## 2 Materials and Methods
### IR Sensor-Based Satellite Products
Estimations with PMW and AMW sensors provide a \"snap-shot\" detection of precipitation fields below the satellite [46], leading to a coarser temporal sampling compared to GEO satellite IR imagery [12]. To counter this, these sensors need to be carried onboard a constellation of LEO satellites [44]; however, for now, microwave sensors onboard LEO satellites give global coverage every 3 h [12]. CMORPH (CPC MORPHing) is a multi-satellite-based and PMW-derived precipitation product developed by the Climate Prediction Centre (CPC) of the NOAA [19]. The CMORPH products used in this study have a 30 min temporal and 8 \(\times\) 8 km\({}^{2}\) spatial resolutions. The CMORPH algorithm uses the estimates derived by PMW sensors, propagates the precipitation fields from the motion vectors determined from IR sensors observations, and uses a morphing technique which smooths the fusion of precipitation-pattern propagations backward and forward in time. Two products, derived from this algorithm, were used in this study:  
* The CMORPH-RT [47], which propagates PMW sensor-based estimates only forward in time making them available in real time;
* CMORPH v0.x based on the morphing method [19]. The Global Satellite Mapping of Precipitation (GSMaP) is a project supported by the Japan Aerospace Agency (JAXA) (Tokyo, Japan) and the Japan Science and Technology Agency (Saitama, Japan) [20]. GSMaP rain-rate estimates were derived from PMW sensor measurements and the motion vectors were determined from successive IR images to propagate rain fields. Moreover, a refining step for the effects linked to the propagation was implemented by the use of a Kalman filter model [48]. Among all of the products presented in [49], four of them were retained with their associated gauge-calibrated versions: the near-real-time version 7 of GSMaP (GSMaP-NRT) based on the original GSMaP v7 algorithm and an instantaneous (GSMaP-Now) version of GSMaP with a half-hourly extrapolation, only forward in time, by using motion vectors determined by geostationary satellites [50]. Furthermore, as [PERSON] et al. [51] detailed, both GSMaP-NRT and GSMaP-Now products have gauge-adjusted versions (GSMaP-NRT-GC and GSMaP-Now-GC, respectively), which we used in this work, with the same latency and gauge-adjusting process. This process is detailed as follows [50]: the gauge measurement was not available in real-time, the gauge-adjusted versions were produced by adopting the error parameters derived from the gauge-corrected satellite precipitation product (GSMaP-Gauge) of the post-real-time product (GSMaP-MVK). Both GSMaP-Gauge and GSMaP-MVK were not used in this work because of their post-real-time latency of 3 days. The four products were given at a spatial resolution of 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\) (11 \(\times\) 11 km\({}^{2}\)). GSMaP-Now and GSMaP-Now-GC have a 30 min temporal resolution while the NRT version has an hourly timestep. The space mission Global Precipitation Measurement (GPM) was launched in 2014 as part of a joint project between NASA and JAXA. In that framework, level 3 satellite precipitation products Integrated Multi-satellite Retrievals for GPM (IMERG) were developed [21]. IMERG provides precipitation fields every 30 min, with a horizontal resolution of 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\) in latitude and longitude. These products emerge from a combination of data collected by IR and PMW sensors from the GPM constellation satellites. In this study, we used two different products from IMERG: IMERG-Early and IMERG-Late, which were both considered as NRT versions but with various post-processing procedures [52]:  
* IMERG-Early (later called EARLY) is the earliest version of the IMERG product available after nominal observation; with approximately 4 h of data latency, the propagation of precipitation fields determined by the observation of IR sensors is applied only forward in time;
* IMERG-Late version (later called LATE) is available after a latency of 14 h and has its precipitation fields propagated forward and backward in time.