Evaluation and Optimization Design for Microclimate Comfort of Traditional Village Squares Based on Extension Correlation Function

The evaluation approaches for microclimate comfort in traditional villages often ignore the year-round impact and the impact from dynamic and static behaviors, as well as the composite impact of wind and heat environments. To solve the problem, this study presents an evaluation and optimization design strategy for microclimate comfort of traditional village squares based on extension correlation function, using field survey, computer simulation, and example analysis. Firstly, the wind and heat environments in the space of the square were measured on the site with an ultrasonic integrated weather station. Secondly, simulation parameters were configured on PHOENICS (computational fluid dynamics software), namely, boundary conditions, wind environment, heat environment, and green plants, and used to simulate the wind and heat environments in the space of the square, followed by a correlation analysis between the simulation results and the measured results. Finally, the extension correlation function was adopted to comprehensively evaluate the microclimate comfort of the preliminary design scheme, and the design scheme of the square was finalized through repeated adjustments. The proposed strategy was verified on an example: Xieduqi square, Zoumatang village, eastern China's Zhejiang Province. The example analysis shows that the proposed strategy is highly operable. The research effectively improves the optimization design of traditional village squares, extends the digital technology system of traditional villages, and greatly drives rural construction in the future.


Research Review.
Traditional Chinese villages, especially those in Jiangsu and Zhejiang, are often blessed with a superior landscape environment, a profound history, and a convenient road transport system, as well as well-established infrastructure and public service facilities. anks to numerous rural revitalization policies (e.g., the project of one thousand demonstration villages and rectification of ten thousand villages, the beautiful village initiative, and the future village initiative), and heavy government investments, traditional villages are constantly attracting a large population from urban areas, and poised to be ideal human settlements in future. In recent years, more and more attention has been paid to microclimate comfort in rural spaces. e precision control of microclimate can create an energy-efficient, environmentally friendly, ecological, and comfortable rural space, which will significantly promote the construction of future villages, and energize the sustainable development of villages.
Microclimate refers to the local climate formed by the influence of the underlying surface. e comfort of microclimate, which can be measured by body comfort, is the satisfactory state of humans in a small-scale climate environment [22]. Microclimate comfort mainly consists of wind comfort and heat comfort. Most of the existing studies have adopted the Beaufort wind comfort criteria and heat comfort criteria, focusing on one of the two comforts. For example, many scholars explored the influence of greening methods (green space, tree arrangement, urban form, street form, and architectural form) over microclimate comfort of the square [1][2][3][4][5][6][7]23]. Some scholars verified the heat comfort in the microclimate of the semiclosed courtyard space through numerical simulation [8,9]. Soflaei et al. [24] adjusted the microclimate comfort of traditional Iranian courtyards, in the light of direction, size, and proportion. Tumini et al. [10] presented an urban renovation design strategy based on the modeling technology of microclimate heat comfort. Contraposing two typical urban spaces (squares and courtyards), Chatzidimitriou and Yannas [11] explained the influence of geometry, landscape elements, and material properties over the heat comfort of pedestrians. rough quantitative simulation, generation, and optimization operations, Qiu and Yu [12] put forward a spatial form design method for urban squares based on the universal thermal climate index (UTCI). Huang [13] improved the Beaufort scale combined with the dynamic and static behaviors on squares, and proposed a way to optimize the spatial form of square space. Yan et al. [14] expounded on the principles and evaluation indices of human heat comfort, and established a human heat adaptation model based on the analysis method for heat comfort data, the dry, humid, and hot climate effects, and the environmental regulation. To sum up, the existing studies have overlooked the year-round impact (e.g., the typical weather days in winter and summer are considered, instead of simulating the climate around the year), the impact from user behaviors (e.g., the obvious difference between dynamic and static behaviors in the adaptability to wind and heat environments), and the composite impact of wind and heat environments on human comfort (e.g., wind is merely treated as an index of heat comfort evaluation, without further deliberation: the wind velocity should not surpass 5 m/s at the height of 1.5 m). Most of spontaneous human activities have difficulty to proceed in an uncomfortable environment. e frequency and quality of public activities are significantly affected by wind velocity, temperature, and humidity. Some of the recent reviews in the field of microclimate comfort are collated in Table 1 to initiate the discussions on a comprehensive perspective.

