Sorghum Module Scope

The sorghum module simulates the growth of a sorghum crop in a daily time-step (on an area basis not single plant). Sorghum growth in this model responds to climate (temperature, rainfall and radiation from the met module), soil water supply (from the soilwat module) and soil nitrogen (from the soiln module). The sorghum module returns information on its soil water and nitrogen uptake to the soilwat and soilnmodules on a daily basis for reset of these systems. Information on crop cover is also provided to the soilwat module for calculation of evaporation rates and runoff. Sorghum stover and root residues are ‘passed’ from sorghum to the residue and soiln module respectively at harvest of the sorghum crop.

A list of the module outputs is provided in the ‘Sorghum module outputs’ section below, but basically the module will predict leaf area development, N% and biomass of stover; depth, N% and biomass of roots; grain N% and biomass; grain yield and N%, grain size and grain number all on a daily basis.

Sorghum Module History

The sorghum module was originally developed from the QSORG model (Hammer and Muchow 1991) with features of the AUSIM model (Carberry and Arbrecht 1991) but has been extensively revised and improved since then.

Sorghum Module Structure

Figure 1: Order of key simulation steps in the sorghum module.

Sorghum Module Components


There are 11 crop stages and nine phases (time between stages) in the sorghum module (Table 1), and commencement of each stage (except for sowing to germination which is driven by soil moisture) is determined by accumulation of thermal time. Each day the phenology routines calculate today’s thermal time (in degree days) from 3-hourly air temperatures interpolated from the daily maximum and minimum temperatures. Thermal time is calculated using the relationship in Figure 1 with the eight 3-hour estimates averaged to obtain the daily value of thermal time (in growing degree days) for the day. Different thermal time relationships are used for development before and during drain-filling. These daily thermal time values are cumulated into a thermal time sum which is used to determine the duration of each phase. Between the stage of emergence and flowering the calculated daily_thermal_time is reduced by water or nitrogen stresses, resulting in delayed phenology when the plant is under stress.

Figure 2: Relationship between temperature and thermal time accumulation. In the sorghum module different relationships are used for development before and during grainfilling.

Table 1: Phenological stages simulated in the sorghum module. 

Stage code Stage name Stage description
1 sow Sowing
2 germ Germination
3 emerg Seedling emergence
4 End_juv End of the juvenile phase
5 fi Floral initiation
6 flag Appearance of the flag leaf
7 flowering Flowering
8 Start_grain_fill Start of linear phase of grain filling
9 End_grain_fill End of linear phase of grain filling
10 maturity Physiological maturity
11 Harvest_ripe Ready for harvest
12 End_crop Crop finished and absent from simulation


The thermal time between sowing and germination is dependent upon soil water status. The phase between germination and emergence includes an effect of the depth of sowing on the thermal time target. The duration between emergence and flag leaf appearance is determined by the total number of leaves destined to appear on the plant, and the rate at which they appear, which is determined by temperature (see below). The total number of leaves is equal to the number in the seed at germination (4) plus the number subsequently initiated at a rate of 21 o Cdays per leaf, until floral initiation is reached. Hence the timing of floral initiation will determine the total leaf number and the timing of the appearance of the flag leaf and flowering. The phase between emergence and floral initiation is composed of a cultivar-specific period of fixed thermal time, commonly called the basic vegetative or juvenile phase. Between the end of the juvenile phase and floral initiation the thermal development rate is sensitive to photoperiod (calculated as a function of day of year and latitude) if the cultivar is photoperiod sensitive. The model assumes that sorghum, as a short day plant, will have a longer phase (dependent upon cultivar) between the end of the juvenile phase and initiation if photoperiods exceed the base photoperiod. There are cultivar-specific fixed thermal time durations for the subsequent phases between flowering and the start of grain fill, between the start and end of grainfill, between the end of grainfill and maturity, and between maturity and harvest ripe. Table 2 gives phenology parameters currently available in the sorghum module.

Biomass accumulation (Photosynthesis)

Each day two estimates of the daily biomass production are calculated, one limited by available water for transpiraton (eqn 1), and the other limited by radiant energy (eqn 2). The minimum of these two estimates is the actual biomass production for the day.

delta_drymatter_transpiration = soil_ water_ supply * transpiration_efficiency eqn 1.

Note: transpiration_efficiency is derived from the transpiration_efficiency_coefficient (=0.009 kPa) and the vapour pressure deficit (vpd) estimated from daily temperatures.

dlt_drymatter_potential = rue *radiation_interception eqn 2.

