Modeling density currents in a typical tributary of the Three Gorges Reservoir, China

Ecological Modelling 296 (2015) 113–125

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Modeling density currents in a typical tributary of the Three Gorges Reservoir, China Jun Ma a,b , Defu Liu c,d, *, Scott A. Wells e, Hongwu Tang a,b , Daobin Ji f , Zhengjian Yang c a

College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China State Key Laboratory of Hydrology–Water Resources and Hydraulic Engineering, Nanjing 210098, China c College of Resources and Environmental Engineering, Hubei University of Technology, Wuhan 430068, China d Engineering Research Center of Eco-environment in Three Gorges Reservoir Region, Ministry of Education, China Three Gorges University, Yichang 443002, China e Department of Civil and Environmental Engineering, Portland State University, Portland, OR 97207-0751, USA f College of Hydraulic & Environmental Engineering, China Three Gorges University, Yichang 443002, China b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 17 June 2014 Received in revised form 22 October 2014 Accepted 26 October 2014 Available online 7 November 2014

The initial filling of the Three Gorges Reservoir (TGR), China, has caused serious phytoplankton blooms in its tributary bays. A two-dimensional, laterally averaged, hydrodynamic and water quality CE-QUALW2 model was used to simulate the hydrodynamics and water temperature of a typical tributary (Xiangxi Bay XXB) of the TGR to study the relationship between phytoplankton and density currents. The CE-QUAL-W2 model was calibrated to data collected in XXB (depth profiles of velocity and water temperature at three locations) from January 2008 through December 2008. The model performed well in simulating (1) flow velocity profiles, (2) unusual water temperature profiles, (3) the plunge point location of the intrusion layer, (4) propagation speed, and (5) the travel distance of the density currents. The model was then used to examine potential factors that affect the density currents, such as water level fluctuations in the mainstem of the TGR, water temperature differences between the mainstem and XXB, and inflow rates to XXB. Therefore, a better understanding of the hydrodynamics of tributaries in the TGR can be used to understand the aquatic ecosystem dynamics of these tributaries. ã 2014 Elsevier B.V. All rights reserved.

Keywords: Three Gorges Reservoir (TGR) Xiangxi Bay (XXB) Density currents Water temperature stratification CE-QUAL-W2

1. Introduction The Yangtze River (China) is the longest river in Asia and the third-longest in the world. It flows for 6418 km (3988 miles) from the glaciers on the Qinghai–Tibet Plateau in Qinghai eastward across southwestern, central and eastern China before emptying into the East China Sea at Shanghai. The Three Gorges Reservoir (TGR), located at the end of the upper Yangtze River, is one of the largest man-made reservoirs in the world with a capacity of 39.3 billion m3, a surface area of 1080 km2, and a watershed area greater than 1 million km2 (Huang et al., 2006). The Three Gorges Project (TGP) has brought substantial social and economic benefits, such as flood control, hydro-power generation, and navigation, for both the catchment region and a large part of the country.

* Corresponding author at: College of Resources and Environmental Engineering, Hubei University of Technology, Wuhan, Hubei 430068, China. Tel.: +86 27 59750009; fax: +86 27 88032271. E-mail address: dfl[email protected] (D. Liu). http://dx.doi.org/10.1016/j.ecolmodel.2014.10.030 0304-3800/ ã 2014 Elsevier B.V. All rights reserved.

However, the TGP will have long-term impacts on the environment. For example, severe algal blooms have been reported in certain tributary bays since the initial impoundment of TGR in June 2003 (Ministry of Environmental Protection of China, 2012). Algal blooms have been observed every year in Xiangxi Bay (XXB), which is the largest tributary in the lower reach of TGR (32 km from Three Gorges Dam) (Fig. 1). Algal blooms are influenced by mass transport (nutrients, trace elements, carbon dioxide) (Daines et al., 2014; Domingues et al., 2011b; Xu et al., 2010), environmental factors (light, temperature) (Chen and Liu, 2010; Cunha and Calijuri, 2011; Domingues et al., 2011a), hydrodynamics (circulation of water, mixing, stratification) (Liu et al., 2012; Zhou et al., 2014), and interactive biochemical kinetics (Kara et al., 2012; Norton et al., 2012; Robson et al., 2008). There is increasing evidence, through analysis of long-term data records, that algal blooms in the tributaries of TGR are sensitive to changes in thermal stratification, hydrodynamics and nutrient loads (Yang et al., 2010). Water temperature is one of the most important physical properties of freshwater systems. Increasing temperature is a main

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Fig. 1. (a) Location of the Three Gorges Reservoir (TGR) in China; (b) location of Xiangxi Bay (XXB) in the TGR outlined in red; and (c) location of the sampling sites in the XXB, where XX00 is near the confluence with the TGR.

