Investigation on hydrothermal processes in a large channel-type reservoir using an integrated physics-based model

On the Earth's surface, rivers are considered as essential systems, from which water resources have been utilized extensively. However, our knowledge on the effect of water conservancy project and the behaviour of a river remains very limited, especially after being dammed (Avijit 2007; Arrifano et al. 2018). Over recent decades, more mega dams have been built in large rivers, with an unprecedented scale of manmade reservoirs being formed. The impoundment and regulation of water in a river can change both the hydrodynamic and thermal regimes, with alterations at both the spatial and temporal spans (Olden & Naiman 2010; Poff & Zimmerman 2010). The fluvial flow and water temperature are basic characteristics of an aquatic ecosystem, together with its physical, chemical and ecological processes.

These processes are also the basic elements of the habitat suitability for fish in a thermal cue for migration, spawning and hatching (Wootton 1990; Angilletta et al. 2008; Wang & Lin 2013). Angilletta et al. (2008) predicted that Chinook salmon in the Rogue River suffered a decrease in mean fitness after a dam construction, which resulted in delay spawning by adults or slowed development by embryos. Tao et al. (2018) pointed that in the Yangtze River, the spawning time of Chinese sturgeon was postponed for about 29 days after the Three Gorges Dam (TGD) was being built. The temperature variation caused by the dam can be far more than that caused by global warming, and it can affect the breeding of fishes significantly (Huang & Wang 2018).

Dam-induced thermal modifications have caused increasing concerns due to the growing awareness of hydro-environments. However, previous attention has been mainly focused on the vertical thermal stratification, which is important in lake-type reservoirs with weak vertical mixing (Yang et al. 2012; Lee et al. 2013; Milstein & Feldlite 2015; Azadi et al. 2018). Thermal stratification is especially meaningful for the selection of operation schemes and water withdrawal to avoid a negative thermal impact on downstream species and agriculture (Caliskan & Elci 2009; Zouabi-Aloui et al. 2015). However, the thermal regime and thermodynamic processes are also modified by the delivery, distribution and retention of heat (Olden & Naiman 2010). With respect to reservoirs built on the mainstream or major branches of mega rivers, the vertical mixing is relatively strong due to the large discharge and the channel shape. The dam-regulated water level can lead to significant changes in the water volume and surface area, elongating the water retention and altering the heat exchange. Therefore, some traditional engineering measurements, such as selective withdrawal, which are useful in a lake-type reservoir with usage of the thermal stratification, become invalid due to the absence of stable stratification in the channel-type reservoirs. Additionally, the complicated topography and dendritic branches along a reservoir affect its thermodynamic processes.

The effect of impoundment of a large reservoir is significant not only within the reservoir, which is a considerable length of a river, but also in a long downstream reach. For example, the Three Gorges Reservoir (TGR) extends more than 600 km, so that the thermal flux and horizontal distributions are more complicated, and a remarkable thermal variation has also been found at a station 690 km downstream of the dam, based on measurements (Zhou et al. 2019). Another example is the Amazon River, where hundreds of dams have been built or proposed to be built (Tundisi et al. 2014). The dams, through regulating water level and discharge, would affect the fluvial and basin environments to a large scale, including impact on fisheries, mercury methylation and forest degradation (Fearnside 2014; Chen et al. 2015; Arrifano et al. 2018). Thus, a detailed understanding of the effect of dam operation on the riverine hydrodynamic and thermal regimes is important for the health of the entire river.

The TGR, initially impounded in 2003, is the largest channel-type reservoir along the Yangtze River, with the total water volume being over 40 billion m³. Since impoundment, the eco-environmental issues, including thermal modifications, have been a major concern (Xu et al. 2011; Zhou et al. 2013; Huang et al. 2015; Wu et al. 2017; He et al. 2018). To date, existing studies have focussed mainly on the tributary reservoirs, where the hydrodynamic processes have been relatively weak with the increased water level and small discharge, and the vertical thermal stratification is the main feature (Yu & Wang 2011; Ma et al. 2015; Ji et al. 2017). The hydrothermal processes along this large channel-type reservoir have not been fully investigated. Zou et al. (2011) found that the outflow temperature of the TGR changed considerably since the dam was built in 2013, based on measured data from 1959 to 2006, and Dai et al. (2012) also predicted that the main reservoir exhibited no stable thermal stratification using a simulation approach. These studies were conducted before the dam started normal operation mode in 2003. The annual maximum of water level increased year by year from 139 m in 2003 to 175 m in 2010, after which the water level was regulated according to the designed scheme. However, only limited research has been carried out for the normal operation of the reservoir after 2010. More importantly, the impact of the regulated water level on the temperature variation has not been fully investigated yet, and the relationship between the two is unknown.

