# Correcting for Mobile X-Band Weather Radar Tilt Using Solar Interference
## 5 Pointing Correction Verification
### Radar QPE and Verification with External Data
#### 5.2.2 Verification Using External Data  
Raingauge network data over England and Scotland were obtained from the Environment Agency and Scottish Environment Protection Agency, respectively, and processed separately using the methods described in [PERSON] et al. [28]. Briefly, this entailed an initial quality control step followed by spatial interpolation of the raingauge values using the multiquadric method to produce 1 km-resolution precipitation grids that were accumulated to an hourly timestep. These 1 km grids match those produced for the radar data in the previous section. In total, there were 233 raingauges within 150 km of the radar site.  
Verification was performed by comparing catchment averages of the hourly gridded radar QPE and raingauge surfaces over the 215 catchments outlined in Figure 7. Of these, 85 catchments (shown with bold outlines on Figure 7) have a mean lowest usable elevation for the radar beam of less than 2 km, indicating that the beam elevation should  
Figure 6: Terrain altitude within 150 km of the radar location, show by the red dot (**left panel**) and the resulting beam blocked fraction for a fixed elevation angle of 0.5\({}^{\circ}\)(**right panel**). The radar is located at a height of 133m above mean sea level (amsl).  
not be considered excessive for these catchments. Several statistical quantities were then computed over each catchment in order to assess different aspects of the performance of the radar QPE.  
The first statistic,  
\[\text{percentage bias}=100\%\frac{\langle p_{i}\rangle-\langle P_{i}\rangle}{ \langle P_{i}\rangle},\]  
assesses the relative difference in the total depths of water between radar and raingauge QPE, where \(p_{i}\) and \(P_{i}\) are the hourly catchment averages of the radar QPE and raingauge interpolation \"truth\", respectively, and angular brackets, \(\langle\cdots\rangle\), denote temporal averaging over all non-missing timesteps. A second statistic,  
\[\text{MAPE}=100\%\frac{\langle|p_{i}-P_{i}|\rangle}{\langle P_{i}\rangle},\]  
was used to assess relative error in the radar QPE. It was chosen in preference to alternatives such as the R\({}^{2}\) efficiency (Nash-Sutcliffe Efficiency) as it is insensitive to the zero-inflated na  
Figure 7: Catchment average performance statistics for the full campaign period, calculated using radar QPEs without the tilt correction (**left column**) and with the tilt correction (**central column**) and showing the difference between the two ((**right column**); shows corrected minus uncorrected). Catchment outlines are also shown on the figures, with a bold outline being used for catchments with lowest usable beam elevations of less than 2 km. The blue dot on all panels is the location of NXPol-1.  
ture of precipitation data (which has a value of zero for a considerable portion of timesteps). A final statistic, the correlation coefficient, \(r\), was used to assess the size of errors in the data independent of any overall bias. Note that the last two statistics are sensitive to the choice of the hourly timesteps used in the calculation. This was deemed to be a relevant timescale over which accurate precipitation data would be needed for modelling flood hydrology in this region.