Comparative study of sol-air temperature models in the tropical island based on measured data

. The sol-air temperature is a hypothetical parameter to reflect the outdoor multi-field coupled thermal environments of air temperature, solar radiation, and long-wave radiation. The simplified model was proposed in code for thermal design of China which ignores the influence of long-wave radiation of sky and surrounding environment. However, the climate is characterized by strong radiation, high temperature and high humidity in tropical islands, and the underlying surface types are mostly sea surface. This may affect the applicability of sol-air temperature models. To explore the above issues, the Davis weather station and Kipp & Zonen solar radiation observation system were used to gather the meteorological and radiation data around the building, which is a case study building near the coastline in Sanya. Also, the dynamic temperature of the external surface of envelope and sea surface was captured. Then, the weather types were classified by clearness index, and the influence of sky and sea surface radiation on the sol-air temperature calculation of each orientation in different sky conditions is analysed. The results show that the sol-air temperature decreased by 1.07-2.44 ℃ on average considering the long-wave radiation of the sky and sea surface, especially in clear sky, with an average decrease of 1.49-3.85 ℃.


Introduction
The sol-air temperature represents the comprehensive heat effect of outdoor solar radiation heat gain, air convection and long-wave radiation heat transfer on the external surface of the envelope. In general, the sol-air temperature calculation has been simplified in different forms to facilitate engineering applications. Chen [1] proposed that the sol-air temperature is equal to the sum of the weighted average of the equivalent solar radiation temperature and outdoor air temperature, the surrounding structure surface temperature and underlying surface temperature, and the sky long-wave radiation temperature. This method is clear in its physical meaning with high calculation accuracy, but the application in building thermal design is less due to the complexity of the formula and input parameters. In Chartered Institution of Building Services Engineers (CIBSE) Guide [2], the empirical formula with independent variables solar radiation, outdoor air temperature, long-wave radiation heat exchange between the external surface of the envelope and the surrounding environment and outdoor wind speed, etc was proposed. In literature [3], the solair temperature model proposed by the former Soviet Union based on local climate characteristics is continued to be applied, which mainly distinguishes the long-wave radiation heat transfer between the surrounding environment and the external surface of the envelope, and between the sky and the external surface * Corresponding author: yinkailii@163.com of the envelope. To simplify the implementation, a further simplified sol-air temperature model was proposed in Code for Thermal Design of Civil Building GB 50176-2016 [4] of China (Code 2016), which mainly considers solar radiation heat gain and air convection heat transfer, ignoring the role of the longwave radiation heat effect of the sky and surrounding environment.
The long-wave radiation heat transfer intensity between the sky and the external surface of the envelope is mainly dominated by local climate, while the intensity between the surrounding environment and the external surface of the envelope is mainly related to the surrounding construction materials. China spans a wide range of latitudes with diverse climate types. As a result, the applicability of the simplified model of sol-air temperature proposed by Code 2016 may change significantly in different regions of China. Based on the observation results of microclimate related parameters on the external surface of an experimental building in Beijing, Lin [5] discussed the influence of solar radiation, long-wave radiation and convective heat transfer on the temperature distribution of the external wall surface, and showed that the long-wave radiation and convective heat transfer were the main reasons for the difference in the temperature of the external surface of wall. Chen [6] took Turpan as the representative city of dry hot and dry cold areas, and selected Xi 'an, Lhasa and Shanghai as the comparison. The influence factor of sky long-wave radiation was imported in the simplified sol-air temperature model, and the results showed that the influence of sky radiation value in Turpan and Lhasa should not be ignored. Yin [7] took a low-latitude island in China as a case study, the total heat transfer coefficient between the outdoor environment and the external surface of the building was modified based on the local climate characteristics, and further obtained the values of the sol-air temperature on the horizontal and vertical surfaces.
The climate in tropical islands is usually characterized by strong radiation, high temperature and high humidity, and the underlying surface type in offshore areas is mainly sea surface. The influence of unique climate characteristics and environment on solair temperature calculation remains to be explored. Therefore, based on the theoretical analysis of the solair temperature calculation model, combined with the measured data in Sanya, we calculated the sol-air temperature with the long-wave radiation factors in the sky and sea surface respectively. Furthermore, the simplified model of Code 2016 and the model considering long-wave radiation heat transfer are compared and analysed. It contributes to improve the accuracy of sol-air temperature in tropical islands.

