Tree selection, courtyard form, and outdoor microclimatic comfort in hot-arid educational spaces: a multi-criteria decision framework

1 Introduction

In hot-arid regions, the thermal performance of educational courtyards has become an increasingly important concern at the intersection of climate adaptation, urban design, and public health (Salameh et al., 2024; Cantón et al., 2014). Unlike residual open spaces, school and university courtyards are routinely occupied for circulation, recreation, informal interaction, and outdoor learning, often during the most thermally demanding periods of the academic day (Sun et al., 2025; Zheng et al., 2024; Xu et al., 2025). Under intense solar exposure and elevated air temperatures, these spaces can therefore shift rapidly from functional social environments to sources of substantial thermal stress (Han et al., 2025; Pasandi et al., 2025; Qiao, 2025). Field investigations in educational environments have documented severe outdoor thermal conditions, including air temperatures of approximately 32 °C–41 °C in Aswan and 30 °C–37 °C in the educational open spaces in Kuala Lumpur, while studies of school courtyards have similarly reported conditions associated with heat stress and outdoor thermal discomfort (Elgheznawy and Eltarabily, 2021; Mahmoud and Abdallah, 2022). The significance of this problem extends beyond localized thermal sensation, as excessive heat can constrain the functional usability of outdoor educational spaces and may discourage their use for educational and recreational activities (Binabid et al., 2024; Antoniadis et al., 2020). However, the extent to which improved thermal conditions influence students’ behavioral patterns, social interaction, participation, or perceptions of inclusiveness depends on additional social and behavioral factors and cannot be inferred directly from microclimatic performance alone. Accordingly, such outcomes are considered potential implications of improved outdoor thermal conditions rather than direct outcomes evaluated in the present study.

Moreover, outdoor thermal stress is intrinsically multidimensional. Air temperature (Ta) characterizes the atmospheric thermal load, T_mrt captures the radiative exposure that frequently dominates daytime heat stress, and physiological indices such as Physiological Equivalent Temperature (PET) integrate these environmental drivers into a Human-centered representation of thermal burden (Taleghani et al., 2015; Abdallah et al., 2025; Abdel-Ghany et al., 2013). Consequently, the central challenge is not simply to reduce outdoor temperature, but to maintain educational courtyards as thermally usable environments during actual periods of student occupancy, under the combined influence of climate, solar exposure, spatial configuration, and time of day (Mahmoud and Abdallah, 2022; Salameh, 2024; Gomaa and Ragab, 2022). Among available passive strategies, urban vegetation has emerged as a particularly important nature-based mechanism for regulating outdoor thermal conditions because it modifies the local energy balance through interacting radiative and physiological processes (El-Bardisy et al., 2016; Gomaa et al., 2025; Zango et al., 2017; Gomaa et al., 2024a). Tree canopies intercept short-wave solar radiation, reduce the radiant load received by pedestrians and surrounding surfaces, and alter the exchange of long-wave radiation, while evapotranspiration redistributes available energy toward latent rather than sensible heat fluxes (Montero-Gutiérrez et al., 2026; Chen et al., 2025). Through these mechanisms, vegetation can modify Ta and T_mrt and, consequently, improve human thermal comfort as reflected by PET (Gomaa et al., 2025; Gomaa et al., 2024b; Matzarakis et al., 1999; Höppe, 1999).

In hot-arid environments, the radiative function of trees is especially important because direct and reflected solar radiation frequently constitute a dominant component of daytime outdoor heat exposure (Ali-Toudert and Mayer, 2007; Chen and Ng, 2013; Detommaso et al., 2021; Pattnaik et al., 2025). A substantial reduction in T_mrt may therefore produce a much larger improvement in physiological thermal stress than the corresponding change in Ta alone (Ragab et al., 2026; Abdelhafez et al., 2026). This evidence establishes vegetation as more than a landscape amenity: it is a passive microclimatic infrastructure whose performance depends on how effectively its physical characteristics interact with the surrounding built environment. However, the thermal benefit of vegetation cannot be inferred from vegetation quantity alone. The cooling performance of a tree is conditioned by canopy diameter, foliage density, leaf area distribution, tree height, foliage height, canopy geometry, and spatial position, all of which influence the continuity of shading, the interception of solar radiation, radiative exchange, and evapotranspiration potential (Zango et al., 2017; Gomaa et al., 2024a; Abdelhafez et al.; Attia, 2006). These characteristics become particularly consequential in courtyards, where the interaction between canopy morphology and solar geometry determines not only the magnitude of cooling but also its temporal distribution. A dense canopy may maintain more continuous shading during critical periods of solar exposure, whereas a more open or differently structured crown may produce a more variable response as solar altitude and exposure change.

Similarly, the position of a tree relative to buildings, exposed ground surfaces, and occupied areas governs the extent to which its canopy can intercept radiation where thermal benefits are most needed (Gomaa et al., 2024a; Gomaa et al., 2024b). Thus, comparable vegetation coverage ratios should not be assumed to produce equivalent thermal outcomes. The relevant design question consequently shifts from how much vegetation should be introduced to which tree characteristics and spatial configurations provide the greatest thermal benefit under defined climatic and morphological conditions. In other words, the evaluation of greening quantity must increasingly give way to the assessment of tree-specific thermal performance. This shift is particularly important because tree cooling is inherently context dependent. The same species may produce substantially different thermal outcomes when deployed under different courtyard orientations, solar-exposure patterns, enclosure conditions, surrounding building configurations, airflow regimes, and times of day. The underlying mechanism is an interaction between tree traits and urban context: canopy density, leaf area, height, and foliage structure define the tree’s potential cooling capacity, whereas courtyard orientation, sky exposure, building arrangement, and solar trajectory determine when and where that potential is realized.

A global meta-analysis of 182 studies across 110 cities similarly demonstrated that tree-cooling efficacy is jointly governed by background climate, urban morphology, and tree traits rather than by vegetation presence alone (Li et al., 2024). This context dependence creates a fundamental limitation for conventional tree selection. A species that produces the greatest reduction in T_mrt or PET under one courtyard orientation may not deliver the same benefit under another, while a scenario producing strong peak-hour cooling may not necessarily provide the greatest temporal stability. Accordingly, the question of which tree is “best” cannot be resolved by identifying the alternative with the largest reduction in a single thermal variable. This limitation exposes a broader methodological weakness in the assessment of vegetation-based thermal mitigation. Existing studies commonly rely on absolute or relative changes in ΔTa, ΔT_mrt, PET, or UTCI to quantify performance. These indicators are indispensable for diagnosing atmospheric, radiative, and physiological responses, but when interpreted independently, they primarily answer one question: How much cooling was achieved? They provide substantially less information about whether the improvement is sustained throughout the occupancy period, whether performance remains consistent when courtyard orientation changes, or whether the tree that performs best in one thermal dimension is also the most balanced overall design alternative. This issue is particularly relevant because vegetation may generate a strong radiative response without producing an equivalent reduction in air temperature, and a high instantaneous cooling effect may not necessarily indicate a stable thermal benefit throughout the day.

Four interconnected gaps emerge from the literature. Firstly, although studies increasingly compare species and planting scenarios, methodological consistency remains limited in evaluating alternative trees simultaneously across multiple dimensions of thermal performance. Secondly, temporal performance remains insufficiently resolved, as many investigations focus on peak-hour conditions or daily averages without explicitly quantifying whether a vegetation strategy maintains a more stable thermal environment throughout the actual period of use. Thirdly, the spatial robustness of tree performance remains underexamined. Species are often evaluated within a single courtyard or urban configuration, leaving unresolved how consistently their cooling performance is maintained when orientation and associated solar exposure change. Finally, even when multiple thermal indicators are reported, the analytical pathway from simulation outputs to a transparent and defensible tree-selection recommendation remains incomplete.

These limitations are particularly consequential in educational courtyards, where the value of a tree depends not only on its ability to reduce peak thermal stress, but also on its capacity to provide a reliable and spatially robust benefit during the period in which students occupy space. To address this gap, this study develops a multidimensional decision framework for evaluating and selecting tree species for thermal improvement in hot-arid educational courtyards. The framework first quantifies the baseline-referenced effects of alternative tree scenarios on Ta, T_mrt, and PET, and then evaluates three complementary performance dimensions. The Tree Cooling Efficiency Index (TCEI) quantifies the magnitude of integrated thermal improvement relative to the corresponding non-vegetated baseline; the Thermal Resilience Index (TRI) assesses the capacity of a vegetation scenario to reduce temporal variability in PET; and the Orientation Sensitivity Index (OSI) quantifies the extent to which cooling effectiveness changes between contrasting courtyard orientations. These dimensions are subsequently integrated through the Composite Thermal Performance Index (CTPI) to produce a comparative ranking and a transparent recommendation.

The contribution and novelty of the study lie in transforming tree selection from a conventional comparison of isolated thermal reductions into a multidimensional, decision-oriented evaluation process. Rather than proposing a single indicator to replace existing thermal variables, the framework differentiates between distinct performance attributes and subsequently integrates them through a composite ranking structure. Its novelty therefore resides in the explicit linkage of baseline-referenced thermal simulation, multidimensional performance indices, composite evaluation, and climate-responsive tree selection.

2 Site description and microclimatic context

Aswan, situated in southern Egypt (24.0889° N, 32.8998° E; elevation 194 m above sea level), covers an administrative area of 34,608.00 km² and experiences a hyper-arid hot desert climate designated as BWh under the Köppen classification system (Kottek et al., 2006; Rubel et al., 2018). The region is characterized by extreme summer heat, mild winters, highly intense solar radiation, and substantial diurnal temperature fluctuations characteristic of continental arid environments. These prevailing atmospheric conditions induce severe localized heat stress during school operational hours, making passive urban cooling and outdoor microclimatic optimization critical for occupants’ thermal comfort.

The empirical investigation was conducted at the Egyptian Japanese School in Aswan (Figure 1), a representative modern educational facility serving as the primary study site. The architectural configuration features two distinct, semi-enclosed courtyards specifically designed to accommodate outdoor student activities, physical recreation, and educational gatherings. Each courtyard possesses an identical spatial footprint of 200 m², yet they exhibit contrasting microclimatic performance due to their asymmetrical orientations: the primary courtyard opens toward the East, whereas the secondary courtyard faces West. This spatial configuration creates differential solar radiation absorption and prevailing wind interaction patterns across the school day, establishing diverse thermal microenvironments for outdoor activities. Accordingly, improvements in the thermal conditions of these spaces may have potential implications for their usability during periods of thermal stress; however, the present study does not directly evaluate occupancy patterns, user behavior, social interaction, or perceived inclusiveness.

