The APSIM-Wheat Module (7.5 R3008)


March 25, 2014
This documentation is compiled from the source codes and internal documents of APSIM-Wheat module by Bangyou Zheng (bangyou.zheng@csiro.au), Karine Chenu (karine.chenu@uq.edu.au), Alastair Doherty (alastair.doherty@daff.qld.gov.au) and Scott Chapman (scott.chapman@csiro.au).

Contents

1 Scope of the APSIM-Wheat module
2 APSIM-Wheat history
3 Phenology
 3.1 Thermal time calculation
 3.2 Sowing-germination phase
 3.3 Germination-emergence phase
 3.4 Photoperiod impact on phenology
 3.5 Vernalisation impact on phenology
4 Biomass accumulation (Photosynthesis)
 4.1 Potential biomass accumulation from radiation use efficiency
  4.1.1 Radiation interception
  4.1.2 Radiation use efficiency
  4.1.3 Stress factor (Temperature, nitrogen, phosphorus (not applied), oxygen (not applied))
 4.2 Actual daily biomass accumulation
5 Biomass partitioning and re-translocation
 5.1 Biomass partitioning
 5.2 Biomass partitioning to Root
 5.3 Biomass partitioning to Head (Pod, Meal and Oil (not applicable in this version))
 5.4 Biomass partitioning to Leaf
 5.5 Biomass partitioning to Stem
 5.6 Re-translocation
6 Grain development
 6.1 Grain number
 6.2 Grain (Meal) demand
 6.3 Pod demand
7 Leaf and node appearance and crop leaf area
 7.1 Node number
  7.1.1 Potential node appearance rate
  7.1.2 Potential node number (daily increase)
  7.1.3 Actual node number (daily increase)
 7.2 Leaf number
  7.2.1 Potential leaf number (daily increase)
  7.2.2 Actual leaf number (daily increase)
8 Leaf area expansion
 8.1 Actual leaf area (daily increase)
 8.2 “Stressed” leaf area
 8.3 Carbon-limited leaf area
9 Root growth and distribution
 9.1 Root depth growth
 9.2 Root length
10 Senescence
 10.1 Leaf number senescence
 10.2 Leaf area senescence
 10.3 Biomass senescence
 10.4 Root senescence
11 Crop Water Relations
 11.1 Crop water demand
 11.2 Potential and actual extractable soil water
 11.3 Crop water supply, i.e. potential soil water uptake
 11.4 Actual soil water uptake
 11.5 Soil water stresses affecting plant growth
  11.5.1 Phenology
  11.5.2 Photosynthesis
  11.5.3 Leaf expansion
 11.6 KL factor
12 Nitrogen
 12.1 Nitrogen supply
 12.2 Nitrogen demand
  12.2.1 Nitrogen demand of Grain
  12.2.2 Nitrogen demand of other parts
 12.3 Nitrogen update, partitioning and re-translocation
  12.3.1 Nitrogen concentrations in wheat parts
  12.3.2 Nitrogen update
  12.3.3 Nitrogen translocation
  12.3.4 Nitrogen re-translocation
 12.4 Nitrogen stresses
  12.4.1 Phenology
  12.4.2 Biomass accumulation
  12.4.3 Leaf appearance and expansion (i.e. leaf number and LAI)
  12.4.4 Grain filling (biomass and nitrogen demand of grain)
13 Phosphorus
14 Temperature
15 Light
16 CO2
17 Vapour pressure deficit (VPD)
A Parameter list of wheat module

1 Scope of the APSIM-Wheat module

The APSIM-Wheat module simulates the wheat growth and development of a wheat crop in a daily time-step on an area basis (per square meter, not per single plant). In this module, the wheat crop Wheat growth and development responds to weather (radiation, temperature), soil water and soil nitrogen, and management practices. The wheat module returns information on its soil water and nitrogen uptake to the soil water and nitrogen modules on a daily basis for reset of these systems. Information on crop cover is also provided to the water balance module for calculation of evaporation rates and runoff. Wheat stover and root residues are ’passed’ from wheat to the surface residue and soil nitrogen modules, respectively at the harvest of the wheat crop.