driving factor for spring algal blooms in XXB (Yang et al., 2012; Yi et al., 2009). Yang et al. (2012) have highlighted the role of weak stratification in the absence of algal blooms in the mainstem. Through long-term field observations, Ji et al. (2010a) have found that density currents occur frequently in tributary arms of the TGR. Density currents are affected by upstream inflows to tributary bays, intrusion flow from the TGR, water temperature, inflow sediment concentrations and water level daily fluctuation (WLDF) (Ji et al., 2010a). Density currents also have significant effects on the stratification structure, transformation and transport of nutrients, phytoplankton blooms, and aquatic ecosystem succession. Disentangling the interplay of those factors (upstream inflows, intrusion flow, water temperature, inflow sediment concentrations and WLDF) with density currents is a significant challenge that calls for further research. Compared with conventional monitoring, which is expensive and time consuming, numerical models are attractive because they can simulate the development and progression of hydrodynamic fields. Numerical models have become widely accepted instruments for predicting and diagnosing hydrodynamic field problems. Moreover, computer models of hydrodynamics and eutrophication can help identify the factors governing the characteristics of density currents and identify potential strategies for controlling phytoplankton blooms. Onedimensional hydrodynamic and eutrophication models and twodimensional vertically averaged hydrodynamic models were developed for XXB to simulate water level, flow velocity, reservoir operation, nutrient dynamics, and phytoplankton growth (Li et al., 2002, 2006; Xiao, 2007; Wang et al., 2009; Ma and Lian, 2011; Xu et al., 2009; Li et al., 2012a; Lian et al., 2013). However, these onedimensional and two-dimensional depth-averaged models were unable to simulate horizontal–vertical density currents along the relatively long and narrow XXB. Several two-dimensional laterally averaged hydrodynamic and ecological models and even a number of three-dimensional models have been developed for XXB (Jiang et al., 2011; Yu and Wang, 2011; Dai et al., 2012). However, details involving density currents were not assessed in these studies.

Therefore, in this study, a two-dimensional laterally averaged hydrodynamic and ecological model focusing on the characteristics of density currents was developed to (1) simulate density currents and water temperature in a typical tributary of the TGR and (2) investigate the potential factors that affect these density currents. 2. Materials and methods 2.1. Study area The Xiangxi River, the largest tributary in the lower reach of the TGR (32 km from Three Gorges Dam), drains a watershed whose area is 3095 km2. It has a length of 94 km and an annual average flow of 47.4 m3/s. It extends from 110
250 E to 111
060 E and from 30
570 N to 31
340 N (Fig. 1). After initial filling in June 2003 to a water level of 135 m, a deep riverine bay formed in XXB, with the lower 24 km submerged by a backwater reach. The backwater reach extended to 40 km when the TGR was filled to a normal water level (175 m). 2.2. Model description and application The CE-QUAL-W2 model is a two-dimensional laterally averaged hydrodynamic and water quality model co-developed by the U.S. Army Corps of Engineers Waterways Experiment Station and Portland State University (Cole and Wells, 2013). As the model assumes lateral homogeneity, it is best suited for relatively long and narrow waterbodies exhibiting longitudinal and vertical water quality gradients. This model has been successfully applied to stratified water systems, including lakes, reservoirs, and estuaries (Afshar et al., 2013; Berger and Wells, 2008; Bowen and Hieronymus, 2003; Choi et al., 2007; Kuo et al., 2006; Lee and Foster, 2013; Park et al., 2014; Wells et al., 2012). The CE-QUALW2 model was selected in this study because it is appropriate for XXB, where lateral variations in velocity and temperature are

J. Ma et al. / Ecological Modelling 296 (2015) 113–125

Boundary Condion

Update Boundary Condion

Iteraon

Equaon of State Compute density field,

Inial Condion

Free Surface Equaon Solve for water surface,

Horizontal Momentum Equaon Solve for horizontal velocity,

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determined by statistical regression equations relating the time of year to the air temperature (Fig. 3). Field data were used to supply inflow temperatures when available. Otherwise, correlations with air temperature were used. A head boundary was used for the downstream boundary condition. Water surface elevation (WSE) field data were obtained from the China Three Gorges Corporation. Downstream temperatures were collected weekly at the mouth of XXB using a multi-probe sensor (Hydrolab DS 5X). All upstream and downstream boundary condition data were specified as daily values. 2.3. Assessment of model performance

Connuity Equaon Solve for vercal velocity,

Advecve-Diffusion Equaon Solve for Temperature,

Fig. 2. Conceptual diagram of solution scheme for CE-QUAL-W2 model.

insignificant (Yang et al., 2010). Additionally, this model is capable of modeling density currents and the longitudinal and vertical temperature structure in XXB. CE-QUAL-W2 is based on the finite difference solution of laterally averaged equations of fluid motion, including the continuity equation, x-momentum equation, zmomentum equation, free surface equation, equation of state, and advective–diffusion equation. Details of these equations are shown in Appendix A. Fig. 2 shows a conceptual diagram of the solution scheme for the CE-QUAL-W2 model. Based on the bathymetric and geometric data for the reservoir, a computational grid for XXB was developed. XXB was represented by 64 longitudinal segments, each 500 m in length, and 109 vertical layers, each 1 m thick, consistent with guidelines for defining the computational grid presented by Cole and Wells (2013). Model widths ranged from 10 to 1300 m. The accuracy of the bathymetry data was confirmed by good agreement between the observed and simulated storage–water elevation curves. CE-QUAL-W2 has several coefficients that may be adjusted in the calibration process. A sensitivity analysis determined that the most sensitive model parameters included the longitudinal eddy viscosity, longitudinal eddy diffusivity, Manning’s roughness coefficient, wind sheltering coefficient, dynamic shading coefficient, the fraction of incident solar radiation absorbed at the water surface, and the light extinction for pure water (Table 1). Most of the values chosen were the recommended default values. Upstream inflows and daily meteorological data were available from measurements obtained from a hydrological station at Xingshan (Fig. 1c), approximately 36 km upstream from the confluence of XXB and the Yangtze River. Inflow temperature data were partially obtained from weekly sampling, and data gaps were

