Study on pollution traceability based on the optimized hydrodynamic model of Tai Lake

C_s

Wind drag coefficient, dimensionless;

TP

Total phosphorus, mg/L;

TN

Total nitrogen, mg/L;

APP

Application software on the phone;

GPS

Global Positioning System;

WER

Water exchange rate; %;

LPT

Lagrange particle tracking.

Sensitive areas, which means areas that will not be directly affected by external pollution and need to provide people with clean water resources in this study, mainly include the Center Area, East Area and East Lake in Tai Lake, especially the East Area, which is the most important area in Tai Lake because there are many drinking water sources. From 2017 to 2019, a major outbreak of cyanobacteria in Tai Lake and a steep rise in the total phosphorus (TP) concentration in a sensitive area attracted the attention of the Chinese government and related researchers (Xu et al. 2019). The temperature, light, hydrodynamic conditions and nutrient concentration threshold are the key factors that cause the flowering of cyanobacteria (Guo et al. 2015; Gong et al. 2017). Synchronous growth pattern of nutrients (TP and TN) and algae in the sensitive area suggests that there is a close relationship between the algal blooms and nutrient transport. However, there are few studies focusing on the hydrodynamic laws of the different parts of Tai Lake (Zhu et al. 2007; Ke et al. 2019), making it impossible to reliably analyze or clarify the transport process of pollution groups (Rabe & Hindson 2017). The research on the transport process of pollution groups is also lagging behind due to the lack of current studies on the main hydrodynamic parameters. Now the ‘water diversion from Yangtze River to Tai Lake’ project is also increasing the degree of influence of Tai Lake (Yu et al. 2018), while studies of wind drag coefficient have gradually unmatured, most developed Tai Lake models still use the wind drag coefficient as a constant (Li et al. 2013b), which has significantly limited the analysis of the transport process of pollution groups.

At present, the coefficient of wind drag can be determined by direct and indirect measurement methods (Bell et al. 2012). The direct measurement method (eddy correlation method), which measures atmospheric motion on the basis of acoustic principles. To be precise, the ultrasonic wind, temperature, and humidity sensor measures the pulsation of wind speed, the pulsation of quantity induced by turbulent motion in the atmosphere and the movement of momentum (Babanin & Makin 2008). Flow velocity is obtained by measuring the covariance between the wind speed and the pulsation of the physical quantity (Garratt 1977). The direct measurement approach is reliable and accurate, but the instrument is accurate and costly. It is therefore widely used in fixed offshore observation platforms in national programs, but is not applicable to specific everyday observations. The indirect measurement method measures the momentum flow based on the average of the meteorological state variables (sea surface temperature, surface air temperature, relative humidity, wind speed, etc.) from the standard marine meteorological observation instrument using the block method to obtain the wind drag coefficient expression (Blanc 2010). This approach has the benefits of low cost and convenience of observation devices, but data measurement time is longer and precision is poor. It cannot represent the extensive changes in the turbulence, and the findings are not entirely objective (Li & Fu 2018). In addition, the indoor experimental determination of the wind drag coefficient is inaccurate due to the difficulty of indoor wind generation and the variations in wind speed (Hwang 2018). Unlike the ocean, Tai Lake does not have a set wind speed, temperature, humidity and surface seawater temperature observation station, leading to greater difficulties in measuring the wind drag coefficient (Luo et al. 2016).

In this study, in-situ experiments of the flow velocity and sediment distribution in Tai Lake were carried out. External input conditions were collected during the experiment period (http://data.cma.cn/). The relationship between wind drag coefficient and wind speed was obtained with the help of the hydrodynamic model, and the degree of influence for the sensitive area from five different sources with the typical wind fields was simulated based on the optimized hydrodynamic model. This study provides scientific analysis for the transport process and traceability of pollution groups, meanwhile giving some suggestions for reducing the environmental risk for the sensitive area.

