Effects of water level fluctuation on thermal stratification in a typical tributary bay of Three Gorges Reservoir, China

Region of interest

Xiangxi River is located in Hubei Province, China. The length of Xiangxi River is 94 km starting from Shennongjia Forest Region to Yangtze River, and the catchment area is approximately 3,095 km². Due to the operation of TGR, the 30 m WLF between the flood and dry seasons results in large variations on the backwater area of the Xiangxi River. The water from the Yangtze River intrudes into the Xiangxi River tributary when the TGR water level (WL) rise, and the maximum backwater area can extend to almost 40 km when the TGR WL reaches 175 m. This backwater area is referred to as Xiangxi Bay (XXB, Liu et al., 2012; see Fig. 1A). XXB is the focus of this study.

Measured data

Inflow discharge data was measured in 2010 from a hydrological station at Xingshan (Fig. 2A). WL data at the most downstream point of Xiangxi River at the intersection with the TGR for 2010 was obtained from the China Three Gorges Corporation (see Fig. 2B). As shown in Fig. 2A, the average inflow was 26.8 m³/s, with a maximum value of 348.8 m³/s on June 8 and a minimum value of 1.6 m³/s on December 9, 2010. From Fig. 2B, the high WL of 175 m was reached in late October and the low WL of 145 m occurred in mid-June. Based on the daily WL data, we calculated the daily WLF by comparing it with the value from the previous day. The daily WLF varied sharply during the flood season, with values ranging from 4.09 m on August 25 to −1.73 m on August 5.

Water temperature and the corresponding depth were measured using a Hydrolab DS5X multi-probe sonde (Hach, Loveland, CO, USA) with a vertical resolution of one m. Vertical profile measurements were taken weekly at sites XXU and XXD, and daily at site XXM.

Daily meteorological data were collected from the Xingshan Hydrological Station. The data show that the average AT was 17.4 °C, with a maximum of 32.4 °C on July 2 and a minimum of 3.2 °C on December 15. The average solar radiation was 127.5 J/m²s with a range from 5.8 to 304.4 J/m²s. The average surface water temperature was 20.1 °C, with a maximum of 31.0 °C on August 2 and a minimum of 11.3 °C on February 17 at site XXM. The surface water temperature, AT and short wave solar radiation in 2010 is shown in Fig. 3. AT from April to September correlated well with surface temperature with a correlation coefficient of 0.86.

Model description

The CE-QUAL-W2 (Cole & Wells, 2017) model is a vertical, 2D, laterally averaged hydrodynamic and water quality model that has been applied successfully in many stratified waterbodies (Sadeghian et al., 2018; Zhang, Sun & Johnson, 2015; Noori et al., 2015; Deus et al., 2013; Thomson & Fine, 2003). Because the model assumes lateral homogeneity, it is well-suited for relatively long and narrow waterbodies, which is the case for the XXB (Ma et al., 2015). Thus the CE-QUAL-W2 model was selected to simulate the hydrodynamic characteristics of XXB.

Simulation conditions and calibration

The model grid for the Xiangxi River was divided into 64 longitudinal segments of 500 m in length, and 109 vertical layers of one m in thickness; the entire water column was configured for a total of 4,385 cells (see Fig. 1B). The maximum depth was 100 m at the most downstream segment (the mainstem Yangtze River), while the depth in the upstream sections was only a few meters. To study the thermal stratification and its seasonal variation, field observation data for a complete year were acquired. Based on available field measurements, the simulated period was from January 1 to December 31 in 2010. The boundary conditions (upstream flow and downstream head) used for the simulation are shown in Fig. 2.