Note rue (radiation-use efficiency) is 1.25 g MJ-1 from emergence to end of grain filling. Radiation interception is calculated from leaf area index and a radiation extinction coefficient, which varies with row spacing (Fig. 3). If row spacing is not supplied in the sowing command, the default row spacing of 0.75 m is used, corresponding to an extinction coefficient of 0.40.

Figure 3: Relationship between the radiation extinction coefficient and row spacing used in the sorghum module.

Biomass partitioning

Daily biomass production is partitioned to different plant parts in different ratios depending on crop stage.

Until the end of juvenile phase the root:shoot ratio is maintained at 1.0, and then decreases to a value of 0.087 at flowering.

Between emergence and flag leaf appearance the proportion of biomass produced that is partitioned to leaf increases exponentially as leaves appear (Fig. 4).

Between the stage floral initiation and flag leaf appearance, the biomass remaining after allocation to leaf is allocated between stem and developing panicle in the ration 1:0.30. After leaf growth has ceased at flag leaf appearance, biomass is partitioned between stem and panicle only until the start of grain filling, whereupon partitioning to grain only occurs. The sorghum module allows a total retranslocation of no more than 15 and 20% of leaf and stem biomass present at the start of grainfilling, respectively

Figure 4: Fraction of daily biomass produced that is partitioned to leaf as a function of leaf number.

Grain demand for carbohydrate (biomass) is calculated as a function of grain number. The number of grains set per plant is determined by the average daily growth rate per plant between floral initiation and the start of grain filling.

Leaf development


Leaf appearance rate is driven by thermal time, the last 3.5 leaves before the flag leaf appear each 20 o Cdays, before which a leaf appears every 41 o Cdays.

Potential LAI is a product of leaf area per plant, number of plants per m2 and the water stress factor for expansion (see water deficits section below). Leaf area per plant is simulated as a sigmoidal function of thermal time since emergence, the parameters of which are cultivar-specific (see Table 2).

Actual LAI is less than the potential LAI if there is not sufficient biomass partitioned to leaf on that day. Maximum specific leaf area (SLA_MAX) defines the maximum leaf area (m 2 ) that can be expanded per gram of biomass, and is set to a value of 450 cm 2 g -1 .

Leaf senescence There are four causes of leaf senesence; age, light competition, water stress and frost. The sorghum senescence routines calculate a senesced LAI for each stress each day and take the maximum of the four values as the day’s total senescence.

This senescence due to age occurs on a per plant basis and is a function of thermal time elapsed since flowering. The parameters defining the rate of whole-plant leaf area senescence due to age are cultivar-specific.

Above an LAI of 4.0 light competition causes leaf area to be lost. The LAI senesced because of light competition is related to the amount LAI exceeds 4.0 (see eqns 3 and 4).

sensLAI_light_fac = 0.008 *(LAI- 4.0) eqn 3.

delta_sensLAI_light = LAI * sensLAI_light_fac eqn 4.

Water stress during crop growth will cause leaf senescence (eqns 5 and 6).

sensLAI_water_fac = 0.05 * (1 – sorghum_swdef(photo)) eqn. 5.

delta_sensLAI_water = LAI * sensLAI_water_fac eqn 6.

Note: the calculation of the water stress factor sorghum_swdef(photo) is descibed in the ‘water deficits’ section below.

Frost senescence. Temperatures between 6.0 and 0 o C will cause a linearly increasing loss of leaf area from 0 to 100% respectively.


From the values of senesced LAI the sorghum module calculates the biomass and nitrogen in that leaf area that is senesced, however a proportion of the carbon and nitrogen of these leaves is retranslocated to stem before senescence.


Tiller number is not dynamically-determined in the sorghum module but is set in the sowing command As temperature during the early part of the season and plant density is known to influence the number of tillers produced, it is necessary for the user to set the potential tiller number given an understanding of the likely tiller number produced. As a guideline in cool environments and/or early sowings under low density where maximum tillering would be expected, tiller number would vary between 1.5 and 2 m -2. With low density this would be around 0.3 tillers m -2 . On the other hand in warm environments or late sowings tiller number could vary between 0.75 and 1 m -2 at low population density and around 0.15 m -2 at high density.

Row Configuration

Sorghum row configuration can be set to solid, single skip or double skip.

