## 2 Materials and Methods
### Model Overview
\[\mathrm{\Delta Yield}=\mathrm{\Delta DAM}\ \times\ P_{y} \tag{5}\]  
where, \(\mathrm{\Delta Yield}\) is the daily change in yield and \(P_{y}\) is a grain filling factor. The soil-water balance module (SAFY-SW), adapted from [24; 29], utilizes a simple 'leaky bucket' model to simulate soil-water balance and includes inputs in the form of precipitation, and losses, in the form of runoff, evapotranspiration (ETR) and deep percolation or drainage. The water balance model assumes no unsaturated flow, and capillary or upward flow only occurs as a result of soil evaporation. A root-growth sub-module was adapted for SAFY to aid the simulation of root water uptake, which is used to compute the plant transpiration [24; 31]. Because of the availability of field specific soil information, Refs. [24; 29; 31] implemented the soil-water balance module for a 5-layer soil profile. We adapted the same architecture for estimating water movement in the soil and water stress during the growing season but utilizing the bulk soil information and a mean soil profile, due to the absence of site specific soil information. Equations (6)-(11) shows the equations in the soil-water balance module. Potential evapotranspiration (PET) is computed as 1.1 times the equilibrium evaporation rate (EET), following [47] and EET is calculated using the Priestly-Taylor equilibrium equation, using albedo (\(\alpha\)), global radiation (\(R_{g}\)) and daily mean temperature (\(T_{avg}\)). The Priestly-Taylor equation only requires a limited number of meteorological inputs. \[\mathrm{EET}=\ R_{g}\times\left(0.0045-0.00437\times\alpha\right)\times\left(T _{avg}+29\right) \tag{6}\]  
\[\Delta\mathrm{DAM}=\mathrm{APAR}\;\times\mathrm{ELUE}\;\times\;\mathrm{F_{T}(T_ {a})}\times\mathrm{WST} \tag{1}\]0  
\[\mathrm{PE}=\left\{ \begin{array}{ll}\mathrm{PET}\times\left(1-0.43\times \mathrm{GAI}\right);&\mathrm{if\ GAI}<1\\ \mathrm{PET}\times\mathrm{e}^{-0.4\times\mathrm{GAI}};&\mathrm{if\ GAI}\geq 1 \end{array} \right. \tag{8}\]  
\[\mathrm{PT}=\left\{ \begin{array}{ll}\mathrm{PET}\times\frac{\mathrm{GAI}}{ 3};&\mathrm{if\ GAI}<3\\ \mathrm{PET};&\mathrm{if\ GAI}\geq 3\end{array} \right. \tag{9}\]  
PE is potential evaporation, PT is potential transpiration, and is computed based on the daily estimated GAI. Potential root water uptake (PRWU) is derived using Equation (10). \[\mathrm{PRWU}=0.00267\times\frac{\mathrm{e}^{62\times\left(\mathrm{SW-WP} \right)}}{\left(6.68-\log(\mathrm{RLV})\right)} \tag{10}\]  
SW is the soil-water content, WP is water availability at wilting point and RLV is the root length density. The actual evapotranspiration (AET) is equal to PT, if PRWU is greater than or equal to PT, i.e., no water stress condition. Where PRWU is less then PT crop transpiration demand is not satisfied and the crop is considered to be experiencing water stress (WST), computed as the ratio of AET to PT. \[\mathrm{WST}=\frac{\mathrm{AET}}{\mathrm{PT}} \tag{11}\]  
An equation is also added to translate AET (in mm.day\({}^{-1}\)) to a latent heat (LH) flux in Watts/m\({}^{2}\) Equation (12). This should enable the model to be compared to equivalent measurements obtained from a flux tower or similar instrument, if available at a site and is an important component of the energy balance. \[\mathrm{LH}=28.94\times\mathrm{\ AET} \tag{12}\]  
A carbon flux module was previously implemented within the SAFY model. The approach estimates the Gross Primary Productivity (GPP) similar to Equation (1) with a modification to the ELUE parameter and inclusion of \(\mathrm{sR_{10}}\), to account for the fraction of the green tissues in the senescence stage. Here, we replaced ELUE by fELUE, a product of ELUE and radiation use efficiency (RUE). RUE takes into account the diffuse fraction of radiation that is not usually considered in crop models, but studies have shown that RUE can be significant in the estimation of productivity; ignoring the parameter may lead to an inaccurate estimation of the fluxes. Equations (13)-(16) outline the equations used to derive GPP [25; 32].