within the present model and outputs, originating mainly from data foundation, spatial scale and anthropogenic influences. In addition, all copula models, marginal distributions and percentile-grading thresholds of the SSRI are trained using station-based data from Shaanxi Province. The finalized index cannot be directly transferred to regions outside Shaanxi. For cross-regional applications, indicator fitting and standardisation procedures must be re-implemented.

First, there are intrinsic limitations of the algorithmic model. ① PCA loadings: piecewise-sensitivity tests reveal stable signs of PCA loadings across different time windows, with only minor numerical fluctuations. Full-period samples are adopted in this study to guarantee overall consistency. ② Min–max normalisation: multi-year climatological extremes are applied to mitigate disturbances from extreme years. Nevertheless, large mountain–basin contrasts across Shaanxi cause global extremes to induce certain distortions in variable distributions for sub-regions. ③ Clayton copula: selected from multiple copula candidates according to Kendall-τ and AIC/BIC criteria. Static-parameter specification represents a conventional modelling simplification, which may yield biases in depicting local co-dependence among partial variables. ④ Regarding the logical concern with vegetation variables: since NDVI is adopted as one of the input variables, direct interpretation based on NDVI would raise the risk of circular reasoning. In this paper, topographic and meteorological factors are treated as core drivers. Partial-correlation analysis with controlled variables is applied to isolate the independent contribution of NDVI, so as to avoid this problem.

Second, scale constraints arising from station observation and spatial interpolation. Interpolation based on 101 national meteorological stations inevitably smooths climatic differences induced by micro-topography. In addition, standard station observations cannot fully reflect the actual thermal perception in mountainous and valley environments, which is a common limitation of station-driven climate evaluation studies. Focusing on provincial-scale macro assessment, this study does not pursue absolute accuracy at micro-topographic point scales.

Third, simplification of indicators and anthropogenic processes. Restricted by data availability, ecological indicators such as negative oxygen ions were not incorporated into the evaluation framework.

Fourth, temporal and spatial dependence of samples. First-order autocorrelation tests for the 31 long-term stations indicate weak temporal dependence at most sites. Comparisons between the Mann–Kendall (M-K) and modified Mann–Kendall (MMK) tests verify the robustness of trend detection results. Station resampling and time-block bootstrap sensitivity analyses are further conducted for copula fitting, confirming that sample dependence exerts limited substantive impacts on copula model selection and dependent parameters. Nevertheless, the mixed station-year dataset does not fully satisfy the independent and identically distributed (i.i.d.) assumption, which may lead to the underestimation of standard errors for model parameters.

4.6. Future Outlook

First, the UTCI validation suffers from threshold sensitivity issues. This study adopts 9–26 °C as the threshold range for UTCI no-thermal-stress conditions, which can well characterize summer thermal environments across areas with different elevations in Shaanxi. Nevertheless, converting continuous thermal-physiological indicators through fixed thresholds inevitably causes information loss. Future studies can conduct multi-threshold sensitivity analysis to quantify the influences of diverse UTCI classification criteria on validation results.

Second, the percentile mapping of the SSRI is anchored to the reference period of 1981–2024. When applied to future climate scenarios or other study regions, the SSRI framework requires recalibration based on updated climatic distributions to reduce scaling drift induced by variations in the reference period.

Third, meteorological stations exhibit spatial autocorrelation. The current treatment of station-year samples as independent observations may interfere with uncertainty estimation. Spatial block bootstrap and other advanced methods can be adopted in future research to evaluate model parameter stability while preserving inherent spatial dependence structures.

Furthermore, although the C-vine model exhibits high goodness-of-fit in model selection, the selection of the vine structure still entails certain uncertainty. Future studies can adopt model averaging methods to further evaluate the impacts of different dependence structures on the SSRI estimation results. Although this study has verified the robustness of core conclusions through station resampling and time-block bootstrap sensitivity analysis to address sample dependence, subsequent research can further improve the estimation of parameter confidence intervals and fully quantify the uncertainty caused by spatial autocorrelation by applying spatial block bootstrap and multi-model averaging approaches.

In terms of data limitations, the annual spatially averaged vegetation data adopted in this study fails to capture intra-summer vegetation dynamics. Incorporating high-resolution remote-sensing datasets such as Sentinel-2 and Landsat is expected to improve the spatiotemporal accuracy of vegetation information. Furthermore, the current SSRI mainly reflects natural climatic suitability. Future research can incorporate socio-economic factors, including transportation accessibility, service facilities and medical resources, to establish a comprehensive evaluation system targeted at tourism planning.

Moreover, multi-source data fusion can be implemented by integrating ground meteorological station observations, automatic mountain meteorological station records, satellite-retrieved land surface temperature and unmanned aerial vehicle (UAV)-based near-surface temperature and humidity measurements. This can densify observational samples in uninhabited areas such as the Qinling-Daba Mountains and northern Shaanxi gully regions and further develop a refined hundred-meter-scale gridded SSRI dataset. Additionally, hourly meteorological time-series data can be utilized to characterize diurnal variations in human thermal perception. Refined datasets of negative air ions, atmospheric comfort level and land use can also be supplemented to optimize the four-dimensional evaluation system and compensate for deficiencies caused by missing variable in the current framework.

