## 1 Introduction  
Fresh water scarcity is one of the main issues examined by climate-change adaptation policies [1; 2]. A common objective of climate change adaptation policies is to identify feasible water management strategies at regional and continental scales to secure the water required for food production, while preserving the ecosystems. This issue is particularly relevant in regions where agricultural irrigation is the main pressure on renewable water resources. In these regions, an assessment of water withdrawal for crop irrigation is fundamental to plan sustainable policies and implement better-informed decisions in water resource management. Irrigation maps at global and continental scales have been developed for spatial statistics of agricultural water demand [3; 4; 5]. However their utility for planning water resources and climate adaptation polices is still limited [6]. In Europe, Regulation (EU) No 1303/2013, consistently with the Water Framework Directive (WFD, 2000/60/EC), has imposed to Member States the implementation of effective procedures for assessing irrigation water volumes, as a prerequisite for the exploitation of structural and investments funds within the EU Common Agricultural Policy [7]. Since direct accounting of irrigation water use is often not feasible, procedures based on crop-water-balance modeling have been proposed for a quantitative assessment of irrigation water use at regional scale [8; 9; 10; 11; 12; 13; 14]. In Mediterranean regions, where rainfall and groundwater capillary rise are negligible in the irrigation season (generally from April to September), evapotranspiration is the key variable of the crop water budget. To this end, the Italian Ministry for Agricultural Policy (MIPAAF) has established a set of guidelines to define estimation methodologies of irrigation volumes as an alternative to direct measurements (ministerial decree 31 July 2015). In order to uniform instruments and methodologies at the national scale, these guidelines catalog the procedures having a sound scientific basis, including those adopted by the irrigation advisory services, available in several Italian Regions [8]. In the case of collective irrigation schemes, the estimation methodology allows to consider the withdrawal water volumes coincident with the net irrigation requirements for crops in \"standard\" conditions as defined by the Food and Agriculture Organization of the United Nations (FAO)-56 study [14], accounting for the actual crop development. Evapotranspiration is often estimated as a function of the daily reference crop evapotranspiration (ET\({}_{0}\)), which is evapotranspiration from a well-watered hypothetical reference crop according to the FAO-56 Penman-Monteith equation [15]. A complete set of meteorological data--including air temperature, wind speed, solar radiation and relative humidity--is required for computing ET\({}_{0}\). Even in highly developed countries, ground weather stations recording variables with consistent accuracy over time are generally available only in a few sites, as part of relatively sparse monitoring networks or very often far from rural areas [16]. In some countries, such as Italy, data availability is also constrained by the fact that the monitoring networks are managed by several regional and national services, which adopt different policies in data storage and distribution. In areas where a monitoring network is available, spatial interpolation procedures can be employed for assessing weather data at the ungauged sites as well as for generating regular gridded data for regional studies, e.g., [17; 18; 19]. In the spatial interpolation of nonlinear models such as ET\({}_{0}\), the best solution is to first interpolate the input variable (e.g., the weather variables) and then, calculate the model output (e.g., ET\({}_{0}\)) [20]. This rule was verified by recent studies applied to the regional assessments of ET\({}_{0}\)[21; 22; 23; 24].