Spatio-Temporal Variation of Heavy Metal Pollution during Accidents: A Case Study of the Heshangshan Protected Water Area, China

Recently, water environmental accidents have occasionally occurred which have had wide-ranging influences, long durations and are difficult to deal with. The development of the social economy, the acceleration of industrialization, the huge discharge of industrial wastewater and the occasional occurrence of ship transportation accidents pose serious threats to the water quality of water inlets and protected water areas. This article applied the two-dimensional water quality model, used a GIS platform and FORTRAN language, and predicted spatio-temporal variations of the iron concentration during a water pollution accident. This research selected the water inlet of Heshangshan Water Plant and the Heshangshan protected water area as the research objective, and assumed a water pollution event had occurred. It was suggested that we should take corresponding emergency measures and relevant solutions to deal with the bad effects of water pollution accidents. The processes mainly included the selection of the study area, the determination of the equation to be used, parameters determination, as well as the identification of the accident scenario and source. The durations of the iron concentration exceeding the standard at the water inlet were 12–18 min and in the protected water area were 16–36 min in four water periods after the accident. In addition, the durations taken for the iron concentration to decrease to the background value in the protected water area were 18–38 min after the accident in four water periods in the accident scenario. Relevant departments should take some contingency measures to avoid fetching water from the intake after the accident within 40 min after the accident and the relevant staff can cancel the warning 40 min after the accident.


Introduction
Considering that 80% of human diseases are related to unsafe drinking water, according to the World Health Organization [1][2][3], drinking water is a major issue that can affect human health [4,5]. In consequence, drinking water safety has attracted the attention of many countries and has become a global strategic issue [6][7][8]. Water inlets are the points where water plants draw water from and protected water areas are the source of drinking water. Therefore, it is indispensable to ensure the water quality safety of water inlets and protected water areas. This paper contributes to producing residents, the water quality of the water inlet is directly related to residents' daily life and body health. Therefore, it is necessary to systematically carry out relevant research and proceed with the prediction of the water inlet and the protected water area in accident scenarios, so as to provide technical guidance and support for the water quality safety of domestic drinking water.
Based on the existing model, spatio-temporal variations of the pollutants of the water inlet and the protected water area in the accident scenario were predicted by using a GIS platform and FORTRAN language. Moreover, the durations of the iron concentration exceeding the standard at the water inlet, and the durations of the iron concentration exceeding the standard as well as spatio-temporal variations of the iron concentration in the protected water area were obtained. This will give a reference for relative research in method and provide strategic suggestions for decision makers in the prevention and treatment of water pollution accidents.

Study Area
In this study, the Heshangshan protected water area was selected as the representative of the Three Gorges Reservoir Area (TGRA). It is the largest protected water area in the TGRA. In addition, the protected water area is the drinking water source of nearly one million residents in Chongqing City, which is the main city in the TGRA. The study area spanned 106 • 31 40" E-106 • 32 25" E, 29 • 30 43" N-29 • 31 22" N and covered 432 km 2 . It belongs to Jiulongpo District, which is located in the southwest of the main city of Chongqing City. The District borders Yuzhong District, Shapingba District, Jiangjin District as well as Bishan County, and faces Nan'an District as well as Banan District across the river. The longest distance from north to south is 36.12 km, and the width from east to west was 30.4 km. The terrain map of Heshangshan is shown in Figure 1. The Heshangshan protected water area was the water intake area of Heshangshan water plant, and the plant withdrew 200,000 t/d of water from the study area and serviced 980,000 residents in Daping, Yangjiaping, Shiqiaopu and Zhongliangshan areas. The water plant also provided domestic water to some areas, such as Yuzhong District and Shapingba District. The water inlet of Heshangshan (106 • 31 54" E, 29 • 31 11" N) was located under the Egongyan Bridge in Chongqing City, near the left bank of the river. According to water quality monitoring data, the water qualification rate of Heshangshan protected water area was about 80% in recent years, which was lower than the desired one of 95%. Pollutants beyond level III of the water quality standard (GB3838-2002) in the protected water area included iron. scenarios, so as to provide technical guidance and support for the water quality safety of domestic drinking water.
Based on the existing model, spatio-temporal variations of the pollutants of the water inlet and the protected water area in the accident scenario were predicted by using a GIS platform and FORTRAN language. Moreover, the durations of the iron concentration exceeding the standard at the water inlet, and the durations of the iron concentration exceeding the standard as well as spatiotemporal variations of the iron concentration in the protected water area were obtained. This will give a reference for relative research in method and provide strategic suggestions for decision makers in the prevention and treatment of water pollution accidents.