Finally, multi-scale refined evaluation can be achieved in spatial and climatic scenario dimensions. Spatially, on the basis of provincial-scale macro zoning, nested fine-scale assessments at municipal, county and scenic spot levels can be conducted to clarify the suitability differentiation of micro-topographic units including villages, valleys and tourist areas. In terms of climate scenarios, multi-model future warming outputs from CMIP6 can be coupled to simulate the spatiotemporal evolution of the SSRI in Shaanxi Province under different emission pathways for the 2050 and 2100 horizons.

5. Conclusions

This study performs dimensionality reduction via dimension-wise PCA to extract five principal components. The ECDF is adopted to construct non-parametric marginal distributions, so as to avoid marginal fitting bias potentially induced by pre-specified parametric distributions. Multiple candidate copula models are employed to characterize the joint dependence structure among the five climatic variables.

Comprehensive selection based on AIC, BIC and Akaike weights demonstrates that the 5-dimensional C-vine copula model obtained through automatic structure selection yields the optimal fitting performance (AIC = −4490.36, Akaike weight = 0.9973). Furthermore, the Monte Carlo-calibrated goodness-of-fit test fails to reject the hypothesis of consistency between the model and observational data (p = 0.175), indicating that this model can reasonably describe the joint probability structure of multi-climatic factors during summer in Shaanxi Province.

First, a nonlinear joint evaluation framework oriented to multi-climatic factors was established, realizing a standardised statistical workflow from multi-indicator information extraction to comprehensive index construction. Five principal components were extracted through dimensionality reduction via segmented PCA. The empirical cumulative distribution function (ECDF) was adopted to fit marginal distributions, effectively avoiding marginal fitting biases induced by preset parametric distribution assumptions. Multiple candidate copula models were further employed to characterize the joint dependence structures among diverse climatic factors. Comprehensive screening based on Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Akaike weights demonstrated that the automatically selected C-vine copula model exhibited the optimal fitting performance (AIC = −4490.36, Akaike weight = 0.9973). The Monte Carlo-calibrated goodness-of-fit test failed to reject the consistency hypothesis between the model and observational data (p = 0.175), indicating that the proposed model can well describe the joint probability structure of multi-dimensional summer climatic factors across Shaanxi Province. All ten candidate parametric distributions were rejected by the Kolmogorov–Smirnov (K-S) test, verifying that the ECDF method effectively eliminates the interference of marginal distribution assumption bias on copula-based modelling. Finally, the SSRI was standardised via percentile mapping based on the empirical CDF derived from the 1981–2020 reference period, endowing the index with explicit probabilistic interpretation and ensuring scale consistency for long-term sequential evaluation.

Second, the SSRI across Shaanxi Province exhibits prominent spatial heterogeneity, forming a distinct spatial pattern with high-value zones in mountainous areas and low-value zones in plains and river valleys. The mid-high elevation areas of the Qinling Mountains and the northern slope of the Daba Mountains constitute the dominant high-suitability regions across the province, benefiting from low summer thermal load, high vegetation coverage and superior thermal environment conditions, with stations including Ningshan, Liuba and Zhenping maintaining persistently high multi-year mean SSRI values. The Huanglong Mountain–Ziwuling region in southern northern Shaanxi also presents considerable summer resort potential, confirming favourable summer climatic suitability in mountainous areas of the southern Loess Plateau. In contrast, the Guanzhong Plain and Hanjiang River Valley serve as relatively low-suitability zones due to constraints imposed by low-altitude thermal environments, intense heat exposure and poor wind ventilation conditions. The aeolian sandy areas of northern Shaanxi show low resort suitability, which is attributed to sparse vegetation coverage, a high frequency of strong solar radiation days and dry-hot climatic characteristics. The substantial spatial disparities indicate that the distribution of summer climatic resort resources in Shaanxi does not follow a single geographical pattern but is co-determined by terrain conditions, thermal environment features, ecological background and extreme weather risks. Overall, the Qinling–Daba Mountains and southern northern Shaanxi mountains represent advantageous regions for summer resort climatic resources, whereas the Guanzhong Plain and northern aeolian sandy areas are relatively constrained in summer climatic suitability.

Third, multi-level validation results verify the favourable independence, stability and application potential of the SSRI. External validation based on ERA5-HEAT UTCI datasets reveals significant but incomplete rank correlation between the SSRI and UTCI (Kendall’s τ = 0.289, p < 0.001), suggesting that the SSRI can further incorporate vegetation coverage, extreme weather risks and climatic stability on the basis of characterizing human thermal comfort. LOOCV yields a consistent classification accuracy of 66.3% ± 10.2%, demonstrating robust evaluation stability of the SSRI across annual sample subsets. Analysis of extremely low-suitability years indicates that the SSRI can effectively capture anomalous climatic conditions, while moderate uncertainties remain under extreme scenarios. In general, the SSRI overcomes the inherent limitations of single thermal-comfort indicators in comprehensively reflecting the characteristics of summer resort climatic resources and can provide a quantitative reference for regional resort resource assessment, climatic suitability zoning and tourism climate risk management.