Model performance was evaluated based on the mean error (ME), the absolute mean error (AME) and the root mean square error (RMSE) statistics. The ME shows model bias. The AME provides an indication of model performance and is one measure of average error. The RMSE is statistically well-behaved and is another indicator of the average difference between observations and predictions. These statistics are commonly used to evaluate the goodness of fit of the model to the observed data (Cole and Wells, 2013; Deus et al., 2013; Lindim et al., 2011; Liu and Chen, 2013; Smith et al., 2014). The goodness-of-fit statistics are calculated as follows: Xn ðX obs;i  X model;i Þ i¼1 (1) ME ¼ n

Xn AME ¼

RMSE ¼

i¼1

jX obs;i  X model;i j

(2)

n

sX ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ðX obs;i  X model;i Þ2 i¼1 n

;

(3)

where n is the number of observations, Xobs,i is the value of the ith observation of parameter X, and Xmodel,i is the predicted value of the ith observation of parameter X. As shown in Fig. 4, the types of intrusion (overflow, underflow, and interflow), the thickness of the intrusion layer at the plunge point, and the travel distances of the intrusion layer were also used to compare field data to model predictions. 2.4. Taguchi method for numerical design of experiments The Taguchi method is a robust design optimization methodology that is widely used in industry (Ghani et al., 2004; Hedayat et al., 1999; Nalbant et al., 2007; Park, 1996; Phadke, 1995). It provides an easy, efficient and systematic approach to optimizing

Table 1 Calibration parameters in CE-QUAL-W2 for XXB application. Parameters

Default value

Value used

Longitudinal eddy viscosity (m2/s) Longitudinal eddy diffusivity (m2/s) Manning’s roughness coefficient (s/m1/3) Wind sheltering coefficient Dynamic shading coefficient Fraction of incident solar radiation absorbed at the water surface Light extinction for pure water (m1) Turbulence closure scheme

1.0 1.0 Variable Variable Variable 0.45 0.45 TKEa

1.0 1.0 0.04 0.9 0.8 0.45 0.45 TKEa

a

Turbulent kinetic energy k–e model.

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Fig. 3. Inflow temperature from regression equations vs. measured field data. (mean error: 0.05
C; absolute mean error: 0.80
C; root mean square error: 1.00
C). Upper left: correlation between mean air temperature and the corresponding water temperatures measured at water surface (from January to June). Upper right: correlation between mean air temperature and the corresponding water temperatures measured at water surface (from July to December).

Fig. 4. Sketch of density current.

the design of experiments. By utilizing this method, one can substantially decrease the time required for experimental analysis because the method efficiently explores the effects of multiple factors on performance and also facilitates the investigation of the influence of single factors to determine the relative influence of each of these factors. The most important step in the design of an experiment is the determination of the principal controlling factors. The main factors affecting density currents in XXB are water temperature differences between the mainstem and XXB, upstream inflow rates, and water level daily fluctuation (WLDF) in the TGR (Ji et al., 2010a,b,b; Yang et al., 2010). The assignment of these factors and levels is shown in Table 3. In this study, the potential impact of these factors on density currents and the ways in which this combination of factors produces different flow patterns were investigated by

applying the CE-QUAL-W2 model. To model the different types of density currents in XXB, the initial conditions of the numerical experiments were set to the same conditions as those occurring during overflow, interflow and underflow on October 5, August 24 and November 25, 2008, respectively. Orthogonal arrays are used for accommodating many design factors simultaneously in the Taguchi method. Statistically, this experimental matrix yields the same information as a full-scale factorial experimental design but with fewer experimental trials. For example, a full set of 27 experimental trials can be reduced to a mere 9 experimental trials. Orthogonal arrays are most often named following the pattern LRuns (LevelsFactors). As described above, the upstream inflow rates of XXB, the water temperature differences, and WLDF were selected as the three factors to be used in an orthogonal experimental design. Thus, a standard orthogonal

J. Ma et al. / Ecological Modelling 296 (2015) 113–125

array of L9 (34) was selected in this study, as shown in Table 4. Four control factors with three levels were contained in nine experimental runs. Because only three factors were selected, the fourth control factor (column) was omitted in the L9 (34) orthogonal array. 3. Model calibration Data from January 2008 to December 2008 were used for model calibration. The model performed well in simulating the types (overflow, underflow, or interflow), thickness of the intrusion layer at the plunge point, travel distances and velocities of density currents intruding from the TGR (Table 2). The model results (Fig. 5, right side) indicate that density currents exist all year. Fig. 5 shows that underflow intrusion occurred on February 16 and November 25; overflow intrusion occurred on April 27 and October 5; and interflow intrusion occurred on May 10, June 26, July 13, August 24, September 15, and October 17. The overall trend of the flow directions in the model results shows good agreement with the observed results (Fig. 5). The simulated velocities were of the same order of magnitude as the observations, generally within 0.1 m/s (Table 2). Table 2 also shows that there was good agreement between the model predictions and the field data on the vertical thickness of the intrusion layer, differing by 9 m or less except on August 24 (20 m) and September 15 (16 m). The modeled longitudinal travel distance of the density currents was slightly larger than measured, with a maximum error of 5.5 km (Table 2, July 13). The average modeled and observed values of the travel distance were almost the same, differing by approximately 2.1 km. The mean flow velocities of the density currents at the plunge point (0.058 m/s) were also consistent with field data (0.052 m/s). Predictions of thermal stratification in 2008 yielded a good match to the measured profiles at 3 sites: XX01 (downstream), XX06 (middle reaches), and XX09 (upstream) (Fig. 6). The model