Calibration is the process of adjusting appropriate model parameters by matching the simulation results with the observed data. When the model can reproduce the observed results well, then it can be applied to simulate different but similar scenarios. Hydrodynamic conditions can be affected by several model parameters, such as the longitudinal eddy viscosity, longitudinal eddy diffusivity by influencing the temperature and hence density, Manning’s roughness coefficient, and the wind-sheltering coefficient. Little adjustment of model parameters or calibration was performed since most of the parameters used in the model were assigned default values. The wind sheltering coefficient was adjusted to 0.9 for Xiangxi River according to a previous study (Ma et al., 2015). This coefficient corrects the wind on the Xiangxi River from the measurement location by reducing the wind 10% throughout the entire waterbody. The model coefficients affecting hydrodynamics used in the study are shown in Table 1 and are largely default model coefficients.

Data analysis

The thermocline refers to the profile of maximum decrease rate of temperature in the metalimnion, and methods for estimating the thermocline from profile data including threshold of temperature and density or a critical gradient (Chung & Gu, 2009). In this study, the temperature-gradient threshold was used to calculate the thermocline parameters (Zhang et al., 2014). The uniform criterion of 0.2 °C/m was selected to determine the thermocline according to previous research on Xiangxi River (Liu et al., 2012). The thermocline depth (TD) and thermocline bottom depth (TB) were used as the scale of thermal stratification. The TD was defined as the depth of the upper most part of the thermocline, and the TB was defined as the depth of the lower most part of the thermocline (Liu et al., 2019), the thermocline thickness was the distance between the TD and the TB. Correlation analysis was performed using R software.

Thermal stratification in Xiangxi River

The seasonal variation in the water temperature at site XXM was analysed using data measured in 2010. As shown in Fig. 4A, the seasonal temperature variation was significant in Xiangxi River. At the surface layer, the minimum water temperature occurred between February and March, then increasing rapidly from April to its maximum value of approximately 31 °C in August. This seasonal variation of the water temperature of the surface layer was also seen in the variation of AT and solar radiation (see Fig. 3). Water temperature decreased from September to December. As the water depth increased, the variation in water temperature significantly trailed the AT variation. The maximum water temperature at different vertical elevations was reached at different times. For example, the maximum water temperature at the surface layer occurred in August, while the maximum water temperature at a depth of 35 m occurred in mid-October.

Figure 4 shows the stratification and destratification processes at site XXM. The water temperature rapidly increased at water depths between 0 and 15 m from 11 to 31 °C between February and August, with an increase of temperature at a rate of 0.1 °C/day. The rate of temperature increase rate was approximately 0.05 °C/day during the same period at a depth of 35 m. However, the maximum rate of increase of water temperature in the deeper layers could be higher than that of the surface layers. For example, the maximum value of the temperature increase rate was 0.23 °C/day (from May 21 to July 14) at a depth of 15 m, while the maximum rate of 0.51 °C/day (from April 16 to May 6) was found at a depth of 25 m. At a depth of 35 m, the increase rate was 1.28 °C/day (from February 1 to 10). This result may, however, be related to the hydrological conditions of Xiangxi River, with large temperature changes originating from inflow currents.

The surface water temperature began to rapidly decrease beginning in September (Fig. 3), and the epilimnion deepened following the reduced surface water temperature. The epilimnion reached a depth of 30 m in September, and the depth increased to 40 m in November. An unstable water temperature structure was observed from February to March, which triggered strong vertical mixing. The surface water temperature reached a minimum value in February. Stratification was therefore weak, and the waterbody was unstable, leading to strong vertical mixing.

The spatial variation in the water temperature of Xiangxi River was evaluated using data from August 9, 2010. As shown in Fig. 4B, there were thermal layers in Xiangxi River, and the thickness of each layer changed longitudinally from upstream to downstream.

Simulation of thermal stratification

Since thermal stratification was observed between April and September, the numerical model results were compared with data measured during this period. As shown in Fig. 5, the model not only reproduced the temperature profile but also the formation and duration of the thermal stratification. The simulated thermocline agreed well with the field-measured data from the downstream to the upstream, with an error of generally less than 1 °C. The simulated model results were consistent with the conclusions drawn by the analysis of measured data.