Numerical models are regarded as a useful tool to assess the impact of dam regulations on the hydrothermal conditions. Dai et al. (2012) applied the longitudinal–vertical two-dimensional model of CE-QUAL-W2, a physics-based model, to the main reservoir of the TGR. However, there was almost no obvious temperature difference in the vertical direction, based on the measurements over annual cycles after the normal operation of the reservoir (Long et al. 2016). Therefore, the CE-QUAL-W2 model was not cost effective for the TGR, and a long-term simulation would be hindered by the high computational cost for the vertical distributions of velocity and temperature. In addition, most of the tributaries were neglected in the model of Dai et al. (2012), which would introduce errors not only from the tributaries’ discharges but also from their storage volumes. Cai et al. (2018) used a new hybrid model to the TGR, which was developed by Toffolon & Piccolroaz (2015) and Piccolroaz et al. (2016) based on the concept of the zero-dimensional box model. Cai et al. (2018) found that the root mean square error (RMSE) of the predicted outflow temperature was as large as 2.45 °C, which is about half of reservoir-induced temperature variation, i.e., approximately 5 °C (Zhou et al. 2019). Thus, the hybrid model is not suitable for the channel-type reservoir, such as the TGR, where the water temperature varies significantly along the channel of the reservoir (Long et al. 2016). To summarize, a physics-based model with appropriate dimensions is necessary to predict the hydrothermal processes in channel-type reservoirs and to evaluate the effects of water impoundment.

This paper presents an investigation of the hydrothermal processes in the TGR under the dam-operation conditions by applying recently measured data and building an integrated physics-based model suitable for channel-type reservoirs. The model consists of a one-dimensional hydrothermal dynamic model and a box model for the main reservoir and sub-reservoirs, respectively. The impact of the dam operation on the hydrothermal processes is investigated, and the relationships between the inflow/outflow temperature difference and the dam-regulated water level are obtained. A brief introduction of the TGR is given in the ‘Study site’ section. Data collection, model building and related methods are presented in the ‘Data and methodology’ section. The results and discussion are shown in ‘Results’ and ‘Discussion’ sections, respectively, including the model-predicted and measured water levels, discharges and temperatures, as well as error analysis and scenario analysis. Finally, the conclusions obtained from the study are outlined in the ‘Conclusion’ section. The method and findings can be used to develop an in-depth understanding of the effects of building large channel-type reservoirs and to better manage the water environment in the Yangtze River and other similar mega rivers.

The TGD is located near the downstream end of the upper reach of the Yangtze River (Figure 1(a)). The Yangtze River, one of the largest rivers in the world, is in a subtropical zone and is influenced by seasonal monsoons. The river is 6,300 km long and has a catchment area of 1.8 × 10⁶ km² (Yang et al. 2006; Avijit 2007), with an annual runoff of 960 × 10⁹m³. The catchment has plenty of eco-resources and is an important human settlement for a population of over 400 million (Yang et al. 2006; EPA China 2015).

The Yangtze River has been heavily managed with more than 50,000 dams being built over the whole catchment. Among these dams, the TGD is the largest one, and more water conservancy projects have been planned during the next few decades (Zhou et al. 2013; Zhou et al. 2015). The TGD regulates approximately 50% of the runoff of the Yangtze River. It was completed in 2003 and then started to impound water. The dam is 2,309 m long, 181 m high, and the crest elevation is 185 m above the Wusong-Datum, a commonly used datum in the Yangtze River Basin. Under the design condition, the projected normal water level (PNWL) is 175 m with the reservoir surface area being around 1,000 km², the total capacity of 40 billion m³, and the flood control capacity of 20 billion m³, approximately. During a series of impoundment tests from 2003 to 2010, the maximum annual water level has been raised gradually to the PNWL of 175 m (Xu et al. 2011), as shown in Figure 1(b).