Tai Lake (119°08′E–122°55′E, 30°05′N–32°08′N) is the third largest shallow lake in China, with a total water surface area of 2,338 km², the maximum and minimum bottom elevation are 1.95 m and 0.75 m, the average water depth of the whole lake is 1.9 m, while the average water depth of the eastern bay is 0.9 m (Yan et al. 2016; Chao et al. 2017). Daily data from the China Meteorological Data Network (http://data.cma.cn/) over the past decade indicate that its average annual evaporation is 1,219 mm and the average annual rainfall of Tai Lake Basin is 1,254 mm in the last 10 years. The wind direction is dominated by the south-eastern monsoon and the north-western monsoon, with wind speeds varying from 0 to 10 m/s. The average wind speed for spring, summer, autumn and winter is 4.62 m/s, 4.2 m/s, 3.5 m/s and 3.87 m/s, respectively. And the overall average wind speed was 4.05 m/s from 2007 to 2017 (Figure 1) (Li et al. 2017b). The development of the water diversion from the Yangtze River to Tai Lake project leads to the amount of water entering the lake increasing, and the water exchange cycle decreasing from 300 days to 170 days (Jiang et al. 2018). Many studies have found that the increased water volume will improve the transport speed of pollutants to the east area, and reduce lake self-cleansing time, leading to the pollution from input lake areas coming to the sensitive area (Wu et al. 2019; Xu et al. 2020).

This study conducted in-situ flow velocity and flow direction measurement experiments in Tai Lake during May 13–15, 2019. Experimental equipment was deployed in Gong Bay, Zhushan Bay, Meiliang Bay, East and Western Coast Areas (Northwest and Southwest Territories), respectively. The coordinates data were obtained every 20 minutes. The key information required for the experiment was the amount of water flowing in and out of the lake (once a day) and the data on the wind field (once an hour) during the experiment, which was published by the Tai Basin Management Bureau of the Ministry of Water Resources (http://www.tba.gov.cn/).

Based on the patent of our team (CN207570760 U), this study launched particle tracking equipment in five major parts of Tai Lake, modified the equipment at 3/4 water level through sandstone to ensure that it does not directly interfere with the wind field and meets the requirements of the ideal water particle. ArcGis and Haversine methods were used to process information from the GPS base station and APP, and calculated the average flow velocity and flow direction every 20 minutes. Based on the hydrodynamic model and boundary conditions, the wind drag coefficient was calibrated with the wind stress equation, combined with the information on the wind field, and the particle transport direction trajectory was confirmed. In order to more clearly express the impact of hydrodynamics on pollution transport, the LPT method was adopted in this study. Based on the assumption that pollutants are conservative substances, the redistribution of pollutants in each part of Tai Lake during the water diversion period was simulated without considering the degradation condition. During the period of water diversion from Yangtze River to Tai Lake with the typical wind field, the transport process of pollution groups was studied (Figure 2).

Hydrodynamic model: To accurately calculate the transport process of the pollution groups, this study employed a hydrodynamic model used in this study that is based on the Navier-Stokes equations of three-way incompressible flow and Reynolds values and was subject to the assumption of Boussinesq and hydrostatic pressure. The finite volume method was applied to calculate the spatial discretization. Its mathematic expression is shown in the equations below (Xu et al. 2020).

For n = 1, 2, 3, … according to Euler's formula with drift term a and diffusion coefficient b. is the normal distribution Gaussian increment of Brownian motion W, which is a continuous Gaussian stochastic process with independent increments in subinterval ⁠.

Considering the time of start and landing of the equipment, the buffer time of one hour is removed. Average surface speed (Figure 3) with Western Coastal Area (16.01 cm/s) > Meiliang Bay (14.40 cm/s) > Gong Bay (12.25 cm/s) > Zhushan Bay (10.7 cm/s) > East Area (9.39 cm/s). The Western Coastal Area has the highest flow velocity and the most obvious range of variations, due to this area being susceptible to the wind field and with rare water vegetation coverage. On the other hand, although the flow velocity is lower in the Bay Area, the average flow velocity is lowest in the East Area because of the many islands and dense aquatic plants. The results show that the flow velocity in Tai Lake is: Western Coastal Area (open lake area) > Meiliang Bay & Gong Bay (open bay area) > Zhushan Bay (near bay area) > East Area (island cluster area).

