Correlation Between the Insolation Shadow Ratio and Thermal Comfort of Urban Outdoor Spaces in Residential Areas in Xi’an
Abstract
1. Introduction
2. Methodology
2.1. Research Framework
2.2. Sites
2.3. Field Investigation
2.3.1. Objectives
2.3.2. Content and Methods
2.4. Selection of Outdoor Thermal Comfort Indicators
2.4.1. Method for Calculating the UTCI Based on Field Measurements
2.4.2. Method for Calculating the UTCI Based on Simulation
2.5. Concept and Calculation Method of the ISR Index
2.5.1. Method for Obtaining ISR Values Through Field Measurements
2.5.2. Method for Obtaining ISR Values Through Simulation
2.6. Validation of the Relationship Between Outdoor Thermal Comfort and the ISR
2.6.1. Spearman Correlation
2.6.2. Sobol Sensitivity Analysis
3. Results
3.1. Field Measurement Results
3.1.1. Measured Results of the Insolation Shadow Ratio for Different Types of Spaces
3.1.2. Measured UTCI Results for Different Types of Spaces
- (1)
- Comparison of measured UTCI data
- (2)
- Analysis of UTCI Differences Between Sunlit and Shaded Areas
- (3)
- Results and Analysis
3.2. Correlation Analysis Between Measured ISR and UTCI
3.3. Simulation Results
3.3.1. Simulated ISR
3.3.2. Simulated UTCI
- (1)
- Comparison of simulated UTCI data
- (2)
- Results and Analysis
3.4. Workflow Efficiency Comparison
3.5. Correlation Analysis Between Simulated ISR and UTCI
3.6. Sensitivity Analysis Between Simulated ISR and UTCI Values
4. Discussion
4.1. Effect of ISR Variation on the UTCI
4.2. Reasons for Differences Between Measured Data and Simulated Data
- (1)
- Nonlinear relationships: The relationship between ISR and thermal comfort is not strictly linear. For instance, excessive solar exposure can increase discomfort in high-temperature seasons, while enhancing comfort in colder seasons. This suggests that the relationship between thermal comfort and ISR is complex, influenced by multiple factors such as season, wind speed, and humidity.
- (2)
- Localized microclimate effects: Factors such as the built environment, vegetation coverage, and surface materials can alter local microclimatic conditions, affecting thermal comfort. Even with the same ISR, variations in material thermal properties (e.g., absorption and reflectivity) can lead to differing surface temperatures, causing deviations in measured results.
- (3)
- Real-world complexity vs. idealized models: Real-world sites often involve numerous interacting factors not accounted for in idealized models. While the simulation primarily considers building-induced shadowing effects, real environments introduce additional uncertainties and overlapping variables, leading to deviations from predicted outcomes.
4.3. Data-Driven ISR Threshold Determination
- (1)
- Measured ISR Threshold Patterns
- (2)
- Simulated ISR Threshold Patterns
4.4. Practical Implementation of ISR Thresholds
5. Conclusions
5.1. Limitations
- (a)
- Data Acquisition Constraints in Complex Urban Environments
- (b)
- Geographic Impact ISR Thresholds
- (c)
- Mono-Variable Model Simplification
- (d)
- Lag Effects between Shading and Thermal Comfort Perception
5.2. Key Findings
- (1)
- Analytical results of the measured data:
- ➀
- A correlation between the ISR and the UTCI was observed across different sites, and it was validated using SPSS based on measured ISR and UTCI data from the actual residential area. The degree of correlation varied among the three sites. Site A and site B exhibited stronger positive correlations, while site C demonstrated a weaker correlation. An exception was observed during the vernal equinox at site C, where the measured ISR and UTCI data showed a negative correlation. Site C exhibited outliers during the vernal equinox. However, this anomaly is likely influenced by complex environmental factors, making it difficult to attribute the phenomenon to a single cause.
- ➁
- The strength of the correlation between the ISR and the UTCI of site A and site C was significantly higher in the sunlit areas than in the shaded areas; however, at site B, it was higher in the shaded areas than in the sunlit areas. The stronger correlation between ISR and UTCI in shaded areas compared to sunlit areas can be explained by two main factors: environmental factors and measurement point distribution. Shaded areas are more influenced by factors like building layout, vegetation, wind speed, and humidity. For example, vegetation in shaded areas can further cool the environment through transpiration, enhancing the ISR–UTCI correlation. Sunlit areas, less affected by these factors, show a weaker correlation. The placement of measurement points and surrounding shading from buildings or vegetation can amplify the impact of ISR on UTCI in shaded areas, especially when these areas are heavily obstructed or influenced by microclimatic conditions. Therefore, this demonstrates that shaded areas are more sensitive to environmental and microclimatic interactions than sunlit areas.