The water level has been regulated according to an operation scheme, as shown in Figure 1(b), concerning multiple factors, including mainly flood control, power generation, waterway navigation and water supply. During the annual cycles since 2010, the water level has been operated between 145 m and 175 m in the wet and dry seasons, respectively. During the wet season, i.e., from June to September, the near-dam water level has been kept at a relatively low level of 145 m, called the flood control water level (FCWL), to provide storage capacity for large floods. From late September to October (the end of the wet season), the reservoir begins to impound water, and the water level rises gradually to 175 m. During November and December, the water level is maintained at a high level for power generation. From January to May, the water level has been lowered down gradually but not below a dry control water level of 155 m to allow for navigation.

The ecological impact of the TGD has become a key issue, in which the thermal regime, as a basic factor, has received much public attention. It has been found from field observations that significant temperature changes have occurred after the TGR impoundment (Yu et al. 2007; Zou et al. 2011). Although attention has primarily been paid to the vertical thermal profiles, field measurements have indicated that there is no obvious stratification in the reservoir (Wang et al. 2011; Cao et al. 2012; Dai et al. 2012; Long et al. 2016). On the other hand, a significant change in the water temperature has occurred along the whole length of the channel-shaped TGR during annual cycles, and the water temperature difference between the inflow and outflow has increased significantly since impoundment (Long et al. 2016).

To investigate the thermodynamic processes in the TGR, a comprehensive data collection and processing exercise was conducted. The data acquired include topographic data covering the entire TGR, as well as the hydrological and meteorological data from 2010 to 2012, the first 3 years after the dam operated with the PNWL.

The cross-sectional shapes vary significantly along the TGR. The inserts in Figure 1(a) show two typical cross-sections: a wide cross-section with a water surface width being more than 2 km and a narrow cross-section with a width being about 300 m. In total, a set of data representing 471 cross-sections along the main channel of the YR and two main tributaries, i.e., the Jialing River and Wu River, were collected. The distance between neighbouring cross-sections varies along the channel, with the values being from 1 km to 3 km. The other 20 minor tributaries have very small discharges, although their storage capacities for water and heat are significant, thus their depth–area–volume relationships are specified for water and heat fluxes.

The daily values of water surface elevation, discharge and temperature were collected along the reservoir. The surface elevation data were acquired from six hydrological gauging stations, namely Cuntan, Qingxichang, Wanxian, Fengjie, Badong and Miaohe, and their locations are shown in Figure 1. Discharge data were acquired from seven hydrological stations along the TGR, including Zhutuo, Beibei, Wulong, Cuntan, Miaohe, Huanglingmiao and Yichang, while the water temperature data were available at eight stations, including Zhutuo, Beibei, Wulong, Cuntan, Badong, Miaohe, Huanglingmiao and Yichang. The meteorological data, including the air temperature, wind and humidity, were acquired from five weather stations along the TGR. The five stations were Shapingba, Wanxian, Fengjie, Badong and Yichang, and the labelled sites 1–5 are shown in Figure 1(a).

Figure 2 shows a schematic view of the model. The model consisted of a one-dimensional hydrothermal dynamic model and a box model, in which the air–water heat fluxes were calculated based on the meteorological conditions, as described in the following subsections: Hydrothermal dynamic model, Box model for the sub-reservoir and Heat flux through the air-water interface. With regard to the TGR, the model domain consisted of the main reservoir (756 km long from the TGD to Zhutuo station) and 22 tributaries, which covered the main dendritic system of the TGR. Two main tributaries, Jialing River and Wujiang River, were included as branch channels in the model because of their considerable contribution of inflow discharge to the reservoir. Thus, a dynamic model was set up to predict the hydrothermal processes in the main reservoir and two main tributaries. With regard to the other 20 minor tributaries, their combined discharge was small, but the total volume was relatively large. The main role of these 20 branches was to provide storage capacity, i.e., storing or releasing water with the seasonal variation in the water level. These tributaries are referred to as sub-reservoirs in the present study. Therefore, the box type model was applied to each minor tributary using a specific depth–area–volume relationship to calculate the water volume and heat budgets.

