Abstract

Previous research studies focused only on data of local air temperature and humidity, ignoring the water body itself, which cannot definitively answer the question of how the Three Gorges Reservoir's (TGR) water affects the local climate overall. To understand the effect of the TGR on the local climate quantitatively, this paper provides an original mathematical hypothesis and proves in theory there is only one way to calculate the transfer of heat and humidity between the TGR and the local air. Based on this mathematical hypothesis, a detailed research method to explore the effects of the TGR's heat and humidity on local climate was formed. A field investigation was conducted and a research site was selected in Chongqing. This study has determined the effects of the TGR's heating or cooling on the air during the measuring period. A mathematical model to assess the effects of heat and humidity from the TGR on local climate was set up. The final results based on the mathematical model show that the average air temperature decreased 0.67 K and the average moisture content increased 0.25 g/kg during the 24 hours measuring time for the area studied.

INTRODUCTION

The Three Gorges Project (TGP) on the Yangtze River is the world's largest hydroelectric power project. By 2010, when the TGP became fully operational, the water storage capacity of the Three Gorges Reservoir (TGR) was 3.93 × 1010 m3 with a normal pool level of 175 m, about 4.5% of the Yangtze's annual discharge (Xu & Milliman 2009). After water collected within the TGR, there was a significant increase in the water surface due to the effect of backwater, leading to a decrease in water flow speed in the reservoir (Yu 2011). Since the TGR began filling with water, some environmental consequences emerged, capturing the attention of researchers and environmental activists around the world. Contentious environmental issues surrounding the TGP have centered on water quality (Hu et al. 2014; Yue &Yuan 2016), fish population (Yi & Yang 2010; Wang & Bi 2016), sedimentation and downstream riverbed erosion (Jia & Shao 2010; Yang & Milliman 2014), geological instability (Peng & Niu 2014; Wang & Chen 2014), carrying capacity of the environment in the reservoir area (Li & Zhang 2016; Wu & Wang 2016) and the situation of the local climate.

After water collected, as a typical river way reservoir, the TGR has an influence on the local climate. The TGR's effect on the local climate has attracted the interest of international scholars (Dai 2008; Chen & Zhang 2009a,2009b). Many comparative analyses and regional climate models have been discussed (Wu et al. 2006). Zhang et al. (2004) simulated the impact of the TGR on the local climate by using a simplified model, and the results showed the influence of the TGR on the climate was limited to 10 km. Gao et al. (2003, 2007) analyzed the changes in land use and land cover that influenced local and regional climates and said such effects could be studied with regional climate models. More specifically, by using the Penn State/NCAR MM5, Miller et al. (2005) conducted multiple layered experiments down to 10 km resolution for 8 weeks duration to simulate the effects of the TGR. The results showed that as a potential evaporating surface, the TGR could cool the surrounding area. Wu et al. (2006) used the regional climate model to simulate the effects of the TGR on the climate of the surrounding areas. The results showed the width and coverage of the TGR did not have significant influence on the local climate, except for cooling over the TGR water body in both June–August (summer) and December–February (winter). However, Sun & Qin (2002) analyzed the climatic features in the Three Gorges dam area. The results showed that warmer winter temperatures in the area were evident. It also suggested the warmer winter temperatures could possibly have some relationship with the water storage of the TGR. Yang & Chen (2002) used meteorological data from five local weather stations to study the climate characteristics in the Three Gorges dam area. The results also showed there were warmer winter temperatures in the dam area. Chen & Zhang (2009a, 2009b) used the temperature observation data of 33 weather stations in the TGR area during the period from 1961 to 2006 to analyze the climate characteristics of temperature changes since the water storage of the TGR began. The results showed that the expanding water surface area of the reservoir seemed to have an effect of increasing temperature during the winter and an effect of decreasing temperature during the summer.

