## 2 Problem Definition
### Data Collection  
The OEL data that has been used in this work have been collected from the smart rainfall system (SRS) which is a network of microwave sensors for satellite down-links developed by the University of Genoa and Artrys, Darts Engineering Srl, Genoa, Italy [24]. The analysis is focused on measurements performed by an SRS sensor installed on the roof of the University of Genoa--DITEN department, characterized by an offset antenna with a parabolic reflector with a diameter of 85 cm, and aligned towards the Turksat 42\({}^{\circ}\) E Constellation. The azimuth and elevation angles of the dish with respect to the sun are 137.09\({}^{\circ}\) and 29.2048\({}^{\circ}\), respectively. The sensor was programmed to receive the signal in the upper Ku band (11.7\(\sim\)12.75 GHz) with vertical polarization [25]. A universal low noise block (LNB), placed on the arm of the parabolic dish, converts the microwave signals from the Ku-band to the L-band. The LNB interface circuit provides the power supply and the 22 kHz tone to select the proper sub-band (10.75 to 11.7 GHz and 11.7 to 12.75 GHz) and polarization. The RF signal, after filtering and amplification, is sent to a detector that converts the power over a 45 dB range into a voltage using logarithmic amplifiers. The LNB interface board consists of a microcontroller that also performs the signals analog-to-digital conversion (ADC) with 10-bit resolution. The microcontroller samples the RF signals 64 times per minute; at the end of each minute, a UDP packet including the input RF power measurement and some information is sent to a central server for further processing. The block diagram of the system is reported in Figure 2 of [26], while the SRS sensing board is shown in Figure 3 [26]. The ground data used as a reference for actual rainfall occurrence were obtained by a dynamically calibrated TBRG manufactured by CAE S.p.A.--San Lazzaro di Savena, Italy--and installed at the Hydraulic Laboratory of the University of Genova--DICCA department [25]. Figure 1 shows a cartographic overview of the position of the dish and the reference rain gauge (TBRG) where the blue circle on the map is the location of the SRS dish, and the red circle is the location of the TBRG. Figure 1: The location of the SRS dish at the University of Genova—DITEN department (blue circle, Lat: 44.4031; Lon: 8.9587; Altitude 70 m.a.s.l.) and TBRG at the Hydraulic Laboratory of the University of Genova—DICCA department (red circle, Lat: 44.3998; Lon: 8.9636; Altitude 45 m.a.s.l.). The blue line represents the ground projection of the path from the dish toward the Turksat 42\({}^{\circ}\) E constellation, chosen for this research. The choice of the instrument providing reference measurement was made considering the high level of accuracy of the DICCA's TBRG, since it has been corrected from the systematic mechanical errors reaching class A performance (according to EN 17277:2019 recommendations) and constantly monitored by the WMO Lead Centre \"[PERSON]\" on Precipitation Intensity laboratory. Figure 4 in [25] provides the percentage relative error as a function of the rainfall intensity. The error is in the range \(\pm\)3% for all the rainfall measurements. Furthermore, its location (Figure 1) is below the SRS microwave downlink considered in this study, at a distance of approximately 500 m from the dish, and is therefore suitable for providing a reasonable indication of the rainfall conditions occurring in the monitored territory. To improve the reference dataset quality, the inter-tip time correction method described by [PERSON] et al. [27] was applied. This processing technique is able to provide more accurate one-minute rainfall measurements, with respect to the coarse method yet very common in operational practice, i.e., the counting of the number of tips performed by the TBRG mechanical sensor over a specified measurement update interval. Such a number is usually associated with a rainfall volume, given the TBRG sensitivity and calibration parameters.