FACTORS INFLUENCING THERMAL STRUCTURE IN A TRIBUTARY BAY OF THREE GORGES RESERVOIR*

YU Zhen-zhen, WANG Ling-lingCollege of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China, E-mail: yuzhenzhen8@126.com

FACTORS INFLUENCING THERMAL STRUCTURE IN A TRIBUTARY BAY OF THREE GORGES RESERVOIR*

YU Zhen-zhen, WANG Ling-ling
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China, E-mail: yuzhenzhen8@126.com

To better understand the factors influencing the thermal structure of tributaries in the Three Gorges Reservoir (TGR), a well validated three-dimensional hydrodynamic and water temperature model was proposed to simulate the water temperature distribution in the Xiangxi Bay, a representative tributary of TGR. The numerical results show that water temperature stratification seasonally occurred in the Xiangxi Bay, with stable vertical temperature profiles. It is found from the numerical experiments that three key factors are responsible for the formation of water temperature structure: (1) very often, the locations of thermocline are mainly determined by wind speeds, and the higher the wind speed is, the deeper the thermocline is located beneath the water surface, which could be expressed by a fitted exponential function, (2) the thermal structure is affected by static stability of water column, and the thermocline becomes closer to the water surface and its thickness increases with the increase of temperature, (3) due to the effect of the thermal density inflow, the water temperature of the hypolimnion tends to be uniform, however, even under the condition of larger inflow discharge, the influence of the inflow on the epilimnion and the thermocline is not significant.

water temperature stratification, numerical simulation, density current, influencing factors, wind force, static stability of water, inflow discharge, Three Gorges Reservoir (TGR)

Introduction

Thermal stratification is one of the most important environmental issues for deep waters, due to its strong effects on physical, chemical, and biological processes. Often in summer, surface water temperature is much higher than that at bottom, consequently, water densities become stacked vertically, forming the upper epilimnion, the bottom hypolimnion, and the metalimnion (thermocline) between them. Note that the thermocline can be regarded as a transition layer with a sharp temperature gradient. Vertical stratification causes weak mixing, which in fact prevents the surface water from supplying substances to the bottom layer. Therefore, nutrients and Dissolved Oxygen (DO) are often confined only in the epilimnion layer, cau-sing a series of water quality problems such as hypoxia[1,2]. In particular, water temperature stratification may speed up the eutrophication and create favorable conditions for algal blooms[3], which may pose a significant adverse impact on the ecosystems in water. On the other hand, large-scale waters are frequently disturbed by human society. Hence, it is of great interest and significance to study the spatial and temporal characteristics of water temperature in human-made water bodies, such as the Three Gorges Reservoir (TGR).

The TGR is the largest reservoir in China and around the world, with a normal pool level of 175 m and a total reservoir storage capacity of 3.93×1010m3. After the impoundment of TGR, there is a significant increase of water level in some tributaries due to the effect of backwater, leading to a decrease of flow speed therein. It is observed that seasonal stratification has occurred almost every year, especially in tributary waters of which the hydrodynamic characteristics are fundamentally similar to that in deep lakes[4]. Both monitoring data and numerical simulation indicated that, water temperature stratification has occurred insome tributary bays of TGR. The Xiangxi River is the first major tributary in the upper reaches of the Three Gorges Dam. It originates from the Shennong Jia forest region in the northwest of Hubei Province, China, and the distance between the Xiangxi Mouth and the Three Gorges Dam is approximately 30.0 km[5](see Fig.1). The Xingshan Hydrological Station is located in the upper reaches of the Xiangxi River with a distance of 32 km to the Xiangxi Mouth. In addition, the Gaolan River is the largest tributary of the Xiangxi River, with a catchment area of 833 km2. After the water level of TGR had been increased up to 135 m in 2003, the Xiangxi River became a typical tributary bay. Unfortunately, algal blooms have been observed in recent years in the central area of the bay in spring season due to the poor hydrodynamics[6].