Experimental apparatus
For analysing the influence of the surrounding environment on the sol-air temperature calculation in the tropical islands, meteorological data and radiation data observation stations were installed near the coastline in Sanya Bay (18.29°N, 109.37°E). In addition, the temperature of the sea surface and the external surface of the target building was monitored, and the observation location and field arrangement are shown in Fig. 1. The radiation data in each vertical orientation were collected by the Kipp & Zonen solar radiation observation station, and the meteorological data were collected by the Davis portable weather station. The temperature data were measured by a high-precision infrared thermometer (testo 845) on the sea surface and the external surface of the case building envelope and recorded manually. The case building selected in this study is close to the coastline and about 100 meters away from the observation stations. The building envelope is wood structure, and the temperature measurement points were located at the central points of the nonpermeable envelope on each observation. The average values of 3 measurements at the same point were taken as the final recording results. The complete records of 5 measuring points on the sea surface and south-facing, north-facing, east-facing and west-facing external surfaces of the building were recorded as a group, and the period of each group was controlled within 5 minutes. The measured height of radiation is about 2 m, and the performance parameters of each instrument are shown in Table 1

Data collection
Data measurement information is shown in Table 2. "√" indicates that data is recorded successfully, and "-" indicates that no data is recorded. Both meteorological and radiation data are automatically recorded by the data collector at hourly time resolution. The surface temperature data were manually measured and recorded. Due to the changeable weather and the complicated night conditions near the coastline, some temperature data at night are recorded once within every two hours. The measurement results are shown in Fig. 2, where the symbols are consistent with Table 1. On May 24, the sky conditions were clear, and on May 25, it was rainy and cloudy. The figure shows a gentle variation in sea surface temperature, between 20.8 ℃ and 31.2 ℃, which is mainly due to the larger heat capacity of water compared to the underlying surface commonly found inland. In addition, the temperature of the sea surface is usually lower than that of external surface of the building during the day and not much different during the night. Generally, the direction of heat radiation transfer is from the external surface of the building to the sea surface, which indicates that the long-wave radiation heat exchange from above has a cooling effect on the building.

Theory of heat balance on external surface of envelope
The definition of sol-air temperature is derived from the heat balance theory of the external surface of the building envelope, and the theoretical expression is shown in Eq. 1.
Where q w is the heat quantity transferred from the external surface of the wall to the internal surface, in W. t sa is the sol-air temperature, t a is the outdoor air temperature, t v is the temperature of the external surface of the building envelope, all in ℃. α w is the total heat transfer coefficient of the external surface of the envelope, in W/m 2 ·K. ρ is the solar radiation absorption rate of the external surface of the envelope. I v is the total solar radiation on the vertical surface, including direct radiation, diffuse radiation and underlying surface reflected radiation, in W/m 2 . σ is Stefan-Boltzmann constant, equal to 5.67×10 -8 W/m 2 ·K 4 . ε os is the systematical emissivity between the external surface of the envelope and the sky. Due to the area of the sky is much larger than the area of the envelope, it can be considered that ε os is equal to ε o , and ε o is the emissivity of the external surface of the envelope. In this case, the envelope of the building is a wooden structure, so the ε o is about 0.9, that is, the ε os is 0.9. ε oi is the systematical emissivity between the external surface of the envelope and the surface of the surrounding structure i, which is approximately considered that ε oi = ε o ·ε i . Where X os is the radiation angle factor of the external surface of the envelope facing the sky, which is 0.5 for vertical surface. X oi is the radiation angle factor of the external surface of the envelope facing the surface of the surrounding structure i. Where T v , T sky and T i are the thermodynamic temperatures of the external surface of the envelope, the sky and the surface of the structure i around the building, respectively, and all in K.