Due to the short time after the complete filling of the TGR (filling to 175 m normal pool mark) in 2010 and the limited availability of monitoring data, there may possibly be some discrepancies in research results for local climate data. Moreover, the cross-effects of ground, vegetation, buildings, and the possible impact of the TGR on the local climate made it difficult to distinguish the impact of the TGR itself (Xu & Tan 2013). Due to the complexity of the problem, different scholars have different opinions about the local climate effects of the TGR. Through the analysis of the references, it can be concluded that previous research studies only focused on air temperature and humidity changes, ignoring the water body itself. This raised the difficult question of why no one could, with certainty, distinguish the TGR water body's effect on the local climate from an integrated effect, because the TGR is only one of many factors effecting local climate. Based on the above analysis, this paper provides an original mathematical hypothesis and a detailed research methodology based on the hypothesis to explore the effects of the TGR's heat and humidity on the local climate.

MATHEMATICAL HYPOTHESIS FOR THE EFFECTS OF TGR'S HEAT AND HUMIDITY ON THE AIR

This paper provides the mathematical hypothesis named ‘sheep counting’, and uses the solution of the mathematical hypothesis to answer the question mentioned above, which is to distinguish the TGR water's effect on the local climate from the integrated effect with certainty. The mathematical hypothesis has proved in theory that there is only one way to analyze the effect of heat and humidity from the TGR on the local climate. The detailed description of the mathematical hypothesis is shown in Figure 1.

Figure 1

Diagram of the mathematical hypothesis of ‘sheep counting’.

Figure 1

Diagram of the mathematical hypothesis of ‘sheep counting’.

Description of the mathematical hypothesis

  • 1.

    There are an infinite number of sheep on the grassland , the sheep on the grassland are located outside of the sheepfolds.

  • 2.

    There are multiple sheepfolds, and there are an infinite number of sheep in each sheepfold , n is the number of sheepfolds.

  • 3.

    The sheep on the grassland and in the sheepfolds are identical and there are no individual differences.

  • 4.

    Each sheepfold has only one gate. All the sheep in or out of the sheepfold must go through the gate, and the number of sheep in or out of the sheepfold is unknown .

Question

In a cycle of 24 hours, what is the effect of a given sheepfold on the numerical change of sheep on the grassland?

Solutions

Step (1): Obviously, it is not reasonable to consider the numerical change of sheep on the grassland itself, because the number of sheep on the grassland is infinite , and it is impossible to know the base of the infinite number, and it is impossible to know the infinite number after a change, so it is impossible to determine the numerical change by considering the sheep change on the grassland. In addition, the numerical change of sheep on the grassland is not only from one given sheepfold , but also from other sheepfolds, and the number of sheep in or out of each sheepfold is unknown (, , is the given number among ), therefore it is impossible to solve the mathematical hypothesis by considering the numerical change of sheep on the grassland itself.

Step (2): It is not feasible to consider the numerical change of sheep from a given sheepfold, because the number of sheep in a given sheepfold is also infinite (, is the given number among ), and the reason why it cannot be solved is the same as step (1).

Step (3): Finally, the only solution of the mathematical hypothesis is the number of sheep in or out of the given sheepfold (, is the given number among ). If the number is determined, the mathematical hypothesis can be solved, and is the only and final solution for the mathematical hypothesis.

In the mathematical hypothesis of ‘sheep counting’, the sheep on the grassland represent the heat or humidity in the local air; the sheep in the sheepfolds represent the heat or humidity from ground, vegetation, buildings, the TGR's water, etc., which affect the local climate. The sheep in or out of sheepfold through the gate represents the heat or humidity transfer between the local air and ground, vegetation, buildings, the TGR's water, etc.

The mathematical hypothesis has proved in theory there is only one way to analyze the effects of heat and humidity from the TGR on the local climate for the first time. The heat and humidity of the local air (sheep on the grassland) are influenced by various factors (sheep in or out of the sheepfolds), such as ground, vegetation, the TGR's water, and buildings, etc. Therefore, according to the above theoretical analysis, if we want to quantitatively analyze the effects of heat and humidity from the TGR's water on the local air, we must take the TGR's ‘water–air’ interface (gate of the sheepfold) as the research object, and analyze the quantity of heat and humidity in or out of the ‘water–air’ interface hour by hour (sheep in or out of the sheepfold through the gate), and then calculate the sum of heat and humidity for a 24-hour cycle. Finally, we can determine the quantitative data of heat and humidity and make the conclusions of cooling or heating, drying or wetting effects of the TGR's water on the local climate.

