# Correcting for Mobile X-Band Weather Radar Tilt Using Solar Interference
## 3 Solar Interference Assessment Methodology
### Application of a Multi-Parameter 2D Gaussian (Bullseye) Fit
This step is essential to provide a robust fit with respect to the peak solar power, as otherwise, the narrow sampling of the solar disk when the SNR threshold is increased allows too much freedom for a five-parameter model to broaden the Gaussian through inflation of the azimuth and elevation widths. If an empirical fit is not possible due to sensitivity limitations, theoretically derived values for the model widths can be used instead; [PERSON] [24] covers how to derive these in great detail. The second modification is to extend the time window used for model fitting to increase the number of observations available. The extension of the time interval has previously been shown to be valid provided that the Sun's solar emissions do not vary significantly during the period being investigated [12]. While this is generally the case for the duration of the project (brown line, Figure 3), the observations here are converted to relative solar flux using the closest available observations from the Dominion Radio Astrophysical Observatory (DRAO) to reduce the impact of variable solar activity on the resulting fit. [PERSON] and [PERSON] [25] previously applied such an approach while using solar interference as an absolute calibration source for the ra  
Figure 2: Bullseye plots for 1 February to 22 March 2017, during which time the SNR threshold was reduced. The solar power delta is the difference between the power observed by the radar and the reference solar power (see Section 3.2 for more details). The red dashed line is the beam ellipse predicted by a 5-parameter fit with the red cross denoting the pointing offset from that fit. All data were collected while NXPol-1 was deployed at Chilbolton Observatory. employ [PERSON]'s [26] approximation for 3 cm wavelength to convert DRAO observations from S-band to X-band, and here we take the same approach, which is as follows:  
\[P_{X}=10\log_{10}(255+0.69(F_{S}-64)) \tag{8}\]  
where \(F_{S}\) is the observed S-band solar flux in solar flux units (sfu), and \(P_{X}\) is the equivalent solar flux at X-band in logarithmic solar flux units (dBsfu). Conversion from absolute observations of solar emission to relative values (termed solar power delta in this work) allows the time windows to be extended without introducing uncertainty due to variability in the Sun's emissions, increasing the number of observations available and allowing cross-comparison of these multi-parameter power fit estimates with the long-duration tilt estimates described in the following section. Figure 3: Solar interference observations identified by the BALTRAD RAVE scansun toolbox. Panel **(A)** shows the difference between radar azimuth and solar azimuth, where each hit is shaded by its radar-measured elevation. Panel **(B)** shows the difference between radar elevation and solar elevation, where each hit is shaded by its radar-measured azimuth. Panel **(C)** indicates the observed logarithmic solar flux (dBsfu) for each observation, shaded by radar azimuth, along with a time series of the converted DRAO observations used as a reference (brown line). Solid vertical lines on each panel indicate the maintenance dates listed in \[\Delta_{\phi}=\sqrt{-\frac{40\log_{10}2}{a_{1}}}, \tag{2}\]0 In total, 2907 solar hits are shown on each panel.