Study Area
In this study, the Heshangshan protected water area was selected as the representative of the Three Gorges Reservoir Area (TGRA). It is the largest protected water area in the TGRA. In addition, the protected water area is the drinking water source of nearly one million residents in Chongqing City, which is the main city in the TGRA. The study area spanned 106°31'40"E-106°32'25"E, 29°30'43"N-29°31'22"N and covered 432 km 2 . It belongs to Jiulongpo District, which is located in the southwest of the main city of Chongqing City. The District borders Yuzhong District, Shapingba District, Jiangjin District as well as Bishan County, and faces Nan'an District as well as Banan District across the river. The longest distance from north to south is 36.12 km, and the width from east to west was 30.4 km. The terrain map of Heshangshan is shown in Figure 1. The Heshangshan protected water area was the water intake area of Heshangshan water plant, and the plant withdrew 200,000 t/d of water from the study area and serviced 980,000 residents in Daping, Yangjiaping, Shiqiaopu and Zhongliangshan areas. The water plant also provided domestic water to some areas, such as Yuzhong District and Shapingba District. The water inlet of Heshangshan (106°31'54"E, 29°31'11"N) was located under the Egongyan Bridge in Chongqing City, near the left bank of the river. According to water quality monitoring data, the water qualification rate of Heshangshan protected water area was about 80% in recent years, which was lower than the desired one of 95%. Pollutants beyond level III of the water quality standard (GB3838-2002) in the protected water area included iron. According to topographic data in the study area, data collection and a field investigation were conducted to obtain the cross-section data of the Heshangshan protected water area. The GIS-based  According to topographic data in the study area, data collection and a field investigation were conducted to obtain the cross-section data of the Heshangshan protected water area. The GIS-based inverse distance weighting method was used to process the terrain to generate the DEM diagram of the Heshangshan protected water area, as shown in Figure 2. inverse distance weighting method was used to process the terrain to generate the DEM diagram of the Heshangshan protected water area, as shown in Figure 2.

Governing Equation
Strictly speaking, the models of water pollution are usually three-dimensional, but the threedimensional model can be simplified to two-dimensional, one-dimensional or even zero-dimensional according to the assumptions of the model and the actual practical requirements. In general, the protected water area in cities and towns is relatively large (for river-type drinking water sources); the depth of the river is far less than the length and width of it. It is usually considered that the distribution of pollutants in the depth direction of the river is uniform, so it can be assumed that the contaminant does not substantially diffuse in the z direction, that is, the concentration diffusion coefficient is approximately zero; and the diffusion coefficient is non-zero in the x and y directions. Therefore, this study used the two-dimensional water quality model [27][28][29].
Water quality control equations in the following conserved form were adopted without considering wind shear stress and the Coriolis force [30][31][32][33]:

Governing Equation
Strictly speaking, the models of water pollution are usually three-dimensional, but the three-dimensional model can be simplified to two-dimensional, one-dimensional or even zero-dimensional according to the assumptions of the model and the actual practical requirements. In general, the protected water area in cities and towns is relatively large (for river-type drinking water sources); the depth of the river is far less than the length and width of it. It is usually considered that the distribution of pollutants in the depth direction of the river is uniform, so it can be assumed that the contaminant does not substantially diffuse in the z direction, that is, the concentration diffusion coefficient is approximately zero; and the diffusion coefficient is non-zero in the x and y directions. Therefore, this study used the two-dimensional water quality model [27][28][29].
Water quality control equations in the following conserved form were adopted without considering wind shear stress and the Coriolis force [30][31][32][33]: where x and y are the longitudinal and transverse flow distances of the river; u and v are the flow velocity of the river in the x and y directions; t is time; h is the water depth; z is the water level; h b is the river bottom elevation; c is the concentration of a pollutant in the reach; ε x , ε y are x, y direction of the eddy viscosity coefficient, respectively; g is the gravitational constant; E x and E y are the sum of the molecular diffusion coefficient, turbulent diffusion coefficient and dispersion coefficient in x and y directions, respectively; n is the roughness of the reach, and q is the interval inflow of the reach.
Si is the sink source term of water pollutant. (In this article, S i = K 1 c + S 0 and K 1 is degradation coefficient and S 0 is foreign exchange).