Both the solar radiation flux and the heat exchange rate through the water-atmospheric surface were determined based on the meteorological condition, including the cloudiness, atmospheric temperature, relative humidity and wind speed. The inflow discharge and water temperature from the mainstream and tributaries were used to specify the upstream boundary conditions, while the measured water level at the TGD was used to specify the downstream boundary condition for the reservoir. The station of Miaohe is located very close to the dam site (16.42 km upstream), and the water depth is large (>100 m). Therefore, the water level at the Miaohe was practically identical to the water level at the dam and was used to specify the downstream boundary condition.

The Manning coefficient was given as a distribution along the reservoir according to the channel properties and a long-term relationship between the water level and discharge. The value range was from 0.0265 to 0.0733, which was in accordance with the previous settings (Zhou et al. 2015). The longitudinal dispersion was calculated using Elder's formula, ⁠. It was found in the pre-running cases that the longitudinal dispersion played a very limited role in the model-predicted temperature distribution in this advection-dominated reservoir. The momentum correct factor was set to 1, considering the momentum situation in the reservoir.

The governing equations were discretized using the Preissmann scheme, and the principle of three-phase algorithm was applied (Islam et al. 2005; Zhu et al. 2011). The meteorological data were interpolated over the model grids. The time step was set to 5 min, with the Courant number being approximately 6, which was determined using a trial and error method. Six months of pre-running was conducted for the model to obtain the initial water elevation, discharge and temperature at each grid in the computational domain. Two pre-running cases were undertaken, one with a 6-month period and the other being a 1-year period. These scenario analyses showed that the predicted variables were convergent.

In Equations (1)–(3), the water discharge is included in the lateral inflow together with its temperature ⁠.

The Huanglingmiao and Yichang stations were the two hydrological stations located closest to the TGD, approximately 8 km and 38 km downstream of the dam. Therefore, the measured water discharge and temperature values at the Huanglingmiao and Yichang were used for the outflow in the current study.

The model-predicted water-level, discharge and temperature values were compared with measured data at the hydrological stations along the TGR (see Figure 3). It can be seen from Figures 3(a)–3(c) that almost all data points are distributed at or near the diagonal lines, which indicates that these model predictions are generally close to the measured results. For all of the three parameters, the correlation coefficients are greater than 0.97, as shown in Figures 3(a)–3(c). The model-predicted and measured water levels are given in Figure 4(a). The comparison shows a satisfactory agreement between the levels over the annual cycles, with correlation coefficients being above 0.99. The water temperature time series are plotted at four stations: two stations in the upstream reach and the other two stations in the downstream reach (see Figure 3(d)). The locations of these stations are shown in Figure 1. The model-predicted temperature values are very close to the measured data points when reproducing the seasonal temperature variations.

Table 1 lists the statistical metrics of the errors in the model-predicted water level, discharge and water temperature. The predicted and measured water levels were compared at six stations along the TGR from the Cuntan to Miaohe stations. The average RMSE of the water level was 0.204 m, the correlation coefficient (CC) value was 0.999, and the relative error (RE) value was approximately 0.5%. The measured discharge data at four stations, i.e., Cuntan, Miaohe, Huanglingmiao and Yichang, were used for verification. The average values of the RMSE, CC and RE were 718.4 m³/s, 0.994 and 1.03%, respectively, indicating good agreement between the model predictions and measurements. With regard to water temperature, the errors were estimated at three stations, i.e. Badong, Huanglingmiao and Yichang. The mean RMSE value was 0.685 °C, and the average of the CC between the predicted and measured data was 0.982. The relative error was less than 5% with an average of 3.23%. In total, the predictions were satisfactory with errors in an acceptable range.