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performance was also evaluated by comparing the simulated results and observations for all paired depths at sites XX01, XX06 and XX09 (Fig. 7), and these comparisons showed excellent model–data agreement. The overall averaged mean error (ME), averaged absolute mean error (AME), and averaged root mean square error (RMSE) were 0.27
C, 0.35
C, and 0.46
C, respectively, at site XX01; 0.16
C, 0.42
C, and 0.58
C, respectively, at site XX06; and 0.09
C, 0.59
C, and 0.74
C, respectively, at site XX09. Most of the vertical profiles have AMEs less than 0.5
C and RMSEs less than 1
C. Based on Cole and Wells (2013), the error statistics show that the model effectively captured the characteristics of thermal stratification. 4. Thermal stratification Site XX01 was selected for illustrating the thermal structure. Fig. 6 depicts the vertical water temperature predictions and modeled profile of XX01 throughout 2008. Weak stratification started in April during spring warming. From June through October, the temperature decreased rapidly in both the surface and bottom zones, whereas temperature in intermediate zones changed little with depth, forming a “step-like” stratified pattern. Fig. 8a,b shows that there were five different water temperature layers at site XX01 and XX06 during the period when interflow and overflow intrusion density currents occurred: (1) a very thin wellmixed layer due to the wind effects, (2) a thermocline due to the density currents, (3) a thick well-mixed layer due to the density current’s intrusion from the mainstem, (4) a thermocline due to density currents and upstream cold mountain inflows, and (5) the hypolimnion due to the upstream cold mountain inflows. The reason for this stratified pattern is that downstream interflow intrusion from the mainstem and upstream underflow from cold mountain streams form two distinct surface and bottom zones. Fig. 8c shows that there were two different water temperature layers at site XX09 during the period when underflow intrusion density currents occurred: (1) a 17-m thick well-mixed layer and

Table 2 Statistics of characteristics of density currents in XXB. Date

Types Observed

2–16 4–27 5–10 6–26 7–13 8–24 9–15 10–5 10–17 11–25

Underflow Overflow Interflow Interflow Interflow Interflow Interflow Overflow Interflow Underflow

Thickness of intrusion layer at plunge point (m)

Travel distance (km)

Velocity at plunge point Mean (range) (m/s)

Modeled

Observed

Modeled

Observed

Modeled

Observed

Modeled

Underflow Overflow Interflow Interflow Interflow Interflow Interflow Overflow Interflow Underflow

40-ba 1–26 3.5–30.5 10–44 3–29 6–49 9–41 0–27 28–65 49-b

37-b 0–28 4.5–28 17–49 3–25 26–56 25–55 0–24 37-b 44.5-b

6.5 22.5 22 22 17 18 18 29.4 22 9.5

7.5 24 25 21 22.5 19.5 23 29.4 22 14.5

0.054 (0.014–0.083) 0.059 (0.008–0.086) 0.071 (0.027–0.101) 0.031 (0.002–0.076) 0.063 (0.032–0.100) 0.064 (0.033–0.110) 0.020 (0.009–0.036) 0.062 (0.004–0.105) 0.051 (0.014–0.070) 0.047 (0.007–0.073)

0.045 (0.004–0.062) 0.059 (0.002–0.078) 0.073 (0.002–0.114) 0.033 (0.002–0.049) 0.067 (0.003–0.103) 0.042 (0.006–0.059) 0.032 (0.002–0.048) 0.087 (0.005–0.135) 0.074 (0.006–0.101) 0.069 (0.001–0.095)

18.7

20.8

0.052

0.058

Average a

b: Bottom.

Table 3 Factors and levels used in the numerical experiments. Symbol

Factors

A B-1 B-2 B-3 C

Upstream inflow rates to XXB (m3/s) Water temperature difference as overflow occurs (
C)a Water temperature difference as interflow occurs (
C) Water temperature difference as underflow occurs (
C) Water level daily fluctuation (WLDF) (m/d)

a

Water temperature difference between surface water of XXB and the well-mixed TGR mainstem.

Level 1

2

3

10 0.6 0.6 0.6 0.5

40.37 1.6 1.1 1.6 1.5

400 3.1 1.6 3.1 3

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J. Ma et al. / Ecological Modelling 296 (2015) 113–125

Table 4 L9 (34) standard orthogonal array table with factors A,B, and C arranged in columns 1–3, respectively. Because only three factors are selected, the fourth control factor (column) is omitted in this study. Experimental run