The approaches used in modeling crop processes balance the need for a comprehensive description of the observed variation in crop performance over diverse production environments and the need to avoid reductionist approaches of ever-greater complexity with large numbers of parameters that are difficult to measure.

A list of the module outputs is provided in the ‘Wheat module output’s section below. Basically the module simulates phenological development, leaf area growth expansion, biomass and N concentration of different crop components (Leaf, Stem, Root and Grain) on a daily basis, as well as. It also predicts grain size and grain number.

2 APSIM-Wheat history

APSIM-Wheat has been developed from a combination of the approaches used in previous APSIM wheat modules:Asseng et al. (1998a,b); Wang et al. (2003); Meinke et al. (19971998). The current version of the model is implemented within the APSIM Plant model framework which is currently used for other crops such as grain legumes and canola. Most of the model constants (species-specific) and parameters (cultivar specific) are externalized from the code (wheat.xml file).

3 Phenology

There are 11 phases in APSIM-Wheat module (Figure 1). The timing of each phase (except from sowing to germination, which is driven by sowing depth and thermal time) is determined by the accumulation of thermal time (TT) adjusted for other factors which vary with the phase considered (e.g. vernalisation, photoperiod, N). The length of each phase is determined by a fixed thermal time (‘thermal time target’), which is specified by “tt_<phase_name>” in wheat.xml. Most parameters of thermal time targets are cultivar-specific.

3.1 Thermal time calculation

The daily thermal time (ΔTT) is calculated from the daily average of maximum and minimum crown temperatures, and is adjusted by genetic and environmental factors. Hence, the duration of phases between emergence and floral initiation is adjusted for photoperiod and vernalisation, using the cultivar-specific parameters “photoperiod factor” (fD, subsection 8) and “vernalisation factor” (fV , subsection 12). Other environmental factors include soil water stress (fW,pheno, subsubsection 95), nitrogen stress (fN,pheno, subsubsection 107) and phosphorus stress (fP,pheno, section 13) in all phases except from Sowing to Emergence (See details below), but they are all parametrized to have to effect in the current released APSIM-Wheat. All factors are bound from 0 to 1.

pict
Figure 1: Phenology in the APSIM_Wheat module. Targets are expressed in adjusted thermal time (subsection 6) and are cultivar-specific parameters. The values given for the reference genotype Hartog.

Crown temperatures are simulated according to the original routines in CERES-Wheat and correspond to air temperatures for non-freezing temperatures. The maximum and minimum crown temperatures (Tcmax and Tcmin) are calculated according to the maximum and minimum air temperature (Tmax and Tmin), respectively.

        {                              2
Tcmax =   2+ Tmax(0.4 + 0.0018(Hsnow − 15) )  Tmax < 0
          Tmax                              Tmax ≥ 0
(1)

       {
T    =   2+ Tmin(0.4 + 0.0018(Hsnow − 15)2)  Tmin < 0
 cmin     Tmin                              Tmin ≥ 0
(2)

where Hsnow is the snow depth (cm). The default value of Hsnow is set to zero in the source codes (Figure 2). For more detail information about subsection 1 and subsection 2, please see the function CWVernalPhase::vernalisation in the APSIM code.

pict

Figure 2: Crown temperature (Tc) in response to air temperature (T) for different snow depth (Hsnow) in APSIM-Wheat. In the released APSIM version, Hsnow equals zero cm.

The daily crown mean temperature (Tc) is calculated by the maximum (Tcmax) and minimum (Tcmin) crown temperature.

     Tcmax + Tcmin
Tc = -----2------
(3)

Daily thermal time (ΔTT) is calculated based on daily mean crown temperature, using three cardinal temperatures (Figure 3). The default values of the cardinal temperatures and relative thermal time are specified by x_temp (0, 26, 34) and y_tt (0, 26, 0), respectively, in the wheat.xml (Figure 3). Other crop modules in APSIM calculate thermal time every 3 hours.