With regard to the temperature variation induced by the dam operation, the model performed very well. The RMSE of model-predicted outflow temperature were 0.605 °C and 0.898 °C at stations of Yichang and Huanglingmiao, respectively, as shown in Table 1. The accuracy of the present model is better than the existing hybrid model, in which the corresponding RMSE was 2.45 °C (Cai et al. 2018). It has also been pointed out by Cai et al. (2018) that the robustness of the hybrid model decreased with strong hydrological variations, such as the dam-induced thermal variation. The main reason is that there is only one temperature value for the whole TGR in that box-based hybrid model, while the temperature varies significantly along the channel-type reservoir, as the measurements shown by Long et al. (2016) and in Figure 3 of the present study. The hydrothermal model used in the present study is able to reproduce the temperature and velocity distributions along the reservoir more accurately. From the viewpoint of computational cost, the present model is still rather effective. For instance, it takes approximately 2 min to complete a 1-year simulation when using a CPU of Intel i7-6700 (3.4 GHz). Therefore, it is feasible for long-term and large-scale simulation in channel-type reservoirs, and potentially for cascade reservoirs in a mega river.

To summarize, the model predictions agreed generally well with the measurements. The relative errors of model-predicted water level and discharge were approximately 0.5% and 1%, respectively, and the error in the temperature was less than 5%. Therefore, the model prediction accuracy is considered satisfactory and can be used for predicting the hydrodynamic and thermodynamic processes in channel-type reservoirs under the dam-operation condition.

Figure 4(a) shows time series of water levels at four stations along the TGR, i.e., Zhutu, Cuntan, Qingxichang and Miaohe, from upstream to downstream with the locations being displayed in Figure 1(a). The water surface profiles along the main reservoir are displayed in Figure 4(b) together with the thalweg elevation. Figure 4(b) also shows the locations of the seven hydrologic stations, which are located 756 km (Zhutuo), 604 km (Cuntan), 479 km (Qingxichang), 289 km (Wanxian), 161 km (Fengjie), 69 km (Badong) and 16 km (Miaohe) upstream from the TGD. The Miaohe station is close to the dam site where the water level is considered to be the same as the near-dam water level.

The red line in Figure 4(a) shows the near-dam water level, which is close to the operating rule (the broken line) specified by the TGD authority. During the dry season, the near-dam water level was kept at the PNWL (175 m), while during the wet season the water level was reduced to the FCWL (145 m), except for the temporal water level increase due to the successive floods. With respect to the water-level regulation, an optimal operational strategy has been proposed and discussed according to practice, including impounding in advance and dynamic water-level control (Li et al. 2010, 2014; Huang et al. 2015). The operating rule of the water level shown in Figure 4(a) was the basic rule adopted in practice.

In Figure 4(a), the time-varying water levels differed from one another at the three upper reach stations: Zhutuo, Cuntan and Qingxichang. At Qingxichang, the water level (the green line) was close to that at Miaohe (the red line) over the annual cycles. However, between the Cuntan (the blue line) and Miaohe, there was a significant water-level difference in wet seasons, while both water levels were kept at approximately 175 m during the dry season. This difference can be explained by the seasonal variation within the backwater area. As shown in Figure 4(b), in the wet season, the backwater limit is near Qingxichang, which was about 120 km downstream from Cuntan. The bed elevation at Cuntan was generally higher than 145 m (the broken red line). Therefore, Cuntan's water level was not controlled by the TGD regulation during the wet seasons. However, in the dry seasons, the backwater appeared upstream of Cuntan due to the higher water level of 175 m. Hence, the water surface was rather flat from Cuntan station to the TGD, which led to the similarity in the dry season's water levels at Cuntan, Qingxichang and Miaohe, also shown in Figure 4(a).

In the reach upstream from Zhutuo to Cuntan, as shown in Figure 4(b), the water level was higher during the wet season (the red line) than the dry season (the blue line). This increase in water level was mainly caused by the larger discharge in the wet season. In contrast, downstream from Cuntan to the TGD, the water level was generally higher during the dry seasons than the wet seasons. The reversed results were due to the water-level regulation of the TGD. Therefore, the dominant factors that control the water level were different in reaches downstream and upstream from Cuntan. In the upper reach from Zhutuo to Cuntan, the seasonal discharges dominated the water level, while in the downstream reach from Cuntan to the TGD, the regulation plays a more important role on the water level.

