Mathematical model for radiation energy from an urban surface penetrating the atmospheric infrared window

Solar Energy 171 (2018) 197–211

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Mathematical model for radiation energy from an urban surface penetrating the atmospheric infrared window

T

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Yongdong Zhanga, Lin Lina, Qing Luoa, Min Chenb, , Yong Dingc, Yafeng Gaoc, Wei Yuc a

Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment, Ministry of Education, Chongqing University, Chongqing 400045, China Chongqing University Cancer Hospital, Chongqing 400040, China c The Faculty of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400045, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Infrared energy Atmospheric infrared window Urban surface Urban thermal environment

This paper established a mathematical model to explore the characteristics of infrared energy of 8–14 μm emitted from an urban surface and analyzed the atmospheric transmittance under actual weather conditions. Then, the amount of infrared energy that penetrated the atmospheric infrared window was determined, based on the coupling analysis of urban radiation energy and atmospheric transmittance. Six typical urban surface materials were researched in this case study. The results showed that the transmittance was changed under different weather conditions and different urban surface materials had different infrared energy penetration of the atmospheric infrared window, which indicated different urban surface materials may have potentially different effects on the urban thermal environment. The results also indicated that the transmittance for different materials was affected not only by atmospheric transmittance but also by the distribution of emitted infrared energy along wavelengths, which provides a new perspective for related researchers to understand the phenomenon.

1. Introduction With China’s rapid economic growth, there is a growing population shift from rural areas to urban areas. In the past several decades, the urbanization process has undergone a notable development in China, with the current level of urbanization reaching 57.4% in 2016 (http:// www.stats.gov.cn/). As the rapid development of urban areas accelerates, the urban thermal environmental problem is becoming more serious. In early summer of 2017, Chongqing, Beijing, Shanghai and other major cities suffered from a serious heat wave, with the highest temperature in Chongqing reaching 41 °C, while most of the other big cities in China also suffered from the heat wave (http://www.tianqi. com/). Why did the urban thermal environment become so serious? How can we understand the change? What are the measurements for the change? First, an understanding of the urban thermal environment requires consideration of the complex relationships among various factors, such as urban morphology, land cover, moisture availability, surface materials, anthropogenic heat, air flow, etc. (Oke et al., 1991). Thus, with the rapid growth of population and urbanization, it is important that more sophisticated, realistic and comprehensive measures for the urban thermal environment need to be developed and applied (Tsitoura and Michailidou, 2016; Massetti and Petralli, 2014; Park and Tuller, 2014). In recent years, related measures included: vegetation

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Corresponding author. E-mail address: [email protected] (M. Chen).

https://doi.org/10.1016/j.solener.2018.06.084 Received 9 February 2018; Received in revised form 20 June 2018; Accepted 21 June 2018 0038-092X/ © 2018 Elsevier Ltd. All rights reserved.

plants (Song and Wang, 2015; Zheng and Zhao, 2016), water arrangements (Syafii and Ichinose, 2016; Theeuwes and Solcerova, 2013), urban layouts (Elmira and Priyadarsini, 2016; Sosa and Correa, 2017), urban ventilation (Ignatius and Wong, 2015; Lee and Wong, 2014), porous materials (Saneinejad, 2014; Van Belleghem, 2014), anthropogenic heat (Peter and Matthias, 2015; Koralegedara and Lin, 2016), and cooling materials (Federico and Beatrice, 2016; Alchapar and Correa, 2016). However, these measures have their own defects. For example, the vegetation plants and water arrangements are limited by the land used for urban development. Usually the land in a city is limited, and there is no more land available for vegetation and water arrangements. Urban ventilation is limited by the urban topography and weather conditions, and the urban layout also affects the effect of urban ventilation. Porous materials are limited by the distribution and the amounts of rainfall in different seasons throughout the entire year. The common feature of these measures is that heat transfer is constrained between the urban surface and the atmosphere or just amidst the atmosphere. For example, water, plants or porous materials absorb sensible heat and lowers the urban surface temperature, which merely changes its energy form from sensible heat into latent heat, so the amount of total heat energy still remains in the atmosphere. In the same way, urban ventilation also transfers energy from one location to another location and the amount of energy is not changed. Cooling