In simulating skip row sorghum the assumption of a horizontally distributed leaf area does not hold. To account for this the equation for calculating the percentage green cover of the plant is changed from equation 1 to equation 2

Eq1 %green cover =  where k is the extinction coefficient of the crop at that row spacing and l is the leaf area index

Eq2 % green cover =  where k is the extinction coefficient of the crop at that row spacing, l = is the leaf area index and s is the skip index (1 for no skipped rows, 1.5 for one skipped row, and 2 for two skipped rows)

With a skip row planting configuration, the wide gap between plants implies that root expansion is multi-directional, allowing more time for the roots to reach the centre of the skip rows. The root expansion front is described by a semi circular front expanding from the base of the plant at a rate of 2 cm per day in all directions. (see the output variable “root_proportion”).


Although in practice it is possible to ratoon sorghum, there are no regrowth routines in sorghum.

Water uptake

To determine the amount of water supply to the crop on any day, first the total available water above the lower limit for all soil layers with roots is summed (eqn 7). If roots are only partially through a layer available soil water is scaled to that portion that contains roots. The kl constant (value differs for each soil layer) is then used to limit the amount of water available on any day (eqn 8). The kl factor is emphirically derived, incorporating both plant and soil factors which limit rate of water uptake.

do layer = 1, deepest_layer (do loop to calculate available water for all layers)

sw_avail = sw(layer) – ll (layer) eqn 7.

sw_supply(layer) = sw_avail * kl (layer) eqn 8.

Soil water demand is calculated as in the ‘biomass accumulation’ section above where potentail biomass production is a function of light interception and rue (eqn 1). This potential biomass production is converted to water demand using transpiration efficiency.

Water uptake is the minimum of the supply and demand.

Water deficits affecting plant growth

Soil water deficit factors are calculated to simulate the effects of water stress on different plant growth processes. Three water deficit factors are calculated which correspond to four plant processes each having different sensitivity to water stress i.e. photosynthesis (photo), phenology (pheno), and leaf-expansion (expansion) (Figure 5).

A water availability ratio is calculated by dividing actual soil water supply (sw – ll) by the potential soil water supply (dul – ll). This ratio is used in the relationships illustrated to derive the stress factors for photosynthesis and leaf expansion. A factor of 0 is complete stress and 1 no stress.

Figure 5: Relationship between daily soil water supply:demand ratio and the level of stress on photosynthesis and leaf expansion.

A fraction of plants (0.044) will be killed each day due to water stress once the cumulative water stress factor for photosynthesis exceeds 4.6.

Nitrogen uptake and retranslocation

In order to calculate nitrogen demand today, first potential biomass production is re-calculated unlimited by water, nitrogen or temperature i.e. as a function of rue and radiation-interception (eqn 2). This dry matter (biomass) is then partition into plant parts according to their current relative weights.

Nitrogen demand by root and flower is the N required to attain a Nitrogen target concentration.

Root Flower
Nitrogen target concentration = 0.002 0.005


Stem Nitrogen demand is N required to achieve a Nitrogen target concentration depending on current phenological stage.

Emergence Flowering
Stem Nitrogen target concentration = 0.055 0.010


Nitrogen demand in the leaf up to Flag leaf stage is N required to keep leaf at target SLN of 1.5. After flag, N Required to maintain SLN.

Grain Demand

Grain Fill rate 0.001 mg/grain / degreeday for first 100 dd

Grain N demand attempts to stay at this fill rate.

Nitrogen supply is the sum of nitrogen available via mass flow (eqn 9) and by diffusion (eqn 10).

no3_massflow (layer) = no3_conc * delta_sw (layer) eqn 9.

no3_diffusion (layer) = sw_avail_frac *no3_conc eqn 10.

note: these layer values are summed to root depth and sw_avail_frac is ratio of extractable soil-water over total soil-water.

If nitrogen demand cannot be satisfied by mass flow then it is supplied by diffusion. Demand can only be exceeded by supply from mass flow (up to the nitrogen uptake maximum

Nitrogen available for uptake is distributed to plant parts in proportion to their individual demands.

Grain N demand is a function of the grain number and a specific N demand per grain.

Nitrogen deficits affecting plant growth

There are three N availability factors (0-1), one each for the photosynthesis, expansion, phenology and grain filling processes. A N concentration ratio is calculated for the stover (stem + leaf) in eqn 14 which is used as a measure of N stress, then different constants are used to convert that ratio to a deficit factor for each of the processes. A factor of 1 is used for effecting grain N concentration, 1.25 for photosynthesis (reduces rue), 0.8 for expansion (reduces leaf area expansion) and 5.75 to slow phenological development. As a value of 1 is no stress and 0 complete stress, phenology is least sensitive to nitrogen deficiency and grain N the most.