Problem-Solving Ideas.
Wind and heat environments have a composite influence on human comfort [15]. For the wind and heat comfort of traditional villages, there is not yet a clear definition of the boundaries, or a composite evaluation method, making it impossible to realize the optimization design of the public space. erefore, it is crucial to establish a composite evaluation strategy for the wind and heat comfort in the public space of traditional villages, considering the impacts from year-round climate, and static, and dynamic behaviors. e extension correlation function provides an innovative tool for developing such a strategy. e function can objectively quantify the degree for an element in the domain of discourse to have a certain attribute, and illustrate the quantitative change and qualitative change of these elements. Yang and Cai [25] developed multiple calculation methods for correlation functions. Among them, the standard domain, transition domain, and zero boundary are suitable for simulating the year-round climate, and the composite correlation function is very fit for evaluating wind and heat comfort comprehensively. erefore, this study presents an evaluation and optimization design strategy for microclimate comfort of traditional village squares based on extension correlation function, using field survey, computer simulation, and example analysis. e research comprehensively considers year-round climate simulation, comprehensive evaluation of wind and heat comfort, and dynamic and static behaviors, breaks through industry technology barriers, and extends the digital technology system of traditional villages. e remainder of this paper is mainly divided into methodology explanation, and case analysis. Methodology Potchter et al 2022 [21] • explanation describes the basic principles, detailed steps and precautions of measurement, simulation and optimal design of micro-climate comfort, in order to provide theoretical support for case analysis. Case analysis takes the Xieduqi square as an example to verify the effectiveness of the above methods more intuitively and concretely.

Methodology Explanation
e evaluation and optimization design for microclimate comfort of traditional village squares based on extension correlation function make full use of digital technologies like oblique photography, panoramic shooting, and information modeling, and generate the optimization design scheme for traditional village squares through the following steps: field measurement of wind and heat environments, simulation of wind and heat environments, preliminary design of microclimate comfort, and composite evaluation of microclimate comfort.
e proposed strategy consists of three modules: field measurement of wind and heat environments (Module 1), simulation of wind and heat environments (Module 2), and composite evaluation and optimization design of microclimate (Module 3). Module 1 measures the wind and heat environments in the space of the target square on the site with ultrasonic integrated weather stations. Module 2 configures simulation parameters, such as boundary conditions, wind environment, heat environment, and green plants, on PHOENICS, simulates the wind and heat environments in the space of the square, and tests the correlations between measured results and simulation results. Module 3 employs the extension correlation function to comprehensively evaluate the microclimate comfort of the preliminary design scheme and finalize the scheme through repeated adjustments ( Figure 1).

Measurement of Wind and Heat Environments
2.1.1. Measurement Time, Locations, and Instruments. In a traditional village, the square is a large, regular shaped, frequently used, and highly open venue, which provides an important space for villagers to carry out public activities and handle public affairs. e microclimate comfort of the square is mainly affected by wind direction, wind velocity, air temperature, relative humidity, and solar radiation [26,27]. To identify the problems of local microclimate, the field measurement of wind and heat environments should be performed on the typical weather days in winter and summer, when the wind is relatively heavy (greater than force 5), and the solar radiation is in place. e measurement locations should be selected by three principles. (1) e balanced distribution of wind velocity: the instruments should cover the typical space as uniformly as possible, and avoid spaces that are highly occluded or enclosed. (2) e diversity of people flows and activities: the instruments should cover as many static and dynamic behaviors in the public space as possible. (3) e reasonability of the number of instruments: the measuring points should be arranged based on the number of available instruments, and at least meet the basic needs of measurement.
Considering the slow velocity and changeable direction of wind in traditional villages, this study chooses an ultrasonic integrated weather station (RS-FSXCS-N01-1). Based on ultrasonic principles, the ultrasonic integrated weather station has no limit on the starting wind velocity, and supports 360°alldimensional measurement. Coupled with solar charging, the instrument can record weather data (e.g., temperature and wind velocity) in the long term. Table 2

Collection of Hourly Climate Data.
e climate data released by the state differ significantly from the actual climate parameters in the target village. e difference would severely suppress the simulation accuracy. is study places one ultrasonic integrated weather station at 1.5 m above the tallest building in the village, with no occlusions in the surroundings. e measurement at this point began at the same moment as the measuring points on the square. In recent years, outdoor activities, such as recreation, shopping, and cultural experience, have gradually increased on traditional village squares. During the measurement, we used a panoramic camera (Insta360 Pro 2) or another fisheye camera [16] to take photos or videos at each measuring point, which record the details about the space state and user behaviors.   synthesize an aerial model of the target traditional village ( Figure 3) [17]. In addition, the information model of the traditional village (.rvt format) was generated semiautomatically, using the Revit software and its Dynamo plug-in ( Figure 4). e numerical simulation was performed on PHOEN-ICS 2019, the first commercial software for computational fluid dynamics (CFD) and heat transfer. e FLAIR module of the software provides various turbulence models, multiphase flow models, multi-fluid models, combustion models, and radiation models. Users can load these programs and models by a little programming. In addition, the software supports parallel computing, and offers diverse postprocessing tools. It is very suitable for simulating rural planning and design.