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material is another research field for further studies of an urban thermal environment, which mainly focus on the materials’ albedo. However, regardless of the types of cooling materials, any urban surface material will absorb solar energy and transform the solar energy into infrared radiation energy, convection energy, and evaporation latent energy. Among the three kinds of energy forms, some portion of infrared radiation energy has the ability to penetrate the atmosphere directly through the atmospheric infrared window. However, the study of cooling materials mainly focuses on the materials’ albedo, which cannot completely determine the energy returning directly to outer space. So, the current measures have some defects, which have led to the problem of a bottleneck for the control of urban thermal environments. New ideas should be explored to discover new ways to control this serious urban thermal environmental problem. The key issue is, how can we control the urban heat transfer directly between the urban surface and outer space, which is the most effective way to adjust the urban thermal environment? Transferring infrared radiation energy from an urban surface to outer space is the ideal way to resolve the problem. But, infrared energy emitted from an urban surface will be absorbed by the atmosphere. Fortunately, the atmosphere provides a window to allow the infrared energy to move into outer space directly, which is called the atmospheric infrared window within the waveband of 8–14 μm. This atmospheric infrared window provides us with a possibility to explore a new way to control the urban thermal environment. Infrared radiation plays an important role in the behavior of the thermal environment (Li et al., 2011; 2012). Infrared radiation heat transfer occurs during a full daily cycle and is the only infrared radiation heat transfer occurring during the night. A deeper understanding of infrared radiation is crucial for modeling the effect of infrared radiation on an urban thermal environment. However, the processes of infrared heat transfers between an urban surface and the atmosphere are complicated and different researchers have tried different ways to treat it. In the aspect of infrared energy emitted from an urban surface, many researchers have regarded the energy as an average value, neglecting the distribution of energy along the wavelength (Liu and Han, 2017; Aguerre et al., 2017). For the calculation of surface temperature, infrared radiation energy is regarded as an integrated part of the energy balance, which is a typical viewpoint for infrared energy as considered in an urban thermal environment (Wei and He, 2013; Nazarian and Kleissl, 2015; Wang and Akbari, 2014; Shui and Liu, 2016). But, when considering the effect of infrared energy on the atmosphere, the problem is more complex. Some researchers assume all the infrared energy has been absorbed by the atmosphere (Chen and Wang, 2017; Cortes and Murashita, 2015). Some papers disregard infrared energy when considering the air energy balance (Peng and Ming, 2015; Chen and Ooka, 2009). However, there is a defect in either assuming the amount of infrared energy has been totally absorbed, or totally disregarded, because it has its own thermal performance when it penetrates the atmosphere. Some researchers have considered the atmospheric transmittance (Coutts and Harris, 2016; Chen et al., 2011), but the atmospheric transmittance was regarded as a constant. In fact, the atmospheric transmittance changes with the atmospheric conditions, especially corresponding to the content of water vapor, CO2 etc. Some researchers studied how water vapor content, CO2 etc. affect atmospheric transmittance (Dai et al., 2016; Zevenhoven and Falt, 2018). However, there is no coupling analysis for urban surface radiation and atmospheric transmittance along the wavelength. Evidently, the infrared energy emitted from an urban surface is partially absorbed by the atmosphere and some parts of the infrared energy will directly penetrate the atmosphere through the atmospheric infrared window. Some researchers have researched the emissivity of an urban surface for infrared radiation, but the emissivity of an urban surface is also regarded as an integral value for the calculation of infrared energy (Wang and Liang, 2009; Yang and Wong, 2016). Actually, the emissivity is one of the key factors to determine the distribution of infrared energy emitted from an urban surface. The emissivity of different urban materials also

changes with the wavelength. Due to the fact that different urban surface materials have different thermal characteristics of infrared radiation, different infrared energy is emitted and correspondingly different energy is penetrated through the atmosphere, which gives us the possibility to explore the potential of different urban surface materials to control an urban thermal environment, combined with the study of cooling materials. When the atmosphere absorbs infrared energy, this energy within the atmosphere will affect an urban thermal environment through downward atmospheric radiation. If we can control the infrared energy that has penetrated the atmosphere through the atmospheric infrared window and the reflected energy, in some constant we can adjust the urban thermal environment at the macro level. So, if urban planners rationally use urban surface materials, considering the performance of infrared radiation penetrated the atmosphere through the atmospheric infrared window and the reflected energy, there is great potential to improve an urban thermal environment. While, the study of reflected energy and cooling materials have been extensively researched, as mentioned previously, in this paper, infrared radiation penetrating the atmosphere was the main point through the coupling analysis, both for emitted radiation energy and atmospheric transmittance, based on wavelength. According to the above analysis, the key point in the whole process is the difference of urban surface materials. For different surface materials, different infrared energy would penetrate the atmospheric infrared window directly to outer space, which is one of the important factors to influence an urban thermal environment. So, the material surface has become a potentially important method to control an urban thermal environment by controlling infrared radiation energy. But, to determine the detailed information required for this factor to affect an urban thermal environment, extensive research is needed on the effect of infrared energy penetrating the atmosphere for different urban materials. This paper includes the following three parts: (1) a mathematical model of coupling analysis, both for infrared energy emitted from an urban surface and transmittance to the atmosphere, which analyzed the entire process in theory for the infrared energy that has penetrated the atmosphere; (2) Field experiments that were carried out in a case study, in which all the parameters needed for the mathematical model were measured; (3) Comparative analyses for infrared energy that has penetrated the atmosphere for different urban surface materials, which indicated different potential abilities for controlling an urban thermal environment. Since the absorption of infrared energy in the atmosphere is mainly caused by water vapor and carbon dioxide etc, which are mainly distributed in the troposphere, and the downward atmospheric radiation to an urban thermal environment which is also constrained in the troposphere (Qiumin and Fang, 2014), the research scale of the atmosphere in this paper is limited to the troposphere. 2. Methodology 2.1. Description of the mathematical model The mathematical model includes sub-model (1) and sub-model (2). Sub-model (1) was mainly used to analyze the infrared energy emitted from an urban surface. The basic principle for sub-model (1) is that under the same weather conditions, the different materials used for an urban surface have different surface temperatures, which are caused by the material’s thermal performance and each surface material has its own emissivity spectrum, which shows its performance of infrared radiation. Combining the factors of surface temperature and emissivity, different surface materials will emit different infrared energy within the atmospheric infrared window. The basic principle for sub-model (2) is that because the atmosphere has a selective absorption in the waveband of the atmospheric infrared window, some of the infrared energy emitted from an urban surface can penetrate the atmosphere directly to outer space. But, the penetrating process is related to the distribution of 198

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Different materials of urban surface Infrared energy emitted from urban surface

Surface temperature

Urban thermal environment control Atmospheric transmittance

Material’s emissivity

Sub-model (1)

Infrared energy

H2O, CO2, etc al

Atmospheric infrared window

Sub-model (2) Troposphere

Infrared energy penetrated atmosphere

Outer space

Fig. 1. Diagram of the mathematical model.

water vapor and carbon dioxide along the altitude in the atmosphere. Thus, this sub-model is used to determine the distribution of water vapor and carbon dioxide along the altitude and finally to determine the transmittance under actual atmospheric conditions. The diagram for the structure of the mathematical model is presented in Fig. 1.