In view of the incomplete tracking time at Zhushan Bay, the flow velocity of the other four installations was simulated for 24 hours. Tai Lake is a typical large shallow lake with no high mountains around it, therefore the wind shelter coefficient was set to 1 (Li et al. 2011), and the roughness coefficient range of Tai Lake was estimated to 0.005–0.05 based on the results of Morales et al. (Morales-Marín et al. 2017). Based on the measured data, the wind speed range during the experiment is 1–12 m/s, then calibrated M and N are 0.8 and 0.17 (Equation (15)), respectively. The average wind drag coefficient is 0.0019, which is slightly higher than the wind drag coefficient of the ocean (Mao & Xia 2017), because the ocean is heavily affected by waves. On the case of the wind drag coefficient being taken as constant and variable values, the calculated velocity of the four particles matches well with the measured velocity (Figure 4). Nevertheless, the variance range of the flow velocity when the C_s is a constant is smaller than that when the C_s is considered as a changing value, will accurately reflect the shift in flow velocity at different wind speeds.

The trajectory of the equipment was confirmed with Arcgis. After the hourly coupling of information on wind stations using the Thiessen polygon, the system's motion trajectory was validated with the Lagrange model. When the drift coefficient a is 1 and the diffusion coefficient b is 0, the simulation results of the transport trajectories of the five devices are highly consistent with the measured motion trajectories (Figure 5). The lake bay area has considerably better simulation performance than other lake areas. This is because the movement under the control of the wind field is not prone to the effect of the flow of water in other regions, which enhances the stability of the local flow system and decreases interference from other external factors. Although the lake area shows the same general trend, it is distorted by the flow of rivers into and out of the lake and the effect of lake currents in other areas, and the distortion is extreme. Since there are a large number of islands in the East, the direction of the water flow is opposite to the actual result. The results further verify that the main factors affecting the flow velocity and direction of large shallow lakes are the terrain and the wind field. With the terrain unchanged for a long time, the direction of the flow and the velocity of the flow depend on the direction of the wind and the speed of the wind. Overall, the optimization of the hydrodynamic model has been completed.

The above model was used to study the transport trajectory and the degree of influence of pollution groups during the diversion period. Set the initial water level, flow rate and discharge from the Wangyu River as 3.3 m, 0 m/s and 200 m³/s, respectively. And the overall volume of water from other rivers to Tai lake amounted to 11 billion m³ in 2017. In each location, the transport process of the pollution groups was simulated by the typical wind fields of southeast wind and northwest wind with the speed of 1–10 m/s. Maximum simulation time was set at 60 d according to the Annual report of water diversion from Yangtze river to lake Tai (2007–2017) (http://www.tba.gov.cn/). At the same time, the average TP (Total phosphorus) and TN (Total nitrogen) from the major sources are determined by the measured data in 2017. Then a simulation study was carried out on the transport process of pollution groups in the main inflow areas with the influence of a conventional wind field, to determine the most important pollution sources for the sensitive area.

The results show that the pollution mass in the northwest lake area is the main source of pollution in the sensitive area at present, and different wind directions and speed will have a significant impact on the pollution source's motion and influence proportion. Under the condition of the southeast wind, the pollution from Wangyu river caused by water flux density will increase relatively, and can achieve about 27%, but the impact and scope will be far less than the northwest to the total (Figure 7-1). Under the condition of the Northwest wind, the pollution from the Northwest Area effect on the sensitive area can reach 65%, and will have a significant impact on the East Area (Figure 7-4), it is because with the northwest wind, water exchange to the East Area will improve rapidly, which is caused by the water diverting from Wangyu river, the group will significantly improve the northwest lake pollution to the east lake area transport velocity, leading to the production of this phenomenon (Li et al. 2011).

