# _remote sensing_
## Appendix A Simple Algorithm for Yield Estimates (SAFY)  
In SAFYsw, biomass accumulation depends on the amount of Photosynthetically Active Radiation (PAR) that is absorbed by the canopy, following Equation (A1):  
\[\Delta\text{DAM}=\text{Rg}\cdot\varepsilon\text{C}\cdot\varepsilon\text{l} \cdot\text{ELUE}\cdot\text{FT(Ta)}\cdot\text{Ks},\] (A1)  
where Rg is the solar radiation, \(\varepsilon\text{C}\) is the climatic efficiency, \(\varepsilon\text{l}\) is the light efficiency, ELUE the effective light use efficiency, which also accounts for stresses not considered in the T other crop modules, and FT is the temperature stress. Ks is the water stress coefficient (an addition of the SAFYsw version of the model), which acts as a modifier of the biomass accumulation. Ks is derived from the actual transpiration to potential transpiration ratio, which are calculated in the water balance module, as specified below. Daily LAI expansion is calculated from the daily accumulated biomass until senescence as in Equation (A2):  
\[\Delta\text{GLAI}+=\Delta\text{DAM}\cdot\text{PL}(\sum\text{Ta})\cdot\text{ SLA},\] (A2)  
where \(\Delta\text{GLAI}+\) is the LAI expansion, \(\text{PL}(\sum\text{Ta})\) is a partition-to-leaf function calculated from the thermal sum and two partition parameters (\(\text{P}_{\text{La}}\) and \(\text{P}_{\text{LB}}\)), and SLA is the specific leaf area. After reaching a thermal sum threshold defined by the senescence parameter \(\text{S}_{\text{TT}}\), the LAI starts decreasing following Equation (A3):  
\[\Delta\text{GLAI}-=\text{GLAI}\cdot(\sum\text{Ta}\cdot\text{S}_{\text{TT}})/ \text{Rs},\] (A3)  
where Rs is the canopy senescence rate. When canopy expansion ends, grain starts accumulating depending on the Py parameter of partition to grain and on the total biomass so far accumulated, as in Equation (A4):  
\[\Delta\text{GY}=\text{DAM}\cdot\text{Py}.\] (A4)  
The SAFYsw version also adds a water balance based on the tipping bucket approach by [38], where an upward flux (evapotranspiration-driven) and a drainage downward flux (gravity-driven) are calculated. An equilibrium evaporation rate (EET) is calculated through the Priestley-Taylor equilibrium equation, using albedo (\(\alpha\)), solar radiation and daytime temperature (T), as in Equation (A5):  
\[\text{EET}=\text{Rg}\cdot(0.0045-0.00437\cdot\alpha)\cdot(\text{T}+29).\] (A5)  
Following [38], potential evapotranspiration (ETp) is 1.1 times EET, and potential soil evaporation (Ep, Equations (A6) and (A7) and potential plant transpiration (Tp, Equations (A8) and (A9) are then calculated considering specific LAI thresholds:  
\[\text{Ep}=\text{ETp}\cdot(1-0.43\text{-LAI});\text{ with LAI}<1,\] (A6)  
\[\text{Ep}=\text{ETp}\cdot\exp(-0.4\cdot\text{LAI});\text{ with LAI}\geq 1,\] (A7)  
\[\text{Tp}=\text{ETp}\cdot(\text{LAI}/3);\text{ with LAI}<3,\] (A8)  
\[\text{Tp}=\text{ETp};\text{ with LAI}\geq 3.\] (A9)Potential root water uptake (RWU) is dependent on water available in each layer above the lower limit of plant water availability (LL, i.e., the wilting point), and is calculated as in Equation (A10):  
\[\text{RWU(I)}=0.00267\cdot\exp(62\cdot(\text{SW(I)}-\text{LL(I)}))/(6.68-\ln( \text{RLV(I)}))\] (A10)  
where I indicates the layer, SW(I) is the soil water content and RLV(I) is the root length density. With a total \(\text{RWU}\geq 0\) of Tp, the actual water uptake is considered equal to potential transpiration (no water stress, actual transpiration equals potential transpiration, Ta = Tp). Otherwise, the transpiration demand is not satisfied and Ta is set equal to the actual uptake (limited by soil water availability), and a water stress coefficient (Ks) is calculated as the ratio Ta/Tp. Ks is used as a linear modifier of biomass accumulation in Equation (A1). The downward flux occurs from a soil layer when the soil water content is above the drained upper limit (DUL, i.e., field capacity).