3 Research methodology

3.1 Multi-criteria thermal performance framework

Outdoor thermal performance in courtyard environments cannot be adequately evaluated using a single environmental variable because human thermal perception results from the combined interaction of air temperature, radiant heat exchange, humidity, and wind conditions. Although previous studies have frequently relied on individual indicators such as Ta or PET, these variables describe isolated aspects of the outdoor thermal environment and cannot fully characterize vegetation’s overall cooling effectiveness.

To overcome this limitation, this study proposes a Multi-Criteria Thermal Performance Framework (MCTPF) that integrates multiple environmental indicators into a unified assessment methodology. The framework was developed to evaluate tree-based cooling strategies in hot-arid school courtyards while simultaneously accounting for the magnitude of thermal improvement, temporal thermal stability, and sensitivity to courtyard orientation. The proposed framework consists of four sequential stages, as illustrated in Figure 2.

The first stage consists of generating high-resolution microclimatic data using the validated ENVI-met model. Three environmental parameters are extracted for each simulation scenario: Ta, T_mrt, PET. These variables represent the primary environmental conditions governing outdoor thermal performance and constitute the input layer of the proposed framework. The second stage evaluates the thermal response generated by each vegetation scenario under the investigated courtyard orientations. Rather than interpreting each climatic parameter independently, the framework evaluates four complementary dimensions of vegetation performance: magnitude of thermal cooling; reduction in radiant heat exposure; improvement in human thermal comfort, and temporal stability of thermal conditions. Each vegetation scenario is compared with the corresponding baseline condition under the same courtyard orientation and simulation period.

The third stage introduces four complementary indices: TCEI, which quantifies the magnitude of overall thermal improvement; TRI, which evaluates the temporal stability of thermal conditions; OSI, which quantifies the dependence of vegetation performance on courtyard orientation; and CTPI, which integrates the individual performance dimensions into a final comparative score. The final stage converts the calculated index values into a comparative ranking of the investigated courtyard–orientation configurations, including tree coverage. This enables the identification of configurations that provide the most favorable combination of cooling efficiency, thermal stability, and orientation robustness.

3.2 Courtyard configurations and vegetation scenarios

The simulation scenarios were developed to evaluate the thermal implications of introducing different tree species into the two existing courtyards of the Egyptian Japanese School in Aswan. The scenario design was structured to preserve the school’s actual spatial configuration while allowing evaluation of the thermal performance of alternative vegetation conditions under the two contrasting courtyard orientations. As described in Section 2, the investigated courtyards have comparable spatial dimensions but differ in their directional exposure, with the East-facing courtyard opening toward the East and the West-facing courtyard opening toward the West. This configuration provided a controlled basis for examining both the thermal contribution of vegetation and the extent to which its performance is affected by courtyard orientation.

For each courtyard, a non-vegetated baseline scenario, designated Sc0, was established to represent the reference thermal condition against which all vegetation scenarios were evaluated. Three alternative vegetation scenarios were then generated by introducing the selected tree species individually into the same courtyard configuration. Sc1 represented Cassia leptophylla, Sc2 represented Ficus nitida, and Sc3 represented Cassia nodosa. The same scenario structure was applied independently to the East-facing courtyard and the West-facing courtyard, thereby enabling direct comparison between the tree alternatives while maintaining the same underlying courtyard geometry and orientation-specific boundary conditions.

To ensure the reproducibility of the numerical simulations, the principal ENVI-met model settings and simulation configurations are summarized in Table 1. The table reports the ENVI-met version (V5.5), computational domain and grid resolution, simulation period and meteorological boundary conditions, building and ground settings, as well as the procedures used for extracting and evaluating the simulated microclimatic variables.

TABLE 1. ENVI-met model configuration, computational settings, surface and soil properties, meteorological boundary conditions, and output-extraction parameters used in the microclimatic simulations.

The resulting ENVI-met models and their corresponding vegetation configurations are illustrated in Figure 3, while the principal characteristics of the selected tree species are summarized in Table 2.

TABLE 2. Characteristics of the tree alternatives represented in the ENVI-met vegetation scenarios, including scientific and common names, taxonomic family, and modeled tree height.

The three tree alternatives were modeled using their respective vegetation representations rather than imposing an artificial common tree geometry. Accordingly, the modeled tree heights differed among the scenarios (12 m for Sc1, 3 m for Sc2, and 5 m for Sc3). These morphological differences were retained because the objective of the study was to evaluate the thermal performance of practical tree alternatives as they would be represented within the investigated courtyard context, rather than to conduct a strictly size-controlled experiment in which species identity is isolated from canopy morphology.

The scenario comparison should therefore be interpreted as an assessment of the integrated thermal performance of each tree alternative together with its associated vegetation morphology. Differences in tree height, canopy structure, foliage distribution, and other vegetation characteristics constitute part of the physical mechanisms through which the investigated alternatives influence shading, radiation interception, evapotranspiration, and local airflow. Accordingly, the results do not represent controlled estimates of species identity alone.

To maintain comparability at the environmental and geometric levels, all vegetation alternatives were introduced into the same courtyard geometries and evaluated under the same meteorological forcing, simulation period, ground and building conditions, receptor locations, and assessment procedures. Each vegetation scenario was compared with its corresponding orientation-matched non-vegetated Sc0 baseline. This baseline-referenced structure controls for the inherent thermal differences between the East-facing and West-facing courtyards and ensures that vegetation-induced changes are evaluated within the same local geometric and environmental context.

The vegetation parameters used in the ENVI-met representations were treated as scenario-defining characteristics and were maintained consistently for each tree alternative across both courtyard orientations. The principal morphological and biophysical parameters used in the vegetation representations are reported in Table 2, including tree height, canopy diameter, leaf area index (LAI), maximum leaf area density (LAD), canopy porosity, number of trees, planting spacing, and foliage albedo. Reporting these parameters explicitly improves the reproducibility of the vegetation scenarios and clarifies the physical basis of the differences observed among the simulated tree alternatives.

The three species were selected because they represent commonly used outdoor tree types in Aswan and provide contrasting vegetation characteristics relevant to courtyard thermal regulation. Cassia leptophylla (Gold Medallion) is a member of the Fabaceae family and is commonly used as a shade or ornamental tree. Ficus nitida (Indian Laurel), belonging to the Moraceae family, is widely used in streetscapes, parks, hedges, and other outdoor settings. Cassia nodosa (Pink Shower), belonging to the Fabaceae family, is commonly used for outdoor shading and in parks and streets. The selected species therefore represent practical vegetation alternatives within the local environmental context rather than hypothetical planting options. Their contrasting morphological and biophysical characteristics were retained in the ENVI-met representations because these properties form part of the physical mechanisms governing species-specific microclimatic performance. Consequently, the simulated differences among the scenarios reflect the combined effects of canopy geometry and vegetation characteristics rather than an artificially standardized tree form.

The scenario matrix was designed to maintain a strict baseline-referenced comparison. Thus, the effect of each tree species was evaluated against the corresponding Sc0 condition within the same courtyard rather than against a common baseline shared by both courtyards. This procedure was adopted because the two courtyards differ in orientation and consequently experience different solar exposure and spatial microclimatic conditions. Comparing each vegetation scenario with its orientation-matched baseline ensures that the calculated thermal improvements represent the contribution of vegetation under the same geometric and environmental context. This orientation-matched baseline structure also provides the analytical basis for the subsequent calculation of the proposed thermal-performance indices. The TCEI quantifies the magnitude of baseline-referenced thermal improvement, while the TRI evaluates the temporal persistence of the thermal benefit and the OSI examines the sensitivity of performance to courtyard orientation. These complementary dimensions are subsequently integrated within the CTPI to support the multidimensional comparison of the investigated vegetation strategies.

The resulting scenario configuration is therefore organized as a two-level comparative design. The first level compares the three tree alternatives within each courtyard orientation, whereas the second evaluates changes in the performance of the same tree scenario between the East-facing and West-facing courtyards. This structure distinguishes between two related but conceptually different questions: which tree provides the greatest thermal improvement under a given courtyard condition, and how robust is that performance when the spatial orientation changes?

The first question is addressed through the direct thermal-response analysis and the cooling-efficiency assessment, whereas the second is explicitly evaluated through the orientation-based comparison incorporated into the OSI. This structured design enables the proposed framework to evaluate not only the magnitude of vegetation-induced cooling but also the temporal and spatial robustness of that cooling performance under contrasting courtyard conditions.

3.3 Outdoor thermal comfort assessment

To translate the simulated microclimatic conditions into an assessment of human thermal exposure, the PET was used as the principal outdoor thermal-comfort indicator. PET was selected because it integrates the effects of air temperature, mean radiant temperature, relative humidity, and wind conditions into a thermophysiological equivalent temperature that can be interpreted in relation to human thermal sensation. Within the present framework, PET was not used as a substitute for the individual microclimatic variables. Rather, it was evaluated alongside Ta and T_mrt to preserve the distinction between the physical modification of the microclimate and the resulting integrated human thermal response. This approach is consistent with the broader multi-criteria framework, which extracts Ta, T_mrt, and PET from each simulation scenario before evaluating the resulting thermal performance.

PET values were calculated using RayMan 1.2 based on the microclimatic conditions obtained from the ENVI-met simulations. The required environmental inputs were derived from the simulated conditions at the designated receptor locations and assessment height, while the human parameters were defined consistently for all scenarios to ensure that differences in PET resulted from the simulated environmental conditions rather than changes in the assumed occupant characteristics. The same human-exposure parameters were therefore maintained across the baseline and vegetation scenarios and across both courtyard orientations. In the RayMan configuration, the reference person was defined as a male with a body mass of 75 kg and a height of 1.75°m, with the clothing insulation parameter set to 0.9 clo. These parameters were held constant throughout the comparative analysis. PET was calculated using this standardized adult reference person to provide a consistent basis for comparing the thermal response of all vegetation scenarios and courtyard orientations. The adopted reference person should therefore not be interpreted as representing the exact physiological characteristics of the children or adolescents who constitute an important user group of the investigated school courtyards. Rather, the standardized parameters were maintained to ensure that differences in PET between scenarios resulted exclusively from differences in the simulated microclimatic conditions. The temporal, geographical, and microclimatic input parameters used for the PET calculations in RayMan are summarized in Table 3.

