## 4 Discussion of the Results Including a Preliminary Attempt of Noise Subtraction
For the typical angles of elevation used during sun-tracking, and assuming a flat atmosphere, this produces attenuation values between 0.12 dB and 0.18 dB for Albis and between 0.1 dB and 0.14 dB for WEI. Regarding noise subtraction, since the log-transformed ratio of sun to noise (_i.e._, the measured quantity) divided by noise is of the order of 9 dB, the typical reduction of the retrieved solar flux is about 0.5 dB smaller than the one presented in Section 3. Adding up, between these two second-order effects, noise subtraction is more influent than the atmospheric correction. Hence, we will attempt noise subtraction on the 22 observations coming from WEI, _Monte Lema_, and Albis. Results are presented and discussed below. The Swiss radar receivers operationally measure system noise every 2.5 min at angles of elevation of 35\({}^{\circ}\) and 40\({}^{\circ}\), respectively. The noise measurements are taken between 60 and 70 km, integrating 120 range bins and 420 pulses within a 10\({}^{\circ}\) sector in azimuth. Each noise measurement is thus the average of 120 \(\times\) 420 = 50,400 raw measurements. We then combine 20 noise measurements, keeping the median out of the 20 values as representative of the noise floor. This is done for both channels separately. In the present example, we use the observed noise value at 40\({}^{\circ}\) elevation, N\({}_{\text{EL40}}\) (namely, the last one before the Sun-tracking started), and subtract it from the observed value, S\({}_{\text{out}}\) (both obviously in linear ADU). The observed value consists of the solar flux, plus an \"unknown\" noise component. In formula: S\({}_{\text{out}}\) = S\({}_{\text{Sun}}\) + N\({}_{\text{unknown}}\). Our estimate after noise subtraction, simply consists of subtracting the nearest-in-time observed value of N from the S values listed in Section 3. Table 7 shows that noise subtraction results in an average decrease of approximately 0.5 dB. An important question: Does this kind of noise subtraction improve the agreement between the weather radar and DRAO? As can be seen in Table 8, there is no improvement in terms of standard deviation of the error. However, one can also ask whether the agreement improves in terms of correlation and for this purpose. Table 9 shows the percentage of explained variance (100 times the square of the correlation coefficient) for both polarizations of Albis, Lema, and WEI. It is worth noting that the number of samples is so small that the degrees of freedom are only 5 (Albis), 4 (_Monte Lema_), and 7 (WEI). Noise subtraction increases the correlation for both channels of WEI and Albis. For _Monte Lema_, the correlation slightly decreases. We conclude that the median-observed noise at angles of elevation of 40\({}^{\circ}\) is not always representative for the real (unknown) noise affecting the Sun signal measurement during the off-line Sun-tracking. For future sun-tracking experiments, we plan to use noise samples as close as possible to the sun signal, both in space and time. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Average Error between Radar** & \multicolumn{3}{c}{**Albis**} & \multicolumn{3}{c}{_Monte Lema_} & \multicolumn{3}{c}{_Weissfulbigipfel_} \\ \cline{2-7}
**and DRAO Reference** & **H** & **V** & **H** & **V** & **H** & **V** \\ \hline S\({}_{\text{Sun}}\) + N\({}_{\text{unknown}}\) (as per Section 3) & \(-1.13\) dB & \(-0.75\) dB & \(-0.18\) dB & \(-0.27\) dB & \(-0.07\) dB & \(-0.24\) dB \\ S\({}_{\text{Sun}}\) + N\({}_{\text{unknown}}\) - N\({}_{\text{EL40}}\) & \(-1.62\) dB & \(-1.25\) dB & \(-0.67\) dB & \(-0.76\) dB & \(-0.58\) dB & \(-0.77\) dB \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Agreement between radar estimates (without and with noise subtraction) and the DRAO reference in terms of average error (Log-transformed values) for both polarization channels.