Equation of Discrete
For Equations (1)-(4), the finite volume method was used to discretize [34]: The SIMPLEC method was used for the discretization of the continuity equation and the momentum equation, and the pressure-weighted interpolation method was used for the pressure correction formula, where α was the relaxation factor of the SIMPLEC method. The discrete equations are shown in Equation (5).
The parameter values are shown in Table 1.

Parameter Determination
After the water quality prediction model was confirmed, the next step was to select and determine the parameters of the water quality prediction model. The accuracy and rationality of the parameter measurement are closely related to the reliability and scientificity of the water quality prediction model. The model is often simplified by certain assumptions for its practical application. There are many factors to be determined; however, the most important ones are the transverse diffusion coefficient and the longitudinal diffusion coefficient. Nowadays, the common parameter estimation methods of the water quality prediction model mainly include the empirical formula estimation method, the data calculation method and the method of directly referring to the data verified by the predecessors. Through investigation and the reviewing of the related literature, the empirical formula method was chosen to estimate the parameters of the water quality prediction model.

. Transverse Diffusion Coefficient
The transverse diffusion coefficient in natural water is denoted as D y , and the following empirical formula is used for calculation [35]: where H is the average water depth of the river; α is the transverse diffusion coefficient of dimension 1; u* is the friction velocity; g is the gravitational acceleration; i is the average hydraulic gradient of the river. The value of the transverse diffusion coefficient can be seen in Table 2.

Longitudinal Diffusion Coefficient
Considering that the longitudinal dispersion coefficient is much larger than the longitudinal diffusion one, the latter coefficient is ignored when they are studied together. Empirical formulas commonly used for the river longitudinal dispersion coefficient are shown in Table 3. Table 3. Calculation method of the longitudinal dispersion coefficient.

Calculation Formula
Note Mcquivey-Keefer Formula

Accident Scenario
This study hypothesized the accident scenario of iron pollution occurring in the Heshangshan protected water area. When drinking water contains too much iron, people who drink it will suffer from a hypoxia symptoms, leading to cell membrane damage, mitochondria membrane damage, electron transport problems and nervous system toxicity, which can be life threatening. In addition, according to the monthly monitoring data of the Heshangshan protected water area in 2016, the iron concentration of it increased rapidly and exceeded the standard in certain months. Therefore, iron was selected as the pollutant in this research.
Since the mobile risk sources in the protected water area included freight vehicles [36,37], this study assumed that a truck with 10 t of 40% ferric chloride overturned on the right bank of the upper boundary of the protected water area, and its pollutants flowed into the water from the bank. Let T = 0 when the accident happened, and all pollutants flowed into the protected water area in 10 min, so this study conducted research and analysis on this accident scenario. It was calculated that the iron concentration entering the water body was 16 mg/L. In addition, the degradation rate constant of the iron pollutants was 0 d −1 .

Determination of Boundary Conditions
In the two-dimensional water quality model, the upstream flow and the downstream water level were selected as boundary conditions of it to ensure the accuracy of the results. In this research, the upstream flow was the daily flow of the Zhutuo hydrological station, and the downstream water level was the water level of the Cuntan hydrological station. Influenced by natural or man-made factors [38,39], the annual variation of flow/water level in Zhutuo hydrologic station and Cuntan hydrologic station is obvious. The trend chart for the daily flow of Zhutuo hydrological station and the water level of Cuntan hydrological station in 2016 is shown in Figure 3. For Zhutuo hydrological station, the maximum daily flow was 29,000 m 3 /s, which occurred in the flood period, and the minimum one was 2770 m 3 /s, which occurred in the dry period. For the Cuntan hydrological station, the daily maximum and minimum water levels were 182.16 m in the flood period and 160.6 m in the down period, respectively.