Thermal stratification was not evident in the downstream section of the XXB in late March, but stratification was significant in the middle and upstream sections during this period. In June, thermal stratification developed at a depth of 10 m in the downstream section of the XXB. The depth of the thermocline increased following the increased surface water temperature such that by August it had increased to a depth between 13 and 20 m. The water temperature difference between the surface water and the bottom was approximately 3 °C in August but completely disappeared by November at the downstream station, which indicated that the duration of thermal stratification in the middle and upstream portions of the XXB was longer than that in the downstream portion, reflecting the influence of the Yangtze River.

The impact of water level fluctuation on thermal stratification

The operation of TGR can cause WLFs which influence the hydrodynamic processes and the thermal regime in the Xiangxi River. Based on hydrological data from 2010, we found that WL significantly varied from June to October. During this period, only consecutive daily WLFs greater than 0.2 m/day were considered (see Table 2). The maximum total WLF was −14.03 m, which occurred from August 2 to August 16. The maximum mean daily WLF was 2.46 m/day, which occurred from July 20 to July 24. This result indicated that the WL rose and fell alternately from late June to mid-August. Then, the WL rose gradually, starting from late August, and reached a maximum elevation in late October.

Thermal stratification structure variation

The analysis of the correlation between TD and TB and the impact factors of AT, daily WLF, WL reveals that AT and WL had a significant effect on the thermocline parameters (see Fig. 6). AT was negatively correlated with TD and TB. The correlation coefficient between AT and TD and TB were −0.70 and −0.79, respectively, indicating that both the TD and the TB deepened with decreasing AT. The correlation between the daily WLF and the TDs was not significant during this period. The WL was positively correlated with the TDs. The correlation coefficient between the WL and TD and TB were 0.67 and 0.94, respectively. It indicates that WL variation had a strong effect on the thermal stratification structure.

The variations of the TD, the TB, the AT and the WL at XXM were evaluated from June to October 2010. As showed in Fig. 7, it was found that the TD was zero to five m with slight changes from June to late September, then below 25 m in October. The TB gradually increased from around 20 m on August 15 to approximately 45 m on October 15. The thermocline thickness varied from 1 to 44 m with a mean value of 18 m. The mean value of thermocline thickness was 19 m from June to late September, then decreased to three m in October. The WL significantly changed from late September to October, demonstrating that both the TD and TB deepened following increasing WL (see Fig. 7B). Hence, water level variations can affect the thermal stratification structure significantly.

The effect of various water levels on thermal stratification

To evaluate the effect of WL on thermal stratification, the CE-QUAL-W2 model was used to simulate different hypothetical situations. Since the WL and thermal stratification varied significantly from June to October in 2010, simulations were performed for the period between June 1st and October 31st. The range of WL was from 145.1 to 174.9 m, AT from 9.5 to 32.5 °C with a mean value of 24.4 °C, the inflow discharge from 6.1 to 348.8 m³/s, and the inflow temperature from 6.8 to 21.5 °C during this period. Hypothetical situations were designed in which WL was the only variable in each design condition. The baseline scenario used the measured field data as boundary conditions. The other two scenarios varied the WLF by ±5%. The other meteorological and hydrological conditions used the measured boundary conditions (see Table 3).

Variations in WLs affected the thermal stratification structure in Xiangxi River (see Fig. 8). The thermocline thickness increased with the increasing WL from June to late September, with little variation in October (see Fig. 8D). Both the TD and the TB increased when the WL increased by 5%, and the TD and the TB decreased when the WL decreased by 5% compared to the baseline simulation (see Figs. 8E and 8F). Hence, WL variation can affect the TD and the TB. As the WL rises, the TD and the TB were deepened. Nowlin et al. (2004) found reservoir stratification was more sensitive to WLFs than a natural lake. Naselli-Flores & Barone (2005) found that different hydrological years may result in different patterns of thermal stratification in summer. Wang et al. (2012) found that a low WL resulted in a higher surface temperature due to a decrease of impounded cold water. These studies indicated that WL variation can affect the thermal stratification, which is consistent with the findings of the current investigation.