RESEARCH METHOD

Heat and moisture transfer on the interface of ‘water–air’

Heat transfer between water and air includes sensible heat and latent heat, which are caused by temperature differences and moisture pressure differences respectively. Figure 2 depicts the heat and moisture transfers between the TGR's water and local air. The sensible heat is mainly determined by the temperature difference of water surface and local air, and latent heat mainly depends on the differences of water surface saturated vapor pressure and vapor pressure in the air. The sensible heat is directly related to water and air temperature. Moisture transfer is an important source of changing air humidity.

Figure 2

Diagram of heat and moisture transfer between the TGR's water and local air.

Figure 2

Diagram of heat and moisture transfer between the TGR's water and local air.

In addition to the exchange of sensible heat and latent heat between the TGR's water and local air, the process of energy exchange on the ‘water–air’ interface also includes the long-wave radiation between the TGR's water and the local atmosphere. The diagram of each part of the energy is shown in Figure 3.

Figure 3

Diagram of energy exchange on the ‘water–air’ interface.

Figure 3

Diagram of energy exchange on the ‘water–air’ interface.

The total heat flux of ‘water–air’ interface can be expressed by heat flux from water to air and from the air to water . The net heat flux is : 
formula
(1)
 
formula
(2)
 
formula
(3)
when is from water to the air, it is positive, otherwise negative. When H is from air to water, it is positive, otherwise negative. Through the comparison of and , the effects of cooling or heating can be precisely determined. When , the TGR's water has a heating effect on the local air; when , the TGR's water has a cooling effect on the local air. So, if , it means the net heat flux is from the air to water. If , it means the net heat flux is from water to air. The specific items are explained as follows: 
formula
(4)
is the long-wave radiation from the atmosphere that is projected to the water surface W/m2 (Weng & Sun 1993); is the air temperature, K; e is the vapor pressure, ; n if it is sunny, ; if it is cloudy, ; is the reflected long-wave radiation from the water surface, , W/m2; is the reflection coefficient of the water surface: 
formula
(5)
where is the long-wave radiation of the water surface, W/m2; is the long-wave emissivity; is the Stefan–Boltzmann constant; is the water surface temperature, K.
The sensible heat , latent heat and moisture transfer between the TGR's water and the local air can be calculated by bulk method (Kondo 1992): 
formula
(6)
 
formula
(7)
 
formula
(8)
where H is the sensible heat flux of ‘water–air’ interface, W/m2; E is the moisture flux of ‘water–air’ interface, g/(m2.s); is the latent heat flux of ‘water–air’ interface, W/m2; is air density, kg/m3 (Zhao 2008); is air specific heat, J/kg.°C; is wind speed, m/s; , are bulk parameters for sensible heat and latent heat: 
formula
(9)
where l is latent heat, , kJ/kg (Hannah et al. 2004); is saturated moisture content under the condition of temperature , g/kg (Lian 2006); is moisture content over the water surface, g/kg, which can be calculated by the following formula: 
formula
(10)
 
formula
(11)
where is saturated moisture pressure under the condition of temperature , ; is air relative humidity, %; p is moisture pressure, ; is local atmospheric pressure, (www.weather.com.cn/).

FIELD MEASUREMENTS

Measuring area selection

The measuring area was selected in Chongqing, one of the municipalities governed by the Chinese central government, which is located in the upper region of the TGR (see Figure 4). The measuring area chosen is relatively open and flat to reduce the influence of the nearby topography. Because the measurement of heat and moisture transfer on ‘water–air’ interface is a complex process, it is influenced by the factors of long-wave radiation, water temperature, air temperature, air vapor, and wind speed over the water, etc.

Figure 4

Points for measuring the effects of heat and humidity from the TGR.

Figure 4

Points for measuring the effects of heat and humidity from the TGR.

