# Dual-Polarization Observations of Slowly Varying Solar Emissions from a Mobile X-Band Radar
## 3 Deriving Solar Flux Values Using Observations of a Mobile Radar Working at the X-Band
### The Swiss Confederation Dual-Polarization X-Band Weather Radar
#### 3.2.2 Assessing the Unpolarized Solar Power in dBm at the Entrance of the Antenna Feed  
The assessment of the measured unpolarized Solar signal at another reference point (outside the radome, and not yet captured by the radar antenna) requires the knowledge of three terms:  
* the multiplicative factor from unpolarized solar radiation to dual-pol channels (dual-polarization loss);
* accurate knowledge of the Rx chain losses, L\({}_{\text{Rx}}\), including dry radome attenuation for both polarizations;
* (finally), since the solar disc is not seen with a constant antenna Gain due to the directive weather radar antenna, the Sun cannot be considered as a point source. As far as the first term is concerned, the factor can easily and reasonably be assumed equal to 2 (that is, by adding 3 dB to the log-transformed scale). As for the Rx chain losses (including the dry radome losses), reference can be made to the measurements performed during the Site Acceptance Test  
Figure 1: Signal received from the Sun (horizontal channel), S\({}_{\text{rp}}\), at the reference point, which is at the entrance of the Low Noise Amplifier (LNA) (see the left-hand term in Equation (3)) over two consecutive winter days. Since the attenuation of the Earth’s atmosphere has not been corrected, a maximum can be observed in correspondence to the largest angle of elevation value. (Locarno airport, autumn 2012); the values are listed in the first line in Table 1. Regarding the last point, since the half power beam width of the antenna is not much larger than the solar disk, the contribution of the outer areas of the disc are underestimated compared to the inner part; hence the observed flux density starts to deviate (decrease) from the integrated flux density observed when a broader-beam antenna (for instance, the DRAO antenna, whose HPBW is 4.5\({}^{\circ}\)) is used. In principle, if the beam axis is pointed precisely towards the center of the disc and the solar disc is uniformly bright, it is possible to quantify such non-point-source, \(\rm{L_{nps}}\). For instance, according to Section 7.1 in Reference [17] or Equation (13), page 161, in Section 2.d in Reference [11], if an apparent diameter of the radio sun equal to 0.57\({}^{\circ}\) and HPBW = 1.3\({}^{\circ}\) are assumed, \(\rm{L_{nps}}\) = 10 Log (0.8954) = 0.29, which we have approximated to 0.3 dB. However, it is worth noting that the uniformly bright S\(\rm{un}\) disc condition is encountered often around the solar activity minimum, but more rarely elsewhere during the solar cycle. The incident solar power at the antenna feed, \(\rm{P_{ant}}\), can be derived simply (in an equation) as:  
\[\rm{P_{ant}}=S_{rp}+3\;dB+L_{Rx}+L_{nps}=S_{rp}+3.3\;dB+L_{Rx}. \tag{4}\]  
where \(\rm{S_{rp}}\) has been estimated using Equation (3). \(\rm{P_{ant}}\) has the same dimension as \(\rm{S_{rp}}\), namely \(\rm{[P_{ant}]}\) = dBm. 2.3 Estimate of the Unpolarized Incoming Solar Spectral Irradiance, \(\rm{I_{3,2}}\), in Solar Flux Units (where \(\rm{O_{2}}\) Attenuation is Neglected)  
As stated in Section 2.2, the DRAO reference values consist of the spectral power per unit of area, which is a quantity that is called irradiance in the radiative transfer theory. However, at microwave frequencies, it is expressed in the Solar Flux Units (SFU), where 1 SFU is equal to \(10^{-19}\) mW\(\cdot\)m\({}^{-2}\cdot\)Hz\({}^{-1}\). Hence, the Rx bandwidth (in Hz) and the antenna equivalent area, \(\rm{A_{eq}}\) (in m\({}^{2}\)) should be known as precisely as possible for the final comparison in order to transform the estimated incident power at the antenna feed, given in dBm, \(\rm{P_{ant}}\), into the incident spectral irradiance at 3.2 cm, \(\rm{I_{3,2}}\), which in the same way as the DRAO reference, is expressed in dBsfu.