TABLE 3. Temporal, geographical, and microclimatic input parameters used for PET calculation in the RayMan model.

The PET calculation was subsequently integrated into the baseline-referenced analytical framework. For each tree scenario, PET was compared with the corresponding Sc0 condition under the same courtyard orientation and assessment period. This allowed the thermal effect of each tree species to be expressed as a relative improvement rather than as an isolated PET value. The resulting PET reductions were then evaluated together with changes in Ta and T_mrt to quantify the overall cooling effectiveness of each vegetation configuration through the proposed TCEI.

In parallel, the temporal behavior of PET was used to assess thermal stability through the TRI, while the differences in TCEI between the two courtyard orientations were used to quantify orientation sensitivity through the OSI. Accordingly, the modeling and thermal-comfort procedures establish a continuous methodological sequence from existing courtyard configuration, vegetation scenario generation, ENVI-met simulation, PET calculation, baseline-referenced comparison, and multidimensional performance evaluation. This sequence ensures that the subsequent performance indices are derived from a consistent set of physically simulated and thermophysiologically interpreted conditions. The final integration of these dimensions through the CTPI is described in the following methodological section.

3.4 ENVI-met model validation

The reliability of the microclimate simulations was assessed through field-based validation of the ENVI-met model. Validation was conducted for the existing courtyard configuration of the Egyptian Japanese School in Aswan before implementing the vegetation scenarios. This procedure was adopted to verify that the numerical model could adequately reproduce the observed thermal conditions of the study site before being used for comparative scenario analysis.

Field measurements were conducted within the school courtyard on 2 Ma y 2023. Air temperature and relative humidity were recorded at hourly intervals over a continuous 24-h period, from 00:00 to 23:00, at a standardized height of 1.6 m above ground level. Measurements were obtained using a HOBO U12 data logger installed within a solar-radiation shielding arrangement at a representative monitoring point in the courtyard.

The measured observations were then compared with the corresponding ENVI-met outputs extracted from the nearest model grid location and equivalent measurement height. The model was driven by the same local meteorological conditions recorded by the Aswan University weather station, thereby enabling a direct comparison between measured and simulated microclimatic conditions under consistent site-specific atmospheric forcing. Model agreement was quantitatively evaluated using the Pearson correlation coefficient (r), coefficient of determination (R ²), mean absolute error (MAE), root mean square error (RMSE), mean bias error (MBE), and mean absolute percentage error (MAPE).

The Pearson correlation coefficient was calculated as Equation 1:where M i and S i represent the measured and simulated values, respectively, M _ and S _ are their corresponding means, and n is the number of paired observations.

r = ∑ i = 1 n M i − M — S i − S — ∑ i = 1 n M i − M — 2 ∑ i = 1 n S i − S — 2 (1)

The coefficient of determination was calculated as Equation 2:

R 2 = ∑ i = 1 n M i − M — S i − S — ∑ i = 1 n M i − M — 2 ∑ i = 1 n S i − S — 2 2 (2)

The mean absolute error was calculated as Equation 3:

M A E = 1 n ∑ i = 1 n S i − M i (3)

The root mean square error was calculated as Equation 4:

R M S E = 1 n ∑ i = 1 n S i − M i 2 (4)

The mean bias error was calculated as Equation 5:

M B E = 1 n ∑ i = 1 n S i − M i (5)

The mean absolute percentage error was calculated as Equation 6:

M A P E = 100 n ∑ i = 1 n S i − M i M i (6)

The validation results are summarized in Table 4 and illustrated in Figure 4.

TABLE 4. Statistical performance of the ENVI-met model in reproducing the measured air temperature and relative humidity during the validation period.

For air temperature, the model demonstrated a very strong correlation with the measured observations, with (r = 0.998) and (R ² = 0.996). The calculated MAE was 1.505 °C, while the RMSE was 1.539 °C. The MBE was −1.505 °C, indicating a systematic tendency of the model to underestimate air temperature. The corresponding MAPE was 4.39%. The regression relationship between the measured and simulated air temperature was Equation 7:

T a , s i m = 0.9975 T a , m e a s − 1.4174 (7)

The slope of 0.9975, which is very close to unity, indicates that the simulated air temperature changes almost proportionally with the measured temperature across the validation range. Thus, the model reproduces not only the direction but also the magnitude of the temporal variations with limited proportional distortion. The negative intercept indicates a systematic offset toward lower simulated values, which is consistent with the negative MBE and the observed tendency of underestimation. Physically, this pattern suggests that the model captures the temporal response of the courtyard thermal environment well but exhibits a small systematic bias in its absolute temperature level rather than a substantial distortion of the diurnal thermal dynamics. The validation statistics also indicate the presence of a systematic component in the air-temperature deviation. In particular, the similarity between the reported absolute MAE and MBE values suggests that the simulation error was predominantly directional rather than entirely random, indicating a tendency toward systematic underestimation of air temperature under the investigated conditions. Accordingly, the high correlation between simulated and measured values should not be interpreted as evidence of the complete absence of model bias. The validation results were therefore used primarily to establish the suitability of the model for comparative scenario analysis, while acknowledging uncertainty in the absolute prediction of individual microclimatic variables.

Relative humidity demonstrated an even stronger agreement between measured and simulated values, with (r = 0.9999) and (R ² = 0.9998). The corresponding MAE was 0.895 percentage points, while the RMSE was 0.941 percentage points. The MBE was −0.895 percentage points, indicating a small systematic underestimation of relative humidity. The MAPE was 3.62%. The regression relationship was Equation 8:

R H s i m = 0.9714 R H m e a s − 0.1661 (8)

The regression relationship for relative humidity shows the same overall pattern of strong proportional agreement, with a slope close to unity and a negative intercept. The near-unity slope indicates that the model closely tracks the temporal changes in relative humidity across the observed range, whereas the negative intercept represents a small systematic displacement of the simulated values toward lower humidity levels. This interpretation is consistent with the negative MBE and indicates that the principal discrepancy is an approximately systematic offset rather than a failure to reproduce the temporal variability of relative humidity. Taken together, the regression slopes close to unity for both validation variables indicate that the ENVI-met model preserved the temporal sensitivity of the measured microclimatic conditions, while the negative intercepts and corresponding negative MBE values reveal a modest systematic underestimation in the absolute simulated levels. The agreement between these regression characteristics and the error statistics is important because it distinguishes a relatively small systematic bias from a larger structural mismatch in the temporal response.

Overall, the high correlation coefficients and coefficients of determination, together with the relatively low MAE and RMSE values, indicate strong agreement between the measured and simulated microclimatic conditions and confirm that the model successfully reproduced the temporal pattern and variability of the observed environment. However, the model showed a systematic negative bias in absolute predictions of air temperature and relative humidity, indicating a tendency to underestimate. Although this bias was limited relative to the overall daily variation, the validation results more strongly support using the ENVI-met model for comparative analysis across alternative vegetation scenarios than for interpreting absolute thermal quantities. Accordingly, the model was considered sufficiently reliable for evaluating the relative thermal effects and comparative performance of the investigated vegetation configurations, while acknowledging uncertainty in the absolute prediction of individual microclimatic variables.

It should be noted that the present validation evaluates the ability of the ENVI-met model to reproduce the measured baseline microclimatic conditions and does not constitute direct field validation of the cooling effects associated with the simulated vegetation scenarios. Field measurements of vegetated courtyard conditions, including changes in mean radiant temperature, wind speed, humidity, and PET, were not available. Accordingly, the subsequent vegetation analysis should be interpreted as an exploratory simulation-based assessment of the comparative thermal performance of the investigated modeled tree configurations. The validation should nevertheless be interpreted within its specific scope. The field comparison was conducted at a single receptor location over one representative 24-h period and was limited to air temperature and relative humidity. Consequently, the validation primarily supports the model’s ability to reproduce the observed near-surface atmospheric conditions under the investigated simulation setup. T_mrt and PET were not directly validated against field globe-temperature or radiant-temperature measurements and should therefore be interpreted as model-derived comparative indicators rather than independently validated absolute quantities.

3.5 Proposed thermal performance indices

The conventional evaluation of vegetation-based outdoor cooling strategies commonly relies on the independent comparison of air temperature, mean radiant temperature, or thermal comfort indices. Although these variables provide essential information regarding microclimatic conditions, their separate interpretation does not fully capture the multidimensional performance of vegetation. A tree species may produce a substantial reduction in mean radiant temperature but a comparatively limited reduction in air temperature, while another species may provide a more balanced thermal response. Similarly, a large instantaneous cooling effect does not necessarily indicate that a vegetation configuration can maintain improved thermal conditions throughout the assessment period. To address these limitations, this study proposes four complementary thermal performance indices within the (MCTPF). The proposed indices distinguish between:

• The magnitude of thermal improvement;
• The temporal stability of the thermal environment;
• The sensitivity of vegetation performance to courtyard orientation; and
• The overall integrated performance of each configuration.

All indices were calculated using the corresponding non-vegetated baseline scenario as the reference condition. Accordingly, each vegetation scenario was compared with the baseline condition under the same courtyard orientation and simulation period.

3.5.1 Tree Cooling Efficiency Index (TCEI)

The TCEI was developed to quantify the overall magnitude of thermal improvement generated by each vegetation configuration relative to its corresponding non-vegetated baseline condition. The index integrates three complementary dimensions of the simulated thermal response: Ta, representing the atmospheric cooling effect; T_mrt, representing the modification of the radiative environment; and PET, representing the resulting integrated human thermal response. All vegetation scenarios were evaluated against the corresponding baseline condition under the same courtyard orientation and assessment period. This orientation-matched baseline comparison ensured that the calculated improvements reflected the simulated effect of the vegetation configuration rather than inherent differences between the two courtyard environments.

For each thermal variable X, the relative thermal improvement of vegetation scenario i under courtyard orientation o was calculated as Equation 9:where R I x , i , o is the relative improvement in thermal variable X, X ¯ 0 , o is the mean value of the corresponding baseline scenario (Sc0) under orientation o, and X ¯ i , o is the mean value of vegetation scenario i under the same orientation. Here, X represents T_a, T_mrt, or PET.