ΔE = Δλ·Eλ = ελ·

When calculating the infrared energy for each wavelength gap, all the infrared energy from 814 μm was totaled, then the total infrared energy could be represented by formula (4):

In sub-model (1), the amount of infrared energy emitted from an urban surface within the 8–14 μm was analyzed. The amount of infrared energy emitted from an urban surface was determined both by emissivity and urban surface temperature. Because the value of emissivity is different at different wavelengths for certain materials, the amount of infrared energy needed to be integrated within 8 ∼ 14 μm aried. This sub-model completed the calculation for the integrated amount of infrared energy within 8–14 μm. According to Plank’s law, μm the energy emitted from a black body for a specific wavelength is determined by:

c1 λ−5 c e 2/(λTs)−1

E=

∑ ΔE

(4)

E - total infrared energy within 8–14 μm emitted from an urban surface, W/m2. According to the above analysis, when the information of surface temperature Ts and emissivity ελ was known, the total infrared energy within 8–14 μm could be determined. The detailed information of Ts and ελ will be discussed in Section 3.

(1) 2.3. Sub-model (2) for atmospheric transmittance

Ebλ - emissive power of a black body below a specific wavelength, W/ (m2 μm). λ - wavelength, μm. Ts -surface temperature, K . c1, c2 -are the constants, c1 = 3.747 × 108 , c2 = 1.439 × 10 4 .

Atmospheric transmittance is related to the distribution of water vapor, carbon dioxide, et al. Water vapor and carbon dioxide are considered the two main factors in determining the transmittance, so the two factors were used to determine the transmittance. Due to the nonuniformity of water vapor and carbon dioxide in the atmosphere, the content is higher at lower levels. As the altitude increases, the content of water vapor and carbon dioxide rapidly decreases. In this paper, according to tropospheric characteristics, the troposphere is divided into different layers with equal measurements of 200 m. So, the height of each layer is: 200 m, 400 m, 600 m······2200 m and the total number of layers is 11. Fig. 2 presents the sketch for the divided layers. The total height of the troposphere considered in this paper is approximately 13.2 km.

So the infrared energy for a specific wavelength emitted from an urban surface is determined by:

Eλ = ελ·Ebλ = ελ·

(3)

ΔE - the infrared energy within one wavelength gap, W/m2 . Δλ - the wavelength gap, Δλ = 0.1 μm.

2.2. Sub-model (1) for infrared energy emitted within 8–14 μm

Ebλ =

c1 λ−5 ·Δλ e c2/(λTs)−1

c1 λ−5 e c2/(λTs)−1

(2)

Eλ - emissive power of an urban surface below a specific wavelength, W/(m2 μm). ελ - emissivity of an urban surface below a specific wavelength.

(1) Determining the transmittance for the factor of water vapor

To calculate the total infrared energy within the waveband of 8–14 μm, the curve of emissivity was dissolved based on the discrete method and the wavelength gap of 0.1 μm was used in this paper, then the infrared energy within one wavelength gap could be expressed by:

The density of water vapor along the height in the atmosphere can be expressed by Zhang (2013): 199

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ρib - density of water vapor at the bottom of layer i , g/m3. ρit - density of water vapor at the top of layer i , g/m3.

Layer 11 (2200 m)

……

The vertical height of layer hi will be revised based on the pressure change and different distance for different direction (Weiwu, 2004),

p xHi = 1.66hi ⎛⎜ i ⎞⎟ p ⎝ 0⎠

Layer 3 (600 m)

xHi - the revised height for water vapor of layer i , m. hi - the vertical height of layer i , m. p0 - the atmospheric pressure at sea level, pa pi - the atmospheric pressure for layer i , pa

Layer 2 (400 m) Layer 1 (200 m)

W = ρi ·xHi

Fig. 2. Drawing of the divided layers.

ρ (h) = ρ0 ·e−h / h1·

0.5

T0 T (h)

(9)

W - the water vapor column in layer i , mm. W is defined as the integration of atmospheric water vapor mass.