Measurement process

The measurements were carried out on 22–23 June 2015. To analyze the effects of heating or cooling, drying or wetting of the TGR's water on the local air, the measuring period needed to be at least 24 hours, which is the shortest possible measuring cycle. For the measurement in this paper, the corresponding measuring cycle was 24 hours and the time interval for the measurements was 1 hour. The measured parameters included: water temperature, solar radiation, air temperature, air relative humidity and wind speed, etc. The local atmospheric pressure was obtained from the Central Weather Bureau. By utilizing the above mathematical hypothesis and research method, the sensible heat, latent heat, long-wave radiation and moisture transfer between the TGR's water and the local air could be analyzed. The instruments used in the field measurements included an infrared radiation thermometer, an environmental supervision instrument, a GPS apparatus, etc. The type of infrared radiation thermometer was a MS6530, which is used to measure water temperature, with a measurement range of −32–535 °C, an accuracy of ±0.5% and a response time of 0.5 second. The type of environmental supervision instrument was a KANOMAX6531. The instrument was used to measure air temperature, relative humidity, and wind speed. For air temperature, the measurement range is −20–70 °C, and the accuracy is ±0.5 °C. For relative humidity, the measurement range is 2–98%, and the accuracy is ±2%. For wind speed, the measurement range is 0.01–30 m/s, and the accuracy is ±2%. The type of GPS apparatus is a N600, which was used to record the altitude at different locations.

RESULTS AND DISCUSSION

Effects of heat and humidity on the ‘water–air’ interface

The measuring period was 24 consecutive hours on 22–23 June 2015. Figure 5 shows the flux curve of sensible heat and latent heat. The transfer direction of heat flux was different during the entire measuring period. The sensible heat flux is always from air to water. However, the latent heat flux can be from water to air or from air to water depending on time. If the entire heat flux during the measuring cycle were totaled, the results would provide the exchange of sensible heat flux on the ‘water–air’ interface. The data for sensible heat flux was 403 KJ/m2.d and the data for latent heat flux was 81 KJ/m2.d. According to the previous definition of transfer direction, the transfer direction of sensible heat and latent heat were opposite. Through the comparison of sensible heat and latent heat, the heat transfer direction was from water to air during the measuring period and the sum data of heat flux was 322 KJ/m2.d.

Figure 5

The curves of sensible heat flux and latent heat flux.

Figure 5

The curves of sensible heat flux and latent heat flux.

Figure 6 shows the curves of long-wave radiation. It can be concluded that the fluctuation of long-wave radiation emitted from the water surface was small, which is related to the stable characteristics of the water temperature. The range of long-wave radiation emitted from the water surface was 444.6–453 W/m2, with the largest gap of 8.4 W/m2, with a mean value of 447.3 W/m2. The range of long-wave radiation from the atmosphere was 456.4–500.3 W/m2, with the largest gap of 43.8 W/m2, with a mean value of 473.9 W/m2.

Figure 6

The curves of long-wave radiations.

Figure 6

The curves of long-wave radiations.

Considering the sensible heat, latent heat and long-wave radiation, the final heat transfer can be analyzed on the ‘water–air’ interface. Figure 7 shows the curves of the final heat flux from water to air and the final heat flux from air to water on the ‘water–air’ interface. From the curves of final heat flux during this measuring cycle, the range of was 328.7–349.8 W/m2 with a mean value of 337.3 W/m2; and the range of was 424.8–472.6 W/m2 with a mean value of 445.6 W/m2. In this paper, the shortest cycle of 24 hours was used as the measuring cycle, so the sum of heat flux in the 24 hour cycle was the final net heat flux: 
formula
 
formula
 
formula
Figure 7

The curves of heat flux on the ‘water–air’ interface.

Figure 7

The curves of heat flux on the ‘water–air’ interface.

Therefore, the conclusion reached was the final heat flux from water to air was smaller than that from air to water during this 24 hour cycle, which means the TGR's water had a cooling effect on the air.

Similarly, it was necessary to analyze the moisture transfer, which occurred on the ‘water–air’ interface. From Figure 8, we found the moisture content of saturated air near the water surface crossed with the moisture content in the air , which means the moisture transfer can be from water to air and also can be from air to water. The range of was 22.9–25.2 g/Kg with a mean value of 23.7 g/Kg. The range of was 21.74–25.11 g/Kg with a mean value of 23.36 g/Kg. The range of moisture transfer was 0.374–9.88 g/m2 · h with a mean value of 1.42 g/m2 · h. By analyzing the above, the conclusion was that the moisture transfer direction was from water to the air during this measuring cycle. In other words, the TGR's water had a wetting effect on the local air and the final quantity of moisture transfer was: ΣD = 34 g/m2 · d.