Setting of Simulation Boundaries.
e square is connected to other spaces in the traditional village. If the simulation boundaries are too large, the computing load would be too high. Under the premise of ensuring analysis accuracy, the top priority in wind and heat environment simulation is to properly set the simulation range of the object. e range is not the boundary conditions of the computational domain. Normally, the simulation range is bounded by the tall buildings, streets, and alleys around the square. e streets and alleys can be properly extended until the paths bend and form an enclosed space.

Parameter Setting for Wind Environment.
According to the requirements of POLIS and COST, two help programs of PHOENICS, we separately determined the length, width, and height, turbulence model, radiation model, grid division, and convergence residual of the computational domain. Referring to the measured data over the village and the perennial data on Weather Spark, we further determined the local weather parameters. Drawing on the standard for green performance calculation of civil buildings (JGJ/T 449-2018), we determined the wind profile function and its values. In addition, the independence and rationality of the grid size was tested by gradually increasing the number and density of grids. e increase was terminated, when the calculation result did not change significantly anymore.

Parameter Setting for Heat Environment.
e simulation parameters of the heat environment were configured similarly as those of the wind environment. In addition, the material parameters of the underlying surface, emission and absorption coefficients of solar radiation, and direct and diffuse solar radiations were determined, according to the standard for green performance calculation of civil buildings (JGJ/T 449-2018), code for thermal design of the civil building (GB 50176-2016), and local specifications. e common data are detailed in Tables 3 and 4.

Parameter Setting for Green Plant Simulation.
Green plants, which are usually porous media, should be modeled separately in Revit or Rhino, and imported to PHOENICS for converting to the Foliage type. e leaf area index, i.e., the ratio of the total area of plant leaves to the unit land area, was determined based on the actual physical characteristics. e drag coefficient is usually 0.15∼0.25 for deciduous trees, 0.2 for forests, 0.5 for a single row of deciduous trees, and 0.6∼1.2 for coniferous trees. e turbulence medication was set to green. Table 5 presents the common plant parameters of traditional villages.

Correlation Test.
e Pearson correlation coefficient of the paired sample t-test is often adopted to measure the correlation between two variables. e value of the coefficient falls between −1 and 1. We corrected the parameters through the simulation of the village environment, and captured their values at an interval of 5 min. e simulation accuracy meets the requirement, only if the simulation value does not significantly vary from the measured value at any   [18]. Otherwise, at least one item in the simulation went wrong, and another round of simulation should be performed.    spatial optimization is the process of improving the comfort level of spatial nodes in the transitional domain from discomfortable to comfortable. In the field of Extenics, two intervals are often available to measure the satisfactoriness of the value of a feature in the domain of discourse U: the satisfactory interval χ 0 � 〈a 0 , b 0 〉, and the acceptable interval x � 〈a, b〉. It is clear that X X 0 .

Composite Evaluation and Optimization
When no transform is implemented, if the value of the object on a feature falls in the acceptable interval 〈a, b〉, then the object has a certain attribute. e degree for the object to have the attribute can be characterized by a real number in (0, +∞). Such objects constitute the positive domain in the extension set. On the contrary, if the value of the object on a feature falls outside the acceptable interval 〈a, b〉, then the object does not have the certain attribute. e degree for the object to lack the attribute can be characterized by a real number in (−∞, 0). Such objects constitute the negative domain in the extension set. If the value of the object on a feature is a or b, then the object is the zero boundary in the extension set. e satisfactory interval χ 0 � 〈a 0 , b 0 〉 is the standard positive domain, which corresponds to the comfort domain; the interval X + � 〈a, a 0 〉 ∪ 〈b 0 , b〉 is the transitional positive domain [25].
Similarly, the negative domain can be divided into a transitional negative domain, and a standard negative domain.
Let R denote the real number domain, and X − � 〈c, a〉 ∪ 〈b, d〉 denote the transitional negative domain. Suppose In this study, the transitional positive domain and the transitional negative domain of Extenics are combined into the transitional domain, which precisely corresponds to the transitional domain of microclimate comfort. Based on the perennial data on Weather Spark, we determined four critical weather parameters of village microclimate, namely, V cold(Winter⟶Spring) , V hot(Summer⟶Autumn) , V hot(Spring⟶ Summer), and V cold(Autumn⟶Winter) ( Figure 5). e weather parameters include wind velocity, wind speed, outdoor air temperature, relative humidity, soil temperature at −3.2 m, intensity of direct solar radiation, and intensity of diffuse solar radiation.