(5)

According to the value of water vapor column W, the transmittance τλi·H2 O for each wavelength in each layer can be determined through the database from Zhang (2013). When the transmittance of each layer is obtained, the total transmittance for the atmosphere can be calculated:

h1- constant, 1/ h1 ≈ 0.45; h - height from sea level, m; ρ (h) - density of water vapor at height h , g/m3; ρ0 - density of water vapor at sea level, g/m3; T0 - air temperature at sea level, K; T (h) - air temperature at height h , K;

n

τλ·H2 O =

∏ τλi·H2 O

(10)

i=1

In the troposphere, the change of air temperature is linear with the height (Chen et al., 2011), so, the air temperature at different height can be expressed by:

T (h) = T0−α·h 0 ⩽ h < h1

(6)

T (h) = T0−α·h1−β (h−h1) h1 ⩽ h < h2

(7)

τλ·H2 O - the total transmittance for the factor of water vapor for a certain wavelength; τλi·H2 O - the transmittance of a certain wavelength for the factor of water vapor in layer i ; n - the number of layers divided for the troposphere, n = 11; (2) Determining the transmittance for the factor of carbon dioxide

α = −0.0065 K/m ; β = −0.0019 K/m ; h1 = 10000 m ; h2 = 20000 m ; The average density of water vapor for each layer is determined by:

ρi =

The atmospheric pressure at different heights can be expressed by Horst (2004):

ρib + ρit (8)

2

p = p0 [1−(0.0065h)/288]5.225

ρi - average density of water vapor for layer i , g/m3;

Soil

Sandstone

(11)

Use the following formula to calculate the pressure for each layer:

Brick

Marble Fig. 3. Typical materials used in the case study. 200

Asphalt pavement

White tile

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Fig. 4. Surface temperatures for the typical materials on the 13th of September 2016.

Fig. 5. Emissivity of the typical materials for 8–14 μm.

pi =

pib + pit

of τλi·CO2 , the following formula is used to determine the total transmittance:

(12)

2

n

pib - the atmospheric pressure at the bottom of a layer i , pa pit - the atmospheric pressure at the top of a layer i , pa .

τλ·CO2 =

i=1

To determine the transmittance for the factor of carbon dioxide, the parameter x Ci was introduced here (Weiwu, 2004):

x Ci = 1.66hi (

pi 1.5 ) p0

∏ τλi·CO2

(14)

τλ·CO2 - the total transmittance for the factor of C2 O for a certain wavelength; τλi·CO2 - the transmittance for the factor of C2 O of layer i for a certain wavelength;

(13)

x Ci - the revised height of carbon dioxide for a layer i , m.

When the τλ·H2 O and τλ·CO2 were determined, the following formula is used to calculate the total transmittance considering both the water vapor and carbon dioxide:

When the parameter x Ci was determined, the transmittance τλi·CO2 for a certain wavelength of carbon dioxide of a layer i can be obtained according to database from Zhang (2013). Based on the transmittance

τλ = τλ·H2 O·τλ·CO2 201

(15)

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8:00, 13 September

0:00, 13 September

20:00, 13 September

16:00, 13 September

Fig. 6. Emitted energy (ΔE ) from typical materials.

8–14 μm, W/m2.

Table 1 Total emitted energy for the typical times (W/m2). Time

0:00 4:00 8:00 12:00 16:00 20:00

Material

2.4. Experimental process

Soil

Brick

Asphalt pavement

Sandstone

Marble

White tile

139.95 137.42 144.85 205.55 190.36 145.75

159.97 154.10 153.98 197.37 200.10 163.62

170.37 161.42 160.44 212.79 219.27 171.89

156.89 150.00 150.34 187.62 189.42 158.31

145.10 139.56 140.74 174.40 177.06 147.53

138.94 135.12 133.24 165.11 167.63 141.74

Based on the previous description of the mathematical model in theory, the final goal is to assess the differences of infrared energy emitted from different urban material surfaces that penetrated the atmospheric window. So the parameters needed in the mathematical model should be known. These parameters include: surface temperature, material’s emissivity (Tang and Qijiang, 2005), atmospheric pressure, air temperature, and water vapor density, etc. The goal of the experiment was to provide parameters needed for the mathematical model. A case study was used to explain the mathematical model in this paper. The data chosen for the experiment was from 0:00 13 Sep to 23:00 13 Sep 2016 and the time interval was one hour. We chose one summer day’s experimental data to demonstrate the mathematical model. The data from the experiment was only to show the function of the mathematical model and the paper was mainly focused on the methodology of the coupling analysis for urban emitted energy and atmospheric transmittance. So, the data for one day was chosen. Based on the mathematical model in the paper, the cases for monthly, seasonal situation, etc. could also be analyzed, but this is not the goal of the paper. In this experiment, six typical urban materials were used (Fig. 3) and the measuring location was in the Shapingba District of Chongqing, one of the municipalities in China. The instruments used in the experiment included: (1) Temperature and humidity instrument

τλ - atmospheric transmittance; According to the infrared energy emitted from an urban surface ΔE discussed in sub-model (1), and combined with the transmittance analyzed above, the amount of infrared energy penetrating the atmosphere can be determined by:

ΔEt = τλ·ΔE

(16)

∑ ΔEt

(17)

Et =

ΔEt - infrared energy that penetrated atmosphere for one waveband gap, W/m2. Et - infrared energy that penetrated the atmosphere for waveband 202

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Fig. 7. Total emitted infrared energy for 8–14 μm at different times on the 13th of September 2016.

Fig. 8. Distribution of air temperature and water vapor density on the 13th of September 2016.

