## Materials and Methods
### Simulation on Full Circular Irrigated Area  
Following the nozzle configuration model, a nozzle configuration was set for a center pivot with the parameters in Table 3. Then, water distributions for the full circular irrigated area (FCIA) of the center pivot with RSPSs and FSPSs installed at intervals of 1.5, 3.0, and 4.5 m were simulated.  
In the processes of FCIA simulation, a total of 191, 96 and 64 sprinklers were used for 1.5-, 3.0- and 4.5-m intervals, respectively. Given that the diameter of the smallest nozzles available was 1.79 mm for the 3 TN series, so the size ranges of used nozzles were 1.79-4.17 mm, 1.79-5.95 mm and 1.79-7.14 mm for the three sprinkler intervals, respectively. The relationship between the sprinkler discharge and opening area of the nozzle is as follows [42]:  
\[q=c\cdot\sqrt{2 gH}\cdot A \tag{9}\]  
where \(q\) is discharge of the sprinkler (m\({}^{-3}\cdot\)s\({}^{-1}\)), \(A\) is the opening area of the nozzle (m\({}^{2}\)), \(g\) is gravitational acceleration (m\(\cdot\)s\({}^{-2}\)), \(H\) is the pressure head (m) and \(c\) is the discharge coefficient. Thus, the water distributions of those sprinkler of unmeasured nozzles in this experiments (except the 2.78-, 4.76-, and 6.75-mm nozzle) could be estimated by means of weighted average based on the  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Configurations**} & \multicolumn{4}{c}{**Configuration Parameters**} & \multicolumn{4}{c}{**Operating Parameters**} \\ \cline{2-9}  & **Sprinkling** & **Pressure of** & **End Gun** & **Pipe** & **Sprinkler** & **Sprinkling** & **Sprinkling** & **Cycle** \\  & **Radius** & **End Sprinkler** & **Diameter** & **Intervals** & **Volumes** & **Intensity** & **Length** \\ \hline Parameters & 300 m & 103 kPa & None & 165 mm & 4.5 m & 10 mm & 10 mm/h & 36 h \\ \hline \end{tabular}
\end{table}
Table 3: Configurations and operating parameters of the simulated center pivot irrigation system.  
three measured ones. The weights were decided by the opening area of the nozzle. Let \(A_{x}\) be the opening area of unmeasured nozzle, for which the subscript \(x\) indicates its nozzle diameter. Then the sprinkling intensity of any point of the unmeasured nozzles could be estimated as:  
\[\left\{\begin{array}{l}I_{x,ij}=I_{278 jj}\frac{A_{x}}{\lambda_{278}}\ (x<2.78)\\ I_{x,ij}=I_{278 jj}\Big{(}1-\frac{A_{x}-A_{x}\lambda_{278}}{A_{426}-A_{278}}\Big{)} +I_{4.76,ij}\Big{(}1-\frac{A_{4278}-A_{x}}{A_{426}-A_{278}}\Big{)}\ (2.78\ <x<4.76)\\ I_{x,ij}=I_{4.76,ij}\Big{(}1-\frac{A_{x}-A_{4.76}}{A_{675}-A_{4.76}}\Big{)}+I_{6.75,ij}\Big{(}1-\frac{A_{6.75}-A_{x}}{A_{6.75}-A_{4.76}}\Big{)}\ (4.76\ <x<6.75)\\ I_{x,ij}=I_{6.75,ij}\frac{A_{x}}{A_{6.75}}\ (x>6.75)\end{array}\right. \tag{10}\]  
where \(I_{x,ij}\) is sprinkling intensity at point \((i,j)\) when the nozzle diameter is \(x\), and \(A_{2.77}\), \(A_{4.76}\) and \(A_{6.75}\) are the opening areas of 2.78-, 4.76- and 6.75-mm nozzles respectively. Following the above procedures, the estimated average radial application patterns for the unmeasured nozzles are shown in Figure 4.  
Water application amounts of any points in the FCIA can be obtained based on mathematical superposition according to the related sprinklers, as defined by the nozzle configuration (Figure 3) and their locations. A total of 16,000 points were generated randomly and their application depths were calculated to assess the CUC. It should be noted that the diameter of the smallest available nozzles was 1.79 mm for the 3 TN series; there will be special cases occurring closer to the pivot. The practically configured nozzles sizes were much larger than that of the theoretical configured nozzle (Figure 3).