Replacement of AFGEN tables

Two approaches were used to replace AFGEN tables. The first approach involves AFGEN tables which highlighted negligible differences among available WOFOST parameterizations for a group of species. In these cases, the tables were substituted with non-editable functions, developed by interpolating the available WOFOST parameterizations for rice and wheat, without introducing any additional parameters. The AFGEN tables replaced according to this approach were those related to specific stem area (SSATB; function of DVS; ha kg1, replaced by Equation (1)), reduction factor of gross assimilation rate (TMNFTB; function of minimum temperature; kg kg1, Equation (2)), dry biomass partitioning to roots (FRTB; function of DVS; kg kg1, Equation (3)) and storage organs (FOTB; kg kg1, Equation (4)), and relative death rates of roots (RDRTB; function of DVS; kg kg1 d1, Equation (5)) and stems (RDRSTB; kg kg1 d1, Equation (5)).

The second approach to replace AFGEN tables involves cases for which marked differences among parameterizations available in literature were observed. In these cases, the differences were in the values assumed by parameters, whereas the shapes (e.g., monotonic decreasing for partitioning to leaves) of the AFGEN functions proposed by different authors were coherent, since reflecting biological features of the plants. This led to the need of introducing functions driven by editable parameters to allow users to modulate the physiological crop responses to temperature and development stage. A set of functions was therefore developed to interpolate the available AFGEN parameterizations -mainly derived from measurements- with the aim of minimizing the number of parameters. These parameters were defined providing them with a clear morphological or physiological meaning, in order to ease the attribution of their values through field measurements and/or literature search. This allowed a consistent reduction of the number of parameters without undermining the degree of adherence of the model to real systems. Temperature effect on thermal time accumulation rate (originally represented by the AFGEN DTSMTB; C-d) was simulated by using the b function proposed by Yin et al. (1995, Equation 6)), driven by the parameters minimum, optimum and maximum temperature for development (Tbase,dev, Topt,dev and Tmax,dev, respectively; C). The same temperature response function (Equation (6), editable through the parameters Tbase,gro, Topt,gro and Tmax,gro, representing cardinal temperatures for growth) was used for the temperature effects on CO2 assimilation (AFGEN TMPFTB; unitless), where maximum rate is represented by the parameter Amax (kg ha1 h1). Changes in Amax during the crop cycle are now simulated without the need of further parameters.

where a = 2 and b = 1.8 for thermal time accumulation and a = 0 and b = 1 for the calculation of thermal limitation to gross photosynthesis. The light use efficiency table (EFFTB; function of daily mean temperature;

kg ha1 h1 J1 m2 s) was replaced by a linear function between two parameters (EFF10 and EFF40; kg ha1 h1 J1 m2 s), representing light use efficiency of single leaves at 10 C and 40 C. The original table describing the evolution of the extinction coefficient for diffuse visible light (KDIFTB; function of DVS; unitless) was substituted by Equation (7), driven by the parameter KDIFmax (unitless), representing the maximum value of KDIF; changes in this parameter simulate the extinction of light along canopies of different cereal species or cultivars.

The AFGEN table describing the changes in specific leaf area (SLA) during crop cycle (SLATB; function of DVS; ha kg1) was replaced by a function returning SLA values which are constant during early stages and decrease exponentially later (Equation (8)). Two parameters are required to adapt this function to different cereal species or varieties: SLA at emergence (SLAem; ha kg1) and at mid-tillering (SLA035; ha kg1).

where f (estimating the ratio between minimum SLA reached by the crop and SLA at mid-tillering) is derived using Equation (9):

This formulation allows model users to specify the value of SLA at tillering instead of the value reached by the variable at the end of the crop cycle (minimum SLA), the former being easier to measure within field experiments. Since the changes discussed above led to a non-editable FOTB function and FSTB (the fraction of aboveground photosynthates partitioned to stems; kg kg1) is e for each DVS e the complement to one of the sum of FOTB and FLTB (the fraction partitioned to leaves), partitioning to the aboveground organs is now completely dependent on the partitioning to leaves (FL, kg kg1). FL is derived by using a function driven by a single editable parameter: partitioning to leaves at emergence (RIPL0; kg kg1) (Equations (10) and (11)). The same concepts behind this type ofrepresentation of allocation patterns to the different plant organs are used in the rice-specific WARM model (Confalonieri et al., 2009a).

with:

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