(Type: S-THB-M002); Measuring range: −40–75 °C (for air temperature), 0–100% (for air humidity); Precision: ± 0.2 °C (for air temperature), ± 2.5%(for air humidity). (2) Wind velocity instrument (Type: SWSET-B); Measuring range: 0–76 m/s; Precision: ± 4%. (3) Solar radiation instrument (Type: S-LIB-M003); Measuring range: 0–1280 W/ m2; Precision: ± 10 W/m2. (4) Atmospheric pressure instrument (Type: S-BPB-CM50); Measuring range: 66–107 kPa; Precision: ± 0.3 kPa.

corresponding solar radiation are shown in Fig. 4. The solar radiation is a typical distribution during September in Chongqing, which showed the radiation intensity was still strong. Due to the different thermal performances of urban materials, the temperature changes were different. The asphalt pavement was affected greatly by the solar radiation and its temperature was much higher than that of another materials. The asphalt’s highest temperature was 48.8 °C, and the temperature change range was 28.0–48.8 °C. The white tile was affected much less by the solar radiation and its temperature was relatively stable. The maximum temperature of white tile was 36.9 °C, and the temperature change range was 22.6–36.9 °C. The temperature change of soil was not very stable at noon. The temperature change of brick, sandstone and marble was located midway between the asphalt pavement and the

3. Result and discussion 3.1. Infrared energy emitted from an urban surface in 8–14 μm The urban surface temperature for the typical materials and the 203

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Fig. 9. Water vapor density for the different layers at typical times on the 13th of September 2016.

Fig. 10. Air temperature for the different layers at typical times on the 13th of September 2016.

Based on the urban surface temperatures, emissivity and sub-model (1), the infrared energy emitted from an urban surface can be determined. The emitted infrared energy was analyzed from hour to hour. Fig. 6 shows the results for typical times. From Fig. 6, the distribution of infrared energy changes along the wavelength at different times was similar, which was determined by the emissivity, wavelength and surface temperatures. The infrared energy emitted by both asphalt pavement and brick was very close to the energy emitted by a blackbody as the emissivity was very close to that of a blackbody, nearly to 1. The infrared energy at a wavelength of 9–10 μm had low value for marble, which corresponded to the same low value in its emissivity. From Fig. 6 (0:00), the average energy for each 0.1 μm of soil, brick, asphalt pavement, sandstone, marble and white tile were 2.33, 2.67, 2.84, 2.61, 2.42, 2.32 W/m2. The biggest value was 22.41% more than the smallest value. When the time was 16:00, the average energy for each 0.1 μm of the six surfaces was 3.12, 3.28, 3.59, 3.11, 2.90 and 2.75 W/m2. The biggest value was 30.55% more than the

white tile and their temperatures were relatively close. The rank of average temperatures for the typical materials was: asphalt pavement (35.0 °C), brick (31.7 °C), sandstone (30.9 °C), marble (30.3 °C), soil (28.2 °C), white tile (28.2 °C). The temperatures of the different materials were the key factors affecting infrared energy emission. The emissivity of the six surfaces for 8–14 μm is showed in Fig. 5. According to the distribution of emissivity, the differences of emissivity for the six typical surfaces for 8.5–11.5 μm were great and the differences for 8–8.5 μm and 11.5–14 μm were not so great. The emissivity of brick and asphalt pavement was stable and the brick was 0.932–0.984 and the asphalt pavement was 0.965–0.978. The emissivity of soil and sandstone had evident changes from 8–14 μm, whose emissivities were 0.856–0.999 and 0.888–0.978 respectively. The emissivity of marble and white tile had the greatest changes from 8–14 μm, and the emissivities of marble and white tile were 0.438–0.998 and 0.749–0.988 respectively. All the analyses above showed the emissivity had significant impact within the wavelength. 204

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Fig. 11. Atmospheric pressure distribution at different times near an urban surface on the 13th of September 2016.

Fig. 12. Atmospheric pressure distribution at different layers (20:00) on the 13th of September 2016.

between the asphalt pavement and the white tile values. Fig. 7 presents the total infrared energy from 8–14 μm for the six materials at the different times. The trend of the emitted energy was the same. In the daytime the emitted energy was much greater than the energy in the nighttime, plus there was the difference for the six materials, which had similar trends analysed in Table 1

smallest value. The infrared energy at 16:00 from the same materials were 33.91%, 22.85%, 26.41%, 19.16%, 19.83%, 18.53% more than that of 0:00 for the corresponding six materials, since the effect of solar radiation, the value of infrared energy from the urban surface at 0:00 was much smaller than that at 16:00. The energy distribution was the integral effect of the related factors of emissivity, wavelength and surface temperatures. For the six surfaces under actual atmospheric conditions, the emitted energy is was highest at 16:00 and the rank for the typical time was: 16:00, 20:00, 0:00 and 8:00 for all the materials except for soil. Table 1 is the total infrared energy from 8–14 μm at the typical time for the six materials. The difference of value at 0:00, 8:00 and 20:00 was not so great, but the value at 16:00 was much greater than others, which was closely related to the surface temperatures. The value of asphalt pavement was highest at the four times, and the value of white tile was lowest at the four times. The other four material values were

3.2. Atmospheric transmittance under actual atmospheric conditions This paper measured surface temperature, air temperature, water vapor density, atmospheric pressure, etc. as parameters used in the submodel (2) from 0:00 13th Sep to 23:00 13th Sep. Fig. 8 presents the distribution of air temperature and water vapor density, which shows the air temperature and water vapor density was at a high level in the daytime as the solar radiation and evaporation was strong. Fig. 9 presents the water vapor density for the different layers at typical times, 205

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Fig. 13. The curves of a water vapor column at different times on the 13th of September 2016.