N_conc_ratio = (N_conc_stover – N_conc_stover_min) / (N_conc_stover_crit – N_conc_stover_min) eqn14.


Root growth and distribution

Root depth is initialised at the depth of sowing. Between emergence and grain filling, the increase in root depth is a daily rate multiplied a soil water availability factor. The daily rate is 10-15 mm/day during emergence and 33mm/day from end-of-juvenile to the start of grain-filling. Root depth is constrained by the soil profile depth. The increase of root depth through a layer can be constrained by known soil constraints through the use of the 0-1 parameter xf, which is input for each soil layer.

Growth of root biomass is partitioned with depth using an exponential decay function from the soil surface and converted to root length density using a fixed specific root length.

Roots are not senesced during the life of the crop, but are incorporated in the soiln module at harvest and distributed as fresh organic matter in the profile

Temperature stress

There are no generic temperature factors, as for water and nitrogen stress, but as discussed in sections above temperature does influence the rate of leaf senescence and radiation use efficiency.

Plant death

All or some of the plants can be killed due to a variety of stresses;

If the crop hasn’t germinated within 40 days of sowing, due to lack of germinating moisture, all plants are killed.

If the crop does not emerge with 150 o Cdays of sowing, because it was sown too deep, then all plants are killed.

If crop is past floral initiation and LAI = 0, then all plants are killed due to total senescence.

If the cumulative phenological water stress factors exceed 25, all plants are killed due to water stress prolonging phenology.

A fraction of plants will be killed by high temperatures immediately following emergence.


The detachment routines in sorghum are disabled in the current code.

Sorghum Module Parameterisation

Crop lower limit (ll), root water extraction constants (kl) and root extension factors (0-1, xf) values are needed for each soil layer


ll = 0.200 0.200 0.200 0.220 0.250 () ! crop lower limit

kl = 012 0.08 0.06 0.04 0.02 () ! kl need calibrating for each crop and soil type

xf = 1.0 1.0 1.0 1.0 1.0 ()

Phenology, leaf area and grainfilling parameters are needed for each cultivar. An example is given below of those for the three generic maturity classes.

Table 2: Cultivar parameters for generic early, mid and late-season cultivars in the sorghum module.

Parameter values for cultivars of maturity classes
Parameter name Parameter units Early Medium Late
tt_emerg_to_endjuv ( o C day) 100 100 100
est_days_endjuv_to_init () 15 20 20
pp_endjuv_to_init 30 30 30
tt_endjuv_to_init ( o C day) 115 120 255
photoperiod_crit1 (hours) 12.3 12.3 12.3
photoperiod_crit2 (hours) 14.6 14.6 14.6
photoperiod_slope ( o C/hour) 25 38.4 38.4
tt_flower_to_maturity ( o C day) 695 695 695
tt_flag_to_flower ( o C day) 100 100 80
tt_flower_to_start_grain ( o C day) 30 30 50
tt_maturity_to_ripe ( o C day) 1 1 1
Main_stem_coeff (1/oC) 2.95 2.88 2.95
Tpla_prod_coef (1/oC) 0.015 0.018 0.018
Tpla_inflection (oC) 320 355.7 400.8
Spla_prod_coef (1/oC) 0.007 0.007 0.005
Spla_intercept -250 -250 -280 -321
dm_per_seed (g) 0.00083 0.00083 0.00083
x_stem_wt vs y_height Mm vs g 0 80

0 2000

0 80

0 2000

0 80

0 2000

Module Dependencies

The minimum module configuration required to run sorghum in APSIM is the inclusion of the report, met, manager, soilwat2, soiln2 and residue2 and sorghum modules.