R I x , i , o = X ¯ 0 , o − X ¯ i , o X ¯ 0 , o (9)

The relative improvements were expressed as dimensionless decimal fractions. Thus, a value of 0.10 represents a 10% improvement relative to the corresponding orientation-matched baseline. For descriptive presentation, these values may be expressed as percentages by multiplying by 100.

Accordingly, the relative improvements in the three thermal indicators were calculated as Equations 10–12:

R I T a , i , o = T a ¯ 0 , o − T a ¯ i , o T a ¯ 0 , o (10)

R I T m r t , i , o = T m r t ¯ 0 , o − T m r t ¯ i , o T m r t ¯ 0 , o (11)

R I P E T , i , o = P E T ¯ 0 , o − P E T ¯ i , o P E T ¯ 0 , o (12)

Because the three thermal indicators do not contribute equally to the interpretation of outdoor thermal performance, equal weighting was not adopted. Instead, a differentiated weighting structure was established according to the analytical role of each indicator within the proposed framework. PET was assigned the highest weight (w P E T = 0.50) because it represents the integrated human thermal response resulting from the combined influence of the outdoor thermal environment. Mean radiant temperature was assigned a weight of w T m r t = 0.30, reflecting the central importance of vegetation shading and radiative modification in hot-arid outdoor environments. Air temperature was assigned a weight of w T a = 0.20, representing the atmospheric component of vegetation-induced cooling. This weighting structure therefore follows a hierarchical interpretation of thermal performance: the integrated human thermal consequence is given the greatest importance, followed by the physical modification of the radiative environment and, subsequently, the atmospheric cooling response.

The weighting coefficients satisfy (Equation 13):

w T a + w T m r t + w P E T = 1 · 00 (13)

Accordingly:

w T a = 0.20

w T m r t = 0.30

w P E T = 0.50

The same weighting structure was consistently applied to all vegetation scenarios and both courtyard orientations. Consequently, differences in TCEI values resulted exclusively from differences in simulated thermal performance rather than from scenario-specific adjustments to the weighting system.

Based on these weighting coefficients, the TCEI was calculated as Equation 14:where T C E I i , o represents the integrated cooling efficiency of vegetation scenario i under courtyard orientation o.

T C E I i , o = 0.20 R I T a , i , o + 0.30 R I T m r t , i , o + 0.50 R I P E T , i , o (14)

The resulting TCEI values were retained on a dimensionless decimal scale. For example, a TCEI value of 0.2506 represents an integrated weighted relative thermal improvement of approximately 25.06%. These raw values were subsequently transformed to a common scale during the normalization procedure used for calculating the CTPI. This distinction between the raw TCEI values and the subsequently normalized CTPI input scores was explicitly maintained to ensure numerical consistency and reproducibility throughout the multi-criteria assessment procedure.

Higher TCEI values indicate greater integrated thermal improvement relative to the corresponding orientation-matched non-vegetated baseline. The index therefore provides a consolidated measure of the overall cooling effectiveness of each investigated vegetation configuration. For transparency and reproducibility, the component improvements in T_a, T_mrt, and PET, together with the resulting TCEI values, were retained as independently traceable quantities. This allows the index to be recalculated directly from the reported thermal-response data and enables the influence of alternative weighting structures to be examined without repeating the underlying ENVI-met simulations. Because PET represents an integrated thermal-comfort response influenced by multiple microclimatic variables, including air temperature and mean radiant temperature, the potential statistical dependence among the thermal-improvement indicators included in the TCEI was explicitly examined.

Importantly, PET was retained as an integrated human thermal-response indicator, while T_a and T_mrt were retained to preserve the underlying physical mechanisms responsible for the observed thermal improvement. Thus, the three indicators were not assumed to be statistically independent; rather, they represent complementary analytical dimensions of courtyard performance, including atmospheric modification, radiative modification, and the resulting integrated human thermal response. To examine the potential influence of correlation among these variables, Pearson correlation analysis was conducted using the relative improvements in T_a, T_mrt, and PET obtained for all vegetation scenarios and courtyard orientations. The results, presented in Table 5, confirmed substantial statistical dependence among the indicators, particularly between relative T_mrt and PET improvements.

TABLE 5. Pearson correlation matrix among the relative thermal-improvement indicators used in the TCEI.

The correlation results confirm that the three variables should not be interpreted as statistically independent predictors. Their simultaneous inclusion in the TCEI therefore does not represent an assumption of statistical independence, but rather a deliberate multidimensional descriptive structure linking physical microclimatic modification with its integrated thermal consequence for outdoor users.

The simultaneous inclusion of Ta, T_mrt, and PET does not aim to construct statistically independent predictors or a statistical predictive model. Instead, the TCEI intentionally combines two complementary levels of interpretation: the underlying physical mechanisms of microclimatic modification, represented by Ta and T_mrt, and the resulting integrated human thermal response, represented by PET. The weighting structure should therefore be interpreted as a decision-based performance aggregation rather than as a statistical model requiring independence among its input variables. Accordingly, the statistical dependence among the three indicators does not invalidate their combined use within the proposed descriptive and decision-support framework, provided that the potential influence of weighting assumptions on the resulting comparative rankings is explicitly examined through sensitivity analysis. To further examine whether the statistical dependence and the adopted weighting structure influenced the final comparative outcome, correlation and sensitivity analyses were conducted to evaluate the stability of the resulting scenario ranking. The robustness of the ranking under alternative reasonable weighting structures was therefore considered as part of the evaluation of the proposed composite framework.

3.5.2 Thermal Resilience Index (TRI)

The magnitude of thermal improvement at a single time does not fully describe the performance of a vegetation configuration. A scenario may produce substantial reductions in thermal stress during specific hours while exhibiting considerable fluctuations during the remainder of the assessment period. To incorporate this temporal dimension, the TRI was developed to evaluate the extent to which each vegetation configuration reduces the temporal variability of outdoor thermal conditions relative to its corresponding non-vegetated baseline. Because PET represents the integrated thermal response of the reference person to the prevailing microclimatic conditions, its temporal variation was adopted as the basis for evaluating thermal resilience. The temporal variability of PET during the assessment period was quantified using the standard deviation Equation 15:where P E T i , o , t represents the PET value for vegetation scenario i, orientation o, and time step t; P E T ¯ i , o is the mean PET value over the assessment period; and nn is the total number of hourly observations Equation 16.where S D P E T , S c 0 , o represents the standard deviation of hourly PET values under the non-vegetated baseline condition for orientation o, whereas S D P E T , i , o represents the corresponding standard deviation under vegetation scenario i.

S D P E T , i , o = ∑ t = 1 n P E T i , o , t + P E T ¯ i , o n − 1 (15)

T R I i , o = S D P E T , S c 0 , o − S D P E T , i , o S D P E T , S c 0 , o (16)

3.5.3 Orientation Sensitivity Index (OSI)

The OSI was developed to quantify the extent to which the cooling efficiency of each vegetation configuration is affected by the spatial orientation of the courtyard. Unlike the TCEI, which measures the magnitude of integrated thermal improvement achieved within a specific courtyard orientation, the OSI evaluates the relative change in cooling performance when the same vegetation configuration is assessed under the alternative courtyard orientation.

Because the objective of the multidimensional assessment was to evaluate the performance of each vegetation configuration separately within Courtyard A and Courtyard B, an orientation-specific formulation of the OSI was adopted. This approach allows the influence of orientation to be expressed relative to the cooling performance achieved within each respective courtyard rather than assigning a single sensitivity value to the vegetation scenario regardless of spatial context. Accordingly, the orientation sensitivity associated with Courtyard A was calculated as Equation 17:

O S I i , A = T C E I i , A − T C E I i , B T C E I i , A (17)

Similarly, the orientation sensitivity associated with Courtyard B was calculated as Equation 18:where T C E I i , A and T C E I i , B represent the cooling-efficiency values of vegetation scenario i in Courtyard A and Courtyard B, respectively.

O S I i , B = T C E I i , B − T C E I i , A T C E I i , B (18)

This formulation explicitly preserves the influence of the courtyard context in the orientation assessment. The same absolute difference in cooling efficiency may represent a different relative sensitivity depending on the level of performance achieved within each courtyard. Consequently, OSI is calculated separately for Courtyard A and Courtyard B, allowing orientation-related performance differences to be retained in the subsequent multidimensional comparison and composite assessment. A lower OSI indicates that the cooling efficiency of a vegetation configuration changes less relative to its performance within the respective courtyard and therefore reflects greater orientation robustness. Conversely, a higher OSI indicates that the cooling efficiency achieved within that courtyard is more strongly affected when compared with the alternative orientation.

It should be noted that the two orientation-specific OSI values are complementary rather than independent measures. Both are derived from the same difference between T C E I i , A and T C E I i , B, but each expresses that difference relative to the cooling performance achieved within its respective courtyard. This enables the orientation effect to be incorporated into the evaluation of each courtyard individually while maintaining a direct comparison between the two spatial contexts.

3.5.4 Composite Thermal Performance Index (CTPI)

The individual indices described above represent complementary dimensions of vegetation performance. However, practical climate-responsive design decisions require the simultaneous consideration of the magnitude of thermal improvement, temporal thermal resilience, and robustness to courtyard orientation. The CTPI was therefore developed to integrate these three dimensions into a single comparative performance measure while preserving the orientation-specific thermal response of each vegetation configuration. The CTPI framework was structured hierarchically. TCEI represents the primary thermal-performance outcome because it directly quantifies the integrated improvement in Ta, T_mrt, and PET relative to the corresponding orientation-matched baseline. TRI represents the temporal stability of the resulting thermal environment, whereas the OSI represents the robustness of cooling performance when the same vegetation configuration is evaluated under different courtyard orientations.