Fig. 14. The changing curves of atmospheric transmittance within 8–14 μm the 13th of September 2016.

Fig. 14 presents the changes for atmospheric transmittance under actual weather conditions during the measuring period. From Fig. 14, the change trend of transmittance at different times was the same. In the waveband of 8–9 μm, the atmospheric transmittance was increasing, which was from around 5% to 45%. In the waveband of 9–11 μm, the atmospheric transmittance was relatively stable, which remained around 55%. In the waveband of 11.8–12.8 μm, there was a peak for the transmittance, which was from around 50%. In the waveband of 13.4–14 μm, the atmospheric transmittance was converging close to zero and not changing with the atmospheric conditions. The reason for the change trend was that water vapor and CO2 have absorption features for infrared energy at different wavelengths. For some wavebands, the absorption is high and for some it is low. As the CO2 is relative stable in the atmosphere, the change is mainly caused by the change in water vapor content, which means more water vapor equals less atmospheric

which changed with actual atmospheric conditions and the change was the key factor for the change in atmospheric transmittance. Fig. 10 presents the air temperature change for the different layers at typical times, which also affected the atmospheric transmittance. Fig. 11 presents the atmospheric pressure distribution at different times near an urban surface, which affected the distribution of water vapor and carbon dioxide. Fig. 12 presents the atmospheric pressure distribution at different layers (at 20:00), which also was one of the parameters to affect the transmittance. According to the above measured parameters, a water vapor column for the experimental period can be determined. Fig. 13 presents the distribution of a water vapor column at different times, which directly determined the transmittance of water vapor. According to sub-model (2) and combined with the measured parameters above, the atmospheric transmittance can be determined. 206

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Fig. 15. Average atmospheric transmittance for 8–14 μm on the 13th of September 2016.

0:00, 13 September

8:00, 13 September

16:00, 13 September

20:00, 13 September

Fig. 16. Infrared energy (ΔEt ) penetrating the atmosphere at typical times.

207

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Table 2 is the total penetrated energy for the typical times (W/m2). Time

0:00 4:00 8:00 12:00 16:00 20:00

Table 4 The difference of penetrated energy compared to white tile and its ratio. W/m2

Material Soil

Brick

Asphalt pavement

Sandstone

Marble

White tile

52.80 47.07 49.64 63.85 62.38 45.82

60.56 52.92 52.88 61.35 65.69 51.55

64.54 55.44 55.10 66.14 71.99 54.15

59.30 51.43 51.55 58.24 62.07 49.81

53.44 46.52 46.92 52.50 56.39 45.03

51.68 45.55 44.91 50.31 53.98 43.80

Table 3 Distribution of penetrated energy (W/m2) with same length of waveband (μm). Time

Waveband

0:00

16:00

Brick

Asphalt pavement

Sandstone

Marble

White tile

8.0–9.0 9.0–10.0 10.0–11.0 11.0–12.0 12.0–13.0 13.0–14.0

6.64 10.37 13.27 11.60 9.10 1.83

8.09 12.65 15.05 12.74 9.97 2.05

8.89 13.61 15.97 13.51 10.43 2.14

7.77 12.10 14.75 12.68 9.97 2.04

8.34 9.00 12.10 12.19 9.77 2.05

7.35 9.74 12.29 11.23 9.18 1.89

8.0–9.0 9.0–10.0 10.0–11.0 11.0–12.0 12.0–13.0 13.0–14.0

7.83 12.70 16.02 13.42 10.40 2.00

8.61 14.10 16.68 13.62 10.59 2.09

9.77 15.64 18.20 14.82 11.35 2.23

7.91 12.97 15.77 13.12 10.27 2.02

8.61 9.75 13.08 12.75 10.16 2.04

7.47 10.44 13.14 11.61 9.45 1.87

Brick

Asphalt

Sandstone

Marble

White tile

0:00

Difference Ratio1 (%)

1.12 2.17

8.88 17.17

12.85 24.87

7.62 14.74

1.75 3.40

0 0

8:00

Difference Ratio1 (%)

4.73 10.54

7.97 17.75

10.19 22.70

6.64 14.79

2.01 4.47

0 0

16:00

Difference Ratio1 (%)

8.40 15.57

11.71 21.70

18.02 33.38

8.09 14.99

2.41 4.47

0 0

20:00

Difference Ratio1 (%)

2.02 4.61

7.76 17.71

10.35 23.64

6.01 13.72

1.24 02.83

0 0

Table 5 The difference of total penetrated energy compared to white tile in a whole day.

Material Soil

Soil

Materials

Soil

Brick

Asphalt

Sandstone

Marble

White tile

Difference (KJ) Ratio1 (%)

373.25 9.11

729.85 17.81

1019.57 24.88

560.41 13.67

118.78 2.90

0 0

8–14 μm, which shows the night and morning times of 0:00–8:00 is the best time for infrared energy to penetrate the atmosphere. But, the daytime, as the water vapor is increasing, is not the best time to penetrate the atmosphere. All the changes of transmittance are dependent upon the atmospheric conditions, mainly the distribution of water vapor, while the carbon dioxide was considered to be relatively stable. These results provide us with a key to better understand infrared energy from urban surfaces to penetrate the atmosphere at different times.