        (|T             0 < T ≤ 26
        {2c6                c
ΔT T =  |( 8 (34− Tc)   26 < Tc ≤ 34
         0             Tc ≤ 0orTc > 34
(4)

pict

Figure 3: Daily thermal time (ΔTT) in response to daily crown temperature (Tc) in APSIM-Wheat.

For each phenological stage, the daily thermal time (TT) is summed from the start of phase and can be reduced by genetic and (fD, subsection 8) and vernalisation factor (fV , subsection 12) and also dependent on environmental factors (photoperiod and temperature). The environmental factors include soil water stress (fW,pheno, subsubsection 95), nitrogen stress (fN,pheno, subsubsection 107) and phosphorus stress (fP,pheno, section 13). The next phenological stage occurs when this adjusted thermal time (TT in subsection 5) reaches the “target thermal time” for the stage considered Figure 1.

  ′   ∑
TT  =   [ΔT T × min(fD, fV)× min(fW,pheno,fN,pheno,fP,pheno)]
(5)

In the current released version, soil water, nitrogen and phosphorus stresses have no effect on phenological development (i.e. parameters fW,pheno = fP,pheno = 1 subsubsection 95, and fN,pheno has values typically above 1 subsubsection 107). So, subsection 5 is reduced to

      ∑
T T′ =   [ΔT T × min(fD,fV)]
(6)

In the output variables of wheat module, TT from the start of each phase is named as “ttafter<phasename>”. For example, the output variable “ttaftersowing” is not the actual thermal time after sowing, but the thermal time adjusted for genetic and environmental factors.

3.2 Sowing-germination phase

The seed germination is determined by soil water availability in the seeded layer (specified by pesw_germ with default value 0 mm). The crop will die if germination has not occurred before a certain period, defined by days_germ_limit in wheat.xml, which has a default value of 40 d.

3.3 Germination-emergence phase

The germination to emergence phase includes an effect of the depth of sowing (Dseed) on the thermal time target. The phase is comprised of an initial period of fixed thermal time during which shoot elongation is slow (the “lag” phase, Tlag) and a linear period, where the rate of shoot elongation (re, C d mm1) towards the soil surface is linearly related to air temperature. Then, the period of emergence (Temer) is calculated by

Temer = Tlag + reDseed
(7)

The crop will die if emergence has not occurred before a certain period, defined by tt_emerg_limit in wheat.xml, which has a default value of 300C d.

Most studies on seedling germination have simply recorded the accumulated thermal time between germination and 50% emergence from a given sowing depth. For the purposes of model parametrization the value of Tlag (shoot_lag) has been assumed to be around 40 C d, while re (shoot_rate) has been derived from studies where thermal time to emergence was measured and where sowing depth was known and it is set to 1.5 C d per mm. This means that at a sowing depth of 40 mm emergence occurs 100C d after germination (40 + 1.5 × 40).

There is the capability of increasing the time taken to reach emergence due to a dry soil layer in which the seed is germinating, through the relationship between fasw_emerg and rel_emerg_rate. Currently this effect is “turned off” in the Wheat.xml file.

3.4 Photoperiod impact on phenology

Photoperiod is calculated from day of year and latitude using standard astronomical equations accounting for civil twilight using the parameter twilight, which is assumed to be -6 (civil twilight) in wheat.xml. Twilight is defined as the interval between sunrise or sunset and the time when the true center of the sun is 6 below the horizon. Other crop modules of APSIM have used -2.2 as twilight parameters. In APSIM, the photoperiod affects phenology between emergence and floral initiation (Figure 1). During this period, thermal time is affected by a photoperiod factor (fD in subsection 5 and subsection 6) that is calculated by

                        2
fD = 1 − 0.002Rp(20− LP )
(8)

where LP is the day length (h), RP is the sensitivities to photoperiod which is cultivar-specific and is specified by photop_sens in wheat.xml. The default value of RP is 3 (Figure 4).

pict

Figure 4: Relationship between photoperiod factor (fD) and day length (LP) with different sensitivities to photoperiod (Rp). The default value of RP is 3.