Factor 1

Factor 2

Factor 3

Factor 4

1 2 3 4 5 6 7 8 9

1 1 1 2 2 2 3 3 3 A

1 2 3 1 2 3 1 2 3 B

1 2 3 2 3 1 3 1 2 C

1 2 3 3 1 2 2 3 1 –

(2) a thermocline due to the upstream cold mountain inflow, forming a “semi-U” stratified pattern. 5. Main factors affecting density currents To conduct an analysis of the relative importance of each factor more systematically, an analysis of variance (ANOVA) was applied to the modeling results. This analysis attempted to clarify the significance levels of the different factors influencing density currents. Tables 5, 7 and 9 show the factors, levels, and experimental results for the overflow, interflow, and underflow scenarios, respectively. Tables 6, 8 and 10 summarize the statistical analysis of the effect of different factors on the travel distance and thickness of the intrusion layer at the plunge point of the overflow, interflow, and underflow, respectively. The K value for each level of a parameter was the average of three values shown in Tables 5, 7 and 9. The range value (R) for each factor was the difference between the maximum and minimum value of the three levels. An F ratio is generally used to examine the significance of the controlling factors, and the calculated ratios are also listed in Tables 6, 8 and 10. A critical F (Fc) ratio corresponding to the L9 orthogonal array with a degree of freedom of 6 can be determined as 3.46 from the Fisher–Snedecor table at the p = 0.10 level. If the F ratio for each factor is greater than the Fc ratio, this indicates that the factor dominates the travel distance or thickness of the overflow with a confidence level of 90%. Experimental and numerical analysis using the Taguchi method showed that as the upstream inflow to XXB increased, both the travel distance and the thickness of the overflow, interflow and underflow intrusion decreased (Tables 6, 8 and 10) because cold mountain inflows from upstream sank to the bottom of XXB as an underflow. Due to conservation of momentum, the travel distance of density flow intrusion from the mainstem of TGR will decrease as upstream inflow increases. Nevertheless, increasing upstream inflows generated large eddies or circulation in XXB (Fig. 5), which can break down thermal stratification. The travel distance and vertical thickness of the intrusion layer at the plunge point of the underflow intrusion increased along with an increase in the temperature differences between the mainstem and XXB (Table 10). The travel distance of overflow intrusion significantly increased as the temperature difference increased. However, the vertical thickness of the intrusion layer at the plunge point of the overflow changed little with increases in the temperature difference (Table 6). Both the travel distance and the thickness of the intrusion layer at the plunge point of interflow increased and then decreased with increasing temperature differences (Table 8), indicating that there was a critical temperature difference. Enhancing density current intrusion will increase water flow velocity and water turbulence intensity and will also generate large eddies or circulation in XXB (Fig. 5), which may be

Fig. 5. Left: observed vertical profiles of flow velocity at sites XX01, XX06, and XX09. Right: modeled longitudinal distribution of flow field and water temperature.

J. Ma et al. / Ecological Modelling 296 (2015) 113–125

Fig. 6. Observed and modeled vertical profiles of water temperature at sites XX01, XX06, and XX09.

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35 y = 0.9654x + 0.9663 (R² = 0.98)

30

Simulated T, ć

25 20 15 10 5 5

10

15

20

25

30

35

Observed T, ć Fig. 7. Observed vs. simulated temperature at sites XX01, XX06, XX09 (number of points used: 151).

helpful in mitigating algal blooms through a deeper mixing depth of the epilimnion. Density currents responded differently to the water level daily fluctuation (WLDF). For overflow intrusion, the travel distance and the vertical thickness of the intrusion layer at the plunge point increased as WLDF increased (Table 6). For interflow, travel distance increased with increased WLDF, but the thickness of the intrusion layer at the plunge point did not change as WLDF changed (Table 8). However, for underflow, the travel distance and the thickness of the intrusion layer at the plunge point first increased and then decreased with increased WLDF (Table 10). Hence, increasing WLDF will increase the travel distance of the density current intrusion. 6. Discussion 6.1. Impacts of density currents on the thermal structures In this study, the two-dimensional hydrodynamic and ecological XXB model fully captured the horizontal–vertical characteristics of density currents after calibration based on one year of field data considered by our research. The model successfully represented the occurrences, longitudinal intrusion length, vertical thickness and types of density currents (Figs. 5 and 6, Table 2), which was not possible for one-dimensional models (Li et al., 2002, 2006; Xiao, 2007; Wang et al., 2009; Ma and Lian, 2011). In contrast to the limited field data and the hydrodynamic profiles monitored by Ji et al. (2010a,b); Ji et al. (2010a,b), Yang et al. (2010), Li et al.

Fig. 8. Typical thermal stratifications in XXB at sites XX01, XX06, and XX09.

(2012b) and Ji et al. (2010c), the model was able to characterize the circulation pattern in XXB, including the influences of upstream inflow and mainstem intrusion (Fig. 5). In this study, the upstream cold mountain inflows usually sank to the bottom of XXB as an

Table 5 The factors, levels and experimental results of overflow scenarios. Experimental run

1 2 3 4 5 6 7 8 9

Factor

Results

A Upstream inflow rates to XXB (m3/s)

B-1 Water temperature difference as overflow occurs (
C)

C Water level daily fluctuation (WLDF) (m/d)

Travel distance (km)

Thickness of the intrusion layer at plunge point (m)

10 10 10 40.37 40.37 40.37 400 400 400

0.6 1.6 3.1 0.6 1.6 3.1 0.6 1.6 3.1

0.5 1.5 3.0 1.5 3.0 0.5 3.0 0.5 1.5

11.5 16.4 20.2 12.3 16.9 18.6 12.5 15.9 18.8

38.9 39.9 39.4 36.9 38.4 38.9 38.4 34.9 36.9

J. Ma et al. / Ecological Modelling 296 (2015) 113–125

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Table 6 Statistical analysis of overflow scenarios. Results

A

B-1

C

Travel distance

K1 K2 K3 R Sum of squared deviations F ratio

16.033 15.933 15.733 0.300 0.140 0.005

12.100 16.400 19.200 7.100 76.740 2.912

15.333 15.833 16.533 1.200 2.180 0.083

Thickness of the intrusion layer at plunge point

K1 K2 K3 R Sum of squared deviations F ratio Fc

39.400 38.067 36.733 2.667 10.667 2.370 3.46

38.067 37.733 38.400 0.667 0.667 0.148

37.567 37.900 38.733 1.166 2.167 0.482

Table 7 The factors, levels and experimental results of interflow scenarios. Experimental run

1 2 3 4 5 6 7 8 9

Factor

Results

A Upstream inflow rates to the XXB (m3/s)

B-2 Water temperature difference as interflow occurs (
C)

C Water level daily fluctuation (WLDF) (m/d)

Travel Thickness of the intrusion layer at distance (km) plunge point (m)