Because TCEI and TRI are calculated separately for Courtyard A and Courtyard B, whereas OSI represents the cross-orientation sensitivity of each vegetation configuration, the CTPI was calculated separately for every scenario–courtyard combination. Thus, each vegetation configuration received an orientation-specific CTPI value for Courtyard A and Courtyard B. The normalized orientation-robustness score derived from OSI was applied to both courtyard-specific CTPI calculations of the same vegetation configuration, while the TCEI and TRI components retained their orientation-specific values. This structure allows courtyard orientation to influence the final composite performance through the directly simulated cooling efficiency and temporal resilience while simultaneously accounting for the overall robustness of the vegetation configuration across both spatial contexts. Before aggregation, the TCEI, TRI, and OSI components were transformed to a common 0–100 performance scale. This normalization step was necessary because the raw indices are expressed on different numerical scales and have different preferred performance directions. The raw index values were therefore not directly aggregated. Instead, each index was first converted into a normalized performance score, ensuring that higher values consistently represented better performance in the final composite calculation. For the two benefit-oriented indices, TCEI and TRI, higher raw values represent better performance. Their normalized scores were therefore calculated using min–max normalization (Equations 19, 20): where N T C E I , i , o and N T R I , i , o represent the normalized cooling-efficiency and thermal-resilience scores, respectively, for vegetation scenario i under courtyard orientation o. The terms T C E I min, T C E I max, T R I min, and T R I max represent the minimum and maximum raw values observed among all evaluated scenario–courtyard combinations.

N T C E I , i , o = T C E I i , o − T C E I min T C E I max − T C E I min (19)

N T R I , i , o = T R I i , o − T R I min T R I max − T R I min (20)

Accordingly, the normalization range for TCEI and TRI was determined from the complete set of six scenario–courtyard observations, comprising Sc1, Sc2, and Sc3 evaluated in both Courtyard A and Courtyard B. Using a common normalization range preserves the relative differences between courtyard-specific performances and prevents the independent rescaling of each courtyard from masking the influence of orientation on the final ranking. Unlike TCEI and TRI, the OSI is a cost-oriented index because lower values indicate greater orientation robustness. The OSI was therefore transformed into a positive orientation-robustness performance score using reverse min–max normalization (Equation 21):where N O R , i is the normalized orientation-robustness score for vegetation scenario i, and O S I min and O S I max represent the minimum and maximum OSI values among the evaluated vegetation configurations.

N O R , i = O S I max − O S I i O S I max − O S I min × 100 (21)

Thus, a vegetation configuration with lower orientation sensitivity receives a higher normalized orientation-robustness score. Because OSI represents the difference in cooling efficiency between Courtyard A and Courtyard B for the same vegetation configuration, the resulting normalized orientation-robustness score is calculated once for each vegetation scenario. The same normalized orientation-robustness score was subsequently assigned to the Courtyard A and Courtyard B CTPI calculations of the corresponding vegetation configuration. This does not imply that the two courtyards have identical thermal performance. Rather, their differences remain explicitly represented through their separate TCEI and TRI values. The orientation-robustness component instead provides an additional configuration-level measure indicating how consistently the vegetation scenario performs when transferred between the two investigated spatial orientations.

After normalization, all three performance dimensions were expressed on a common 0–100 scale, with higher values consistently representing more favorable performance. The CTPI was then calculated as a weighted linear combination of the normalized cooling-efficiency, thermal-resilience, and orientation-robustness scores (Equation 22):where w C, w R, and w O represent the weighting coefficients assigned to cooling efficiency, thermal resilience, and orientation robustness, respectively, (Equation 23) and:

C T P I i , o = w C N T C E I , i , o + w R N T R I , i , o + wO N O R , i , o (22)

w C + w R + w O = 1 (23)

A differentiated weighting structure was adopted rather than equal weighting because the three indices do not have identical positions within the conceptual hierarchy of the proposed framework. Cooling efficiency represents the primary functional outcome of vegetation-based thermal modification and directly reflects the magnitude of improvement achieved relative to the non-vegetated baseline. Thermal resilience and orientation robustness represent complementary robustness characteristics that qualify the consistency of this primary thermal performance across time and spatial orientation. Accordingly, cooling efficiency was assigned the highest weight (w C = 0.50), while thermal resilience and orientation robustness were assigned equal secondary weights (w R = 0.25 and w O = 0.25, respectively). This weighting structure follows a hierarchical performance rationale in which the primary objective—achieving meaningful thermal improvement—receives half of the total decision weight, whereas the remaining half is distributed equally between temporal and spatial robustness. Equal secondary weights were retained for TRI and orientation robustness because no empirical evidence within the present dataset justified assigning systematic priority to temporal stability over spatial transferability, or vice versa. The adopted weights represent normative decision preferences based on the conceptual hierarchy of the proposed framework rather than empirically derived universal coefficients. Accordingly, these weighting values should be interpreted as transparent decision parameters for the present assessment rather than as universally applicable constants for vegetation-performance evaluation.

Accordingly, the final CTPI equation was:

C T P I i , o = 0.5 C N T C E I , i , o + 0.25 R N T R I , i , o + 0.25 O N O R , i , o (24)

A higher CTPI value indicates a vegetation configuration that provides a stronger overall combination of cooling effectiveness, temporal thermal resilience, and robustness to courtyard orientation under the investigated conditions. The CTPI is not intended to replace established thermal-comfort indicators such as PET. Rather, it functions as a multidimensional decision-support metric that integrates complementary aspects of vegetation performance within the same analytical framework. The individual TCEI, TRI, and OSI values were retained and reported separately from the composite CTPI to maintain transparency and allow the contribution of each performance dimension to be independently examined. Because weighting in multi-criteria assessment inevitably involves a degree of decision preference, the robustness of the resulting ranking was further examined through weighting-sensitivity analysis. Alternative weighting structures were tested while maintaining the unit-sum constraint (w C + w R + w O = 1) to determine whether reasonable changes in the relative importance assigned to cooling efficiency, temporal resilience, and orientation robustness altered the comparative ranking of the evaluated vegetation configurations. The adopted weighting structure of 0.50, 0.25, and 0.25 was retained as the primary decision model, while the sensitivity analysis was used to evaluate the stability of the resulting rankings under alternative decision priorities.

3.5.5 Index application and comparative ranking

The proposed indices were subsequently applied to each scenario–courtyard combination following the calculation procedures described above. TCEI and TRI were calculated separately for each courtyard orientation, whereas OSI was derived for each vegetation configuration from the difference in cooling efficiency between the two orientations. The resulting indices were normalized where required and integrated through the CTPI to support the final comparative ranking.

TCEI and TRI were calculated independently for each scenario–courtyard combination because they represent performance under a specific orientation. In contrast, OSI was calculated once for each vegetation configuration because it represents the difference in cooling efficiency between Courtyard A and Courtyard B. The resulting orientation-robustness score was therefore incorporated into the CTPI calculation for both courtyard-specific evaluations of the same vegetation configuration. The final CTPI was calculated separately for each scenario–courtyard combination rather than as a single value for each vegetation configuration. This approach preserves the effects of courtyard orientation on cooling efficiency and thermal resilience while accounting for the overall orientation robustness of each vegetation alternative.

The mathematical definitions, input variables, interpretation, and preferred direction of each index are summarized in Table 6. A complete worked example illustrating the calculation of relative thermal improvements, TCEI, TRI, OSI, normalization, orientation robustness, and CTPI is provided in the revised methodology to demonstrate the numerical consistency and reproducibility of the proposed framework. The resulting indices support a multidimensional comparison of the modeled vegetation alternatives based on cooling efficiency, temporal stability, and orientation robustness. Because the vegetation alternatives were not morphologically standardized, the results represent the performance of the complete modeled configurations, including their associated morphological and canopy characteristics, within the investigated courtyard contexts.

TABLE 6. Conceptual structure and performance criteria of the proposed indices for evaluating tree-specific cooling efficiency, temporal thermal resilience, orientation robustness, and integrated thermal performance.

4 Results and discussion

4.1 Baseline-referenced microclimatic response and cooling performance

The thermal response of the two courtyards was first evaluated by comparing each vegetation scenario directly with its corresponding non-vegetated baseline condition (Sc0). This baseline-referenced approach ensured that the thermal contribution of vegetation was assessed within the same courtyard geometry, orientation, and environmental conditions, thereby avoiding direct comparison between absolute thermal conditions that inherently differed between the East-facing and West-facing courtyards. The assessment focused on Ta, T_mrt, and PET, representing the atmospheric, radiative, and integrated human thermal-response dimensions of outdoor thermal performance, respectively. According to Figure 5, the assessment period from 08:00 to 15:00 was selected to represent the regular daytime operational period of the investigated school, during which the outdoor courtyards are relevant to student and staff activities. The analysis was therefore focused on the hours of practical school occupancy rather than the complete 24-h simulation period, allowing the thermal performance of the vegetation scenarios to be evaluated under conditions directly relevant to the intended use of the courtyards.

Across both courtyards, all vegetation scenarios produced a consistent simulated downward shift in Ta, T_mrt, and PET relative to the corresponding Sc0 baseline, although the magnitude of improvement differed according to the modeled vegetation configuration and courtyard orientation. Among the investigated modeled configurations, Sc2 (Ficus nitida) consistently produced the greatest simulated cooling response, followed by Sc3 (Cassia nodosa) and Sc1 (Cassia leptophylla). This comparative ranking should be interpreted within the specific ENVI-met vegetation representations, courtyard geometries, and meteorological conditions examined in this study rather than as definitive evidence of the intrinsic cooling superiority of the individual tree species.

The relative magnitude of improvement also differed among the three thermal variables. Reductions in Ta were comparatively modest, whereas substantially larger improvements were observed in T_mrt. This pattern indicates that the principal cooling contribution of the investigated tree scenarios was associated with modification of the radiative environment through shading and interception of solar radiation rather than with large reductions in ambient air temperature. The concurrent reduction in PET demonstrates that these changes in the physical microclimate translated into measurable improvements in the integrated thermal conditions experienced by occupants. Across the evaluated scenarios, the relative improvements were therefore generally greatest for T_mrt, followed by PET and Ta.

The comparison between the two courtyard orientations further confirmed that vegetation performance was orientation-dependent (Figure 6). During the occupied time, Sc2 (Ficus nitida) achieved the greatest overall thermal improvement in both courtyards. In the east-facing courtyard, Sc2 reduced Ta, T_mrt, and PET by approximately 5.2%, 37.88%, and 25.39%, respectively, relative to the corresponding baseline. In the west-facing courtyard, the corresponding relative improvements were approximately 4.57%, 25.48%, and 15.35%, respectively.