3.3. Infrared energy penetrating the atmosphere

transmittance. From Fig. 14, the transmittance at 0:00 was the highest, and the lowest was at 12:00. The average transmittance at 0:00, 4:00, 8:00, 12:00, 16:00 and 20:00 from 8–14 μm was 36.85%, 33.29%, 33.43%, 30.18%, 32.40% and 30.64%. According to the distribution of the transmittance, if the energy emitted from the surface materials is greater in the high region of transmittance, it means more energy is being released to outer space. Fig. 15 presents the average atmospheric transmittance within

In the previous sections, infrared energy emitted from urban surfaces and the atmospheric transmittance under actual weather conditions was determined. In this section, infrared energy penetrating the atmosphere was analyzed. To briefly analyze the problem, typical times were chosen. Fig. 16 presents infrared energy penetrating along the wavelength. From Fig. 16, the change trend of penetrated energy was the same, which was similar to the change trend of transmittance. The

Fig. 17. Distribution of total penetrated energy at the different times. 208

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Fig. 18. Total emitted energy, penetrated energy and their ratio.

listed in Table 5. The biggest difference for total penetrated energy of 1019.57 KJ and the highest ratio 1 can reach 24.88%. The total energy emitted by an urban surface and the total energy penetrated for the experimental period are shown in Fig. 18. E represents the total energy emitted by an urban surface; Et represents the total energy penetrating the atmosphere. Et / E represents the ratio of energy penetrated to total emitted energy. The penetrated energy changed with time and was determined by the factors of energy emitted and the atmospheric transmittance. Based on the data in Fig. 18, the ratio of Et / E was different, and the ratio (%) for soil, brick, asphalt pavement, sandstone, marble and white tile was 33.04, 33.17, 33.16, 33.13, 32.19 and 32.57. The ratio value here represents the transmittance for certain materials, which was determined both by the distribution of emitted energy and atmospheric transmittance. So, the transmittance for certain materials was not only determined by atmospheric transmittance but was also related to the distribution of emitted energy. To explain this phenomenon, transmittance for different materials at different times are listed in Table 6. This indicates the results showing that at the same time the transmittance for different materials was different, which is also under the condition of the same atmospheric transmittance. The reason for this problem is the emitted energy was changed with the wavelength based on Fig. 6. For a certain material at different times, the transmittance for a material was also changed, which was caused by both atmospheric transmittance and a changed distribution of emitted energy at different times. Evidently, the data in Table 6 was affected by the distribution of emitted energy along with the wavelength. So, the transmittance for the materials was not determined only by the atmospheric transmittance. This was the important discovery in this paper. However, the penetrated energy can be determined only by the atmospheric transmittance under the condition that the emitted energy from all kinds of material is assumed to be even distribution. Under this assumption, the emitted energy is changed into a horizontal line. Of course, the total amount remains the same. Fig. 19 presents the horizontal distribution of emitted energy under the condition of the same total emitted energy, which means there was no change along the wavelength. Transmittance for different materials under horizontal distribution was the same, which was only determined by the atmospheric transmittance. Under this situation, the transmittance had nothing to do with the material itself. The transmittance for materials determined only by the atmosphere is listed in Table 7. The comparison of Table 6 and Table 7 shows the difference for the transmittance. The research results show that transmittance for

Table 6 The transmittance (%) for different materials for typical times. Time

0:00 8:00 16:00 20:00

Material Soil

Brick

Asphalt pavement

Sandstone

Marble

White tile

37.73 34.27 32.77 31.44

37.86 34.34 32.83 31.51

37.88 34.35 32.83 31.51

37.80 34.29 32.77 31.46

36.83 33.33 31.85 30.53

37.20 33.71 32.20 30.90

penetrated energy for asphalt pavement was the highest. Table 2 is the total penetrated energy for the typical times, which is determined by the emitted energy and atmospheric transmittance. The transmitted energy at 16:00 was the highest, although the transmittance at this time was not the highest. The rank of penetrated energy for the typical times was: 16:00, 0:00, 8:00, and 20:00. Table 3 is the distribution of penetrated energy with the same length of waveband for 0:00 and 16:00, which shows the penetrated energy was much different under the condition of the same length of waveband. The result indicates that urban materials chosen should consider the distribution of penetrated energy. If emitted energy is more focused on the waveband of high atmospheric transmittance, more infrared energy will be released to outer space under the condition of the same amount of emitted energy. Fig. 17 presents the distribution of total energy penetrated at different times. Comparing penetrated energy to emitted energy (see Fig. 6), the trends of the two kinds of energy are different. As the penetrated energy is associated with not only the emitted energy, but the atmospheric transmittance, which has its own distribution performance. According to Fig. 17, at around 0:00, there is the highest transmittance, although the emitted energy is relatively low, a relatively high amount of penetrated energy can also be obtained. In the daytime, although the atmospheric transmittance is relative low, the emitted energy is much higher, so is the corresponding high penetrated energy. In order to show the differences of penetrated energy, Table 4 lists the different amounts compared to white tile, which is the lowest value for penetrated energy. There are differences, both for the time and the category of materials. Ratio 1 is defined as follows:

Ratio 1 = (other material−white tile)/white tile The difference of penetrated energy of materials for the whole day is 209

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0:00, 13 September

8:00, 13 September

16:00, 13 September

20:00, 13 September

Fig. 19. Horizontal distribution of emitted energy.

deviation for the penetrated energy. Deviation is defined as:

Table 7 Transmittance for material under the horizontal distribution of emitted energy. Time

0:00

4:00

8:00

16:00

20:00

Transmittance

36.85

33.29

33.43

32.40

30.64

Deviation = (Ep1−Ep2)/Ep1 Ep1– penetrated energy considered atmospheric transmittance and distribution of emitted energy (W/m2); Ep2– penetrated energy only considering atmospheric transmittance (W/m2); Table 8 represents the penetrated energy only considering the atmosphere transmittance, which is used in many other references. The deviation in Table 8 indicates that when the distribution of emitted energy is more uneven, the deviation is bigger based on Fig. 6. So the deviation of marble and white tile is relative small, and the other four is much bigger based on the above analysis.