10 10 10 40.37 40.37 40.37 400 400 400

0.6 1.1 1.6 0.6 1.1 1.6 0.6 1.1 1.6

0.5 1.5 3.0 1.5 3.0 0.5 3.0 0.5 1.5

8.4 14.5 12.7 10.3 13.1 12.4 11 9.5 9.6

41 46 49 37 49 47 33 43 38

Table 8 Statistical analysis of interflow scenarios. Results

Factors

A

Travel distance

K1 K2 K3 R Sum of squared deviations F ratio

11.867 11.933 10.033 1.900 6.976 0.884

9.900 12.367 11.567 2.467 9.502 1.204

10.100 11.467 12.267 2.167 7.202 0.912

Thickness of the intrusion layer at plunge point

K1 K2 K3 R Sum of squared deviations F ratio Fc

45.333 44.333 38.000 7.333 94.889 1.101 3.46

37.000 46.000 44.667 9.000 141.556 1.642

43.667 40.333 43.667 3.334 22.222 0.258

underflow. In contrast, the density current intrusion from the mainstem (TGR) entered XXB from 4 different vertical locations at the mouth of XXB: from the surface layer on April 27 and October 5, from the upper-middle layer on May 10, June 26, and July 13, from the lower-middle layer on August 24, September 15, and October 17 and from the bottom layer on February 16 and November 25. When the intrusion entered XXB from the surface or bottom, it tended to induce a clockwise circulation or an anticlockwise circulation, respectively (Fig. 5). If the intrusion entered from the upper-middle or lower-middle layer, it would separate into two circulation patterns and cause an anticlockwise circulation in the upper layer and a clockwise circulation in the lower layer (Fig. 5). All the clockwise circulation would affect the upstream underflow. These water circulation patterns shown by this study were not

B-2

C

observed in other 2-D and 3-D models previously applied to XXB (Li et al., 2012a; Xu et al., 2009). Stratification patterns in XXB displayed unusual temperature stratification patterns compared with natural lakes (Wetzel, 2001). There was a “semi-U” thermal structure in the upstream reaches (site XX09 on November 25 in Fig. 8c) and a “step-like” stratification in the mid- and lower reaches of XXB (site XX01 on June 26 in Fig. 8a and site XX06 on October 5 in Fig. 8b). Usually, stratification in the relatively shallow upstream reaches was much stronger than that in the downstream reaches (April 28, May 10, June 26, July 13, August 24, September 16, and October 5 in Fig. 6), a finding that represents a contrast to traditional views (Yu and Wang, 2011). These unusual thermal patterns were due to the occurrences of dynamic density currents in the side arm (XXB). Generally, the intrusion from the

122

J. Ma et al. / Ecological Modelling 296 (2015) 113–125

Table 9 The factors, levels and experimental results of underflow scenarios. Experimental run

1 2 3 4 5 6 7 8 9

Factor

Results

A Upstream inflow rates to the XXB (m3/s)

B-3 Water temperature difference as underflow occurs (
C)

C Water level daily fluctuation (WLDF) (m/d)

Travel Thickness of the intrusion layer at distance (km) plunge point (m)

10 10 10 40.37 40.37 40.37 400 400 400

0.6 1.6 3.1 0.6 1.6 3.1 0.6 1.6 3.1

0.5 1.5 3.0 1.5 3.0 0.5 3.0 0.5 1.5

12.6 16.9 20.2 14.3 17.4 19.4 10.4 14.4 18.4

82 84 88 84 86 84 56 56 94

Table 10 Statistical analysis of underflow scenarios. Results

Factors

Travel distance

K1 K2 K3 R Sum of squared deviations F ratio

16.567 17.033 14.400 2.633 11.847 0.417

12.433 16.233 19.333 6.900 71.660 2.523

15.467 16.533 16.000 1.066 1.707 0.060

Thickness of the intrusion layer at plunge point

K1 K2 K3 R Sum of squared deviations F ratio Fc

84.667 84.667 68.667 16.000 512.000 1.274 3.46

74.000 75.333 88.667 14.667 394.667 0.982

74.000 87.333 76.667 13.333 298.667 0.743

mainstem of the TGR could not influence the upstream reaches significantly, and the upstream cold mountain inflows, which originated from Shennongjia Forest, flowed out of XXB from the bottom (Fig. 5). Accordingly, in the relatively shallow upstream portion, the well-mixed upper layer of warm water and the bottom cold water formed a “semi-U” thermal pattern (Fig. 8c). In the mid and lower reaches of XXB, when the intrusion from the mainstem of the TGR entered from the middle layer at the mouth of XXB, it destroyed the thermal stratification, producing unusual vertical profiles such as the “thermocline–mixed–thermocline” profile (site XX06 on September 16 in Fig. 6). If the water surface layer was mixed by high wind speeds but was still far away from interflow intrusion layers, then a four-layer “mixed–thermocline–mixed–thermocline” profile would be formed (site XX06 on April 28, June 26, and July 13 in Fig. 6). If the upstream underflow rate was very large and the bottom water was well-mixed, a five-layer thermal structure as “mixed– thermocline–mixed–thermocline–mixed” would be observed (site XX01 on June 26 in Fig. 8a and site XX06 on October 5 in Fig. 8b). When the intrusion from the mainstem of the TGR entered from the surface layer at the mouth of XXB, it destroyed the thermal stratification of XXB in the entire upper layer; additionally, the underflow water cooled the bottom layer, so that the whole XXB showed a “semi-U” thermal structure (Fig. 6 on October 5). Yang et al. (2010) also monitored the process through which a “step-like” pattern shifted to a “semi-U” during the impoundment after the flood season when the density current intrusion entered XXB from the surface layer. When the underflow intrusion from the mainstem of TGR intruded from the bottom, a large-scale anticlockwise circulation was induced, and the thermal stratification in the whole domain of XXB was weakened (Fig. 6 on February 16 and November 25). Ji et al. (2010a,b); Ji et al. (2010a,b) and Yang et al. (2010) also mentioned that this stratification was weakened during the winter when the side arm experienced underflow both from the upstream