3.5 Vernalisation impact on phenology

In APSIM, vernalisation effects phenology between emergence and floral initiation (Figure 1). During this period, thermal time is affected by a vernalisation factor (fV in subsection 5 and subsection 6).

Vernalisation is simulated from daily average crown temperature (Tc), daily maximum (Tmax) and minimum (Tmin) temperatures using the original CERES approach (Figure 5).

ΔV  = min(1.4− 0.0778Tc,0.5+ 13.44 -------Tc------2)  when, Tmax < 30∘CandTmin < 15∘C
                                (Tmax − Tmin + 3)
(9)

pict

Figure 5: Relationship between vernalisation (ΔV ) and maximum (Tmax) and minimum (Tmin) temperature.

Devernalisation can occur if daily Tmax is above 30 C and the total vernalisation (V ) is less than 10 (Figure 6).

                                          ∘
ΔVd = min(0.5(Tmax − 30),V ) when, Tmax > 30 CandV < 10
(10)

pict

Figure 6: Relationship between devernalisation (ΔV d) and maximum temperature (Tmax) when the total vernalisation (V ) is less than 10.

The total vernalisation (V ) is calculated by summing daily vernalisation and devernalisation from Germination to Floral initiation (Composite phase Vernalisation in Figure 1).

    ∑
V =    (ΔV  − ΔVd)
(11)

However, the vernalisation factor (fv) is calculated just from Emergence to Floral initiation (Composite phases eme2ej in Fig. 1).

fV = 1 − (0.0054545RV + 0.0003)× (50− V )
(12)

where RV is the sensitivities to vernalisation, which is cultivar-specific and is specified by vern_sens in wheat.xml. The default value of RV is 1.5 (Figure 7)

pict

Figure 7: Relationship between cumulated vernalisation (V ) and vernalisation factor (fV ) and for different sensitivities to vernalisation (RV ). The default value of RV is 1.5.

4 Biomass accumulation (Photosynthesis)

The daily biomass accumulation (ΔQ) corresponds to dry-matter above-ground biomass, and is calculated as a potential biomass accumulation resulting from radiation interception (ΔQr, subsection 13) that is limited by soil water deficiency (ΔQw, subsection 30).

4.1 Potential biomass accumulation from radiation use efficiency

The radiation-limited dry-biomass accumulation (ΔQr) is calculated by the intercepted radiation (I), radiation use efficiency (RUE), diffuse factor (fd, paragraph 4.1.3), stress factor (fs, subsubsection 18) and carbon dioxide factor (fc, paragraph 22).

ΔQr  = I × RU E × fd × fs × fc
(13)

where fd, fs and fc are defined in the wheat.xml file. In the current version of APSIM-Wheat, only Leaf produces photosynthate. Diffuse factor (fd) equals to 1 (paragraph 4.1.3), so that subsection 13 can be:

ΔQr  = I × RU E × fs × fc
(14)

4.1.1 Radiation interception

Radiation interception is calculated from the leaf area index (LAI, m2 m2) and the extinction coefficient (k) (Monsi and Saeki2005).

I = I0(1 − exp (− k× LAI × fh)∕fh)
(15)

where I0 is the total radiation at the top of the canopy (MJ) which is directly imported from weather records; fh is light interception modified to give hedge-row effect with skip row. fh could be calculated based on the canopy width, but is not used in the current version of APSIM (i.e. fh = 1). So, subsubsection 15 is reduced to.

I = I0(1− exp(− k × LAI))
(16)

Extinction coefficient (k) varies with row spacing,

k = h (W )
    e   r
(17)

where Wr is the row spacing which is specified by the user (in the APSIM interface, the .sim or .apsim file); he is a function of rowing spacing which is defined for both green leaf and dead leaves by parameters x_row_spacing, y_extinct_coef in the wheat.xml file (Figure 8) and is linearly interpolated by APSIM. In the current version of APSIM-Wheat, no impact of row spacing is considered (Figure 8)

pict

Figure 8: Values of extinction coefficient for different row spacings.

