## 1 Introduction  
The accurate spatial modelling of rainfall distribution has a widely recognized value among scholars and practitioners of different scientific and engineering fields (e.g., hydrology, water balances and resources management, regional impacts of global change, etc.) [1, 2, 3, 4, 5]. Moreover, sustainable landscape management requires spatially interpolated data, whose outcomes are strictly related to models and geostatistical parameters adopted. In fact, temperature and rainfall patterns significantly contribute to the configuration of natural vegetation types [6] and affect the suitability of territory to specific crops. Moreover, an accurate mapping rainfall distribution represents a key data input in modelling and monitoring the effects of climate change [7, 8]. Referring to these mentioned uses of spatial rainfall models at different timescales, it is worth highlighting their fundamental role in the parametrization of crop models simulating crop growth as well as in the implementation of hydrological models aiming at flood forecasting [9]. A prerequisite for implementing the spatial rainfall distribution is the availability of official climate databases with sufficient temporal and spatial completeness. Indeed, to implement reliable hydrological or environmental models, there is the need to accurately assess the choice and set-up of spatial interpolation models that can affect the obtained results introducing significant errors. Rainfall is not a regular phenomenon and is characterized by high spatial variability. Usually, meteorological networks are widely dispersed in a territory without a defined sample scheme. Moreover, rain gauge networks just collect point estimates, and in most cases, their number is quite limited [10; 11]. Thus, there is the need to estimate rainfall values at unrecorded locations using the values at surrounding sites [12] to spatially interpolate the original discrete point measurements so as to obtain continuous surfaces. Notwithstanding the possibility of using different precipitation products as rainfall proxies, rain gauge databases today represent the primary reference to implement hydrological models [13], largely because of the temporal consistency of these data that in most cases are multi-decades time-series. In the last two decades, several authors have attempted to identify the most reliable and accurate method of spatial rainfall interpolation in different geographical areas and spatial domains (continental, national, regional, local) [9; 10; 11; 14; 15; 16]. Referring to the spatial interpolation of the rainfall phenomenon, we have to consider that the most reliable interpolator may vary depending on the different regions in which it is applied [3; 17]. In the scientific literature, several spatial interpolation methods have been proposed and compared by scholars to map rainfall data in a reliable way in various world areas. There is no recent comprehensive review analysing the spatial interpolators tested for rainfall spatialisation to our best knowledge. Indeed, the work of [PERSON] and [PERSON] [18] found more than fifty spatial interpolation models applied in the estimation of spatial rainfall spatial distribution. The spatial interpolation methods can be classified as deterministic/stochastics and probabilistic, either applied to a global or a local scale. The comparison of deterministic (multiple empirical regressions [19; 20]; splines [21]; inverse distance weighting, IDW [22; 23; 24; 25]) with geostatistical algorithms [26; 27]) can be considered one of the most common in the climatology field of research. Several authors pointed out that the geostatistical approach, based on the regionalised variables [26; 28; 29], can lead to a more reliable estimate of rainfall distribution than the deterministic ones [12; 17; 30; 31; 32; 33].