# Study of the Dynamic Adaptive Calculation Method for River Water Environmental Capacity
## 3 Methodology
### Dynamic Adaptive Calculation Method for Water Environmental Capacity
#### 3.2.2 Calculation Model and Method
Then,  
\[C=C^{\prime}\exp(-\frac{Kx}{u}) \tag{7}\]  
\[C^{\prime}=\frac{C_{0}\exp(-\frac{K(L-x)}{u})Q_{0}+C_{p}Q_{p}}{Q_{0}+Q_{p}} \tag{8}\]  
where \(L\) is the length of the upstream and downstream section of a river; \(K\) is the water quality degradation coefficient; \(u\) is the flow rate; when there is only one sewage outlet or  
Figure 4: The schematic diagram of the section-end control model. the sewage outlet is generalized as shown in Figure 3; and \(C=C_{s}\), the water environmental capacity \(W=Q_{p}C_{p}\), shown in the following:  
\[W_{i}=(Q_{i}+q_{i})C_{s}-Q_{i}C_{s}f(x_{i}-x_{i-1}) \tag{2}\]0  
(4) Subsection summation model [44]  
Water function zoning is divided into several sections according to the sewage outlet, water intake, and tributary inlet as the control section, and the water quantity and pollutants meet the law of material conservation before and after the control section. There are \(n\) water intakes, sewage outlets, and tributary inlets in the water function zoning, and the functional zoning is divided into \(n+1\) section, as follows:  
One-dimensional water quality model:  
\[W_{i}=(Q_{i}+q_{i})C_{s}-Q_{i}C_{s}f(x_{i}-x_{i-1}) \tag{2}\]1  
where \(C_{x}\) is the pollutant concentration, mg/L; \(x\) is the longitudinal distance along a river, m; \(u\) is the average velocity of the channel section under the design flow, m/s; and \(C_{0}\) is the concentration of pollutants in the initial section, mg/L. The material balance equation is as follows:  
\[W_{i}=(Q_{i}+q_{i})C_{s}-Q_{i}C_{s}f(x_{i}-x_{i-1}) \tag{2}\]2  
where \(Q_{i-1}\) is the inflow flow of the \(i\) river section, m\({}^{3}\)/s; \(Q_{i}\) is the discharge of section \(i\), m\({}^{3}\)/s; \(C_{i-1}\) is the initial mass concentration of pollutants in the \(i\) river section, mg/L; \(C_{i}\) is the mass concentration of pollutants in reach \(i\), mg/L; \(x_{i}\) is the distance from the \(i\) control section to the lower section of the functional zoning, m; and \(W_{i}\) is the WEC for section \(i\), g/s. The flow balance equation is as follows:  
\[W_{i}=(Q_{i}+q_{i})C_{s}-Q_{i}C_{s}f(x_{i}-x_{i-1}) \tag{2}\]3  
where \(q_{i}\) is the discharge volume or tributary flow or water intake flow of the sewage outlet for the \(i\) river section, m\({}^{3}\)/s. The WEC for the \(i\) river section is as follows:  
\[W_{i}=(Q_{i}+q_{i})C_{s}-Q_{i}C_{s}f(x_{i}-x_{i-1}) \tag{2}\]4  
where \(u_{i}\) is the velocity of the \(i\) river section, m/s. The WEC of the river is \(W=\sum\limits_{i=1}^{n+1}W_{i}\), the available water environmental capacity is as follows:  
\[W_{i}=(Q_{i}+q_{i})C_{s}-Q_{i}C_{s}f(x_{i}-x_{i-1}) \tag{2}\]5  
2. Water environmental capacity calculation parameters  
(1) Design hydrological conditions  
1) Yearly scale design hydrological conditions involve determining the design flow based on the frequency of the driest month and the frequency of all months. The frequency of the driest month involves selecting the monthly flow data from the long series of a hydrological station and frequency analyzing the driest month flow of each year as the empirical point data. Similarly, the frequency of all months involves selecting the monthly flow data from the long series of a hydrological station and frequency analyzing the monthly average flow of all months of each hydrological year as the empirical point data. The theoretical frequency curve is then obtained by two frequency arrangement methods, and flow values corresponding to 90%, 75%, and 50% design frequencies are adopted. 2. Wet, normal, and dry periods represent the design hydrological conditions. The design flow is calculated according to the frequency of the water period and a typical year. The idea of calculating the design flow of a water period according to its frequency involves selecting a long series of monthly flow data from a hydrological station. Based on current research habits in the field of hydrology, a hydrological year is divided into wet, normal, and dry periods.