Figure 5 shows the water discharge flowing into and out of the TGR. It can be seen that the discharge is characterized with a significant seasonal variation. During the wet seasons, the peak flood discharge entering the reservoir was greater than 65,000 m³/s, while the maximum discharge leaving the reservoir was less than 45,000 m³/s. This operation relieved the flood risk for the downstream region, but at the same time the water elevation increased significantly inside the reservoir, as shown in Figure 4. Another noticeable phenomenon was the increase in the minimum discharge during the dry season. The inflow discharge ranged from 3,000 to 5,000 m³/s, while the outflow discharge was between 6,000 and 7,000 m³/s. The supplemented water was used for power generation and downstream waterway navigation during the dry season.

Figure 6 shows the TGR inflow and outflow water temperatures over three annual cycles, as well as their difference. The method of monthly moving average was used to remove short-term fluctuations, shown as thick lines in Figure 6. In general, both the inflow and outflow temperatures varied seasonally over the annual cycles. The minimum water temperature was approximately 10 °C, which occurred in the dry season from January to March, while the maximum water temperature could reach up to 25 °C during the wet season from July or September. The range of the seasonal temperature variation was approximately 15 °C. The water temperature increased rapidly in spring and decreased in autumn.

As seen in Figure 6, there was a significant difference between the inflow and outflow water temperatures. The outflow temperature showed an obvious phase lag when compared to the inflow temperature. The lag time could reach up to 2 months, which occurred in the dry season. As a result, there was an increase in temperature before February, and a decrease after that. The temperature difference could be greater than 5 °C in the early dry season and the early wet season, which was approximately one-third of the range of the annual temperature variation. However, before the TGD was built, the water temperature values in these two locations varied in a nearly synchronous manner (Zou et al. 2011). The temperature phase lag was due to its spatial (longitudinal in this case) and temporal variations, which were closely related to the operation of the dam. In addition, for the inflow water temperature, short-term fluctuations were also significant with periods of less than a month. However, with regard to the water leaving the TGR, the temperature distributions were rather smooth with very weak fluctuations, which was attributed to the mixing processes in the TGR.

With the dam-regulated water-level and seasonal discharge variation, the water volume in the TGR changed significantly over time, as shown in Figure 7. Both the total volume of TGR and the component of sub-reservoirs are presented. There are 22 sub-reservoirs in total (see Figures 1(a) and 2). It can be seen from Figure 7 that the two volumes varied with both seasonal and short-term fluctuations. The seasonal variations were caused by the water-level regulation, while the short-term fluctuations were attributed to flooding events. The maximum volume of the TGR was approximately 45 × 10⁹ m³, which occurred in the dry season when the near-dam water elevation was kept at 175 m. During the wet season, the water volume decreased to approximately 23 × 10⁹ m³. The active volume was approximately 22 × 10⁹ m³, which was the flood control storage capacity of this reservoir, i.e., the effective storage capacity. The volume of all sub-reservoirs was approximately 10 × 10⁹ m³, accounting for nearly 20% of the volume of the TGR, while the active volume of sub-reservoirs was approximately 6 × 10⁹ m³, which accounted for more than 25% of the total active volume of the reservoir. This significant capacity of the storage indicates that the sub-reservoirs play an important role in the main reservoir's hydrodynamic and thermodynamic regime.

A scenario analysis was conducted to identify the impact of the dam operation on the thermal condition of the TGR. Four scenario runs were carried out with different water-level regulations, as listed in Table 2. These water-level variations were set according to the historic water levels since the initial impoundment of the reservoir was started, which are shown in Figure 1(b). Scenario S1 was carried out according to the condition before the construction of the TGR. The initial impoundment was represented by scenario S2, which occurred from 2003 to 2006, with the water level varying between 135 m and 140 m, as shown in Figure 1(b). Scenario S3 was set for the second stage of the impoundment in 2007 and 2008, when the water level changed from 145 to 155 m. Scenario S4 was for the normal regulation after 2010, when the FCWL (145 m) and PNWL (175 m) were used during the wet and dry seasons, respectively. The variation range increased from 5 m to 30 m in the progressive stages of impoundment. To diagnose the impact of the water-level regulation, the same incoming discharge process was imposed for all four scenarios.