4.1.2 Radiation use efficiency

RUE (g MJ-1) is a function of growth stages which is defined by parameters x_stage_rue and y_rue in wheat.xml (Figure 9) and linearly interpolated by APSIM. In the current version of APSIM-Wheat, RUE equal to 1.24 from emergence to the end of grain-filling and does not vary as a function of daily incident radiation as in the model NWHEAT.

pict

Figure 9: Radiation use efficiency (RUE) for different growth stages.

4.1.3 Stress factor (Temperature, nitrogen, phosphorus (not applied), oxygen (not applied))

Actual daily radiation-limited biomass accumulation can be reduced by a stress factor (fs, subsection 13 and subsection 14). This stress factor is the minimum value of a temperature factor (fT, photo, paragraph 20), a nitrogen factor (fN photo, subsubsection 108), a phosphorus factor (fP photo) and an oxygen factor (fO photo).

fs = min(fT, photo, fN, photo, fP, photo, fO, photo)
(18)

No phosphorus stress fP,photo and oxygen stress fO,photo are applied in the current version of APSIM-Wheat. So, subsubsection 18 is reduced to

f =  min(f      , f      )
 s       T, photo  N, photo
(19)

The temperature factor fT, photo is a function of the daily mean temperature and is defined by parameters x_ave_temp and y_stress_photo in the wheat.xml (Figure 10). Values are linearly interpolated by APSIM. The temperature stress is applied from sowing to harvest.

                 Tmax-+-Tmin
fT, photo = hT, photo(   2     )
(20)

pict

Figure 10: Temperature factor in response to mean daily temperature.

The nitrogen factor fN,photo is determined by the difference between leaf nitrogen concentration and leaf minimum and critical nitrogen concentration.

                 ∑    CN − CN,min
fN,photo = RN,photo  ---------------
                 leafCN,crit − CN,min
(21)

where CN is the nitrogen concentration of Leaf parts; RN,expan is multiplier for nitrogen deficit effect on phenology which is specified by N_fact_photo in the wheat.xml and default value is 1.5.

The CO2 factor For C3 plants (like wheat), the CO2 factor of APSIM is calculated by a function of environmental CO2 concentration (C, ppm) and daily mean temperature (Tmean) as published by Reyenga et al. (1999)

fc = (C-−-Ci)(350+-2Ci)
    (C + 2Ci)(350− Ci)
(22)

where Ci is the temperature dependent CO2 compensation point (ppm) and is derived from the following function.

Ci =-163-−-Tmean
    5 − 0.1Tmean
(23)

pict

Figure 11: CO2 factor in response to the CO2 level (C) for different mean air temperatures.

Diffuse factor (not used in the current version) The daily diffuse fraction was calculated using the functions suggested by Roderick (1999):

( Rd                     Rs
|{ Rs = Y0            f orRo ≤ X0
| RRds = A0 + A1 RRso    f orX0 <  RRso ≤ X1
( RRds = Y1            f orRRso > X1
(24)

where

A0 = Y1 − A1X1
 A1 = XY11−−YX00-
(25)

where Ro is the daily extra-terrestrial solar irradiance (i.e. top of the atmosphere); Rd and Rs are the daily diffuse and global solar irradiance at the surface, respectively. X0, X1, Y 0 and Y 1 are four empirical parameters.

X0 = 0.26,    Y0 = 0.96,  Y1 = 0.05,and
X1 = 0.80 − 0.0017|φ|+ 0.000044|φ|2
(26)

where φ is latitude.

Ro is derived from this function

R0 = 86400×-1360×-(ϖ-×-sin(φ)×-sin(θ)+-cos(φ-)×-cos(θ)×-sin(ϖ0-))-
                            1000000π
(27)

where ϖ0 is the time of sunrise and sunset, which derives from any solar declination (θ) and latitude (φ) in terms of local solar time when sunrise and sunset actually occur (http://en.wikipedia.org/wiki/Sunrise_equation)

ϖ0 = arccos(− tan(φ )tan(θ))
(28)

Solar declination (θ) can be calculated by

             2π
θ = 23.45sin(365.25-(N − 82.25))
(29)

where N is day of year.

fd is calculated by a function of the diffuse fraction which is not implemented in current wheat module, (i.e. fd = 1).

