## 2 Materials and Methods
### Forecasting Models
#### 2.3.2. Agrohydrological Model Setup  
The irrigation advisory service of MAGDA rests on the SPHY model [61], whose irrigation module has been improved and adapted for delivering short-term and mid-term forecasts (up to 5 days ahead) of Irrigation Water Requirements (Figure 3). Figure 2: MAGDA domain configuration and data assimilation setup. (**A**) shows the three nested WRF domains used for the Italian and French demonstrator sites, and (**B**) for the Romanian site. The outermost domain (D01) covers approximately 30–60\({}^{\circ}\)N and 20\({}^{\circ}\)W–30\({}^{\circ}\)E in (**A**), and 30–60\({}^{\circ}\)N and 0–50\({}^{\circ}\)E in (**B**), with a horizontal resolution of 22.5 km. The intermediate domain (D02) spans roughly 35–55\({}^{\circ}\)N and 10–20\({}^{\circ}\)E in (**A**), and 35–55\({}^{\circ}\)N and 10–40\({}^{\circ}\)E in (**B**), at 7.5 km resolution. The innermost domain (D03) focuses on the pilot areas, ranging from approximately 39\({}^{\circ}\)N to 50\({}^{\circ}\)N and 0\({}^{\circ}\) to 15\({}^{\circ}\)E in (**A**), and from 42\({}^{\circ}\)N to 48\({}^{\circ}\)N and 20\({}^{\circ}\)E to 30\({}^{\circ}\)E in (**B**), with 2.5 km resolution. Latitude and longitude tick labels are shown for both panels. (**C**) illustrates the forecast configuration for hydrological and irrigation applications, where 3 DVAR assimilation is applied at 18:00, 21:00, and 00:00 UTC, followed by a 120-h free forecast starting at 00:00 UTC. (**D**) presents the rapid-update scheme adopted for convective storm forecasting, involving 3-hourly 3 DVAR cycles and a 12–24-h forecast horizon to enhance short-term storm prediction. Irrigation Water Requirement (IWR) is defined here as the supplemental water needed to meet crop water demand that is not fulfilled by rainfall and existing soil moisture. IWR is computed as:  
\[IWR=ET_{c}-ET_{c,act}=ET_{c}-(P_{eff}+ET_{sm}) \tag{1}\]  
where ET\({}_{c}\) is the crop reference evapotranspiration under non-stress conditions, and Et\({}_{c,act}\) is the actual crop evapotranspiration. P\({}_{eff}\) is the effective precipitation, and ET\({}_{sm}\) is the fraction of the soil water content at the root-zone that is taken by crops for evapotranspiration (also known as the Root Zone Water Supply). The component \(P_{eff}+ET_{sm}\) is the total of water available from rainfall and soil moisture that is used at each timestep to meet the crop water requirement. Under stress conditions for which rainfall and soil moisture stored in the root-zone (\(P_{eff}+ET_{sm}\)) do not match the crop water requirements (ETc), the \(P_{eff}+ET_{sm}\) component may be similar to the crop evapotranspiration computed by using satellite-based evapotranspiration methods. Conceptually, the SPHY model used in MAGDA adopts a simplified 1D leaky-bucket approach, which simulates the dynamics of soil water content in the root-zone domain by considering the main inflows (rainfall) and outflows (interception, actual evapotranspiration, and drainage) that account in the soil-crop-atmosphere continuum (Figure 4A). The water balance in the root-zone domain is computed as:  
\[\Delta SM=Inf-D-ET \tag{2}\]  
being SM the soil moisture in the root zone in water depth, Inf is the fraction of the rainfall that infiltrates into the root zone after canopy interception is discounted, D is the volume of water outflowing the root zone due to vertical or lateral drainage, and ET is the actual evapotranspiration. Drainage is computed using a power-law relationship:  
\[D=k\cdot EWC^{p} \tag{3}\]  
where EWC (mm/day) refers to the Excess Water Content or amount of water that exceeds the soil's field capacity after accounting for precipitation inflows within the root zone (saturation-excess approach). Parameters k and p define the soil drainable-water retention curve of a soil, with k being the diffusivity coefficient (mm\({}^{2}\)/day) and p the moisture diffusivity exponent (dimensionless).