- (2)
- Analytical results of the simulation date:
- ➀
- The ISRs of site A on the four typical solar term days showed negative correlations with the UTCI, of different degrees.
- ➁
- The ISRs of site B showed positive correlations with the UTCI on the spring and autumn equinoxes and negative correlations on the winter and summer solstices.
- ➂
- The ISRs of site C on the four typical solar term days showed positive correlations with the UTCI, of different degrees.
- ➃
- The magnitude of the ISR variations had a direct impact on the range of outdoor thermal comfort fluctuations. As the ISR differences increased, the UTCI fluctuations became more pronounced, suggesting ISR as a potentially key factor in shaping the thermal environment of outdoor spaces.
5.3. Contributions
- (1)
- Theoretical Innovation: We propose the ISR as a novel morphometric index that quantifies solar shade dynamics and their nonlinear coupling with UTCI-based thermal comfort. This metric establishes an intuitive visualization framework linking shadow coverage (0–1 normalized) to physiological heat stress thresholds (9–26 °C UTCI).
- (2)
- Design Praxis Transformation: The ISR enables direct conversion of thermal comfort requirements into implementable shade design parameters and reduces the technical threshold of thermal environment optimization.
- (3)
- Build A New Research Pathway: We establish a dynamic solar exposure analysis framework that integrates field microclimate measurements and simulated data with GAM-based threshold modeling. Although the present study focuses on Xi’an, the ISR computation protocol—grounded in local solar trajectories and parametric solar–shadow modeling—is directly transferable to other cold-region contexts.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
22 December 2022 | Panoramic Picture |
---|---|
8:00–10:00 | |
12:00–14:00 | |
16:00–18:00 |
21 March 2023 | Panoramic Picture |
---|---|
8:00–10:00 | |
12:00–14:00 | |
16:00–18:00 |
22 June 2023 | Panoramic Picture |
---|---|
8:00–10:00 | |
12:00–14:00 | |
16:00–18:00 |
Time | Winter Solstice | Spring Equinox | Summer Solstice | Autumnal Equinox | |
---|---|---|---|---|---|
Site A | 8:00 | 0.941 | 0.943 | 0.942 | 0.943 |
9:00 | 0.940 | 0.942 | 0.943 | 0.942 | |
10:00 | 0.937 | 0.941 | 0.943 | 0.940 | |
11:00 | 0.934 | 0.937 | 0.942 | 0.937 | |
12:00 | 0.917 | 0.930 | 0.939 | 0.924 | |
13:00 | 0.775 | 0.877 | 0.903 | 0.836 | |
14:00 | 0.406 | 0.724 | 0.800 | 0.673 | |
15:00 | 0.038 | 0.531 | 0.685 | 0.480 | |
16:00 | 0.000 | 0.404 | 0.571 | 0.372 | |
17:00 | 0.000 | 0.328 | 0.535 | 0.301 | |
18:00 | 0.000 | 0.311 | 0.395 | 0.353 | |
Site B | 8:00 | 0.711 | 0.821 | 0.822 | 0.809 |
9:00 | 0.643 | 0.771 | 0.847 | 0.756 | |
10:00 | 0.538 | 0.703 | 0.841 | 0.677 | |
11:00 | 0.365 | 0.580 | 0.788 | 0.539 | |
12:00 | 0.142 | 0.434 | 0.747 | 0.396 | |