4.2 Actual daily biomass accumulation

The actual daily biomass accumulation (ΔQ) results from water limitation applied on the potential radiation-driven biomass accumulation (ΔQr). This water-limited biomass (ΔQw) is a function of the ratio between the daily water update (Wu, subsection 93) and demand (Wd, subsection 31) capped by

ΔQw  = ΔQrfw,photo = ΔQr Wu-
                        Wd
(30)

where fw,photo is the water stress factor affecting photosynthesis (subsubsection 96); Wu is the actual daily water uptake from the root system (which corresponds to the soil water supply (Ws) capped by Wd), Wd is the soil water demand of Leaf and Head parts (section 11).

When the soil water is non-limiting (fw,photo = 1, i.e. Wd Ws), biomass accumulation is limited by the radiation (ΔQ = ΔQr, subsection 32). When the soil water is limiting, biomass accumulation is limited by water supply (ΔQ = ΔQw).

The water demand (Wd, in mm) corresponds to the amount of water the crop would have transpired in the absence of soil water constraint, and is calculated from the potential biomass accumulation from RUE (ΔQr, subsection 13). Following Sinclair (1986), transpiration demand is modeled as a function of the current day’s crop growth rate, estimated by the potential biomass accumulation associated with intercepted radiation (ΔQr, see subsection 13), divided by the transpiration efficiency.

Wd = ΔQr--− R
        TE
(31)

where R is respiration rate and equals to zero in the current version of APSIM-Wheat, TE is transpiration efficiency (subsection 88). See section 11 for more details about water demand and supply.

The daily biomass accumulation (ΔQ) corresponds to dry matter above ground biomass is limited by the radiation interception (ΔQr, subsection 13) or by soil water deficiency (ΔQw, subsubsection 97), so that daily biomass accumulation can be expressed as:

      { ΔQ    W  = W
ΔQ  =      r    u    d
        ΔQw   Wu < Wd
(32)

where Ws is water supply, Wd is the soil water demand from the shoot, limited by radiation interception (subsection 11.1). In the current APSIM-Wheat, Wd is actually only directly affected by the soil water demand of the leaf (subsection 11.1). Wu and Wd are calculated by soil module of APSIM.

5 Biomass partitioning and re-translocation

5.1 Biomass partitioning

In the wheat module, wheat is divided into four components or parts: Root, Heat, Leaf and Stem (Figure 12), and is derived from a more generic plant module (meaning that it has some parts not used or has a terminology, better adapted to other crops). Leaf includes only leaf blades. Stem is defined in a functional rather than a morphological manner and includes plant stems, leaf sheaths and stem-like petioles (not applicable for wheat). Head is divided into Grain and Pod (which correspond to spike without the grain). Then grain are separated into Meal and Oil (not used). The structure of wheat parts is shown in Figure 12.

pict
Figure 12: The hierarchical structure of wheat parts. Texts in the parentheses are classes of parts. The gray box indicates a plant part not used in wheat.

On the day of emergence, biomass in plant parts (Root, Head, Leaf, Stem, Pod, Meal and Oil) are initialized by root_dm_init (set at 0.01 g plant-1 in the wheat.xml file), leaf_dm_init (0.003 g plant-1), stem_dm_init (0.0016 g plant-1), pod_dm_init (0 g plant-1), meal_dm_init (0 g plant-1), oil_dm_init (0 g plant-1), respectively. Daily biomass production (subsection 32) is then partitioned to different plant parts in different ratios that vary with crop stage. Overall, Root biomass are calculated with a shoot:root ratio from the above-ground biomass (ΔQ; Figure 13). Then the above-ground biomass are partitioned into the different plant parts hierarchically, with biomass being attributed first to Head, then Leaf and finally Stem. This means that all parts might not have the biomass demand satisfied if the biomass production is limited.

pict
Figure 13: Biomass partition rules in the APSIM-Wheat module. Texts in the parentheses are partitioning methods of different organ types. The above-ground biomass (ΔQ) is used to calculate Root biomass based on a shoot:root ratio, and is then partition to (1) Head based on the demand from Pod and Grain, and then (2) Leaf (proportion of the remaining biomass), and (3) Stem. Re-translocation occurs during grain filling, when the biomass accumulation doesn’t satisfy Head demand. Biomass from Stem and Pod are then used to satisfy the Head demand (Pod and Grain).

