## 2 Materials and Methods
### Description of the Precipitation Products
#### 2.1.2 Radar Networks  
In this study, data from two radar networks were used: the Meteo-France PANTHERE rain-rate composite product [26; 27] and the OPERA pan-European composite product [28]. Both of these products are mainly based on observations from the national radar network when focussing on rainy events over France but some differences exist in data treatments or instruments, which can impact the rain estimates. The ARAMIS French radar network [13] is composed of 31 Doppler radars that use various frequencies (or bands): 5 are in the S-band, 20 are in the C-band, and 6 are in the X-band [29] (see Figure 1). An additional C-band radar, operated by the company NOVIMET, is located at the Mont Vial summit (43.89\({}^{\circ}\) N, 7.15\({}^{\circ}\) E) in south eastern France, and two other radars, located at the Paris-Charles de Gaulle and Nice airports, contribute to the French PANTHERE product [30]. Moreover, two partner radars which do not take part in the ARAMIS network are used within the PANTHERE product (both are located on the Jersey Island and at the station La Dole/Geneva at the France-Switzerland border). The data processing took into account polarimetric and reflectivity parameters sampled on a polar grid with a resolution of 240 m \(\times\) 0.5\({}^{\circ}\)[29]. For the C- and S-band radars, a radius of 100 km around the radar position was considered for the measurement of  
Figure 1: Positions of the radars of the ARAMIS network (plus symbols) considered in the PANTHERE product. Radars of the OPERA product are identified with small blue circles. Additional coloured circles are used to indicate the type of the radar and an extension of measurement: the C-band (magenta, 100 km), S-band (yellow, 100 km), and X-band (green, 60 km) radars. The C- and S-band radars are only considered in the OPERA product and those located close to the French borders are indicated with dashed-dotted black circles. precipitation amounts, whereas a range of about 200 km around the radar position was used for precipitation detection [31]. The X-band radars were used as gap-fillers [27]. The sampling volumes were produced every 5 min and were built from three to five scans at a low-elevation angle (ranging from 0\({}^{\circ}\) to 3\({}^{\circ}\)) repeated every 5 min and from two to three scans at high-elevation angles (from 3\({}^{\circ}\) to 15\({}^{\circ}\)) [29]. These raw scans were received and processed by the French national centre according to the different steps detailed in [26]. [PERSON] and [PERSON] [27] provided a flow diagram that describes the different steps used in the data processing of the operational radar observations to obtain the rain-rate product:  
* A ground-clutter identification by using pulse-to-pulse fluctuation of the radar reflectivity with further analysis for pixels adjacent to an identified clutter pixel;
* Non-meteorological echoes and precipitation-attenuation corrections from polarimetric modules;
* A partial beam-blockage correction by numerically simulating the interaction between the radar wave propagation and the ground by using orographic maps and long-term precipitation accumulation to identify trees and anthropogenic structures;
* A vertical profile of reflectivity correction deriving from ratios of hourly rainfall accumulation at different elevation angles and using these ratios to determine an optimal vertical profile reflectivity scheme from a predefined set;
* A gas-attenuation correction depending on the wavelength used and the altitude above the sea level;
* The synchronization or correction for advection;
* A weighted linear combination of the corrected reflectivity measurement at different elevation;
* The reflectivity (\(Z\)) conversion to rain rate (\(R\)) by using the \(Z\)-\(R\) relationship \(Z=200\cdot R^{1.6}\), the 5 min rainfall accumulation;
* The rain-gauge adjustment. In our case, we used the aggregated 15 min PANTHERE dataset provided by the company Weather-Measures.