Fig.1 Map of the basin and the modeling region for Xiangxi Bay

As is known, water temperature distribution is affected by some factors such as meteorological conditions, hydrodynamics and reservoir operations, and cannot be continuously measured in detail. By contrast, numerical models may provide a cost-effective method for evaluating hydrodynamic characteristics and water temperature status[7-9]. A number of modeling researches can be found in the literatures on thermal structures in large-scale water bodies. In the early 1970s, two vertical one-dimensional (1-D) models - the MRE and MIT models - were established based on the convection-diffusion equation, aiming to simulate vertical water temperature profiles in large water bodies. Subsequently, Stefan et al. used the method of energy balance to determine the vertical water temperature in lakes and reservoirs. Recently, Deng et al.[10]developed a laterally averaged twodimensional (2-D) water temperature model for the Ertan Reservoir, and the formation, growth and erosion of the thermocline were studied. Ferrarin and Umgiesser[11]proposed a 2-D shallow water model to address the same issue for a lagoon, adopting an additional scalar transport equation, and considering short and long wave radiation, heat flux by evaporation/ condensation and convection process at the free surface. Ji et al.[12]studied the temperature distribution in the Shangyoujiang Reservoir, using a 2-D model with the Fourier expansion. Politano et al.[13]studied the three-dimensional (3-D) temperature dynamics at the McNary Reservoir, and the primary goal of that study was to better understand atmospheric, hydrodynamic and structural conditions that may generate high temperatures at the dam creating thermal stress for downstream migrating juvenile fish. Additionally, the effects of water temperature on the exchange of DO, biological and chemical mass were also numerically studied by some researchers. For instance, Bell et al.[14]simulated the seasonal variations of the temperature and DO profiles of a British lake, the model coupled a 1-D thermal model with a 2-layer DO model, and deep-water anoxia problem was analyzed under different conditions of wind, air temperature and radiation. The long-term effect of global warming on water temperature, DO and nutrients in reservoirs was also reported[15].

However, existing researches are limited to the distributions of water temperature as well as a few water quality parameters. They overlooked a systematic description of driving mechanism for water temperature structure. In this article, the authors aim to elucidate the temperature changes in the Xiangxi Bay, focusing on the key factors that affect the thermal structure. A 3-D hydrodynamic and water temperature model is developed and verified through the measured and theoretical data. By assessing a range of alternatives for the parameters concerned such as wind speeds, solar radiation and inflow discharge, the factors influencing the water temperature structure are rather thoroughly investigated.

1. Method and application

1.1Numerical model design

The 3-D model employed in this study was derived from the conventional Navier-Stokes equations[16]. In the horizontal plane, theξ?ηbody fitted coordinate system was used. To properly deal with sharp bathymetry gradients, theσcoordinate system was adopted in the vertical direction

wherezis the distance from free surface to a specific point,ζis the elevation of surface above the reference plane (z=0),dis the water depth under the reference plane, andσranges from -1 at bottom to 0 at surface. The governing equations can be expressed as

where u, v, ω are the velocity components in the ξ, η, σ directions, respectively, t is the time, H is the total depth, f is the coefficient of Coriolis force, g is the acceleration of gravity, T is the water temperature, νtis turbulent viscosity coefficient (νt=cμk2/ε), σTis Prandtl number, ρ is water density, ρ0is the reference ambient density, gξ, gηare the Lamé coefficients, k is the turbulent kinetic energy, ε is the energy dissipation, P is the production term of turbulent kinetic energy, G is the buoyancy term, Rfis flux Richardson number, σk, σε, c1ε, c2εand c3εare empirical constants (=1.0, 1.3, 1.44, 1.92 and 0.8, respectively), and S is the heat sources term.

In addition, the “physical” vertical velocity w in the Cartesian coordinate system is related to ω by the following relationship

The vertical temperature distribution was computed from a balance between incoming heat from solar short-wave and atmospheric long-wave radiation, and the outflow of heat through convection, evaporation and back radiation, the net increase in heat resulted in an increase in water temperature[17].

The computational domain included the XiangxiBay (32 km) and a part of the mainstream of TGR (40 km). Because the highest water level is 175 m in TGR, contour to a maximum of 200 m was selected from the topographic data (see Fig.2). There are 4 open boundaries: the upper mainstream inflow section, the Three Gorges Dam outflow section, the upper Xiangxi Bay inflow section and the Gaolan Mouth inflow section. The orthogonal curvilinear grid system used here is shown in Fig.3, with the horizontal grid of 394×649, and 20 layers evenly distributed in the vertical plane.

