# Correcting for Mobile X-Band Weather Radar Tilt Using Solar Interference
## 4 Results of the Tilt Estimation Method
* The estimated elevation offsets of the two approaches agree very closely (within 0.05\({}^{\circ}\)) despite the limitations of the bullseye fit due to averaging through time, which increases confidence in the results. * The magnitude of the inclination is significant enough (>0.1\({}^{\circ}\)) to impact radar observations through time without being such a severe deviation from the previous period (>0.5\({}^{\circ}\)) as to prompt immediate intervention. * The bullseye figure has a v-shaped distribution of points, with more-extreme elevation offsets also having more positive azimuth offsets. This is a particularly unusual distribution of points, even for a system with tilt, and is an indication that the offsets (either tilt/fixed or both) have changed through time, particularly as the solar flux delta is high within these distributions. * Further evidence of time-variant offsets are the broad distribution of points across an extended elevation offset range (>1.0\({}^{\circ}\), the typical maximum bullseye size given the radar sensitivity during the project) between 60\({}^{\circ}\) and 120\({}^{\circ}\) azimuth and the time-series plot (Figure 3), where the distribution of points is clearly asymmetric around the summer solstice. In the case of a system with a constant tilt through time, you would expect a more-symmetrical distribution as the azimuths sampled within the radar volume during spring are the same as those sampled during autumn. Period 8 is unique in the dataset as it is the only period to be longer than the 16 week interval recommended by [PERSON] et al. (2016) and is also the only time period during which offline raster scans were taken, which act as a complementary assessment. A total of ten raster scans (Table A1) were undertaken across a 3-day period from 14 to 17 September 2020, covering elevation angles from 5 to 40 degrees and an azimuth range of 173 degrees (94\({}^{\circ}\) to 267\({}^{\circ}\)). These results also show the elevation offset to be azimuthally dependent, where the fitted tilt model has a declination of 288.4\({}^{\circ}\), an inclination of 0.51\({}^{\circ}\) and a fixed elevation offset of 0.74\({}^{\circ}\)(Figure A1). While these are roughly comparable to the results of the analysis of solar hits collected during normal operation of the radar, there is a factor of two increase in the inclination compared to the period as a whole. This is accompanied by a subtle shift in the declination, perhaps indicating the radar platform as a whole or some component of it (trailer/scaffold etc.) sank during this time period (see later discussion). Given the significant change in magnitude and the length of the data record for Period 8, it has been split into two periods (5 November 2019 to 15 June 2020 and 15 June 2020 to 14 October 2020) to derive the final correction. The final 16 weeks of the period (from 15 June 2020) were analysed separately, and a tilt model of 261\({}^{\circ}\) declination, 0.48\({}^{\circ}\) inclination and 0.58\({}^{\circ}\) offset was derived, which is similar to the raster scan observations if refraction correction is applied to those results. The results are not a closer match, as the split into two time periods does not fully characterise the changes in pointing offsets occurring during this period. Alternative approaches to characterising the variable tilt during Period 8 were explored, including a short-duration (7-day) moving window approach and splitting the period into shorter arbitrary time windows, but given the potential non-linearity of the tilting system (it is not clear whether the changes are step-changes at fixed points in time or rather more gradual changes that may or may not have a constant rate of change) and the greater uncertainty of small time windows for tilt estimation, the simple approach of an arbitrary split was used for the final correction. The final fitted tilt model for the first part of Period 8 is shown in Table 4, which shows the final corrections used for all of the time periods.