Sc3 (Cassia nodosa) provided the second-highest cooling performance. Its relative improvements in the East-facing courtyard were approximately 4.01% for Ta, 29.3% for T_mrt, and 19.66% for PET, compared with approximately 3.63%, 20.44%, and 11.98%, respectively, in the West-facing courtyard. Sc1 (Cassia leptophylla) generally exhibited the lowest thermal improvement among the evaluated vegetation scenarios, producing relative reductions of approximately 3.20%, 20.33%, and 13.44% in Ta, T_mrt, and PET, respectively, in the East-facing courtyard. In the West-facing courtyard, the corresponding improvements were approximately 2.90%, 15.89%, and 9.78%, respectively.

The hourly baseline-referenced reductions shown in Figure 7 provide a more detailed interpretation of the temporal development of vegetation-induced cooling. Across the investigated scenarios, the cooling effect generally became more pronounced during the daytime period as solar exposure and radiative loading increased, with the strongest responses occurring during the critical daytime assessment window. This temporal pattern was particularly evident for T_mrt and PET, confirming that the primary thermal contribution of vegetation was associated with the modification of the outdoor radiative environment and its consequent effect on human thermal perception. For Sc2 (Ficus nitida), the strongest cooling response was observed in the East-facing courtyard. During the critical daytime period, the scenario achieved maximum reductions of approximately 2.0 °C in Ta, 18.1 °C in T_mrt, and 10.4 °C in PET, based on the differences between the corresponding baseline and vegetation-scenario maximum values during the assessment period. In the West-facing courtyard, the corresponding maximum reductions were approximately 2.0 °C in Ta, 13.8 °C in T_mrt, and 7.8 °C in PET. These differences confirm that the thermal benefit achieved by the same vegetation scenario was influenced by courtyard orientation, particularly with respect to radiative exposure and its effect on PET.

The same overall hierarchy was observed for the remaining vegetation scenarios, although with lower cooling magnitudes. For Sc3 (Cassia nodosa), the maximum reductions during the assessment period reached approximately 1.6 °C in Ta, 14.4 °C in T_mrt, and 8.0 °C in PET in the East-facing courtyard, compared with approximately 1.6 °C, 10.8 °C, and 6.0 °C, respectively, in the West-facing courtyard. Sc1 (Cassia leptophylla) exhibited the lowest overall cooling response, with maximum reductions of approximately 1.1 °C in Ta, 10.4 °C in T_mrt, and 5.6 °C in PET in the East-facing courtyard and approximately 1.1 °C, 7.8 °C, and 4.2 °C, respectively, in the West-facing courtyard. Thus, the scenario hierarchy observed in the temporal profiles was maintained in the baseline-referenced cooling analysis. Sc2 consistently generated the strongest overall thermal improvement, followed by Sc3, whereas Sc1 produced the smallest reductions. More importantly, the substantially larger reductions in T_mrt relative to Ta demonstrate that the comparative performance of the vegetation scenarios was primarily governed by their capacity to modify solar and long-wave radiative exposure, with these radiative changes subsequently producing substantial improvements in PET.

When the baseline-referenced cooling responses were aggregated over the critical daytime assessment period, the overall thermal performance of each vegetation scenario became more apparent, as summarized in Figure 8. Rather than emphasizing individual hourly or peak reductions, this aggregation provides an integrated representation of the sustained thermal improvement achieved during the period of greatest thermal stress. Sc2 (Ficus nitida) achieved the greatest overall thermal improvement across the three principal thermal indicators in both courtyard orientations, reflecting its consistently stronger cooling performance throughout the assessment period. Sc3 (Cassia nodosa) provided intermediate improvements, whereas Sc1 (Cassia leptophylla) exhibited the lowest overall cooling performance.

4.2 Integrated thermal performance: cooling efficiency, temporal resilience, and orientation robustness

The first performance dimension, represented by the TCEI, provides an integrated measure of the baseline-referenced relative improvements in Ta, T_mrt, and PET. The TCEI values are expressed on a decimal scale, with higher values indicating greater integrated thermal improvement. As shown in Figure 9, a consistent cooling-efficiency hierarchy was observed across both courtyard orientations. Sc2 (Ficus nitida) achieved the highest TCEI values, followed by Sc3 (Cassia nodosa) and Sc1 (Cassia leptophylla). In Courtyard A, the TCEI values were 0.251, 0.194, and 0.135 for Sc2, Sc3, and Sc1, respectively. The corresponding values in Courtyard B were 0.162, 0.128, and 0.102, respectively. These results indicate that the Sc2 modeled vegetation configuration produced the greatest integrated thermal improvement under both investigated courtyard conditions. However, because the vegetation alternatives were represented using their respective modeled morphological characteristics, including differences in tree size and canopy properties, this result should not be interpreted as a pure species-identity effect independent of these characteristics. Rather, it represents the combined thermal performance of each modeled vegetation alternative within the investigated built and climatic context.

The comparison between the two courtyards further demonstrates that cooling efficiency was influenced by orientation. The TCEI of Sc2 decreased from 0.251 in Courtyard A to 0.162 in Courtyard B, while Sc3 decreased from 0.194 to 0.128 and Sc1 from 0.135 to 0.102. Thus, Courtyard A consistently exhibited greater integrated thermal improvement across all vegetation configurations, although the comparative hierarchy among the alternatives remained unchanged. These findings indicate that courtyard orientation influenced the magnitude of the simulated vegetation-induced cooling response without altering the relative cooling-efficiency ranking of the modeled alternatives. The differences between the two courtyards also demonstrate that cooling efficiency and orientation robustness represent distinct performance properties. A vegetation configuration may achieve strong cooling performance under both orientations while still exhibiting substantial differences in the magnitude of its performance between the two spatial contexts. The TCEI therefore quantifies the magnitude of integrated thermal improvement within each courtyard but does not independently represent either the temporal stability of thermal conditions or the robustness of cooling performance to changes in orientation. These complementary dimensions are subsequently evaluated through the TRI and OSI.

The temporal dimension of vegetation performance was evaluated using the TRI, which examines the extent to which each vegetation configuration reduces the temporal variability of PET relative to the corresponding baseline condition. As illustrated in Figure 10, the TRI extends the interpretation of thermal performance beyond cooling magnitude by evaluating whether vegetation contributes to a more temporally stable thermal environment throughout the assessment period.

A positive TRI indicates that the temporal variability of PET was lower under the vegetation scenario than under the corresponding Sc0 baseline, while higher values indicate a greater reduction in temporal variability and therefore stronger temporal thermal resilience. This dimension is particularly relevant in hot-arid educational environments, where sustained thermal stability may be important in addition to the magnitude of instantaneous cooling. The TRI results demonstrate that temporal resilience varied according to both vegetation configuration and courtyard orientation. In Courtyard A, Sc3 (Cassia nodosa) achieved the highest TRI value (0.143), closely followed by Sc2 (Ficus nitida) (0.142), while Sc1 (Cassia leptophylla) recorded a lower value (0.123). The differences between Sc2 and Sc3 in Courtyard A were therefore very small, indicating broadly comparable temporal stabilization performance under this orientation.

In Courtyard B, TRI values were substantially lower for all vegetation configurations, reaching 0.019 for Sc2, 0.018 for Sc3, and 0.015 for Sc1. These results indicate that the ability of vegetation to reduce temporal PET variability was considerably weaker in Courtyard B than in Courtyard A. The combined TRI results therefore demonstrate that temporal resilience did not follow an identical pattern across the two courtyard contexts. While Sc3 produced the highest TRI in Courtyard A, Sc2 achieved the highest value in Courtyard B. Sc1 consistently exhibited the lowest temporal resilience among the investigated configurations. This finding further supports the need to evaluate temporal performance independently rather than assuming that the vegetation configuration producing the greatest cooling magnitude will necessarily produce the greatest temporal stability under all spatial conditions.

Together, the TCEI and TRI results demonstrate that cooling efficiency and temporal resilience represent related but non-identical dimensions of vegetation performance. A high TCEI indicates substantial baseline-referenced thermal improvement, whereas a high TRI indicates a greater reduction in temporal PET variability. Accordingly, the most favorable vegetation configuration cannot be identified solely through the magnitude of cooling but must also consider the stability of thermal conditions throughout the assessment period.

The third performance dimension, orientation robustness, was evaluated using the OSI, with the results presented in Figure 11. Unlike the TCEI and TRI, which were calculated separately for each scenario–courtyard combination, the OSI evaluates the relative difference in cooling efficiency between Courtyard A and Courtyard B for the same vegetation configuration. The resulting OSI therefore represents the sensitivity of each modeled vegetation alternative to changes in courtyard orientation. Because lower OSI values indicate smaller differences in cooling efficiency between the two courtyard orientations, lower values represent greater orientation robustness. The calculated OSI values were 0.272 for Sc1, 0.428 for Sc2, and 0.409 for Sc3.

Accordingly, Sc1 (Cassia leptophylla) exhibited the greatest orientation robustness, followed by Sc3 (Cassia nodosa), whereas Sc2 (Ficus nitida) exhibited the greatest orientation sensitivity. These results indicate that the cooling performance of Sc1 changed least between the two investigated courtyard contexts, while Sc2 experienced the largest relative difference in cooling efficiency. This result introduces an important distinction in the interpretation of overall vegetation performance. Sc2 achieved the highest TCEI under both courtyard orientations, indicating the strongest integrated cooling efficiency. However, its OSI value of 0.428 indicates that this cooling performance was also the most sensitive to changes in courtyard orientation. Conversely, Sc1 achieved the lowest TCEI values but demonstrated the greatest orientation robustness, with the lowest OSI value of 0.272. Sc3 occupied an intermediate position, combining intermediate cooling efficiency with an OSI of 0.409.

Taken together, the three indices reveal a clear trade-off among cooling magnitude, temporal resilience, and robustness to spatial context. Sc2 produced the strongest integrated cooling efficiency under both courtyard conditions, Sc3 achieved the highest temporal resilience in Courtyard A, while Sc1 demonstrated the greatest robustness to changes in courtyard orientation. These differences should be interpreted as differences among the complete modeled vegetation alternatives, in which canopy morphology and associated vegetation characteristics jointly influence shading, radiation interception, evapotranspiration, and the resulting simulated microclimatic response.