5.2 Biomass partitioning to Root

Firstly, some biomass are allocated to the root as a ratio of daily available biomass (ΔQ, subsection 13). The so-called ’magic’ fraction of biomass going to Root is calculated from a stage-dependent function, but is independent on pedo-climatic factors (Figure 14). All biomass in the Root is considered as structural fraction, meaning that it cannot be re-translocated to other parts later on.

ΔQroot = ΔQ × RRoot:Shoot
(33)

where ΔQroot is the daily increment in Root biomass; and RRoot:Shoot is the ratio root:shoot biomass, which is defined by x_stax_stage_no_partition and y_ratio_root_shoot in wheat.xml (Figure 14).

(which is specified in wheat.xml )

pict

Figure 14: Relationship between ratio of root and shoot and growth stage.

5.3 Biomass partitioning to Head (Pod, Meal and Oil (not applicable in this version))

Then all or part of available biomass (ΔQ) are partitioned into Heads according to total demand of Heads (Meal, Oil and Pod). Meal and Pod demands are calculated by subsection 49 and subsection 52. Oil demand always equals to zero in the current version of the APSIM-Wheat module. Biomass directly partitioned in Pod or Grain is considered as structural and cannot be re-translocated, however the biomass providing from re-translocation is accumulated as non-structural biomass. The Pod non-structural biomass can then be re-translocated into Grain (See subsection 5.6).

ΔQhead = min(ΔQ,DgDgrain + Dpod)
    ΔQgrain = DheadΔAhead
     ΔQpod = DDhpeadΔAhead
(34)

where ΔQhead is the daily available biomass for Head, Dhead, Dgrainand Dpod are demands for Head, Grain and Pod, respectively (see subsection 6.2 and subsection 6.3). ΔQgrain and ΔQpod are biomass increment of Grain and Pod, respectively.

5.4 Biomass partitioning to Leaf

Then, the remaining biomass (after the partitioning to the Heads) are partitioned into Leaf based on a stage dependent function (Figure 15). Leaf biomass is considered as structural and thus cannot be re-mobilised.

ΔQ     = (ΔQ − ΔQ    ) ×F
   leaf            head    leaf
(35)

where ΔQleaf is the daily increment in Leaf biomass; and Fleaf is the fraction of available biomass partitioned to the leaf, which is defined by x_stage_no_partition and y_frac_leaf in wheat.xml (Figure 15).

pict

Figure 15: Relationship between fraction of leafLeaf and growth stage.

5.5 Biomass partitioning to Stem

Finally, the whole remaining biomass (if any) are partitioned into Stem (Figure 13). Until the stage “start of grain filling”, 65% of this biomass is distributed to structural biomass (Figure 16), while remaining 35% is allocated in un-structural biomass. Afterwards, all new biomass allocated to Stem is for non-structural biomass (which can re-mobilised).

ΔQstem = ΔQ − ΔQhead − ΔQleaf
(36)

ΔQstem.structural = ΔQstem ×hstructual
(37)

ΔQstem.non−structural = ΔQstem × (1− hstructual)
(38)

where ΔQstem is the daily increment in Stem biomass; ΔQstem.structural is the structural biomass of Stem; ΔQstem.nonstructural is the non-structural biomass of Stem; and hstructual is the fraction of Stem biomass distributed to structural biomass which depends on the growth stage (S). hstructual is specified by stemGrowthStructuralFraction and stemGrowthStructuralFractionStage in wheat.xml, with a default value of 0.65 before beginning of grain filling and 0 after.

pict

Figure 16: Relationship between fraction of structural and unstructural biomass in Stem.