Predict Processes
The reason for choosing the water inlet as the research objective is as follows. The water inlet is the place from which the water plant draws water, and the iron concentration at this location is very important for the water quality of the water plant and people's drinking water safety. The durations for the iron concentration exceeding the standard of the water inlet and the protected water area were predicted. In addition, the spatio-temporal variation of the iron concentration in the four water periods and the durations from the time of the accident to the time when the iron concentration in the protected water area dropped to the background value were predicted and analyzed. Specifically, the durations of the iron concentration exceeding the standard in the protected water area were the durations when the maximum concentration of iron in the protected water area could not meet the standard. Only when the maximum concentration of iron in the protected water area met the standard, could the protected water area meet the standard.
The following is the basic condition of iron pollution concentration prediction and the setting and selection of the source term. In this study, the background value of iron in the protected water area is 0.1 mg/L and the standard value of it is 0.3 mg/L. Moreover, the four water periods concerned were, namely, the dry period, down period, flood period and storage period. The first period is from the end of October to the end of March, the down period extends to June 10, the flood period is from June 10 to the end of September, and then the last one is extends to the end of October. In 2016, the average flows of the protected water area in the four water periods were 3330 m 3 /s, 5031 m 3 /s, 16083

Predict Processes
The reason for choosing the water inlet as the research objective is as follows. The water inlet is the place from which the water plant draws water, and the iron concentration at this location is very important for the water quality of the water plant and people's drinking water safety. The durations for the iron concentration exceeding the standard of the water inlet and the protected water area were predicted. In addition, the spatio-temporal variation of the iron concentration in the four water periods and the durations from the time of the accident to the time when the iron concentration in the protected water area dropped to the background value were predicted and analyzed. Specifically, the durations of the iron concentration exceeding the standard in the protected water area were the durations when the maximum concentration of iron in the protected water area could not meet the standard. Only when the maximum concentration of iron in the protected water area met the standard, could the protected water area meet the standard. The following is the basic condition of iron pollution concentration prediction and the setting and selection of the source term. In this study, the background value of iron in the protected water area is 0.1 mg/L and the standard value of it is 0.3 mg/L. Moreover, the four water periods concerned were, namely, the dry period, down period, flood period and storage period. The first period is from the end of October to the end of March, the down period extends to June 10, the flood period is from June 10 to the end of September, and then the last one is extends to the end of October. In 2016, the average flows of the protected water area in the four water periods were 3330 m 3 /s, 5031 m 3 /s, 16,083 m 3 /s and 10,393 m 3 /s, and the flow rate of the four water periods increased successively. Moreover, the time step of this study was set as one minute.

Durations of the Iron Concentration Exceeding the Standard at the Water Inlet
The velocity was an important factor to determine the diffusion rate of pollutants; the larger the velocity was, the faster the diffusion of pollutants would be, and so the sooner the pollutants reached the water inlet, the sooner the iron concentration of the water inlet met level III of water quality standards. The velocity of the water inlet was different in different water periods; in the dry period, the velocity was less than that in the down period, and the velocity of the water inlet in the down period was less than that in the flood period. Moreover, the velocity of the storage period was the largest, so the durations of the iron concentration exceeding the standard at the water inlet in the four water periods decreased successively. The starting time for pollutants to make the iron concentration of the water inlet exceed the standard in the dry period is the sixth minute after the accident, the starting time of the down period is the third minute, that of the flood period is the second minute, and the starting time in the storage period is the time of the accident. Moreover, the time when the maximum iron concentration of the water inlet occurs is the 15th minute, 10th minute, 8th minute and 5th minute after the accident in the four water periods.
The predicted results show that the polluted durations at the water inlet in the four water periods were 18 min, 15 min, 13 min, and 12 min, respectively. In conclusion, the larger the flow rate, the shorter the duration of the iron concentration exceeding the standard at the water inlet and the smaller the influence of the accident, as is shown in Figure 4. period was less than that in the flood period. Moreover, the velocity of the storage period was the largest, so the durations of the iron concentration exceeding the standard at the water inlet in the four water periods decreased successively. The starting time for pollutants to make the iron concentration of the water inlet exceed the standard in the dry period is the sixth minute after the accident, the starting time of the down period is the third minute, that of the flood period is the second minute, and the starting time in the storage period is the time of the accident. Moreover, the time when the maximum iron concentration of the water inlet occurs is the 15th minute, 10th minute, 8th minute and 5th minute after the accident in the four water periods.
The predicted results show that the polluted durations at the water inlet in the four water periods were 18 min, 15 min, 13 min, and 12 min, respectively. In conclusion, the larger the flow rate, the shorter the duration of the iron concentration exceeding the standard at the water inlet and the smaller the influence of the accident, as is shown in Figure 4. Based on the above results, we suggest that the water inlet be closed for 20 min in the dry period and for 15 min in the remaining three water periods to ensure the safety of drinking water.