13:00 | 0.000 | 0.310 | 0.718 | 0.296 | |
14:00 | 0.000 | 0.299 | 0.709 | 0.300 | |
15:00 | 0.000 | 0.285 | 0.755 | 0.272 | |
16:00 | 0.000 | 0.282 | 0.836 | 0.260 | |
17:00 | 0.000 | 0.288 | 0.786 | 0.309 | |
18:00 | 0.000 | 0.305 | 0.655 | 0.354 | |
Site C | 8:00 | 0.000 | 0.292 | 0.866 | 0.437 |
9:00 | 0.029 | 0.724 | 0.988 | 0.767 | |
10:00 | 0.354 | 0.811 | 0.970 | 0.816 | |
11:00 | 0.548 | 0.815 | 0.938 | 0.814 | |
12:00 | 0.559 | 0.810 | 0.936 | 0.808 | |
13:00 | 0.557 | 0.809 | 0.936 | 0.809 | |
14:00 | 0.526 | 0.814 | 0.938 | 0.815 | |
15:00 | 0.406 | 0.808 | 0.969 | 0.807 | |
16:00 | 0.129 | 0.803 | 0.990 | 0.802 |
Time | Winter Solstice | Spring Equinox | Summer Solstice | Autumnal Equinox | ||||
---|---|---|---|---|---|---|---|---|
Min | Max | Min | Max | Min | Max | Min | Max | |
8:00 | −1.1 | 0.16 | 2.43 | 2.81 | 18.92 | 21.57 | 20.1 | 20.55 |
9:00 | −0.99 | 0.02 | 6.87 | 7.38 | 23.08 | 28 | 20.83 | 20.87 |
10:00 | −0.07 | 0.41 | 6.29 | 6.56 | 23.19 | 29.54 | 21.51 | 23.2 |
11:00 | −2.45 | −2.09 | 7.87 | 9.43 | 25.16 | 31.62 | 22.34 | 23.86 |
12:00 | 1.3 | 3.55 | 7.02 | 13.88 | 26.12 | 33.32 | 22.34 | 24.46 |
13:00 | −1.28 | 2.23 | 9.27 | 21.77 | 27.45 | 34.01 | 22.36 | 27.26 |
14:00 | 3.1 | 7.14 | 13.21 | 26.01 | 28.32 | 34.19 | 22.78 | 27.75 |
15:00 | 4.07 | 6.8 | 12.09 | 21.79 | 29.81 | 36.14 | 22.36 | 26.09 |
16:00 | 1.04 | 2.71 | 11.65 | 20.38 | 30.87 | 37.73 | 23.89 | 26.78 |
17:00 | 3.73 | 3.81 | 10.46 | 17.19 | 32.09 | 38.09 | 23.95 | 25.18 |
18:00 | 2.98 | 4.44 | 11.38 | 12.49 | 32.21 | 36.79 | 24.26 | 24.27 |
Time | Winter Solstice | Spring Equinox | Summer Solstice | Autumnal Equinox | ||||
---|---|---|---|---|---|---|---|---|
Min | Max | Min | Max | Min | Max | Min | Max | |
8:00 | −0.95 | 0.16 | 2.48 | 2.81 | 18.92 | 21.3 | 20.15 | 20.55 |
9:00 | −0.88 | 0.02 | 6.93 | 7.38 | 23.08 | 27.66 | 20.83 | 20.87 |
10:00 | −0.02 | 0.41 | 6.29 | 6.53 | 23.19 | 29.18 | 21.51 | 23.01 |
11:00 | −2.45 | −2.13 | 7.87 | 9.25 | 25.16 | 31.26 | 22.34 | 23.68 |
12:00 | 1.3 | 3.29 | 7.02 | 13.13 | 26.12 | 32.84 | 22.34 | 24.21 |
13:00 | −1.28 | 1.82 | 9.27 | 20.41 | 27.45 | 33.57 | 22.36 | 26.71 |
14:00 | 3.1 | 6.66 | 13.21 | 24.66 | 28.32 | 33.88 | 22.78 | 27.19 |
15:00 | 4.07 | 6.49 | 12.09 | 21.42 | 29.81 | 35.87 | 22.36 | 25.66 |
16:00 | 1.04 | 2.52 | 11.65 | 20.17 | 30.87 | 37.49 | 23.89 | 26.45 |
17:00 | 3.73 | 3.8 | 10.46 | 17.14 | 32.09 | 38 | 23.89 | 25.04 |
18:00 | 3.15 | 4.44 | 11.51 | 12.49 | 32.21 | 36.78 | 24.26 | 24.27 |
Time | Winter Solstice | Spring Equinox | Summer Solstice | Autumnal Equinox | ||||
---|---|---|---|---|---|---|---|---|
Min | Max | Min | Max | Min | Max | Min | Max | |
8:00 | −0.63 | −0.24 | 2.57 | 2.69 | 19.94 | 20.7 | 20.27 | 20.4 |
9:00 | −0.62 | −0.31 | 7.06 | 7.21 | 25.99 | 26.92 | 20.84 | 20.85 |
10:00 | 0.1 | 0.25 | 6.38 | 6.46 | 27.36 | 28.37 | 22.06 | 22.59 |