Compared to the studies of flow velocity (Table 1) in recent years, it has been found that the results for flow velocity would be influenced by different research methods, observation time, wind speed, water level and terrain under the lake. First, the flow velocity measured by the field observation method (Wang et al. 2017) will be larger than the laboratory experiments, because the laboratory experiment (Han et al. 2019) underestimated the importance of the wind field, which is a significant scientific gap between field observations and laboratory experiments (Li et al. 2017b). Then the in-situ measurement method was adopted in this study, with similar conditions to the experiment, the flow velocity is larger than that measured by Jalil (Jalil et al. 2018) due to that the fixed point monitoring device will make the local flow velocity smaller in the monitoring area. Therefore, the in-situ measurement belongs to a new kind method of field observation.

Second, different seasons indicate different wind speeds and water levels. Wu's (Wu et al. 2015) study showed similar results, stated that the wind speed effect is more than 50% and the flow velocity would rise with an increase of wind speed. Tai Lake is a typical large-shallow lake under human control (Liu et al. 2018), so the water level variability is minimal, which means the water level effect is limited. Meanwhile, the statement from Jalil and Wang that (Wang et al. 2017; Jalil et al. 2018) proved that the water level impact rate is much lower than the wind speed.

In particular, we can find that different parts (Whole Lake, Meiliang Bay and East Lake) have different flow velocities, which is mainly related to the terrain under the lake, but the regions have been unchanged for a long time. So it should be noted that different methods is the mainly subjective factor that influences flow velocity measurement, and different wind speeds is the mainly objective factor which influences flow velocity measurement. Based on the results of the flow velocity in this study, it is supported that the method of in-situ measurement can be well applied to the flow velocity measurement, and can provides reliable data for hydrodynamic model optimization.

Tai Lake is a typical large shallow lake at the middle and lower reaches of the Yangtze River, and its flow velocity is primarily determined by the wind-driven and influent-effluent current (Li et al. 2013a). The wind-driven current has a more significant influence on the flow velocity relative to the influent-effluent current (de Faria et al. 2016), and its influence degree on the flow velocity of the lake has reached 90%. The wind-driven is induced by the movement of the wind to the surface layer of the lake and the pressure on the back of the wave. Under the influence of viscous energy, surface layer water forces bottom layer water to push forward (Chao et al. 2017). Wind tension plays a key role in this process. The wind drag coefficient is a crucial parameter that can assess the transfer rate of momentum between the atmosphere and the aquifer. In large shallow lakes where the main driving condition of the flow velocity is the wind energy, but the wind drag coefficient is still considered as constant in most mathematical models (Gibbs et al. 2016).

Based on the discussion in Factors that influenced the flow velocity and pollution traceability, we can see that the flow velocity of Tai Lake is primarily determined by the wind field (Deng et al. 2017). Flow velocity is achieved through the conversion of wind energy momentum, two essential parameters (wind drag coefficient and wind shelter coefficient) are involved in this process (Demchenko et al. 2017). However, the coefficient of wind shelter in previous studies was set to 1 due to there have no mountain barrier around Tai Lake (Li et al. 2015), since wind drag coefficient is the most important to simulate the water transport process.

The natural wind field over Tai Lake changes very frequently, and there are more complex connections when wind field in different parts due to the large area of Tai Lake (nearly 2,338 km²). For the purpose of a reliable transport process to the pollution groups, the sensitivity study between the flow velocity and the wind drag coefficient was determined to simulate (Ramos-Fuertes et al. 2013). In order to express more intuitively the effect of different wind drag coefficients on the result of pollution transport, the next section of this study simply analyzed and discussed it through the experimental and model results.

The sensitivity degree between the flow velocity and the wind drag coefficient determines the dynamic transport of the particles. According to the average error results in Figure 8, it is presumed that the points A and A’ are in the wind field I and travel under the direction of two wind drag coefficients to points B and B’. The transport trajectory of B and B’ changed radically due to the II wind field, and finally reached C and C’ respectively. In this case, the distance was L’ > L > >0. The wind field in nature often changes (Cyr 2017), which has a significant impact on model prediction results and hinders the study of the transport process of the pollution group. It is of great significance to maintain the high sensitivity between flow velocity and wind drag coefficient for future prediction research.