The results therefore demonstrate that the vegetation alternative producing the greatest thermal improvement is not necessarily the alternative whose performance is least affected by changes in spatial orientation. This multidimensional differentiation provides the principal justification for evaluating cooling efficiency, temporal resilience, and orientation robustness independently before combining them within the CTPI. Overall, the integrated analysis establishes the basis for the subsequent composite evaluation. The TCEI quantifies the magnitude of baseline-referenced thermal improvement within each courtyard, the TRI evaluates the reduction in temporal PET variability, and the OSI quantifies the sensitivity of cooling efficiency to changes in courtyard orientation. Together, these complementary indices transform the analysis from a simple comparison of cooling magnitudes into a structured assessment of multiple thermal-performance attributes.

Importantly, the framework does not assume morphological equivalence among the investigated practical vegetation alternatives. Instead, it retains their respective modeled vegetation characteristics and interprets the resulting differences within the specific courtyard geometries, climatic conditions, and ENVI-met representations investigated in this study. Accordingly, the OSI should be interpreted as a measure of the orientation robustness of each modeled vegetation configuration within the investigated context rather than as a universal indicator of the inherent orientation sensitivity of a tree species. This interpretation provides the basis for the subsequent CTPI analysis, in which cooling efficiency, temporal resilience, and orientation robustness are normalized and integrated to support the final comparative evaluation.

4.3 Composite Thermal Performance Index (CTPI) and multidimensional tree ranking

The preceding analysis demonstrated that the thermal performance of the investigated vegetation configurations cannot be adequately represented by a single performance criterion. While the TCEI quantifies the magnitude of integrated thermal improvement, the TRI evaluates the temporal stability of the resulting thermal environment, and the OSI describes the extent to which cooling performance changes between the two courtyard orientations. These complementary dimensions were therefore integrated using the CTPI. To ensure comparability among indices with different numerical ranges and preferred directions, the TCEI and TRI values were transformed to a common 0–100 benefit-oriented scale, whereas the OSI was converted into an orientation robustness score (ONOR), where higher values indicate greater robustness. The normalized indicators were then integrated for each scenario–courtyard combination, allowing the thermal performance of each modeled vegetation alternative to be evaluated separately in Courtyard A and Courtyard B.

The CTPI was calculated using a weighted aggregation structure in which cooling efficiency received the greatest weight, as presented in Equation 24. This weighting structure assigns primary importance to integrated cooling efficiency because the principal objective of the vegetation intervention is to improve the outdoor thermal environment. Temporal resilience and orientation robustness were assigned equal secondary weights because they represent complementary dimensions of performance: the ability to maintain stable thermal conditions over time and the ability to retain cooling effectiveness under changing spatial orientation. Appendix 1 presents the complete multidimensional performance results and CTPI values for all six scenario–courtyard combinations. The results reveal substantial differences in multidimensional thermal performance among the investigated scenario–courtyard combinations. The highest CTPI was obtained by Sc2 (Ficus nitida) in Courtyard A, with a score of 74.75, followed by Sc3 (Cassia nodosa) in Courtyard A with 59.10 and Sc1 (Cassia leptophylla) in Courtyard A with 57.06. The superior performance of Sc2 in Courtyard A was primarily associated with its maximum normalized cooling-efficiency score (CNTCEI = 100) and near-maximum temporal-resilience score (RNTRI = 98.99). However, the results also demonstrate an important trade-off between cooling magnitude and orientation robustness. Although Sc2 produced the greatest integrated cooling performance, it exhibited the highest orientation sensitivity (OSI = 0.428) and consequently received the lowest orientation robustness score (ONOR = 0). In contrast, Sc1 exhibited the lowest orientation sensitivity (OSI = 0.272) and therefore achieved the maximum orientation robustness score (ONOR = 100). Its lower cooling efficiency, however, limited its overall CTPI relative to Sc2 in Courtyard A.

Sc3 demonstrated an intermediate orientation response (OSI = 0.409) but achieved the highest TRI value in Courtyard A (0.143), resulting in the maximum normalized temporal-resilience score (RNTRI = 100). Consequently, Sc3 achieved the second-highest CTPI in Courtyard A (59.10), slightly exceeding Sc1 (57.06). This result confirms that the composite framework does not simply reproduce the ranking obtained from cooling efficiency alone but captures trade-offs among cooling magnitude, temporal stability, and orientation robustness. A strong orientation effect is also evident in the CTPI results. All three vegetation configurations achieved substantially higher composite performance in Courtyard A than in Courtyard B. The CTPI of Sc2 decreased from 74.75 in Courtyard A to 21.06 in Courtyard B, while Sc3 decreased from 59.10 to 12.46, and Sc1 decreased from 57.06 to 25.00. These differences demonstrate that courtyard orientation substantially influenced the overall thermal performance achieved by the modeled vegetation configurations. Within Courtyard A, the CTPI ranking was:Where as within Courtyard B, the ranking was:

S c 2 > S c 3 > S c 1

S c 1 > S c 2 > S c 3

This change in ranking is particularly important because it demonstrates the value of evaluating vegetation performance separately within each spatial context. Although Sc2 consistently produced the greatest magnitude of thermal improvement, its relatively high sensitivity to orientation reduced its composite performance under the less favorable courtyard condition. Conversely, Sc1 benefited from its substantially greater orientation robustness and consequently achieved the highest CTPI in Courtyard B despite having lower TCEI values.

Overall, the CTPI results confirm that no single vegetation configuration can be considered universally optimal independently of courtyard orientation and decision priorities. Sc2 (Ficus nitida) in Courtyard A represents the highest-performing scenario–courtyard combination under the adopted weighting structure, primarily because of its superior integrated cooling efficiency and strong temporal resilience. However, Sc1 (Cassia leptophylla) demonstrates the greatest robustness to orientation, while Sc3 (Cassia nodosa) provides a strong balance between cooling efficiency and temporal thermal stability in Courtyard A.

The proposed multidimensional framework therefore moves beyond conventional single-variable comparisons by explicitly revealing the trade-offs among cooling effectiveness, temporal resilience, and orientation robustness. Importantly, the resulting rankings represent the comparative performance of the complete modeled vegetation alternatives—including their associated canopy and morphological characteristics—under the specific climatic and courtyard configurations investigated, rather than the intrinsic thermal superiority of tree species independently of their physical characteristics.

The multidimensional structure underlying the composite assessment is further resolved through the decision matrix presented in Figure 12. Rather than representing the investigated vegetation alternatives solely through a single composite ranking, the matrix decomposes their performance into the individual thermal dimensions contributing to the final CTPI. The comparison includes the relative improvements in Ta, T_mrt, and PET, together with the TCEI, TRI, OSI, and their corresponding normalized performance scores. The comparative multidimensional performance and the resulting CTPI-based ranking across the two courtyard orientations are further summarized in Figure 13. This representation makes it possible to identify the specific strengths and limitations of each vegetation configuration under each courtyard orientation. The results confirm that Sc2 (Ficus nitida) exhibited the strongest cooling-related performance under both courtyard orientations. In Courtyard A, Sc2 achieved the largest improvements in Ta (5.02%), T_mrt (37.88%), and PET (25.39%), resulting in the highest TCEI value (0.251) and the maximum normalized cooling-efficiency score C N T C E I = 100. It also achieved a TRI of 0.142 and an R N T R I of 98.99, producing the highest CTPI among all scenario–courtyard combinations (74.75). In Courtyard B, Sc2 maintained the highest TCEI (0.162), although its temporal resilience decreased substantially (TRI = 0.019), resulting in a lower CTPI of 21.06.

Sc3 (Cassia nodosa) demonstrated an intermediate cooling profile but the strongest temporal resilience under Courtyard A conditions. Its TRI reached 0.143, corresponding to the maximum normalized resilience score (R N T R I = 100). Combined with a TCEI of 0.194 and an orientation-robustness score of 12.12, Sc3 achieved a CTPI of 59.10 in Courtyard A. However, its performance declined considerably in Courtyard B, where the TRI decreased to 0.018 and the CTPI reached 12.46, the lowest value among the evaluated scenario–courtyard combinations.

In contrast, Sc1 (Cassia leptophylla) demonstrated the greatest orientation robustness, reflected by the lowest OSI value (0.272) and the maximum orientation-robustness score (O N O R = 100). Although Sc1 exhibited the lowest TCEI values in both courtyards (0.135 in Courtyard A and 0.102 in Courtyard B), its strong robustness contributed substantially to its composite performance. Consequently, Sc1 achieved a CTPI of 57.06 in Courtyard A and 25.00 in Courtyard B. These results demonstrate that superior orientation robustness can partially compensate for lower cooling efficiency and temporal resilience within the multidimensional assessment framework.

The decision matrix therefore confirms that the final CTPI is not governed by a single performance dimension. Sc2 achieved the highest overall performance in Courtyard A because its dominant cooling efficiency and strong temporal resilience compensated for its comparatively low orientation-robustness score. Conversely, Sc1 benefited from its superior orientation robustness despite its lower cooling-efficiency performance. Sc3 occupied an intermediate position under Courtyard A conditions because of its strong temporal resilience and moderate cooling performance, but its composite performance decreased substantially under Courtyard B conditions. As illustrated by the CTPI-based ranking in Figure 13, the preferred vegetation configuration changes according to courtyard orientation and the balance among the three underlying performance dimensions.

These findings demonstrate that the proposed framework moves beyond selecting vegetation solely according to maximum cooling magnitude. Instead, it reveals the trade-offs among cooling efficiency, temporal resilience, and orientation robustness, allowing vegetation performance to be evaluated within the specific spatial context in which it is applied. The resulting ranking should therefore be interpreted as representing the performance of the complete modeled vegetation configurations, including their associated morphological characteristics, under the investigated climatic conditions and courtyard geometries, rather than as a universal ranking of tree species independent of context.

4.4 Sensitivity analysis of CTPI to weighting structure

A sensitivity analysis was conducted to examine the influence of alternative weighting structures on the Composite Thermal Performance Index (CTPI) and the resulting ranking of vegetation configurations. Because the CTPI is a multi-criteria decision metric, its ranking may vary according to the relative importance assigned to cooling efficiency, temporal thermal resilience, and orientation robustness. The analysis was performed at the scenario–courtyard level, considering the six individual scenario–courtyard combinations rather than aggregated species-level values. This approach preserves the demonstrated influence of courtyard orientation on vegetation performance. The underlying normalized component scores (CNTCEI, RNTRI, and ONOR) were retained unchanged, and only the weighting coefficients were modified. Therefore, the analysis isolates the influence of decision priorities without altering the ENVI-met simulations, PET calculations, thermal improvements, performance indices, or normalization procedure.

