# Also in the Article

2.3. Model

Procedure

The Environmental Fluid Dynamics Code (EFDC) was applied in the Minjiang River, including hydrodynamics, water ages, and water quality [17]. It was originally developed by the Virginia Institute of Marine Science as authorized by US EPA. EFDC has been successfully applied to a wide range of environmental studies simulating circulation, density or thermal stratification, sediment transport, eutrophication, and water quality in numerous lakes, rivers, wetlands, estuaries, and coastal regions [27,28,29].

In this paper, EFDC used orthogonal curvilinear coordinates, allowing grid sizes to vary and fit the estuary coastline (Figure 1). A total of 2743 grid cells existed in the study domain with grid size varying from 50 m to 1000 m (Figure 1) with three uniform vertical sigma layers. The actual cell size and shape resulted from grid optimization and orthogonality. Most importantly, EFDC included water age, sediment transport, and water quality. The 15 state variables in the water column were simulated by the water quality model, which contains green algae, three types of carbon (refractory particulate organic carbon, labile particulate organic carbon, dissolved organic carbon), five types of nitrogen (refractory particulate organic nitrogen, labile particulate organic nitrogen, dissolved organic nitrogen, NH4+, nitrate, and nitrite nitrogen), four types of phosphorus (refractory particulate organic phosphorous, labile particulate organic phosphorus, dissolved organic phosphorous, total phosphate), DO and chemical oxygen demand. The bottom topography data were obtained from FPNASC and interpolated into the model grids. The time step was set to 60 s to satisfy the Courant–Friedrich–Levy (CFL) criterion. The model was run on 1 December 2012. In order to make the output stable, the results were extracted from 0:00 on 1 January 2013.

Atmospheric boundary conditions: mainly consider the wind field (wind speed and direction), air pressure, temperature, relative humidity, evaporation, rainfall, solar radiation and cloud cover, data from China Meteorological Network; daily rainfall and evaporation data from the YBHC in 2013.

Upper boundary conditions: the upper boundary of the model was the measured discharge of Shuikou Hydropower Station, and the daily temperature data of Xiapu hydrological station was used; water quality boundary was determined according to the conventional water quality monitoring section value.

Tributary boundary conditions: three tributaries of Meixi, Xiyuanxi, and Dazhangxi have hydrological stations, whose flows were provided by hydrological stations. The boundary conditions of other tributaries were obtained by analogy according to the catchment area of each tributary. The water quality boundary conditions of tributaries were generalized to the sub-basins where each tributary was located according to the calculated number of pollutants into the river.

Open sea boundary conditions: the tidal level, salinity, and temperature were provided by the hydrodynamic model of Shuikou Hydropower Station—Minjiang open sea (Mazu Island and Xiquan Island). The tidal level was calculated by the global tidal model TPXO 6.2 developed by Oregon State University. The harmonic results were verified by the measured data of the Huangqi hydrological station, and the average absolute error was within 0.1 m [30]. The downstream water quality boundary was determined according to the conventional water quality monitoring section value.

Due to the lack of parameter values of atmospheric settlement and sediment release, according to the relevant reference [31], the dry and wet settlement in the atmospheric boundary in this paper adopted the mean value, and the sediment release adopted the release value with an uneven spatial and temporal distribution.

According to the data of 2013 (environmental statistics, statistical yearbook, and key monitoring units), the total inflow of COD, NH4+, TN, and TP in the lower reaches of Minjiang River in 2013 were 102363 t y−1, 11267 t y−1, 21168 t y−1, and 1778 t y−1 respectively; The proportions of COD, NH4+, TN, and TP of point source were 82%, 81%, 74%, and 64% respectively.

River nutrients, DO, salinity, and temperature were set based on observed values from the measured results, and the water surface elevation were set at 2.5 m. The model was initially run for several days for each flow condition to obtain a dynamic equilibrium condition. The flow field, salinity, and water concentration distribution under this equilibrium condition were then used as the initial condition for the model calibration so that the model could be ‘hot’ started [24].

The data from 2012 and 2013 were selected to calibrate and validate the established model. The WQ model contains more than 100 parameters, and the calibration values of the main parameters were shown in Table 1. From the results of calibration and validation, it can be seen that the model could reasonably reflect the change process of DO.

Main water quality parameters of the Minjiang River model.