Table 8 Penetrated energy only considered atmospheric transmittance and its deviation (%). Time

Material

Soil

Brick

Asphalt pavement

Sandstone

Marble

White tile

0:00

Ep2 Deviation

51.57 2.35

58.94 2.67

62.77 2.73

57.81 2.52

53.46 0.05

51.20 0.94

8:00

Ep2 Deviation

48.42 2.46

51.47 2.67

53.63 2.70

50.25 2.52

47.04 0.27

44.54 0.83

4. Conclusions

16:00

Ep2 Deviation

61.67 1.14

64.83 1.32

71.03 1.33

61.36 1.14

57.36 1.72

54.30 0.60

20:00

Ep2 Deviation

44.66 2.54

50.13 2.75

52.66 2.74

48.50 2.62

45.20 0.38

43.43 0.85

The paper established a mathematical model to explore the characteristics of infrared energy of 8–14 μm emitted from the urban surface and determined atmospheric transmittance under the actual weather conditions. Then, the amount of infrared energy that penetrated the atmospheric infrared window was determined. Six typical urban surface materials were studied in the case study. The results showed that different urban surface materials had different amounts of infrared energy penetrating the atmospheric infrared window, which indicated the

materials was also affected by the materials themselves. Then, there is the difference between the two transmittances, which shows the 210

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different urban surface materials had different effects on an urban thermal environment when considering the factor of infrared energy. The results also indicated that if urban planners rationally used urban surface materials and considered the performance of infrared energy penetrating the atmosphere through the atmospheric infrared window, there may be potential to control the urban thermal environment. This is a new concept, which needs more researchers to give their attention to in the future. The main conclusions are as following:

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(1) The transmittance for different materials in this paper indicates that the transmittance was not only determined by the atmosphere but also by the distribution of emitted energy. If the distribution of emitted energy was more uneven, the deviation was greater, which provides a new concept for researchers in the field. The distribution of emitted energy was affected by surface temperature and emissivity. Only under the assumption the emitted energy was horizontal distribution, then the transmittance for materials was determined only by atmospheric transmittance. (2) The method of coupling analysis, both for emitted radiation energy and atmospheric transmittance based on wavelength, was established and the penetrated energy through the atmospheric infrared window was determined. The calculating mothod of penetrated energy is an excellent supplement for the further study of reflected energy or cooling materials, which mainly focuses on the matetrials’ albedo. (3) Since the distribution of emitted energy is uneven, under the condition of the same amount of emitted energy, materials that have a greater distribution of energy within the wavelength with higher atmospehric transmittance should be priority considerations, which means these materials will release more energy directly to outer space. The distribution of emitted energy within the wavelength can be analyzed through the mathematical model in this paper. Acknowledgements The authors would like to thank the National Natural Science Foundation of China (51578086; 51178481; 5151101134); Chongqing Fundamental and Advanced Research Projects (CSTC2014jcyjA90018) and the National Key Research and Development Program of China (2016YFC0700705) for their financial support, without which this research paper would not have been possible. References Alchapar, Noelia L., Correa, Erica N., 2016. The use of reflective materials as a strategy for urban cooling in an arid“OASIS” city. Sustain. Cities Soc. 27, 1–14. Aguerre, J.P., Fernández, E., Besuievsky, G., 2017. Computing urban radiation: A sparse matrix approach. Grap. Models 91, 1–11. Peter, Boehmea, Matthias, Bergerb, 2015. Estimating the building based energy consumption as an anthropogenic contribution to urban heat islands. Sustain. Cities Soc. 19, 373–384. Van Belleghem, M., 2014. Validation of a coupled heat, vapour and liquid moisture transport model for porous materials implemented in CFD. Build. Environ. 81, 340–353. Chen, Jiaqi, Wang, Hao, 2017. Analytical approach for evaluating temperature field of thermal modified asphalt pavement and urban heat island effect. Appl. Therm. Eng. 113, 739–748. Chen, X., Wei, H., Yang, P., et al., 2011. An efficient method for computing atmospheric radiances in clear-sky and cloudy conditions. J. Quant. Spectrosc. Rad. Transf. 112, 109–118. Hong, Chen, Ooka, Ryozo, 2009. Study on mitigation measures for outdoor thermal environment on present urban blocks in Tokyo using coupled simulation. Build. Environ. 44, 2290–2299. Coutts, Andrew M., Harris, Richard J., 2016. Thermal infrared remote sensing of urban heat:Hotspots, vegetation, and an assessment of techniques for use in urban planning. Remote Sens. Environ. 186, 637–651. Cortes, Aiza, Murashita, Yuji, 2015. Numerical evaluation of the effect of photovoltaic cell installation on urban thermal environment. Sustain. Cities Soc. 19, 250–258.

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