Figure 8

The curves of the moisture transfer.

Figure 8

The curves of the moisture transfer.

From the data of heat and moisture flux on the ‘water–air’ interface, this paper, for the first time, distinguished the TGR's effect on the local climate from the integrated effect with certainty.

Assessment of heat and humidity from the TGR on local climate

Heat and moisture transfer for selected local area

Through the previous field investigation, the effects of heat and humidity were known, but how is the change of the local air temperature and moisture content measured in quantity? In order to assess the effects of heat and humidity from the TGR on local climate, the areas affected by the TGR should be ascertained. As the effects of heat and humidity from the TGR on the local area are limited, so the area affected by the TGR is also constrained. In this paper, the local area was selected with a width of 2.5 km from the edge of the TGR and a height of 3 km (Figure 9) (Xu 2003; Li 2008; Liu 2010). The total horizontal area for the selected area is 229.8 km2.

Figure 9

Selected local area along the TGR.

Figure 9

Selected local area along the TGR.

Within the selected local area, the water surface area of the TGR needed to be known. As the form of the water surface of the TGR is not uniform, the different sections were measured, and the total area was determined from the sum of all the sections. Through measuring the TGR's width and the length in each section, the total water surface area of the TGR was obtained (Figure 10). The red points in Figure 10 were the measuring points for each section. All the surface area measurements were carried out at the same time corresponding to the measurement of heat and humidity. The total water surface area was calculated to be 18.3 km2.

Figure 10

Water surface area of the TGR for the different sections. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/wcc.2018.067.

Figure 10

Water surface area of the TGR for the different sections. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/wcc.2018.067.

Based on the previous investigation of heat and moisture transfer from the ‘water–air’ surface, the total effects of heat and moisture from the TGR on the local area can be calculated (Table 1).

