# Dual-Polarization Observations of Slowly Varying Solar Emissions from a Mobile X-Band Radar
## 5 Discussion  
It was previously observed that \"raw\", original data cannot be used for an accurate assessment of absolute calibration, because the noise contribution to the detected signal is not negligible. Noise subtraction is necessary as without doing that one would erroneously conclude that the X-band radar is positively biased by approximately 1.6 dB (plus atmospheric attenuation), while the radar \begin{table}
\begin{tabular}{c c c c} \hline  & **DRAO** & **N\({}_{\mathbf{subtr}}\) Hor.** & **N\({}_{\mathbf{subtr}}\) Ver.** \\ \hline Median & 24.36 dBfu & 24.00 dBfu & 24.00 dBfu \\ Average & 24.37 dBfu & 23.99 dBfu & 23.91 dBfu \\ St. dev. & \(\pm\)0.120 dBfu & \(\pm\)0.344 dBfu & \(\pm\)0.321 dBfu \\ \hline \end{tabular}
\end{table} 
Table 2: Main statistical parameters of the three curves shown in Figure 2.  
Figure 2: The red curve represents the daily solar flux values measured by the Dominion Radio Astrophysical Observatory (DRAO) in Canada at 10.7 cm and extrapolated to the X-band. The other four curves show the values retrieved by the Swiss Confederation mobile weather radar. estimates on average, are almost bias-free. However, this fact is only valid for the average value. The small residual negative bias is not constant as it can be over or underestimated. The dispersion of the difference can be assessed, for instance, by using the standard deviation. The results of such a procedure are given in Table 3, where shows: (1) the vertical polarization is slightly better than the horizontal one for both the the Sun + Noise values and after noise subtraction; (2) the standard deviation of the difference increases for both polarizations after daily noise subtraction. Hence, it seems better to subtract a constant noise value than trying to estimate and subtract it daily and subtract on a daily basis. In order to confirm this important conclusion, an attempt could be made to quantify the agreement between the DRAO and the radar-retrieved (original vs. Noise-subtracted) estimates from another viewpoint, that is, in terms of correlation. Table 4 shows the explained variance, which is 100 times the square of the correlation coefficient between the DRAO reference and the radar estimates: again, the original (sun + noise) values give a better score for both polarizations. It is possible to conclude that it is better to subtract a constant noise value than a daily-retrieved one, even in terms of correlation. In other words, our estimate of the noise power that affects the solar signal is still not optimal: if it were possible to improve the estimate of the noise, then a decrease in the dispersion of the error and an increase in the correlation should be expected. Estimating background noise is a crucial part of the sun radiation observations (as previously stated, we used the term _background noise_ to refer to the signal detected at the receiver reference point without any contribution from the sun and a good estimate of background noise is still a difficult task. A visual confirmation of our conclusions is presented in Figure 3, which shows solar flux values after having subtracted the average value of each curve. In this way, the DRAO curve shows a zero mean, and the radar curves are all unbiased. It can be seen that, compared to the DRAO reference, the original sun+noise observations (thin lines) are \"smoother\" and agree better with the DRAO reference, while noise subtraction seems to introduce small \"artificial peaks and valleys\". In both cases, the vertical channel estimates agree (slightly) better with DRAO than the horizontal ones. In fact, once the residual bias has been subtracted, it is (even) easier to see that all the radar-retrieved curves capture and reproduce the slowly varying component of the sun, even at 3.2 cm. However, it would be better to compensate atmospheric attenuation before subtracting an average value since the attenuation depends on the angle of elevation of the sun. For instance, attenuation was around 0.22 dB on 2 February, 0.10 on 21 June and 0.16 dB on 30 September.