*2.4. GRISO*

The Random Generator of Spatial Interpolation from uncertain Observations (GRISO) [81,82] is an improved kriging-like technique implemented by the International Centre on Environmental Monitoring (CIMA Research Foundation) to provide rainfall rate estimates. As input, GRISO uses the data from the Italian rain gauge network composed by roughly 3000 tipping bucket gauges (the number can change because of new instrument installation or malfunctioning of the available ones). While, in general, the rain gauge temporal sampling can change, instrument-by-instrument, ranging between 1 to 60 min (the minimum sampling time for Italian rain gauges is set to 15 min), the minimum detectable rain amount is equal to 0.2 mm. The GRISO technique preserves the rainfall rate values measured at the gauge location, allowing for a dynamical definition of the covariance structure associated with each rain gauge by the interpolation procedure. Each correlation structure depends both on the rain gauge location and on the accumulation time considered. Furthermore, GRISO is adopted in the H SAF validation procedure in comparison with European ground data [63] and respect to Dual-frequency Precipitation Radar (DPR) precipitation product [72]. The GRISO data available are provided over a regular grid (1 km × 1 km) with an hourly time step.

#### *2.5. Parallax Correction*

As highlighted in Sections 2.1 and 2.2, IT GR has higher spatial resolution than SEVIRI (i.e., 1 km versus to 4 km). The first step to correctly match ground-based radar and satellite observation is the upscale of the IT GR data to the SEVIRI resolution. Preliminarily, it has to be highlighted that satellite observations of the top surface of clouds is affected by the parallax effect (parallax error), which results in a dislocation of the ground mapped position. The parallax error is a function of three factors that is latitude, longitude, and height of the cloud other than the radius of Earth. While latitude and longitude of the cloud and radius of Earth are known, the height of the cloud has to be determined.

To this end, the TB measured by SEVIRI channel 9 (TB10.8) is matched with the vertical profiles of temperature provided by European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) data [83–85]. The ERA-Interim data are provided on the same grid of SEVIRI over 37 not equi-spaced pressure levels (from 10 to 1000 hPa corresponding to altitudes ranging from 0 to 16 km about with spatial resolution between 240 and 1400 m about) with a time resolution of six hours (i.e., four runs of the model per day). For each SEVIRI instantaneous field of view (IFOV), the TB10.8 is compared with the corresponding and closest in time vertical profile of temperature provided by ERA-Interim in order to estimate the cloud top height. At this point, the formula reported by Equation (1) can be applied to quantify the parallax displacement as function of longitude and latitude:

$$
\Delta\gamma(\lambda,\phi) = \frac{P\cdot\sqrt{1-\cos^2\lambda\cdot\cos^2\phi}}{P\cdot\cos\lambda\cdot\cos\phi-1} \cdot \frac{\eta}{R} \tag{1}
$$

where *P* = 1 + *<sup>H</sup> <sup>R</sup>* with *H* distance between satellite and Earth surface (~36,000 km), *R* radius of Earth, *h* height of cloud top, λ and φ longitude and latitude, respectively. Once that Δγ(λ,φ) is calculated, it can be converted in number of SEVIRI IFOV displacement both in longitude and latitude. The cloud is then moved to the correct position. The parallax displacement can be marked over the Mediterranean area depending on the cloud top height.

Figure 2 shows the parallax displacement (in km) as function of latitude, longitude and cloud top height. The parallax displacement for low clouds is almost constant around 2.3 km, regardless of the coordinates (latitude, longitude) of the measurement point. For higher cloud top, the displacement becomes significant (up to 15–20 km), depending also on the geographical position. The displacement varies by about 5/6 km for cloud heights of 11/14 km moving from south to north (i.e., from 36◦N to 46◦N and at a given longitude). Moving from west to east (and, therefore, at the same latitude), the variability of the parallax displacement is more limited (from about 1.5 to 2 km).

**Figure 2.** Parallax displacement as function of latitude, longitude, and cloud top height.