Table 1

Total heat and moisture transfer for the selected local area

TimeHeat transfer (KJ/m2.h)Moisture transfer (g/m2.h)Total heat transfer (KJ/ h)Total moisture transfer (Kg/ h)
10:00–11:00 26.44 3.73 4.84 × 108 ↓ 6.84 × 104 ↑ 
11:00–12:00 37.67 0.48 6.90 × 108 ↓ 8.82 × 103 ↑ 
12:00–13:00 40.16 6.67 7.36 × 108 ↓ 1.22 × 105 ↑ 
13:00–14:00 30.93 12.86 5.67 × 108 ↓ 2.36 × 105 ↑ 
14:00–15:00 74.08 9.52 1.34 × 109 ↓ 1.74 × 105 ↑ 
15:00–16:00 86.85 6.18 1.59 × 109 ↓ 1.13 × 104 ↓ 
16:00–17:00 83.72 1.76 1.53 × 109 ↓ 3.22 × 104 ↓ 
17:00–18:00 84.91 1.86 1.56 × 109 ↓ 3.40 × 104 ↓ 
18:00–19:00 52.06 1.58 9.54 × 108 ↓ 2.89 × 104 ↑ 
19:00–20:00 38.95 5.26 7.14 × 108 ↓ 9.64 × 104 ↑ 
20:00–21:00 67.35 1.18 1.23 × 109 ↓ 2.17 × 104 ↓ 
21:00–22:00 56.19 2.38 1.03 × 109 ↓ 4.37 × 104 ↓ 
22:00–23:00 31.45 9.39 5.76 × 108 ↓ 1.72 × 105 ↑ 
23:00–00:00 28.41 2.13 5.20 × 108 ↓ 3.91 × 104 ↑ 
00:00–1:00 34.41 2.21 6.30 × 108 ↓ 4.06 × 104 ↓ 
1:00–2:00 18.71 1.83 3.43 × 108 ↓ 3.35 × 104 ↑ 
2:00–3:00 25.26 0.37 4.63 × 108 ↓ 6.85 × 103 ↓ 
3:00–4:00 20.80 0.78 3.81 × 108 ↓ 1.43 × 104 ↑ 
4:00–5:00 21.75 0.20 3.98 × 108 ↓ 3.58 × 103 ↓ 
5:00–6:00 17.12 0.67 3.14 × 108 ↓ 1.23 × 104 ↑ 
6:00–7:00 7.17 4.42 1.31 × 108 ↓ 8.11 × 104 ↑ 
7:00–8:00 15.87 1.40 2.91 × 108 ↓ 2.57 × 104 ↑ 
8:00–9:00 25.03 0.78 4.59 × 108 ↓ 1.42 × 104 ↓ 
9:00–10:00 60.42 9.88 1.11 × 109 ↓ 1.81 × 105 ↓ 
TimeHeat transfer (KJ/m2.h)Moisture transfer (g/m2.h)Total heat transfer (KJ/ h)Total moisture transfer (Kg/ h)
10:00–11:00 26.44 3.73 4.84 × 108 ↓ 6.84 × 104 ↑ 
11:00–12:00 37.67 0.48 6.90 × 108 ↓ 8.82 × 103 ↑ 
12:00–13:00 40.16 6.67 7.36 × 108 ↓ 1.22 × 105 ↑ 
13:00–14:00 30.93 12.86 5.67 × 108 ↓ 2.36 × 105 ↑ 
14:00–15:00 74.08 9.52 1.34 × 109 ↓ 1.74 × 105 ↑ 
15:00–16:00 86.85 6.18 1.59 × 109 ↓ 1.13 × 104 ↓ 
16:00–17:00 83.72 1.76 1.53 × 109 ↓ 3.22 × 104 ↓ 
17:00–18:00 84.91 1.86 1.56 × 109 ↓ 3.40 × 104 ↓ 
18:00–19:00 52.06 1.58 9.54 × 108 ↓ 2.89 × 104 ↑ 
19:00–20:00 38.95 5.26 7.14 × 108 ↓ 9.64 × 104 ↑ 
20:00–21:00 67.35 1.18 1.23 × 109 ↓ 2.17 × 104 ↓ 
21:00–22:00 56.19 2.38 1.03 × 109 ↓ 4.37 × 104 ↓ 
22:00–23:00 31.45 9.39 5.76 × 108 ↓ 1.72 × 105 ↑ 
23:00–00:00 28.41 2.13 5.20 × 108 ↓ 3.91 × 104 ↑ 
00:00–1:00 34.41 2.21 6.30 × 108 ↓ 4.06 × 104 ↓ 
1:00–2:00 18.71 1.83 3.43 × 108 ↓ 3.35 × 104 ↑ 
2:00–3:00 25.26 0.37 4.63 × 108 ↓ 6.85 × 103 ↓ 
3:00–4:00 20.80 0.78 3.81 × 108 ↓ 1.43 × 104 ↑ 
4:00–5:00 21.75 0.20 3.98 × 108 ↓ 3.58 × 103 ↓ 
5:00–6:00 17.12 0.67 3.14 × 108 ↓ 1.23 × 104 ↑ 
6:00–7:00 7.17 4.42 1.31 × 108 ↓ 8.11 × 104 ↑ 
7:00–8:00 15.87 1.40 2.91 × 108 ↓ 2.57 × 104 ↑ 
8:00–9:00 25.03 0.78 4.59 × 108 ↓ 1.42 × 104 ↓ 
9:00–10:00 60.42 9.88 1.11 × 109 ↓ 1.81 × 105 ↓ 

Note: water surface area = 18.3 km2.

Mathematical model of assessment of heat and humidity from the TGR on local climate

Heat and moisture transfer was through the water–air interface, and the heat and moisture is from water surface to air, changing the air temperature and air moisture content. With the movement of air, the effects of heat and moisture from the TGR expand to the local area. In order to assess the effects of heat and moisture from the TGR in the selected area, a mathematical model was established to calculate the change of air temperature and moisture content. The horizontal distribution of air temperature and moisture content is assumed to be even, and is changed only with the height (Sheng 2003). When there is a layer at the height z from the ground and there is an infinite small thickness , then the energy within the layer is: 
formula
(12)
where T is air temperature within the layer , ; A is surface area for the selected local area, .
The air can be regarded as the normal gas, then: 
formula
 