Fig.2 Topography of Xiangxi Bay

Fig.3 Gird generation of computational domain

The governing equations were numerically solved, using a finite difference method for the spatial discretization on staggered grids. The velocity and water level were obtained at each time step by the Alternative Direction Implicit (ADI) algorithm. Considering the interaction between flow and water temperature, the hydrodynamic equations and the temperature transport equation were coupled. The convergence criterion depended on the type of norm that was used for the determination of the residual, and the value of residual was set to be smaller than 10-5for energy equation and 10-3for all other equations.

The initial condition of the flow was so-called “cold start”. However, an isothermal water temperature structure (11.18oC) in March 2007 was observed and set as the initial conditions. The boundary conditions for most parameters were based on measurements. The inflow boundary conditions of flow consisted of the measured discharges at Guizhou, Xingshan and Jianyang Ping in 2007, and the measured water levels just in front of the Three Gorges Dam as the outflow boundary condition. The shear stress by wind and the heat exchange between surface and atmosphere were appropriately taken into account in the model. The inflow boundary conditions of water temperature came from the measured temperature data of the Miao River, and a zero gradient condition for outgoing flow was used at the downstream boundary. The monthly average meteorological data between 1997 and 2000 in the Yichang City (a city nearest to the Three Gorges Dam) were adopted, including air temperature, relative humidity, sky cloudiness and solar radiation. Some values such as back radiation and heat loss due to evaporation were obtained from empirical formulas.

Fig.4 Comparisons of temperature profiles between simulation and measurement

1.2Simulation results

The spatial and temporal distributions of water temperature were simulated from March to May in 2007. The measured data[18]at the Xiakou Town in the Xiangxi Bay were used to verify the model results. As is shown in Fig.4, where the vertical ordinate is water levelZ, it is obvious that the model could accurately capture the onset of stratification, mixed depth and water temperature. However, there are also slight differences in the water temperature for some portions of the water body. This is due to the inaccurate estimation of heat fluxes that mainly depend on the quality of meteorological data. Basically, we come to the conclusion that, the simulated temperature results could be accepted as a good approximation of actual temperature status.

Fig.5 Simulation results of water temperature distribution in May, 2007 (oC)

The simulation results show that there was a temperature stratification during the spring of 2007 in the Xiangxi Bay. For example, as is shown in Fig.5 for May, 2007, where the horizontal ordinate is distancedand the vertical ordinate is elevationH, the longitudinal differences of water temperature were small, and the horizontal surfaces of temperature were almost isothermal, however, the vertical water temperature differences were significant. Along with the increase of air temperature, solar radiation enhances correspondingly, leading to an imbalance between the source and sink of heat - i.e., the water body is in a state of heat absorption. Thus, the water temperature of the upper layers increased quickly, while the water of lower layers became relatively colder because of the weak thermal conductivity. On the other hand, the water temperature of the upper portion tended to be uniform under the influence of external factors, while the bottom water could experience small disturbances and still kept the original temperature. Then the thermocline existed between them, where the rate of temperature change with depth is great. From the simulation results of May 2007, it is found that the thermocline was located some 3.0 m beneath the water surface, with an approximately 4.5 m thick and a temperature gradient of 0.53oC/m.

Fig.6 Numerical experiments domain of interest

2. Numerical experiments and discussion

The vertical temperature structure in the Xiangxi Bay is indeed a reflection of differences in density of water. It is mainly affected by the interaction of internal and external factors in the bay. Based on the hydrological and meteorological characteristics of the Xiangxi Bay, three major influencing factors were analyzed and discussed through numerical experiments. In order to improve the computational efficiency, the local water region located 2.0 km south of Xiakou Town was used to illustrate the environmental sensitivity (see Fig.6).

2.1Effect of wind force on water temperature stru

cture

The wind could be the main driving force for hydrodynamics, especially, for shallow waters[19,20]. In this section, Koutitas’ analytical solution for winddriven flow in tanks was used to verify the basic performance of our 3-D hydrodynamic model. An idealized rectangular tank was modeled, with an area of 1 250 m×400 m, and a depth of 2 m. Assume that there was a constant wind (5 m/s) acting on the surface, and a vertical circulation would be produced. High resolution in space is necessary: the horizontal grid was 10 m×5 m, and the number of layers in vertical direction was 10. Here, the Coriolis force was neglected and a constant eddy viscosity coefficient was adopted. The simulation was carried out until a steady state circulation was achieved. It was observed from Fig.7 that there was good agreement between the simulated and the analytical velocitiesuat different depthsI. Therefore, the proposed model is capable of simulating wind-driven flow, which gives further support to the use of our model to simulate the effect of wind force on the water temperature structure in the Xiangxi Bay.