Durations of the Iron Concentration Exceeding the Standard for the Protected Water Area
The faster the velocity of water in protected water area was, the faster the diffusion rate of the pollutants was, and the shorter the duration of the iron concentration exceeding the standard in protected water area would be. In this study, the velocities of water in the four water periods decreased successively, so the length of exceeding the standard in the four water periods decreased Based on the above results, we suggest that the water inlet be closed for 20 min in the dry period and for 15 min in the remaining three water periods to ensure the safety of drinking water.

Durations of the Iron Concentration Exceeding the Standard for the Protected Water Area
The faster the velocity of water in protected water area was, the faster the diffusion rate of the pollutants was, and the shorter the duration of the iron concentration exceeding the standard in protected water area would be. In this study, the velocities of water in the four water periods decreased successively, so the length of exceeding the standard in the four water periods decreased in turn. The durations of the iron concentration exceeding the standard in the four water periods were 36 min, 28 min, 17 min and 16 min, respectively. Moreover, the maximum iron concentration in the protected water area occurred at the tenth minute after the accident.
Trends shown in Figure 5 indicate that the iron concentration in the protected water area declined over time after the accident and decreased with the increase in flow rate. In other words, the larger the flow rate was, the faster the iron concentration decreased, and the easier it was to meet the water quality standard. Trends shown in Figure 5 indicate that the iron concentration in the protected water area declined over time after the accident and decreased with the increase in flow rate. In other words, the larger the flow rate was, the faster the iron concentration decreased, and the easier it was to meet the water quality standard.
Considering that the over-standard time of the iron concentration in the protected water area covered this of the water inlet, according to the national relevant regulations, it is recommended that relevant departments should take some contingency measures to avoid fetching water from the intake after the accident within 40 min in dry period, 30 min in the down period and 20 min in the remaining two water periods after the accident.

Spatio-temporal Variations of Iron Concentration in the Protected Water Area.
The spatio-temporal variation of the iron concentration in the protected water area was from the occurrence of the accident to the decrease in the iron concentration in the protected water area to the background value. In the protected water area, the water velocity and the spatio-temporal variations of the iron concentration were positively correlated. That is, the higher the flow rate, the faster the diffusion of iron pollutants in the protected water area, and the easier it was for the iron concentration in the protected water area to return to the background value.
The following are the simulation results of the dry period, down period, flood period and storage period. In this research, the abscissa axis is represented by I, J is the vertical axis; C is the concentration of the pollutant. In addition, the iron concentration of the protected water area in the four water periods could reach the background value (0.1 mg/L) with 38 min, 28 min, 18 min, and 16 min after the accident in the above scenario, respectively.
In the dry period, the maximum iron concentration in the protected water area was 16.22 mg/L, at the tenth minute after the accident. Thirty-eight min after the accident, the iron concentration decreased to the background value ( Figure 6). Considering that the over-standard time of the iron concentration in the protected water area covered this of the water inlet, according to the national relevant regulations, it is recommended that relevant departments should take some contingency measures to avoid fetching water from the intake after the accident within 40 min in dry period, 30 min in the down period and 20 min in the remaining two water periods after the accident.

