## Materials and Methods
### Water Distribution Measurements  
The water distribution was measured with a series of catch cans [20; 30; 37; 38]. The catch cans for the measurement of the RSPS water distribution were arranged in a matrix according to ISO 8026 [39] and ASCE S398.1 [40]. The spacing among the catch cans was 150 cm \(\times\) 150 cm and, in total, 196 catch cans were arranged in 14 \(\times\) 14 rows (Figure 1(a)).  
Because the FSPS results in multiple, clearly separate streams, previous studies proposed many catch can arrangements to measure the water distribution [20; 30; 41]. In these experiments, we adopted a radiation arrangement, like [PERSON] et al. [41]. As shown in Figure 1(b), in total, there were eight radial lines constituted by catch cans. The total number of catch cans used for FSPS water distribution measurements was 344; the intervals between the catch cans were 25 cm.  
The radial data series were converted into matrix data by using mathematical model of interpolating cubic splines, according to [PERSON] et al. [42] and [PERSON] et al. [43]. The algorithm for cubic spline interpolation to calculate the water depth of a point in a matrix is as following: Point \(D\) is  
Figure 1: Schematic of the experimental system for measuring water distribution of rotating and fixed spray plate sprinklers.  
Figure 2: Catch can arrangements for measurements of water distribution with rotating (**a**) and fixed (**b**) spray plate sprinklers. Asterisks indicate the locations of sprinklers.  
a matrix point located between two adjacent radial lines, and its coordinate is (\(x_{D}\), \(y_{D}\)). \(P_{1}\), \(P_{2}\), \(P_{3}\), and \(P_{4}\) are the four nearest points to point \(D\) on the two adjacent radial lines, and their coordinates are (\(x_{1}\), \(y_{1}\)), (\(x_{2}\), \(y_{2}\)), (\(x_{3}\), \(y_{3}\)), and (\(x_{4}\), \(y_{4}\)), respectively. The water depths in those measured points are \(h_{1}\), \(h_{2}\), \(h_{3}\), and \(h_{4}\), respectively. Thus, their distance away from point \(D\) is as follows:  
\[r_{i}=\sqrt{\left(x_{i}-x_{D}\right)^{2}+\left(y_{i}-y_{D}\right)^{2}}\;(i=1, 2,3,4) \tag{1}\]  
where \(r_{i}\) is the distance from point \(D\) to \(P_{i}\). The water depth of point \(D\) (\(h_{D}\)) can be expressed as following:  
\[h_{D}=C_{1}h_{1}+C_{2}h_{2}+C_{3}h_{3}+C_{4}h_{4} \tag{2}\]  
where \(C_{1}\), \(C_{2}\), \(C_{3}\), and \(C_{4}\) are calculated as following:  
\[\left\{\begin{array}{l}C_{1}=\frac{\left(r_{2}r_{3}\mu_{2}\right)^{2}}{\left( r_{2}y_{4}\right)^{2}+\left(r_{1}r_{4}\mu_{2}\right)^{2}+\left(r_{1}r_{2}r_{3} \right)^{2}}\\ C_{2}=\frac{\left(r_{1}r_{3}\mu_{2}\right)^{2}}{\left(r_{2}y_{4}\right)^{2}+ \left(r_{1}r_{3}\mu_{2}\right)^{2}+\left(r_{1}r_{2}r_{3}\right)^{2}}\\ C_{3}=\frac{\left(r_{1}r_{2}\mu_{2}\right)^{2}}{\left(r_{2}y_{4}\right)^{2}+ \left(r_{1}r_{3}\mu_{2}\right)^{2}+\left(r_{1}r_{2}r_{3}\right)^{2}}\\ C_{4}=\frac{\left(r_{1}r_{2}\mu_{2}\right)^{2}}{\left(r_{2}y_{4}\right)^{2}+ \left(r_{1}r_{3}\mu_{2}\right)^{2}+\left(r_{1}r_{2}r_{3}\right)^{2}}\\ \end{array}\right.\right. \tag{3}\]  
Finally, the water distribution measured by method of radial lines was converted into a form of 14 \(\times\) 14 matrix data, which was same as the measurement of RSPS. The converted matrix data was used for further analyses.  
The opening diameter of the catch can used was 98 mm. The water volume collected in each catch can was measured immediately after each irrigation experiment.  
Sprinkling uniformity was evaluated using the Christiansen coefficient of uniformity [44]:  
\[CUC=\left(1-\frac{\sum\limits_{i=1}^{n}\left|h_{m}-h_{i}\right|}{n\cdot h_{m }}\right)\times 100\% \tag{4}\]  
While _CUC_ is the Christiansen coefficient of uniformity, \(n\) is the number of observations, \(h_{m}\) is the average water depth of all observations, and \(h\) is the water depth of the \(i\)-th observation.