Figure 8(a) shows a comparison between the inflow and outflow temperatures without the regulation of the TGR. It can be seen that almost all data points are located near the diagonal line, which indicates that there was no significant temperature difference between the inflow and outflow. This finding is very different from the other three conditions. Even in the initial stage of impoundment, as shown Figure 8(b), differences between the inflow and outflow temperatures were obvious. When the water temperature increased, the outflow temperature was lower than the inflow temperature, and vice versa. As a result, a loop curve was formed, which indicated the seasonal phase lag between the inflow and outflow. With a further impoundment in the TGR, as shown in Figures 8(c) and 8(d), the phase lag became more significant. Therefore, it can be concluded from the scenario analysis that the dam operation played an important role on temperature variation.

To quantify the relationship between the water-level regulation and temperature variation, a regression analysis was conducted. In Figure 9(a), the lag time between the inflow and outflow temperatures was regressed against the water level using an exponential function. It can be seen that the lag time was less than 5 days when the water level was 50 m. If the water level was increased to 150 m, the lag time would be increased over 30 days. Furthermore, if the water level was up to 175 m, then the time lag would be approximately 60 days. With regard to this regressed curve, the correlation coefficient was 0.91, so that it can be considered reliable to represent the relationship between the water level and temperature lag time.

The maximum temperature difference between the inflow and outflow can also be predicted using an exponential formula against the TGD-regulated water level (see Figure 9(b)). When the water level was regulated at approximately 50 m, the temperature variation was approximately 1 °C. If the water level was increased to 150 m and 175 m, the temperature variations were 3.5 °C and 5 °C, respectively. In Figure 9(b), the orange data points represent a higher temperature of outflow than inflow, while the blue points represent the lower temperature. Both data points fitted with the regressed exponential formula generally very well, with a correlation coefficient of approximately 0.89.

The hydrothermal processes in a large channel-shaped reservoir, the TGR, were investigated based on a series of field measurements and a physics-based integrated numerical model predictions. The model domain covered both the main reservoir and sub-reservoirs. The numerical model was satisfactorily verified against the measured data, with mean relative errors of 0.54%, 1.03% and 3.23% with regard to water levels, discharges and temperatures, respectively. With such close agreement, the model was considered a reliable tool for predicting the governing hydrodynamic and thermodynamic processes. The model was then used to simulate the hydrothermal processes in the TGR to investigate the impact of the regulated water level on the inflow and outflow temperature lags. The key findings were obtained from both the field measurements and model simulations are summarized below.

In this channel-shaped reservoir, the water level varied seasonally under the joint effect of dam operation and water discharge. The backwater limit moved between Cuntan and Qingxichang seasonally by the water-level regulation rule. Within the backwater reach, the surface elevation was mainly controlled by the dam operation, at 175 m and 145 m in the dry and wet seasons, respectively. In contrast, upstream from the backwater limit, the water level was higher in the wet season than the dry season, caused by the seasonal variations in the normal water depth determined by the discharge.

With the reservoir's function of flood control in the wet season, the outflow discharge was controlled under 45,000 m³/s, although the inflow discharge could be over 65,000 m³/s. In the dry season, the outflow discharge was increased up to 6,000 m³/s from a small inflow discharge. The component of sub-reservoirs accounted for approximately 20% of the total water volume and approximately 25% of the total active volume, which was an important contributor to the TGR.

The seasonal temperature variation dominated the reservoir's thermal regime. From both field measurements and model predictions, a significant seasonal phase lag was found between the inflow and outflow temperatures, especially during the dry seasons. The lag time can reach up to 2 months with an increase and decrease in the temperature of up to 5 °C. Scenario analysis showed that the phase lag and difference between the inflow and outflow temperatures were closely related to the dam operation. The range of temperature difference increased with a rising water level. Two regressed exponential curves were used to represent functions of the inflow/outflow lag time and maximum temperature difference against the dam-regulated water level. If the water level was 50 m, then the lag time was less than 5 days and the temperature difference was only approximately 1 °C. When the water levels increased to 150 m and 175 m, the lag times were 30 and 60 days, and the temperature difference increased to 3.5 °C and 5 °C, respectively. The outcome of this study, especially the newly regressed relationships, could be useful for developing better environmental and ecological management measures of large reservoirs.

This research was supported by the National Key Research and Development Program of China (2016YFC0502204, 2016YFA0600901) and the National Natural Science Foundation of China (51779121). The authors are grateful to the funders for their support.