Spatio-temporal Variations of Iron Concentration in the Protected Water Area.
The spatio-temporal variation of the iron concentration in the protected water area was from the occurrence of the accident to the decrease in the iron concentration in the protected water area to the background value. In the protected water area, the water velocity and the spatio-temporal variations of the iron concentration were positively correlated. That is, the higher the flow rate, the faster the diffusion of iron pollutants in the protected water area, and the easier it was for the iron concentration in the protected water area to return to the background value.
The following are the simulation results of the dry period, down period, flood period and storage period. In this research, the abscissa axis is represented by I, J is the vertical axis; C is the concentration of the pollutant. In addition, the iron concentration of the protected water area in the four water periods could reach the background value (0.1 mg/L) with 38 min, 28 min, 18 min, and 16 min after the accident in the above scenario, respectively.
In the dry period, the maximum iron concentration in the protected water area was 16.22 mg/L, at the tenth minute after the accident. Thirty-eight min after the accident, the iron concentration decreased to the background value ( Figure 6). During the down period, the maximum iron concentration in the protected water area was 16.71 mg/L at the tenth minute after the accident. At 28 min after the accident, the iron concentration was 0.1 mg/L (Figure 7). During the down period, the maximum iron concentration in the protected water area was 16.71 mg/L at the tenth minute after the accident. At 28 min after the accident, the iron concentration was 0.1 mg/L (Figure 7). In the flood period, the maximum iron concentration in the protected waters was 17.95 mg/L at the same time as in the first two water periods and decreased to the background value in the eighteenth minute (Figure 8). In the flood period, the maximum iron concentration in the protected waters was 17.95 mg/L at the same time as in the first two water periods and decreased to the background value in the eighteenth minute ( Figure 8). In the flood period, the maximum iron concentration in the protected waters was 17.95 mg/L at the same time as in the first two water periods and decreased to the background value in the eighteenth minute (Figure 8). The maximum iron concentration was 14.77 mg/L at the fifth minute after the accident in the storage period, and the iron concentration reached 0.1 mg/L at the sixteenth minute ( Figure 9). The maximum iron concentration was 14.77 mg/L at the fifth minute after the accident in the storage period, and the iron concentration reached 0.1 mg/L at the sixteenth minute (Figure 9). By predicting the spatio-temporal variations of the iron concentration of the protected water area in the four water periods, it could be concluded that the higher the velocity, the less time it took for the iron concentration in the protected water area to reach the background value. At this time the water body has returned to normal state, the relevant managers can cancel the early warning.

Conclusions
Water pollution accidents seriously affect the safety of human life. Ensuring water safety of water inlets and the protected water area is necessary to protect people's health. In this study, the planar two-dimensional water quality model was adopted to predict the spatio-temporal variations of the iron concentration in a certain accident scenario for the water inlet of the Heshangshan Water Plant and the Heshangshan protected water area. An iron pollution accident was assumed to have By predicting the spatio-temporal variations of the iron concentration of the protected water area in the four water periods, it could be concluded that the higher the velocity, the less time it took for the iron concentration in the protected water area to reach the background value. At this time the water body has returned to normal state, the relevant managers can cancel the early warning.

Conclusions
Water pollution accidents seriously affect the safety of human life. Ensuring water safety of water inlets and the protected water area is necessary to protect people's health. In this study, the planar two-dimensional water quality model was adopted to predict the spatio-temporal variations of the iron concentration in a certain accident scenario for the water inlet of the Heshangshan Water Plant and the Heshangshan protected water area. An iron pollution accident was assumed to have occurred in the protected water area. Then, the durations of the iron concentration exceeding the standard at the water inlet, those in the protected water area, and the spatio-temporal variations of iron concentration in the protected water area were analyzed. The conclusions were as follows.
The durations of the iron concentration exceeding the standard at the water inlet were 12-18 min in the four water periods after the accident. The relevant departments should take some contingency measures to avoid fetching water from the intake after the accident for 40 min after the accident. Furthermore, the durations of the iron concentration exceeding the standard in the protected water area were 16-36 min in the four water periods. In addition, the durations of the iron concentration decreasing to the background value in the protected water area were 18-38 min after the accident in the four water periods in the accident scenario. As a result, the relevant staff can cancel the warning 40 min after the accident.
This research can provide decision makers with fast and effective methods regarding water inlets and protected water areas. Moreover, it helps to mitigate the influence of accidents on the drinking water quality of residents after accidents. However, there are still some areas to be improved in this study. In the future, the longitudinal diffusion of pollutants and the biological damage of the water pollution accidents can be further considered [40,41].