General expression
According to Section 3.1.1, a general expression for the sol-air temperature can be computed. As shown in Eq. 2, it is assumed that there are no structures around the building except the underlying surface.
Where q s and q r are the long-wave radiation heat transfer between the sky and the external surface of the wall, and between the underlying surface and the external surface of the wall respectively, in W. Eq. 3 is a simplified solair temperature model proposed in Code 2016, which ignores the influence of q s and q r .

Sky long-wave radiation
According to Eq.1, the precondition for calculating the long-wave radiation heat transfer between the sky and the external surface is to determine the sky effective temperature and the external surface temperature. The temperature of external surface of the wall is provided by the measured data, and the sky effective temperature is usually determined by the empirical formula.
Eq.4 is a widely used method for calculating the sky effective temperature, derived from the radiation and heat balance between the air near the ground and the atmosphere.
T sky = ε air (1/4) T a (4) Where ε air is the emissivity of air near the ground, which is usually calculated by the dew point temperature, as shown in Eq.5. T a is the outdoor thermodynamic air temperature, in K.

Sea surface long-wave radiation
The long-wave radiation heat transfer between the sea surface and the external surface of the building is calculated as shown in Eq.6 q r = σε or X or [(T sea 4 -T v 4 )] (6) According to the definition of ε or , it is necessary to determine the emissivity of the sea surface first.The emissivity of the water surface with a thickness greater than 0.1 mm is 0.96 in the temperature range of 0~100 ℃. Then, ε or = 0.81. Where X or is the radiation angle factor of the external surface of the wall facing the sea surface, and 0.5 is taken for the vertical wall.

Results
Based on the theoretical analysis of the sol-air temperature model and the statistical processing of the measured data, the sol-air temperature values on each orientation were calculated by different relational expression. Fig. 3 shows the comparison of the calculation results of the simplified model of Code 2016 (M0), the model with sky long-wave radiation (M0 & sky), the model with sea long-wave radiation (M0 & sea) and the model with both sky and sea long-wave radiation (M0 & sky & sea). It indicates that the calculation of the sol-air temperature including the long-wave radiation of the sky and sea surface, the results show a decrease trend in Sanya in May. That is, the long-wave radiation heat transfer in the sky and sea has a certain cooling effect on the building during the day. Moreover, the influence of sea surface on sol-air temperature is more significant than that of the sky. For the south-facing orientation, the average result of M0 is 35. 05   In order to further explore the variation of sol-air temperature at different sky conditions, the weather types based on the sample data were first classified by the clearness index, and then the results of sol-air temperature at different sky conditions were analyzed and compared. The clearness index is the ratio of the global solar radiation to the extraterrestrial radiation on a horizontal surface, which reflects the clear condition of the sky. The classification rules are shown in Table 3. The distribution of the calculated results of each sol-air temperature model at different weather types is illustrated in Fig. 4. It shows that the sol-air temperature decreases with the decrease of clearness index. For the

Conclusions
In this paper, meteorological and radiation data are collected and integrated in Sanya. Taking a wooden building near the coastline as a case study, the temperature data of the external surfaces and sea surface were measured and collected. Based on the above measured data and theoretical analysis, the difference between the calculated results of each sol-air temperature model was compared. Furthermore, the weather types were divided by clearness index, and the performance of these models at different weather types was analyzed and compared. The main conclusions are as follows: 1 The measured data indicate that the daily variation fluctuation of sea surface temperature in tropical islands is relatively low, ranging from 20.8 ℃ to 31.2℃. Meanwhile, the long-wave radiation of sea surface has obvious cooling effect on the building surface in daytime.
2 It is suggesting that the sky and sea long-wave radiation factors should be applied to the sol-air temperature model in tropical islands. 3 The performance of each sol-air temperature model in different weather types is different. On clear sky conditions, long-wave radiation from the sky and sea surface has the most significant influence on sol-air temperature calculation, which is recommended not to be ignored. The sol-air temperature decreased by 1.49-3.85 ℃ on average considering the long-wave radiation of the sky and sea surface in clear sky.