Preliminary Spatial Design.
Spatial design adjusts and optimizes the design elements of the traditional village square through addition, deletion, and replacement, aiming to formulate a new design scheme. e design elements belong to such types of points, lines, surfaces, and masses. Among them, points and lines have a negligible impact on the microclimate. As an important feature of design elements, the material has a major impact on the simulation of the heat environment. erefore, this study extracts, classifies, and grades the design elements in various excellent design cases similar to our project, considering the types of horizontal plane, vertical plane, mass, and material. In this way, a complete list of design elements was prepared for traditional village squares (Table 6).

Wind Comfort Indices and Evaluation.
Based on the influence of microclimate comfort on behaviors, the activities on the square are either static or dynamic. e static behaviors include sitting, chatting, and playing cards; the dynamic behaviors include recreation and sports activities, such as roller-skating, dancing, and working out. Considering the Beaufort wind comfort criteria, as well as the age and the activity type of different users in different seasons [19], this study takes 5 m/s as the maximum comfortable wind velocity, and defines the comfort level of different wind velocities: 0∼0.  (Table 7).

Heat Comfort Indices and Evaluation.
e UTCI, which comprehensively considers the spatiotemporal distribution of microclimate elements like wind, heat, humidity, and solar radiation, applies to the evaluation of the outdoor heat environment [20]. us, the study takes UTCI as the indicator of heat comfort [21]. e evaluation criteria are recorded in Table 8. e comfortable interval (no heat stress) is equivalent to the temperature range of 9°C∼26°C, and recorded as level 6. e temperature range of 0°C∼9°C is recorded as level 5. e rest can be obtained by analogy.

Composite Comfort Evaluation.
e wind and heat comfort was compositely evaluated by the composite correlation function. Let λ 1 , λ 2 , . . ., λ m be the weight coefficients Journal of Environmental and Public Health 7 of microclimate features c 1 , c 2 , . . ., c m , and satisfy m i�1 λ i � 1. e composite correlation [25] can be calculated by Before the calculation, all features must be normalized to the SME value range. en, the experts of urban-rural planning and architecture were invited to determine the weights of wind and heat comfort. Expert surveys found that for ordinary traditional villages, the weights of wind and heat

Generation of Final Design
Scheme. e preliminary design scheme was adjusted continuously according to the microclimate evaluation results. e scheme was viewed as the final design scheme, when the following condition was fulfilled: in the transitional domain, the microclimate comfort of the design scheme meets the requirements of all types of dynamic and static behaviors, and satisfies the physiological and psychological requirements of villagers and tourists; the modified design elements have practical functions and aesthetic beauty. As a key component of the village design, the final design scheme would contribute immensely to the future development of the village.