The bottom roughness coefficient and wind field parameters were calibrated and verified through the field monitoring values of model-related parameters and relevant references. The final roughness parameter was 0.015–0.03 m, the wind drag coefficient was 3 × 10−3, and the wind occlusion coefficient was 1. The hydrodynamic calibration mainly verified the tidal level, flow, temperature, and salinity. The measured data of hydrological stations and tidal stations from January to December 2012 were used for model parameter calibration, and then the measured data from January to December 2013 were used for model parameter verification. Minjiang hydrodynamic model tidal level verification diagram in 2013 (Wenshanli, Jiefang Bridge, Xianan, and Baiyantan: two high tidal levels and two low tidal levels per day) was shown in Figure 3 and Table 2. Compared with the measured value and model simulation value, the average error was less than 0.17 m, the average absolute error was less than 0.23 m, and the average absolute error was less than 0.20 m accounted for 50.60%. The results show that the simulated tidal level of each station was in good agreement with the measured value. Minjiang hydrodynamic model flow verification in 2013 (Zhuqi and Wenshanli) was shown in Figure 4. Compared with the measured value and model simulation value, the relative error of Zhuqi station flow was 14.86%, the relative error of the Wenshanli station flow was 24.95%. It could be seen that there was a certain error between the simulated flow and the measured value. The simulation value of the Wenshanli station in the North Channel was slightly larger in the flood period of the Minjiang River, mainly because the South Channel beach had a certain flood discharge capacity in the discharge period, while the model had some shortcomings in the shoreline generalization. The flow in other periods was in good agreement. The overall simulation error was within the acceptable range. Taking Zhuqi flow as upstream inflow, the diversion ratio of the North Channel was calculated. The measured annual average value of diversion ratio of the North Channel was 24.69%, while the simulated annual average value was 23.97%. The relative error was 28.46%. The hydrodynamic model could basically reflect the diversion status of the South Channel and the North Channel.

Tidal level calibration results for Wenshanli (a), Jiefang Bridge (b), Xianan (c) and Baiyantan (d).

Discharge calibration results of Zhuqi (a) and Wenshanli (b).

Statistics of tidal level simulation error in the lower reaches of the Minjiang River in 2013.

The water temperature error of the hydrodynamic model of the Minjiang River in 2013 was shown in Table 3. Compared with the measured value and the simulated value, the average absolute error of all stations was 1.04 °C. The model accurately simulated the temporal and spatial distribution of the water temperature of the Minjiang River, indicating that the model could reasonably calculate the heat exchange process. Wenshanli and Zhuqi were not affected by saltwater. The salinity verification diagram of Baiyantan was shown in Figure 5. After removing individual points, the average relative error of salinity is 23.20%, the salinity simulation value of Baiyantan was basically consistent with the measured value.

Salinity calibration results of Baiyantan.

Statistical analysis of water quality simulation errors in 2013.

Note: Obs. Mean represents the observation average, Sim. Mean represents the simulated average, Relative Error (RE) calculation method is as follows: $RE=1N∑n=1NOn−PnO¯×100%$, N is the number of observed and predicted values, $On$ is the nth observed value, $Pn$ is the nth predicted value, $O¯$ the average observed value.

The model was mainly calibrated and verified the water quality state variables, including DO, TN, TP, NH4+, and BOD5. The important water quality parameter values of the water quality module were shown in Table 1, mainly based on the calibration results, the previous field hydrological and water quality synchronous monitoring, and the research results of the Minjiang River related model [7] and other waters [32]. The error analysis of verification results of each monitoring point in the Minjiang River (Figure 1) was summarized in Table 3.

The relative error range of DO concentration (Table 3) at each monitoring station was 3.86% to 36.83%, of which Xiaxiyuan, Zhuqi, Kuiqi, and Min’an stations were within 17.00%. The absolute error between the average concentration of DO at the monitoring point and the simulated average concentration was within 0.50 mg L−1, indicating that the simulation results were good.

Due to the complex transport process of nutrient variables (TN, TP, and NH4+), the relative error was larger (Table 3). The average annual relative errors of TN, TP, NH4+, and BOD5 concentrations in all monitoring points were 10.30%, 16.25%, 30.50%, and 29.81%, respectively, and the results were within the acceptable range. Overall, the nutrient simulation results were in good agreement with the measured values, which basically reflected the spatial variation of nutrient deficiency in upstream water and poor water quality in the North Channel.

In order to further meet the research on the low oxygen problem in the downstream water body, the hourly frequency of DO calculated by the model was compared with the DO value of the automatic monitoring station, as shown in Figure 6. According to the DO simulation values of Zhuqi (a) and Wenshanli (b) in 2013, the comparison of the automatic monitoring station values with the flow and temperature (Figure 6), it could be seen that DO was significantly positively correlated with the runoff and was significantly negatively correlated with the temperature. The continuous hypoxia phenomenon mainly occurred in the period of high temperature and low flow. At the same time, the DO simulation value could also reflect the short-term hypoxia phenomenon in the downstream of the early flood discharge, such as October 13–19 (Julian day: 285–291), December 17–21 (Julian day: 350–354).

Relationship between simulated and measured DO values and flow and temperature changes in Zhuqi (a), Wenshanli (b) in 2013.

The verification results show that the established mathematical model of the Minjiang River water environment could better describe the hydrodynamic and temporal and spatial variation of water quality in the lower reaches of the Minjiang River and could fully reflect the real-time variation of DO in the Minjiang River.

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