Within the manager file the following syntax is used for harvest and planting the sorghum crop:

if (sorghum.stage_name = ‘harvest_ripe’ and sorghum.plant_status = ‘alive’) then

sorghum harvest

sorghum kill_crop

sorghum end_crop


if (sorghum.plant_status = ‘dead’) then

report do_output

sorghum harvest

sorghum end_crop


if (day > 120 and day < 240 and sorghum.plant_status = status_out ) then

sorghum sow plants = 15 (p/m2), sowing_depth = 50 (mm), row_spacing = 0.35 (m), cultivar = early

, fertile_tiller_no = 1.5, skip = double


(note: row_spacing and skip in sowing command is optional)

Sorghum Module Outputs

Table 3: The following Sorghum variable can be output through the report module

Variable Name Units Description
stage current phenological stage
leaf_no number of fully expanded leaves
leaf_no_dead no of dead leaves
leaf_area (max_leaf = 1000) mm 2 leaf area of each leaf
height mm canopy height
root_depth mm depth of roots
rlv -3 root length per volume of soil in each soil layer
hi Harvest index
plants plants/m 2 plant density
grain_no grains/plant grain number
grain_size g individual grain wt
cover_green 0-1 fraction of radiation reaching the canopy that is intercepted by green leaves
cover_tot 0-1 total crop cover fraction
lai_sum leaf area index of all leaf material live + dead
tlai tot lai
slai area of leaf that senesces from plant
lai m 2 /m 2 live plant green lai
tlai_dead m 2 /m 2 total lai of dead plants
root_wt g/m 2 root biomass
leaf_wt g/m 2 leaf biomass
stem_wt g/m 2 stem biomass
grain_wt g/m 2 grain biomass
grain_wt g/m 2 grain biomass
dm_green (max_part = 6) g/m 2 live plant dry weight (biomass)
dm_senesced (max_part = 6) g/m 2 senesced plant dry wt
dm_dead (max_part = 6) g/m 2 dry wt of dead plants
yield kg/ha grain yield dry wt
biomass kg/ha total above-ground biomass
dlt_dm g/m 2 the daily biomass production
dlt_dm_green (max_part = 6) g/m 2 plant biomass growth
n_green (max_part = 6) g/m 2 plant nitrogen content
n_senesced (max_part = 6) g/m 2 plant n content of senesced plant
n_dead (max_part = 6) g/m 2 plant n content of dead plants
dlt_n_green (max_part = 6) g/m 2 actual n uptake into plant
dlt_n_retrans (max_part = 6) g/m 2 nitrogen retranslocated out from parts to grain
dlt_n_detached (max_part = 6) g/m 2 actual n loss with detached plant
dlt_n_dead_detached (max_part = 6) g/m 2 actual n loss with detached dead plant
swdef_pheno 0-1 water deficit factor for phenology
swdef_photo 0-1 water deficit factor fo photosynthesis
swdef_expan 0-1 water deficit factor for leaf expansion
ep (num_layers) mm water uptake in each layer
cep mm cumulative water uptake
sw_demand mm total crop demand for water
sw_supply mm total supply over profile
esw_layr (num_layers) mm plant extractable soil water
n_conc_stover % sum of tops actual n concentration
n_conc_crit % sum of tops critical n concentration
n_grain_pcnt % grain n concentration percent
n_uptake_grain g/m 2 n uptake by grain
n_uptake g/m 2 cumulative total n uptake by plant
n_uptake_stover g/m 2 n uptake by stover
no3_tot g/m 2 total no3 in the root profile
n_demand g/m 2 sum n demand for plant parts
n_supply g/m 2 n supply for grain
n_supply_soil g/m 2 n supply from soil
n_fix_pot g/m 2 potential N fixation
nfact_photo N deficit factor for photosynthesis
nfact_grain N deficit factor for grain N content
nfact_photo 0-1 Nitrogen stress factor for photosynthesis
nfact_expan 0-1 Nitrogen stress factor for cell expansion
dlt_tt o Cday daily thermal time
das days after sowing

Sorghum Module Validation

The following are some examples of module validation.

Katherine – effects of water deficit



Gatton – differences in applied nitrogen. The rate of 240 kgN/ha is in the LHS graphs and 0 kgN/ha on the RHS.




Hammer, G. L., & Muchow, R.C. (1991). Quantifying climatic risk to sorghum in Australia’s semi-arid tropics and subtropics: model development and simulation. In Climatic Risk in Crop Production: Models and Management for the Semi-arid Tropics and Subtropics, eds R.C. Muchow & J.A. Mellamy. Ch. 16, Wallingford, CAB International, pp 205-32.

Carberry, P.S. & Abrecht, D.G. (1991) Tailoring crop models to the semi-arid tropics. In Climatic Risk in Crop Production: Models and Management for the Semi-arid Tropics and Subtropics, eds R.CT. Muchow & J.A. Bellamy. CAB International, Wallingford, pp 157-82.