11:00 | −2.34 | −2.22 | 8.37 | 8.86 | 29.48 | 30.47 | 22.83 | 23.3 |
12:00 | 2.02 | 2.72 | 9.12 | 11.51 | 30.49 | 31.8 | 23.02 | 23.69 |
13:00 | −0.16 | 0.93 | 13.41 | 17.36 | 31.4 | 32.61 | 23.96 | 25.5 |
14:00 | 4.39 | 5.65 | 17.54 | 21.59 | 32.36 | 33.2 | 24.41 | 25.97 |
15:00 | 4.94 | 5.8 | 13.05 | 20.79 | 34.55 | 35.28 | 23.57 | 24.74 |
16:00 | 1.58 | 2.1 | 12.17 | 19.83 | 36.33 | 36.97 | 24.82 | 25.73 |
17:00 | 3.75 | 3.78 | 10.58 | 17.06 | 37.55 | 37.8 | 24.35 | 24.73 |
18:00 | 3.52 | 3.97 | 11.78 | 12.13 | 32.27 | 36.75 | 24.26 | 24.27 |
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Time Period | Winter Solstice—ISR | Spring Equinox—ISR | Summer Solstice—ISR |
---|---|---|---|
8:00–10:00 | 9.7% | 46.33% | 12.66% |
10:00–12:00 | 40.66% | 87.16% | 30.45% |
12:00–14:00 | 43.97% | 93.53% | 23.94% |
14:00–16:00 | 1.06% | 67.67% | 67.21% |
16:00–18:00 | 0% | 43.59% | 41.08% |
Reference Day | Site A (Average ISR) | Site B (Average ISR) | Site C (Average ISR) |
---|---|---|---|
Winter Solstice (22 December) | |||
Spring Equinox (21 March) | |||
Summer Solstice (22 June) | |||
Autumn Equinox (23 September) |
Reference Day | Site A (UTCI-Mean) | Site B (UTCI-Mean) | Site C (UTCI-Mean) |
---|---|---|---|
Winter Solstice (22 December) | |||
Spring Equinox (21 March) | |||
Summer Solstice (22 June) | |||
Autumn Equinox (23 September) |
Site A UTCI | Site B UTCI | Site C UTCI | ||||
---|---|---|---|---|---|---|
Si | ST | Si | ST | Si | ST | |
Winter ISR | 1.0388 | 1.0388 | 0.9943 | 0.9948 | 0.9715 | 0.9711 |
Summer ISR | 0.9974 | 0.9974 | 0.9871 | 0.9871 | 1.0030 | 1.0030 |
Spring ISR | 1.0088 | 1.0088 | 0.9834 | 0.9835 | 1.0030 | 1.0030 |
Autumn ISR | 1.0060 | 1.0060 | 0.9994 | 0.9986 | 0.9808 | 0.9808 |
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Song, J.; Liu, Y.; Chow, D.H.C.; Liu, B.; Cho, S. Correlation Between the Insolation Shadow Ratio and Thermal Comfort of Urban Outdoor Spaces in Residential Areas in Xi’an. Buildings 2025, 15, 1995. https://doi.org/10.3390/buildings15121995
Song J, Liu Y, Chow DHC, Liu B, Cho S. Correlation Between the Insolation Shadow Ratio and Thermal Comfort of Urban Outdoor Spaces in Residential Areas in Xi’an. Buildings. 2025; 15(12):1995. https://doi.org/10.3390/buildings15121995
Chicago/Turabian StyleSong, Jie, Yu Liu, David Hou Chi Chow, Bo Liu, and Seigen Cho. 2025. "Correlation Between the Insolation Shadow Ratio and Thermal Comfort of Urban Outdoor Spaces in Residential Areas in Xi’an" Buildings 15, no. 12: 1995. https://doi.org/10.3390/buildings15121995
APA StyleSong, J., Liu, Y., Chow, D. H. C., Liu, B., & Cho, S. (2025). Correlation Between the Insolation Shadow Ratio and Thermal Comfort of Urban Outdoor Spaces in Residential Areas in Xi’an. Buildings, 15(12), 1995. https://doi.org/10.3390/buildings15121995