# On the Use of Bright Scatterers for Monitoring Doppler, Dual-Polarization Weather Radars
## 2 Materials and Methods
### The Dual-Polarization, Doppler Radar Located on Monte Lema at an Altitude of 1625 m
#### 2.2.4 Differential (Horizontal/Vertical) Radar Reflectivity  
A first polarimetric observable that can be measured by the MeteoSwiss dual-polarization radar is the differential radar reflectivity, \(Z^{dr}\). This is the Log-transformed ratio between the copolar reflectivity measured at the horizontal, \(ZH\), and vertical, \(ZV\), polarizations; hence, it is expressed in dB, and a \(Z^{dr}\) of 0 dB means that \(ZH=ZV\). In formula form:  
\[Z^{dr}=10\ Log\left(\frac{ZH}{ZV}\right). \tag{5}\]  
This ratio was introduced by [PERSON] and [PERSON] [18] to obtain a better estimate of rainfall, since it contributes to reducing the uncertainty associated with rain drop size distributions. In fact, the additional information associated with \(Z^{dr}\) is remarkable; however, a proper calibration is crucial for successful quantitative applications. [PERSON] [19], for instance, showed that \(Z^{dr}\) should be estimated within 0.2 dB to obtain improved rainfall estimates based on \(Z\) and \(Z^{dr}\). It is possible to use the so-called birdbath scan (angle of elevation of 90\({}^{\circ}\)) on rainy days when the altitude of the 0\({}^{\circ}\) isotherm is high enough to be outside the range that is affected negatively by the T-R limiter recovery time to monitor the differential reflectivity backscattered by liquid drops (\(Z^{dr}\) should be 0 dB). Another (more uncertain approach) is to derive the mean differential reflectivity value of light rain echoes (for example, \(20\leq ZH\leq 22\) dBZ) well below the bright band (which should be around 0.3 dB). Offline Sun observations acquired while tracking the Sun [20,21] are more accurate, but only the receiving chain is monitored, and nothing is therefore known regarding the transmitting path. It is shown in Table 3 (4) in Reference [13] that the standard deviation of six (seven) Sun tracking observations (performed between 2 November 2013 and 21 March 2016) for the MeteoSwiss Monte Lema (Albis) radar is 0.08 (0.04) dB. An interesting and valid alternative to offline Sun-tracking is the automatic daily \"Sun-check\" [10]: this is an operational monitoring technique that is based on the analysis of solar signals in the polar volume radar reflectivity data produced during the operational weather scan program. It has the advantage of the weather radar scan program not being interrupted; the disadvantage is that the antenna beam axis very rarely hits the center of the Sun: consequently, the Sun-to-Noise ratio of each hit can be significantly worse than for Sun tracking. This is partly compensated for by the fact that only one estimate out of many daily hits is retrieved. In Reference [11] (Table 4), the standard deviation of the daily differential reflectivity during an active solar period in 2014 was 0.06 dB for Monte Lema (220 days) and 0.05 dB for the Albis radar (204 days); the dispersion of the difference between H and V during the same set of 100 days in 2014 was 0.06 dB for Albis and 0.08 dB for the Finish ANJ radar (see Table 3 in Reference [22]). In a recent manuscript that reviews several aspects of the monitoring of dual-polarization receiver using solar hits found in operational scans [12], a dispersion as low as 0.02 dB was found for ANJ. These figures refer to a shorter period, namely April 2015. If the antenna is not in an environment with small changes in Temperature, then differential reflectivity can easily vary by a few tens of dB [23]: in Figures 4 and 5, page 1890, in Reference [23], it is shown that a 23 K change in temperature (lasting 8 h) occurred at the S-band Firestone site (on 15 January 2015) and a 0.2 dB drift in \(Z^{dr}\) was observed. Regarding the quantization process, it is worth noting that differential reflectivity is only defined on condition the inequality in (1) is satisfied for both the H and V polarizations. If not, DN is set to 0. The number of radar bins that contain a valid value of differential reflectivity is obviously smaller than for the H or V reflectivity (however, it could be at least the same).