For the Xiangxi Bay model, fifty layers were distributed in the vertical direction. According to the field data (at the Xingshan Hydrological Station) from April 20 to May 4, 2007, the time average discharge from the upstream boundary was around 50 m3/s, and a water level of 149 m was taken as the downstream boundary condition. Meanwhile, the measured temperature and the meteorological data were used to provide the necessary initial and boundary conditions. First, at least 1 week spin-up run was executed to obtain appropriate initial conditions until hydro-dynamics and temperature both reached a dynamic steady state. Then, the simulation was continued for a total of 14 d, using a time step of 60 s. Adopting the same initial and boundary conditions, the authors compared the water temperature profiles under different wind speed conditions. It is shown that the stratification is closely related to the wind speeds, in terms of the stratification pattern and the locations of thermocline (see Fig.8). Normally, the abrupt changes in vertical water temperature are mainly due to the action of wind, moreover, the location of thermocline depends on the characteristic of wind - e.g., the higher the wind speed, the deeper the thermocline.

Fig.8 Water temperature profiles under different wind speed conditions (Wind direction: east)

Fig.9 Relationship between the wind speed and the thermocline location (Wind direction: east)

About 50 percent of the heat (from solar radiation mainly) is absorbed by the water surface of the Xiangxi Bay, and the remainder exponentially decays with depth, causing uneven distribution of water temperature in the vertical direction. However, the upper water layers could be mixed under the influence of the wind force, because wind can stir the warmer water down to a critical depth where turbulence is notably dissipated - i.e.,the interface between epilimnion and thermocline[21]. From the simulation results in Fig.8, where the vertical ordinate is water depthD, when the wind speeds were lower than 2 m/s, the water temperature profiles showed a nearly exponential decay with depth, and the thermocline could not be observed clearly. If the wind speeds reached 3 m/s, a thermocline with a thickness of about 5 m was observed at 2.3 m below the water surface. As the wind speeds became 4 m/s and 5 m/s, the locations of thermocline transferred to 4.65 m and 7.76 m under the water surface, respectively.

In Fig.9 the simulated average depths of thermoclineDA(i.e., the center locations of thermocline) under the wind speedsvchanging from 3 m/s to 5 m/s are presented. An exponential function could be fitted to express the relationship between the wind speed and the locations of thermocline. According to estimate, once the wind speeds reached 9.1 m/s, the average depth of thermocline would appear at about 38 m below the water surface, which means that the wind has the ability to mix the entire water body. At this point, the vertical water temperature would tend to an isothermal distribution and the thermocline would disappear.

Table 1 Static stability of a water body at difference temperature

Fig.10 Locations of thermocline under different water temperature conditions

Fig.11 Time-histories of inflow discharge in Xiangxi Bay (2007)

Fig.12 Simulation results of velocity distribution on 23 April, 2007

2.2Effect of static stability of water on water temperature structure

There is generally a positive relation between static stability and temperature, because for example, water density should decrease but dshould increases as temoperature increases (when water temperature ＞ 3.94C). As is shown in Table 1, for a water body with 10 m depth (dz=10m) under different background temperatures, assume that there is always a constant temperature difference of 1.0oC between surface and bottom, then the static stability would increase as the background temperature increases. Therefore, the capability of resisting mixing would increase along with the increase of temperature.

Our simulations for Xiangxi Bay’s water temperature structure further support the above-mentioned viewpoint. Focusing on the effect of the static stability of water on the temperature structure, the authors carried out a series of numerical experiments, by only enhancing the intensity of solar radiation while using constant conditions of wind speed (3 m/s), wind direction (East), and inflow discharge (50 m3/s). Figure 10 shows three representative water temperature profiles at different times: for the surface water temperatures of 16.98oC, 17.85oC and 18.73oC, respectively, the surface mixing depths were 2.33 m, 1.91 m and 1.55 m underwater, and the thicknesses of the thermocline were 3.88 m, 4.29 m, 4.65 m. It means that when the temperature increases, the static stability of water would gradually increase. Therefore, it is concluded that in the Xiangxi Bay, since high-temperature water is more resistant to mixing, the upper epilimnion generally becomes thinner in summer than that in spring, meanwhile the thickness of the thermocline increases correspondingly.