Case Analysis
e feasibility of our strategy was demonstrated with Xieduqi square, Zoumatang village, eastern China's Zhejiang Province as the example. Founded more than 1,000 years ago, the village is encircled by several rivers, making it a typical water town in the lower reaches of the Yangtze river. Over the history, 76 villagers received the title of Jinshi, the highest and final degree in the imperial examination in Imperial China. erefore, the village is hailed as the largest cradle of Jinshi in China, and recognized as the famous Chinese historical and cultural village, and Chinese traditional village. It is located at the center of the village, the Xieduqi square was originally an artificially excavated river channel. e square gets its name for the 30 m-long oval pier next to the river channel, which looks like the belly button of a crab (the literal meaning of Xieduqi). e square is surrounded by 1-2 story ancient buildings in the style of eastern Zhejiang. e main streets run from east to west. On the river bank lies a long pavilion for tourists and residents to rest temporarily ( Figure 6).
Step 1. Field measurement of wind and heat environments e wind and heat environments were measured from 9am to 5pm on December 25 th , 2020, using five ultrasonic integrated weather stations. One ultrasonic integrated weather station was placed at 1.5 m above the tallest building in the village, with no occlusions in the surroundings. e other four stations were, respectively, deployed inside the long pavilion, beneath the ancient tree, at the east entrance of the square, and at the west entrance of the square (Figures 7-9).
Step 2. Simulation of wind and heat environments Referring to the simulation method in Section 2.2, the wind and heat environments at each measuring point of the square were simulated based on the weather parameters on December 25 th , 2020. e simulation results are displayed in Figure 10 and Table 9.     Step 3. Comparison between simulation results and measured results Step 4. Perform composite evaluation and optimization design rough a year-round simulation of the Xieduqi square, it was learned that the wind velocity is small in summer due to the occlusion by the 1-2 story buildings on the south. In winter, the north wind is not effectively blocked, making it difficult to carry out static activities in the long pavilion. To solve these two problems, we provided a spatial optimization strategy for the square: (1) the village committee needs to buy back the two residential buildings on the south of the square, which are not inhabited for a long time and are inconsistent in style with the surroundings, at a reasonable price, and transform them into lawns; (2) a skylight needs to be opened on the top of the long pavilion, and provided with sun blinds that can be opened or closed at any time; (3) to block wind in winter, a transparent windscreen needs to be arranged on the northside in the long pavilion, which can be  opened or closed at any time; (4) a winter outdoor activity area needs to be designed to the north of the long pavilion, and provided with temporary furniture (Figure 11). e location and area of the skylight and windscreen will be adjusted constantly according to simulation results. None of these renovations affect the ancient buildings, historical landscapes, or related structures. All renovation measures target the newly built elements. e microclimate comfort of the renovation scheme was simulated and evaluated. Figures 12 and 13      at any measuring point was greater than 0.5, a sign of strong correlation. ere is no significant difference between the two sets of results (P > 0.05), i.e., the simulation is sufficiently accurate (Tables 10 and 11). velocity, wind comfort, UTCI, and composite comfort of the scheme, facing the critical weather condition V hot(Spring⟶ Summer) in the transitional domain from spring to summer. As shown in Figure 12, the additional lawns significantly accelerate the wind velocity on the square in summer. e wind moved faster than 1 m/s at any node in the key space for dynamic and static behaviors. e fast wind could carry away a huge amount of heat. Besides, these nodes had high wind comfort.
As shown in Figure 13, after continuous adjustments, the UTCI of any space in the square was smaller than 32°C, corresponding to the level of moderate heat stress. at is, the outdoor activities have a high heat comfort. For the main areas of the square, composite comfort was always above 1.5. e most comfortable state appeared inside and on the north of the long pavilion. Frequent recreation, entertainment, and ancient village experience activities can be arranged in these areas.

Conclusions
e evaluation and optimization design for microclimate comfort of traditional village squares based on extension correlation function make full use of digital technologies like oblique photography, panoramic shooting, and information modeling, and generate the optimization design scheme for traditional village squares through the following steps: field measurement of wind and heat environments, simulation of wind and heat environments, preliminary design of microclimate comfort, and composite evaluation of microclimate comfort.
(1) In order to realize year-round climate simulation, the four critical weather parameters of traditional villages in a certain area can be determined by using the "transition domain" in the extension correlation function and the weather data of the Weather Spark website over the years. ey were recorded as V cold(Winter⟶Spring) , V hot(Summer⟶Autumn) , V hot(Spring ⟶Summer), and V cold(Autumn⟶Winter) .
(2) A series of parameter values were determined in microclimate comfort simulation, including the length, width, and height of the calculation area, turbulence model, discretization equation, radiation model, grid division, convergence residual, solar absorption and radiation coefficient, plant leaf area index, and drag index. (3) Wind comfort (LAWS), with 5 m/s as the limit value, was divided into 10 levels, and established the corresponding relationship between wind speed and season, and user age and the activity type. According to −40°C, −27°C, −13°C, 0°C, 9°C, 26°C, 32°C, 38°C, and 46°C, heat comfort (UTCI) was divided into 10 levels, and the comfort zone (i e, no thermal stress) was from 9°C to 26°C. (4) A comprehensive evaluation method of microclimate comfort in traditional village was proposed, based on the comprehensive correlation function and the inform function of PHOENICS. Wind and heat comfort must be normalized to the SME value range, and their weights are both equal to 0.5. (5) A digital technology system for evaluating microclimate comfort in traditional villages has been established. e relevant software and hardware were drone (DJI Phantom 4 pro v2.0), DJI pilot, ContextCapture, Panoramic Camera (Insta360 Pro 2), Revit, Dynamo, Rhino, PHOENICS, and ultrasonic integrated weather station (RS-FSXCS-N01-1). e following work will be implemented in the future: (1) To determine the weight of wind and heat comfort for traditional villages with special comfort evaluation needs; (2) To explore methods for establishing traditional village information models more quickly, automatically, and in batches; (3) To expand to the method of microclimate comfort evaluation of traditional village streets, courtyards, and indoor spaces of public buildings.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.