**
****WINSORG Methods & Materials**

**Model construction**

WINSORG, the new process-based crop model of sorghum, like WIMOVAC, is
written in Microsoft’s object oriented Visual Basic and uses mechanistic, biochemical
equations to predict carbon dioxide assimilation at the leaf level, which is scaled up to
the canopy level (Farquhar *et al*., 1980; Collatz *et al*., 1992; Humphries and
Long, 1995). Within the new model assimilated carbon compounds were to be accumulated over
time and partitioned to leaves, stems, grains and roots at different rates for each growth
stage, based on the partitioning coefficients of CERES-Sorghum (Bonhomme and Ruget, 1991;
Jegu, 1994; Medeiros, 1997). The duration of growth stages was to be determined by the
elapsed accumulated thermal time from sowing, above a base temperature.

The relationship between growth stages of sorghum, CERES-Sorghum and
WINSORG, is as illustrated in Table 1, Appendix I. Partitioning coefficients and leaf
expansion minimum temperature were based on the sorghum variety Keller, after Bonhomme and
Ruget, 1991; Jegu, 1994 and the thesis of Medeiros (1997) (Table 2, Appendix I). The
values of elapsed thermal time for growth stage 3 and for the combined duration of stages
6 and 7 were taken from Medeiros (1997). Elapsed thermal times for the other stages and
the onset of leaf and stem senescence were estimated by regression analysis to give the
best fit to measured data of sorghum dry weight and leaf area index development for the
sorghum crop grown in Catania in 1993 (Table 3, Appendix II). At this stage, the site data
used for model construction consisted of site latitude, plant density, measured daily mean
air temperature and sowing and harvest dates. Parameter values are listed in Table 4 of
Appendix I.

**Model parameterisation for other sites**

Model predictions of sorghum dry matter and LAI were compared with four
sets of measured data of sorghum grown in four other locations in Europe, from the
Medeiros thesis. The daily mean air temperatures measured for each site were used as
simulation inputs.

For each site the model was parameterized with the values of latitude, plant density,
sowing and harvesting dates for each location (Medeiros, 1977) (Table 5, Appendix I).

The type of growth data available for testing WINSORG varied. The data from the
Policoro and Guadiano sites were only of above ground dry matter and leaf area index.
However, the data for Thebes and Lusignan also included stem and leaf dry weight.

Resulting r^{2} values from regression analysis of compared measured and
predicted dry matter production and leaf area index for each site are listed in Table 6,
Appendix I.

**
**Model development - Temperature effects

The slope coefficient of the regression equations for the fit of
measured to predicted data from Policoro, Lusignan, Thebes and Catania were used to
determine a low temperature stress effect on dry matter production, analogous to those
used in the CERES–Sorghum model. Using the reciprocal of the slope of regression for
each site, plotted against the mean temperature for the 35-day period following crop
emergence at each site, the relationship for a low temperature stress effect was
determined with an r^{2 }value of 0.95.

The low temperature stress effect is expressed by Equations 1 and 2.

CarbonGain = LTFactor * CarbonGain (Eq. 1)

LTFactor = (0.147 * T_{M}) – 2.44 (Eq. 2)

where LTFactor is the low temperature factor and T_{M} is the
daily mean temperature.

The low temperature stress effect was found by Medeiros to only occur
below a threshold temperature. The value of this threshold was determined to be 18^{o}C
for WINSORG, by comparing the effect of changing the threshold value on model simulations
for Lusingnan.

The regression slopes for the fit of data from Policoro, Guadiano,
Thebes and Catania were similarly used to determine the relationship for high temperature
enhancement of dry matter production, also with an r^{2 }value of 0.95. The high
temperature enhancement effect can be expressed by Equations 3 and 4.

CarbonGain = HTFactor * CarbonGain (Eq. 3)

HTFactor = (0.199 * T_{M}) – 1.84 (Eq. 4)

where HTFactor is the high temperature factor.

The range over which the high temperature enhancement has an effect was
determined to be from above 29 ^{o}C to 34 ^{o}C within WINSORG by
comparing the effect of changing the threshold value on model simulations for Guadiano.

**Water stress effects**

Using the data from the Medeiros thesis, WINSORG was adapted to
simulate the effects of water stress on a sorghum crop grown in Catania, Italy in 1993.
Soil parameter values are listed in Table 7, Appendix I.

Growth data consisted of above ground, stem and leaf dry matter, and leaf area index,
measured at intervals during the growing season, at four levels of water stress. For the
control crop measurements the crop was considered to be non-water stressed, at 100% Etmax,
POT. Crops were measured at three other levels of water stress STR1, STR2 and STR3, with
the latter being the least water stressed. The amount of rainfall and irrigation for each
treatment are listed in Table 8, Appendix I.

Other parameter values, determined by trial and error were the threshold leaf water
potential for stomatal conductance effects (–500 J Kg^{-1}) and threshold
leaf water potential for leaf expansion (-250 J Kg^{-1}). To give a reasonable fit
to the data at water-stressed levels, particularly the decrease in leaf area index, the
carbon gain to leaves at leaf water potentials below the threshold level for leaf
expansion, was assumed to be equal to –0.1 of carbon gain. In addition, the
partitioning coefficient to stems, at leaf water potentials below the threshold, was
assumed to be 2/3 of the partitioning coefficient at non-water stressed levels. This
simulated a decrease in the shoot:root ratio, found to occur under water stressed
conditions

Model simulations are compared with observed data in Figures 1a to 1d, Appendix II and
regression coefficients are listed in Table 9, Appendix I.

**Model simulations for sorghum grown at four sites**

WINSORG, with the above adaptations was used to simulate the growth of sorghum for four
other sites around southern Europe, using rainfall/irrigation data and the soil parameters
(listed in Table 10, Appendix I) for each site, in addition to the parameters listed in
Table 5, Appendix I.

**
****Model Testing**

Using data from the contract partners of ISA, Bari, Italy the model was
tested against data for a sorghum crop grown in Rutigliano, in 1997, using the parameter
values listed in Table 11, Appendix I. The variety of sorghum grown was MN 1500 (not
Keller).