A

B-3

C

and the mainstem. These “semi-U” pattern and “step-like” patterns were monitored and mentioned by Yang et al. (2012). 6.2. Influencing mechanism and implication of TGR operation on the density currents Through experimental and numerical analysis, we found that the travel distance of density currents was largely dominated by the temperature differences between the mainstem and XXB, followed by WLDF and then by inflow flow rates (Tables 6, 8 and 10). This result occurred because, first, temperature differences (density differences) were the cause of density currents (Chien and Wan,1999); the greater the temperature difference, the more water would be entrained and the longer it could travel. Second, the continuous propagation of density currents requires large flow rates. WLDF will produce larger flow rates and larger density currents entering XXB. Third, when upstream inflows from cold mountain streams sink to the bottom of XXB as an underflow and meet the density flow intrusion from the mainstem, shear effects and mixing occur at the interface. Therefore, the intensity of density current intrusion will diminish and eventually disappear as mixing occurs. Thus, upstream inflows will then prevent the development of a density current intrusion from the mainstem of the TGR. In contrast, WLDF is a more controllable factor because it can be used to influence the density currents and further break down stratification. Thus, changing current reservoir operation rules by controlling the magnitude and frequency of WLDF may be an effective way to mitigate algal blooms in the tributaries of the TGR. As Zhang et al. (2012) and Chen et al. (2013) have stated, density currents in XXB are vital to mass transport, physicochemical changes (Li et al., 2012b), and phytoplankton communities (Fang et al., 2013) in the aquatic ecosystems. Liu et al. (2012) has found that the development of thermal stratification in XXB is the major cause of

J. Ma et al. / Ecological Modelling 296 (2015) 113–125

seasonal variation in mixing depth and that a density current intrusion from the TGR is the major cause of short-term variation in mixing depth. Intense phytoplankton blooms are associated with a rapid increase of the ratio of euphotic depth to mixing depth during the spring and summer. Yang et al. (2010) discussed the influence of the impounding process of the TGR on eutrophication in XXB and addressed the control of the algal blooms in the side arms through the operation of the TGR. The water fluctuations in the TGR could dilute the algal blooms by increasing the water exchange between the CJ and XXB. In contrast, the fluctuations could restrict the algal blooms by destroying the stratification caused by density currents. During the fluctuation period, enhanced density currents will travel further and deeper. Hence, the mixing depth (Zmix) rapidly increases and exceeds the euphotic depth (Zeup), and the algae are mixed into a much deeper and darker environment according to the critical depth theory (Sverdrup,1953; van Ruth et al., 2010). The smaller the value of Zeup/Zmix, the more rapidly the algal blooms would disappear. Oliver et al. (1999) have suggested a range of 0.20– 0.35 for the critical ratio value of Zeup/Zmix. Accordingly, understanding the dynamics of density currents, the mechanisms of algal blooms, and the relationships between algal blooms and reservoir operations could assist in exploring strategies for preventing and controlling algal blooms. Hence, the hydrodynamic and water quality model of the TGR will be necessary to evaluate how reservoir operations can affect the ecosystem and control nuisance algal blooms and what operational strategies could control the algal blooms most efficiently.

x-Momentum equation Zz

@UB @UUB @WUB @h gcosa @r þ þ ¼ gBsina þ gcosaB  dz @x r @x @t @x @z 1 @Bt xx 1 @Bt xz þ þ qBUx þ r @x r @z

h

(A.2)

t xx ¼ Ax

@U @x

(A.3)

t xz ¼ Az

@U @z

(A.4)

z-Momentum equation 0 ¼ gcosa 

1 @P r @z

(A.5)

Free surface equation Bh

Zh

Zh

h

h

@h @ ¼ UBdz  @t @x

qBdz

(A.6)

Equation of state   r ¼ f T w; FTDS; FSS

(A.7)

Advective–diffusion equation

7. Conclusions The CE-QUAL-W2 model performed well in simulating the unusual thermal stratification of XXB and can be used in the future with in situ monitoring to better understand the importance of density currents for algal dynamics. The CE-QUAL-W2 model can accurately simulate the types, travel distance, thickness of the intrusion layer at the plunge point and circulation of intruding density currents. The main factors affecting density currents in XXB are water temperature differences between the mainstem and XXB, upstream inflow rates, and daily fluctuations in water level. The model theoretically confirmed the long-term existence of density currents and indicated that density currents have a major hydrodynamic impact in the tributary bays of the TGR.

@BF @UBF @WBF @ðBDx @F=@xÞ @ðBDz @F=@zÞ þ þ   @t @x @z @x @z ¼ q F B þ SF B

This research was supported financially by the National Natural Science Foundation of China (Grant Nos. 51179095, 51179205, 51209123), the University Graduate Research and Innovation Projects in Jiangsu Province (Grant No. CXZZ12_0245), and China Scholarship Council (File No. 201206710027). The authors would like to thank Dr. Chris Berger, Department of Civil and Environmental Engineering, Portland State University, and two anonymous reviewers for their valuable reviews and comments. The authors also extend their thanks to all of the members of the Engineering Research Center of Eco-Environment in the Three Gorges Reservoir Region, Ministry of Education, China Three Gorges University for participating in the field monitoring.