The baseline weighting structure assigned the greatest importance to cooling efficiency (0.50), while temporal resilience and orientation robustness received equal weights (0.25 each). Six alternative structures were subsequently examined, including cooling-, resilience-, and robustness-priority structures, together with three balanced combinations emphasizing two performance dimensions simultaneously. All weighting structures satisfied the unit-sum constraint. These weights represent explicit normative decision preferences rather than empirically derived universal coefficients. The resulting rankings are summarized in Table 7. Under the baseline structure, Sc2–A (Ficus nitida) achieved the highest CTPI (74.75), followed by Sc3–A (59.10) and Sc1–A (57.06). Sc2–A retained the first position under cooling-priority, resilience-priority, and cooling–resilience balanced structures, reflecting its strong cooling performance and near-maximum temporal resilience. In contrast, when orientation robustness received substantial importance, Sc1–A (Cassia leptophylla) became the preferred alternative, followed by Sc1–B under the robustness-priority structure.

TABLE 7. Sensitivity analysis of the Composite Thermal Performance Index (CTPI) under alternative weighting structures, showing the weights assigned to cooling efficiency, thermal resilience, and orientation robustness and the resulting scenario rankings.

• Sc1–A, Sc2–A, and Sc3–A refer to Scenarios 1, 2, and three in Courtyard A, respectively.

Bold values indicate the baseline weighting structure.

The results therefore demonstrate that the CTPI ranking is sensitive to explicitly defined decision priorities, particularly when orientation robustness is strongly emphasized. Sc2–A represents the preferred alternative when cooling efficiency and/or temporal resilience are prioritized, whereas Sc1–A becomes preferable when robustness across contrasting courtyard orientations is the dominant objective. Sc3–A remained competitive because of its strong temporal resilience but did not achieve the highest rank under the examined weighting structures. Overall, the sensitivity analysis confirms that the proposed framework does not impose a universally optimal vegetation choice. Instead, it provides a transparent mechanism for adapting tree-selection decisions to different thermal-design priorities while preserving the spatial influence of courtyard orientation.

4.5 Decision framework for climate-responsive tree selection

The preceding analyses demonstrate that climate-responsive tree selection in hot-arid courtyards cannot be based solely on the magnitude of cooling achieved by a vegetation scenario. The investigated configurations exhibited different combinations of cooling efficiency, temporal thermal resilience, and sensitivity to courtyard orientation. The proposed framework therefore translates these multidimensional results into a structured decision pathway linking the candidate tree scenarios to the proposed performance indices and their resulting Composite Thermal Performance Index (CTPI) scores, as illustrated in Figure 14. The framework evaluates each vegetation scenario through three complementary dimensions. The Tree Cooling Efficiency Index (TCEI) quantifies integrated baseline-referenced thermal improvement based on the relative changes in Ta, Tmrt, and PET. The Thermal Resilience Index (TRI) evaluates the temporal stability of thermal performance, while the Orientation Sensitivity Index (OSI) quantifies the variation in cooling efficiency between the two courtyard orientations. These indicators are subsequently normalized, with orientation sensitivity converted into a benefit-oriented robustness score, and integrated into the CTPI for comparative decision-making (Table A1).

The results demonstrate an important distinction between thermal effectiveness and decision robustness. Sc2 (Ficus nitida) achieved the strongest cooling efficiency and temporal resilience, particularly in Courtyard A, where it obtained the highest CTPI value (74.75). However, its relatively high orientation sensitivity (OSI = 0.428) resulted in the lowest orientation-robustness score. Conversely, Sc1 (Cassia leptophylla) exhibited the lowest orientation sensitivity (OSI = 0.272) and the maximum orientation-robustness score, despite its comparatively lower cooling efficiency. The preferred configuration also depended on courtyard orientation. In Courtyard A, Sc2 achieved the highest CTPI (74.75), followed by Sc3 (59.10) and Sc1 (57.06). In Courtyard B, the ranking changed, with Sc1 achieving the highest CTPI (25.00), followed by Sc2 (21.06) and Sc3 (12.46). These results confirm that the same vegetation configuration can exhibit substantially different integrated thermal performance depending on its spatial context.

The framework establishes a transparent pathway from candidate vegetation scenarios through thermal-performance assessment, normalization, and CTPI integration to a context-specific design recommendation. It therefore does not identify a universally optimal tree species. Under the investigated climatic and geometric conditions, Ficus nitida represents the strongest option where maximum cooling efficiency and temporal resilience are prioritized, particularly in Courtyard A, whereas Cassia leptophylla may be preferable where robustness across contrasting courtyard orientations is given greater importance.

The decision implications should nevertheless be interpreted within the scope of the variables evaluated in this study. The framework directly supports vegetation selection according to simulated microclimatic improvement, temporal thermal resilience, and orientation robustness. Potential effects on occupancy, user satisfaction, social interaction, and inclusiveness were not directly evaluated and should therefore not be interpreted as demonstrated outcomes. Overall, the framework provides a transparent transition from microclimatic simulation to climate-responsive design selection by integrating cooling magnitude, temporal stability, and spatial robustness while allowing the final recommendation to respond to specific courtyard conditions and design priorities.

4.6 Study scope and morphological comparability

Several considerations should be taken into account when interpreting the comparative results and the resulting tree-selection framework. The investigated vegetation scenarios represent practical modeled tree configurations rather than a strictly controlled species-comparison experiment. Tree height, crown dimensions, canopy structure, and leaf-area characteristics were therefore not standardized across scenarios. Consequently, the observed differences in thermal performance reflect the combined effects of species-related characteristics and their associated morphological representations in ENVI-met. The results should thus be interpreted as comparisons of complete modeled vegetation configurations rather than intrinsic species effects independent of morphology.

Nevertheless, all scenarios were evaluated under the same simulation framework, courtyard geometries, climatic forcing, assessment period, and calculation procedures, and each was compared with its corresponding orientation-specific non-vegetated baseline. This provides a consistent basis for relative comparison under the investigated conditions. Future studies could standardize parameters such as tree height, crown projection, leaf area index, leaf area density, and canopy porosity to distinguish species-specific effects from morphology-mediated thermal effects.

The interpretation of PET also requires consideration of the intended school users. Because children and adolescents differ from adults in body size and thermophysiological characteristics, absolute PET values calculated using a standard reference person may not precisely represent individual thermal perception. However, identical reference-person parameters were applied consistently across all scenarios and orientations, making the relative differences in PET appropriate for the present comparative assessment. Future research could incorporate age-specific physiological parameters.

The broader applicability of the ranking is limited to the investigated educational facility, the two courtyard orientations, and the hot-arid climatic conditions of Aswan. The resulting hierarchy should therefore not be interpreted as universally applicable. Although the weighting sensitivity analysis examined the influence of alternative decision priorities, it did not address uncertainties related to weather variability, seasonal conditions, vegetation physiological responses, or different courtyard geometries. Further testing across multiple seasons, climatic regions, meteorological conditions, and courtyard configurations is therefore required.

Finally, the model validation was based on baseline measurements of air temperature and relative humidity at a single location over a 24-h period. While this demonstrated the model’s ability to reproduce observed temporal patterns under baseline conditions, it did not directly validate vegetation-induced thermal responses. In particular, T_mrt, wind conditions, PET, and the magnitude of vegetation-induced cooling were not independently validated against field measurements. The findings should therefore be interpreted primarily as comparative simulation-based evidence of the relative performance of the modeled vegetation configurations under the specific investigated conditions. Future research should multi-day and multi-location measurements under both vegetated and non-vegetated conditions to validate vegetation-induced changes across a broader range of microclimatic and thermal-comfort variables.

5 Conclusion

This study developed a Multi-Criteria Thermal Performance Framework (MCTPF) for evaluating climate-responsive vegetation strategies in hot-arid educational courtyards. The framework integrates cooling efficiency, temporal thermal resilience, and orientation robustness through the Tree Cooling Efficiency Index (TCEI), Thermal Resilience Index (TRI), Orientation Sensitivity Index (OSI), and Composite Thermal Performance Index (CTPI), thereby providing a multidimensional basis for comparing vegetation performance across different courtyard orientations.

The results demonstrated clear differences among the investigated vegetation configurations. Sc2 (Ficus nitida) achieved the strongest overall cooling performance, with the highest TCEI values in both courtyards (0.251 in Courtyard A and 0.162 in Courtyard B), and obtained the highest overall CTPI score of 74.75 in Courtyard A. In contrast, Sc1 (Cassia leptophylla) demonstrated the greatest robustness to changes in courtyard orientation, with the lowest OSI value of 0.272, whereas Sc2 exhibited greater orientation sensitivity (OSI = 0.428). These findings demonstrate that the preferred vegetation strategy depends not only on the magnitude of thermal improvement but also on the temporal stability and spatial robustness of that performance. The proposed framework therefore provides a transparent decision-support approach for vegetation selection by making the trade-offs among cooling efficiency, temporal resilience, and orientation robustness explicit. Rather than identifying a universally optimal tree configuration, the framework enables vegetation strategies to be evaluated according to clearly defined thermal-design priorities and the spatial context in which they are applied.

Model validation demonstrated strong agreement between simulated and measured air temperature (T_a), with R ² = 0.996 and MAE = 1.505 °C, as well as relative humidity under the investigated baseline conditions. However, T_mrt, wind conditions, PET, and vegetation-induced thermal responses were not independently validated. Model validation demonstrated strong agreement between simulated and measured temporal patterns of air temperature and relative humidity under the investigated baseline conditions. However, T_mrt, wind conditions, PET, and vegetation-induced thermal responses were not independently validated; therefore, the findings should be interpreted primarily as comparative simulation-based evidence of the relative performance of the investigated configurations rather than as fully validated predictions of absolute thermal conditions. Future research should validate the framework through multi-variable field measurements under both vegetated and non-vegetated conditions and examine its applicability across different seasons, climatic contexts, and courtyard geometries.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fbuil.2026.1956270/full#supplementary-material

Supplementary material Supplementary material at the source

Footnotes

Edited by: Amar Bennadji (SFHEA), Hanze University of Applied Sciences, Netherlands

Reviewed by: Qisheng Han, Henan Institute of Science and Technology, China

Zainab Khalid, University of Baghdad, Iraq