# Rain Monitoring with Polarimetric GNSS Signals: Ground-Based Experimental Research
## 3 Results and Discussion
### Statistical Results of G27 Satellite in 2015
#### 3.1.3 Comparison with Weather Station  
Figure 8a,c show the comparison between accumulated phase shift with accumulated rainfall observed from four nearby weather stations (Lishui, Danyang, Jintan and Jurong). In Figure 8a, it is obvious that only Jurong has rain during the GPS signals receiving period. Moreover, the trend of Jurong's data is somewhat similar to that of accumulated phase shift with a correlation coefficient of  
Figure 7: Examples of phase shift (red solid line with values indicated by the right \(y\) axis) from two rainy days compared with radar reflectivity (interpolated along GPS rays, whose value is shown by color scale and height is represented by left \(y\) axis) and path-averaged rain rate (”pink+” line with values indicated by the left \(y\) axis) calculated from radar reflectivity: (**a**) on 6 July 2015; (**b**) on 10 August 2015; (**c**) sky plot of G27 at this selected time.  
0.9709. In Figure 8c, their correlation coefficients with the data from these weather stations Lishui, Danyang, Jintan, and Jurong are 0, 0.3039, 0.9433, and 0.9114, respectively. This indicates that their accumulations have some relations, even though rain gauge is a point observation while phase shift is a linear measurement. The correlation coefficient here refer to the Person correlation coefficient, whose formula is  
\[R_{XY}=\frac{\sum\limits_{i=1}^{n}\left(X_{i}-\overline{X}\right)\left(Y_{i}- \overline{Y}\right)}{\sqrt{\sum\limits_{i=1}^{n}\left(X_{i}-\overline{X} \right)^{2}}\sqrt{\sum\limits_{i=1}^{n}\left(Y_{i}-\overline{Y}\right)^{2}}} \tag{9}\]  
where \(n\) is the number of sample \(X\).  
It is obvious that the rain gauges variation of rain is only temporal, but for the phase the location and extension of precipitation also plays an important role. If the rain gauge is close to GPS ray and rain area, and this area is not large and sparse, the rain rate from rain gauge can represent the whole area's rain rate. Otherwise, error is inevitable and the comparison is complex. For example, in the case of 6 July 2015, the rain area covers Jurong station during the observing period, and the GPS rays come across this rain area, getting close to Jintan station. However, there is no rain in the other three stations. Thus, Jurong station's correlation coefficient is highest, up to 0.9433. In the case of 10 August 2015, there is no rain in Lishui station and Danyang station during the observing time. When GPS ray is close to Jintan station, it is found that the rain area covers this station from radar echoes. Therefore, Jintan station's result is the best. When checking each GPS ray with radar precipitation echo, it can be  
Figure 8: Cases of accumulated phase shift compared with accumulated rainfall observed from four weather stations and calculated from radar, respectively: (**a**,**b**) on 6 July 2015; (**c**,**d**) on 10 August 2015.  
found that the weather station, showing the best result, is basically more close to GPS ray. Therefore, the distribution of rain has an effect on this comparison analysis.  
Comparisons of accumulated phase shift and accumulated rainfall obtained by different methods (retrieved from radar reflectivity and the best result of rain gauges from four weather stations) can be seen in Figure 8b,d. Though the rain rate from radar is path-averaged, which is obtained from the average of path radar reflectivity, it can also reflect the feature of rain along the GNSS ray. The correlation coefficient between accumulated phase shift and accumulated rainfall from radar is up to 0.9745 in Figure 8b and 0.9519 in Figure 8d, which are both better than the results with rain gauges. This is due to the fact that rainfall from radar is accumulation of path-averaged rain rate, which matches with GPS signals in space.