2

Az ¼ C m

k

(A.9)

e 





¼ B C e1 P þ C e2 þ Pe k k





@kB @kBU @kBW @ Az @k @ Az @k þ þ  B B  @z s k @z @x s k @x @t @x @z ¼ BðP2 þ G  e þ Pk Þ " P 2 ¼ Az

Az

 (A.11)

2 # (A.12)

(A.13)

Cf U 3 ð0:5BÞ

(A.14)

st

Pe ¼

@U @z

(A.10)

N2

G¼

Continuity equation (A.1)



@eB @eBU @eBW @ Az @e @ Az @e þ þ  B B  @t  @x @z @z  s e @z @x s e @x 2 e e

Pk ¼

Appendix A.

(A.8)

TKE (turbulent kinetic energy) model



Acknowledgments

@UB @WB þ ¼ qB @x @z

123

10C 1:25 U4 f ð0:5BÞ2

(A.15)

124

Cf ¼

J. Ma et al. / Ecological Modelling 296 (2015) 113–125

g C2

¼

gn2 1=3

Rh

sffiffiffiffiffiffiffiffiffiffiffiffiffi g dr N¼  r dz

(A.16)

(A.17)

where U and W are the laterally averaged velocity components (m/ s) in each of the x and z directions, B is the width of the water body (m), t is the time (s), g is the gravitational acceleration (m/s2), a is an angle and tan a is defined as the channel slope, r is the density (kg/m3), P is the pressure (N/m2), t xx is the turbulent shear stress acting in the x direction on the x face of the control volume (N/m2), t xz is the turbulent shear stress acting in the x direction on the z face of the control volume (N/m2), Ax is the longitudinal eddy viscosity (m2/s), Az is turbulent eddy viscosity (m2/s), h is the free water surface location (m), q is the lateral boundary inflow or outflow per cell volume (1/s), Bh is the time and spatially varying surface width (m), h is the total depth (m), f ðT w; FTDS; FSS Þ is the density function dependent on water temperature, total dissolved solids or salinity, and suspended solids, F is the laterally averaged constituent concentration (g/m3), Dx and Dz are the temperature and constituent dispersion coefficients in the x and z directions, qF is the lateral boundary inflow or outflow mass flow rate of the constituent (g/m3s), SF is the source/sink rate term for the constituent concentrations (g/m3s), Cm is an empirical constant, k is the turbulent kinetic energy (in the TKE model), e is the turbulent energy dissipation rate, P2 is the turbulent energy production from boundary friction, G is a buoyancy term, Pk, Pe are production terms from boundary friction, C is a Chezy friction factor, n is a Manning’s friction factor, Rh is the hydraulic radius, N is the Brunt–Vaisala frequency, s is the turbulent Prandtl number, and Cm and Ce are constants in the TKE model. Typical values of the empirical constants in the above model are s k = 1.0, s e = 1.3, s t = 1.0, Cm = 0.09, C1e = 1.44, and C2e = 1.92. References Afshar, A., Shojaei, N., Sagharjooghifarahani, M., 2013. Multiobjective calibration of reservoir water quality modeling using multiobjective particle swarm optimization (MOPSO). Water Resour. Manag. 27, 1931–1947. Berger, C.J., Wells, S.A., 2008. Modeling the effects of macrophytes on hydrodynamics. J. Environ. Eng. 134 (9), 778–788. Bowen, J.D., Hieronymus, J.W., 2003. A CE-QUAL-W2 model of neuse estuary for total maximum daily load development. J. Water Resour. Plann. Manag. 129 (4), 283–294. Chen, B., Liu, H., 2010. Relationships between phytoplankton growth and cell size in surface oceans: interactive effects of temperature, nutrients, and grazing. Limnol. Oceanogr. 55 (3), 965–972. Chen, Y., Liu, D., Yang, Z., Wang, Y., Ji, D., Zhang, P., Li, Y., 2013. The impacts of the stratified density currents on supply pattern of main nutrients in Xiangxi River. Acta Scientiae Circumstantiae 33 (3), 762–770 (in Chinese). Chien, N., Wan, Z., 1999. Mechanics of Sediment Transport. ASCE, Reston, Virginia, pp. 913. Choi, J.H., Jeong, S.A., Park, S.S., 2007. Longitudinal-vertical hydrodynamic and turbidity simulations for prediction of dam reconstruction effects in Asian monsoon area. J. Am. Water Resour. Assoc. 43 (6), 1444–1454. Cole, T.M., Wells, S.A., 2013. CE-QUAL-W2: A Two-dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model, Version 3.71. Department of Civil and Environmental Engineering, Portland State University, Portland, OR. Cunha, D.G.F., Calijuri, M.d.C., 2011. Limiting factors for phytoplankton growth in subtropical reservoirs: the effect of light and nutrient availability in different longitudinal compartments. Lake Reserv. Manag. 27 (2), 162–172. Dai, L.Q., Dai, H.C., Jiang, D.G., 2012. Temporal and spatial variation of thermal structure in Three Gorges Reservoir: A simulation approach. J. Food Agric. Environ. 10 (2), 1174–1178. Daines, S.J., Clark, J.R., Lenton, T.M., 2014. Multiple environmental controls on phytoplankton growth strategies determine adaptive responses of the N:P ratio. Ecol. Lett. 17 (4), 414–425. Deus, R., Brito, D., Mateus, M., Kenov, I., Fornaro, A., Neves, R., Alves, C.N., 2013. Impact evaluation of a pisciculture in the Tucuruí reservoir (Pará, Brazil) using a two-dimensional water quality model. J. Hydrol. 487, 1–12.

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