2.3Effect of inflow discharge on water temperature

structure

Since reservoir operations may regulate hydraulic and hydrological regime, it is necessary to examine the sensitivity of water temperature structure to flow boundaries conditions. The Xingshan and Jianyang Ping Hydrological Station, which are located in the upper reaches of the Xiangxi River Basin, the measured time-histories of dischargeQfrom the two hydrological stations are shown in Fig.11. According to the simulation results, it is found that the phenomenon of thermal density flow could appear in the Xiangxi Bay. For example, the Xiangxi Bay exhibited temperature stratification on April 23, 2007, under the discharge condition of 173.2 m3/s (the sum of discharge from the two hydrological stations), as is shown in Fig.12, the lower temperature flow from the upstream with a velocity of 0.054 m/s dived to the bottom of the bay at first and then moved forward in the form of an undercurrent with a decreased velocity of 0.042 m/s. As temperature stratification exists in the surrounding body of water, the thermal density flow would prone to enter a water layer with the same temperature, so an interlayer flow with a velocity of 0.036 m/s is formed about 10 m under the surface.

Fig.13 Water temperature profiles under different inflow discharge conditions (Wind speeds: 3m/s, Wind direction: east)

To analyze the effect of inflow discharge on the vertical water temperature distribution, here the authoes simulated a range of alternatives for inflow discharges, ranging from 0 m3/s to 200 m3/s. Similarly, the other environmental conditions should be unchanged - i.e., constant wind force and solar radiation were considered for all scenarios. As is shown in Fig.13, the inflow discharge mainly affects the bottom hypolimnion, not the epilimnion or the thermocline.With the increase in discharge, the hypolimnion has more uniform temperature with depth. For instance, the hypolimnion shows a water temperature difference of 0.41oC if there is no inflow, however, when the inflow discharge reaches 200 m3/s, the difference should be significantly reduced to 0.16oC. As was mentioned earlier, the Xiangxi Bay is in possession of the phenomenon of thermal density flow, which could result in the stronger turbulence at the hypolimnion, and then the temperature of hypolimnion would tend towards homogenization.

3. Conclusions

Water stratification is a universal phenomenon in deep waters, but it is difficult to evaluate quantitatively and continuously through field work. The authors aimed to numerically examine the relationship between stratification and environmental factors. In this study, a 3-D hydrodynamic and water temperature model has been developed, by coupling continuity, momentum, state, temperature transport, and the turbulent equations. After appropriate calibration, the model was applied to simulate the water temperature in the Xiangxi Bay, a tributary of the TGR that is suffering from the seasonal stratification. Moreover, under different hydrological and meteorological conditions, the effects of wind force, static stability of water and inflow discharge on the water temperature structure were quantitatively investigated.

For the first time, this research demonstrated that in the tributary waters of huge reservoir: (1) wind is a major limiting factor for the formation of a thermocline in the Xiangxi Bay. A deeper thermocline would be formed with the stronger wind force, if wind can not mix the entire bay. The relationship between the locations of thermocline and the wind speeds could be expressed as an exponential function, (2) the static stability of water also plays a significant role in influencing thermal structure in the water column. The static stability would become relatively larger when the temperature increases. Thus, it is difficult for the wind force to produce deeper vertical mixing, the locations of the thermocline are close to the water surface and its thickness increases, meanwhile, the epilimnion becomes thin, (3) in addition, for the Xiangxi Bay the inflow discharge mainly affects the hypolimnion due to the existence of thermal density flow, on the contrary, and the epilimnion and the thermocline are not sensitive to the boundary conditions. Such points can not only enhance our understanding of the stratification phenomenon, but also serve as a scientific reference for sustainable reservoir management.

Acknowledgement

The authors would like to express their appreciation to Dr. Mao Jing-qiao for his suggestions.

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January 6, 2011, Revised May 28, 2011)

* Project supported by the National Natural Science Foundation of China (Grant No. 41001348), the “Qinglan Project” of Jiangsu Province.

Biography: YU Zhen-zhen (1982-), Female. Ph. D. Candidate

WANG Ling-ling,

E-mail: wanglingling@hhu.edu.cn

2011,23(4):407-415

10.1016/S1001-6058(10)60130-8