formula
(13)
The atmosphere pressure is changed with height z, then: 
formula
Combined with Equation (13), then: 
formula
(14)
Air temperature is also changed with height z, then: 
formula
(15)
where is air temperature near the ground; β = 0.65 K/100 m.
According to Equation (15), there is: 
formula
(16)
Combined with Equations (14) and (16), then: 
formula
(17)
Integrate Equation (17), then: 
formula
(18)
When , , the c can be obtained: 
formula
Put c into Equation (18), then: 
formula
(19)
Combined with Equations (12) and (13), then: 
formula
(20)
Put Equation (19) into Equation (20), then: 
formula
(21)
Put Equation (16) into Equation (21), then: 
formula
(22)
Integrate Equation (22) from the ground to the top of the selected area, then: 
formula
(23)
where is the air temperature near the ground outside of the selected area, assuming this air temperature has not been affected by the TGR; is the total energy in the research area under the assumption that there is no effect by the TGR.
Based on Equation (23), the total energy in the research area can be calculated under the assumption that there is no effect by the TGR. According to the in Table 1, the total energy in the research area affected by the TGR can be calculated by: 
formula
(24)
and can also be expressed by: 
formula
(25)
where , is the air temperature and pressure near the ground within the research area with the effect of the TGR: 
formula
Combined with Equations (24) and (25), then: 
formula
(26)
According to Equation (26), the air temperature of affected by the TGR within the research area can be calculated.
The final change of air temperature can be expressed by: 
formula
(27)
Figure 11 shows the air temperature change caused by the TGR, corresponding to the period of the measuring cycle. According to the distribution of the temperature change, the average air temperature decreased 0.67 K in the period of 24 hours within the selected area.
Figure 11

Air temperature change caused by the TGR.

Figure 11

Air temperature change caused by the TGR.

The following is the mathematical model of the assessment of air humidity.

According to the relationship between moisture content and pressure along the different heights (Zhang 1994), the moisture content at height z can be expressed as follows: 
formula
(28)
where is the air moisture content near the ground that is outside of the selected area, assuming this air moisture content has not been affected by the TGR.
The total moisture from the ground to height z for the research area can be expressed by (Liu 1997): 
formula
(29)
According to Equation (19): 
formula
(30)
Combining Equations (28)–(30): 
formula
(31)
where W is the total moisture from the ground to the top of the selected area under the assumption that there is no effect from the TGR.
According to the total moisture transfer in Table 1, the moisture from the ground to the top of the selected area affected by the TGR can be determined: 
formula
(32)
According to Equation (32), the under the effect of the TGR can be calculated. Then: 
formula
(33)

The distribution of is presented in Figure 12. The average moisture content increased 0.25 g/kg in the period of 24 hours within the researched area.

Figure 12

Change of moisture content caused by the TGR.

Figure 12

Change of moisture content caused by the TGR.

CONCLUSIONS

This paper presents a mathematical hypothesis which, for the first time has proved, in theory, that there is only one way to analyze the effects of heat and humidity from the TGR on the local climate. This paper provides the detailed methodology utilized, based on mathematical hypothesis, to examine the effects of heat and humidity from the TGR on the local climate. Through field investigation, the effects of the transfers of sensible heat, latent heat, long-wave radiation, moisture, etc. on the interface of the TGR's water and air were analyzed. The final heat flux from water to air was less than that from air to water during the measuring period. The results showed the TGR's water had a cooling effect on the air during the measuring period, and the TGR's water had a wetting effect on the air during the measuring period. From the data of the mathematical model of assessment, the average air temperature decreased 0.67 K and average moisture content increased 0.25 g/kg in the period of 24 hours within the selected area. Since the time the TGR has been in full operation with a normal pool level of 175 m has been very short, more experiential data needs to be collected to better understand the effect of the TGR on the local climate. This paper has primarily focused on the mathematical hypothesis and new research methodology, to explain the mechanism of the effect of the TGR on the local climate. The long term effects of the TGR on the local climate need continued research. This calls for a long term project to be undertaken.

ACKNOWLEDGEMENTS

The authors would like to thank the National Natural Science Foundation of China (51578086; 51408079; 5151101134); Chongqing Fundamental and Advanced Research Projects (CSTC2014jcyjA90018) and Research on the Key Technology and Demonstration of Improving Indoor Physical Environment in Existing Public Buildings (2016YFC0700705) for their financial support, without which this research paper would not have been possible.

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