The model is mainly optimized on the wind drag coefficient, which can make more accurate judgment on the water flow velocity and direction, help to determine the transport process of the pollution group. However, due to the lack of wind field information in many water areas, the application scope of the model may be reduced.

Nearly a decade of research shows that, pollution control, water diverting and ecological system restoration are the main methods (Gao et al. 2017a; Dai et al. 2018; Yan et al. 2018) to reduce the ecological and environmental risks in sensitive areas (Table 2). Based on the results of the simulation of pollution flux traceability under typical wind field, it was found that the higher the wind speed, the shorter the time for the pollution group to reach the sensitive area, and the much greater pollution flux will enter the sensitive area from the Northwest Area and Gong Bay. At this time, continuous water diversion will promote the eastward velocity of the pollution from the Northwest Area. Although the water from the Wangyu River can effectively prevent pollution in the West Lake Area to the sensitivity area, but when the water quality of the Wangyu River is poorer than the Sensitivity Area, the self-purification time of the pollutants is significantly reduced, which may cause the environmental risks (Han et al. 2015). Now the water quality (TP 0.10 mg/L; TN 1.74 mg/L) from Wangyu River is really much higher than East Area (TP 0.065 mg/L; TN 1.2 mg/L), meanwhile, Gong Bay is much closer to the Sensitive Area (especially to the East Area), so the positive benefits from the water diversion have not been really reflected now (Huang et al. 2016; Gao et al. 2017b). Meanwhile the standard of the water evaluated to the rivers and lakes in China shows a big difference, such as the II class water quality in rivers is TP 0.10 mg/L, this is much higher than the standard in III class of lakes (TP 0.05 mg/L), this is also an important reason which led to the TP risk of Tai Lake in recent years.

In the future, it is suggested that the pollution load from the major inflow areas should be reduced, the pollution control and ecological restoration methods combined, and the water quality standard of the rivers around Tai lake improved, especially the water quality standard of Wangyu river (TP < 0.065 mg/L; TN 1.2 mg/L), so as to make the project of ‘diverting from the Yangze river to Tiahu lake’ play a much more useful role.

• (1)

  The measured results by in-situ experiment showed that the speed monitoring method of the platform obtained a smaller value of flow velocity than the actual one. And the average flow velocity is ranked as Western Coastal Area (16.01 cm/s, open lake area) > Meiliang Bay & Gong Bay (14.40 cm/s and 12.25 cm/s, open bay area) > Zhushan Bay (10.7 cm/s, narrow bay area) > East Area (9.39 cm/s, island cluster area), but the terrain under the lake has been unchangeable for a long time, so wind speed is the mainly objective factor that influences flow velocity and pollution transport.

• (2)

  Based on the in-situ measurement experiment and the hydrodynamic model of Tai Lake, the calculated wind drag coefficient was 0.001–0.0028 when the wind speed (10 m over the water surface) was 1–12 m/s. With the help of the surrounding wind station information and the Thiessen Polygon method, the model in this study can well validate the actual transport track of the monitoring device, which can satisfy the transport simulation of the pollution groups with the constantly changing wind field in the future.

• (3)

  The different wind fields will significantly affect the transport process of pollution groups in each inflowing lake area. Under northwest wind conditions, the pollution flux proportion from Northwest Area and Gong Bay is 65 and 17%, respectively; under southeast wind conditions, the pollution flux proportion from Northwest Area and Gong Bay is 48 and 27%, respectively. Namely, pollution control for the upstream watershed of the Northwest Area and improvement of the water quality (TP < 0.065 mg/L; TN 1.2 mg/L) from the Wangyu river to Tai Lake are the effective methods to reduce the pollution risks for the sensitive area in the future.

The authors thank the Chinese National Science Foundation (No. 51879070), supported by ‘the Fundamental Research Funds for the Central Universities, the World-Class Universities (Disciplines), the Characteristic Development Guidance Funds for the Central Universities and the Fundamental Research Funds for the Central Universities (No. 2019B44214) and PAPD.

All relevant data are included in the paper or its Supplementary Information.