5.6 Re-translocation

If the supply in assimilate (daily biomass increase) is insufficient to meet Grain demand, then re-translocation may occur to meet the shortfall (Figure 13). The biomass re-translocation first occurs from the Stem non-structural biomass. From the start of grain filling, the wheat module allows a total re-translocation of up to 20% of Stem biomass per day. If required, biomass can then be re-translocated from the Pod non-structural biomass. The re-translocated biomass is used to fulfill the Grain and Pod demands (subsection 6.2 and subsection 6.3) and is accumulated as non-structural biomass.

Ddiff,head = (Dgrain − ΔQgrain )+ (Dpod − ΔQpod)
(39)

where Ddiff,head is the unfulfilled demand from the plant, Dgrain and Dpod are the demands from Grain and Pod (subsection 6.2 and subsection 6.3), and ΔQgrain and ΔQpod are the daily increments in biomass accumulated to Grain and Pod (before re-translocation; subsection 34).

ΔQretrans,stem = min(Ddiff,Qstem.non−structural × 20%)
(40)

where ΔQretrans,stem is the dry biomass re-translocated from Stem, and Qstem.nonstructural is the non-structural part of the Stem biomass (subsection 38).

Ddff,head = Ddiff,head − ΔQretrans
(41)

where Ddff,head is updated value of the unfulfilled demand from the head.

ΔQretrans,pod = min(Ddiff,head + Qpod,non−structural)
(42)

where ΔQretrans,pod from pod is the dry biomass re-translocated from Pod, and Qpod,nonstructural is the non-structural part of the Pod biomass.

Ddff,head = Ddiff,head − ΔQretrans,pod
(43)

where Ddff,head is updated value of the unfulfilled demand from the head.

ΔQretrans = ΔQretrans,stem + ΔQretrans,pod
(44)

where ΔQretrans is re-translocated biomass within the plant.

                                    Ddiff,grain
ΔQgrain.non−structural=ΔQretranstograin = Ddiff,head-ΔQretrans
(45)

               -Ddiff,pod-
ΔQretranstopod = Ddiff,headΔQretrans
(46)

ΔQ                ΔQ          − ΔQ
   pod.non−structural=    retranstopod     retrans,pod
(47)

where ΔQgrain.nonstructural and ΔQpod.nonstructural are the daily increment in the non-structural part of Grain and Pod biomass; ΔQretranstograin and ΔQretranstopod to pod are the daily biomass re-translocated to Grain and Pod; Ddiff,grain and Ddiff,pod are the unfulfilled demand of Grain and Pod, which are calculated as (Dgrain ΔQgrain) and (Dpod ΔQpod), respectively.

6 Grain development

6.1 Grain number

The number of grains per plant (Ng) is determined by the stem weight at anthesis.

Ng = RgWs
(48)

where Qs is the stem dry weight at anthesis, Rg is the grain number per gram stem which is specified by grain_per_gram_stem in wheat.xml, with default value at 25 grain g-1.

6.2 Grain (Meal) demand

The Grain demand (or Meal demand, Dg) is calculated in the growth phase postflowering (from flowering to end of grain filling Figure 1). Dg equals to 0 before flowering.

Dg = NgRphg (Tmean )fN,grain
(49)

where Ng is the grain number, Rp is the potential rate of grain filling (0.0010 grain-1 d-1 from flowering to start of grain filling (Figure 1); 0.0020 grain-1 d-1 during grain filling (Figure 1)), hg(Tmean) is a function of daily mean temperature which affects the rate of grain filling (0-1) and is defined by parameters x_temp_grainfill and y_rel_grainfill in wheat.xml and linearly interpolated by APSIM (Figure 17).

fN,grain is a nitrogen factor to grain filling.

f      = hN,-potenh        ∑    -----CN-−-CN,min----    (0 ≤ f    ≤ 1)
 N,grain   hN, min N,grainstem,leafCN,crit × fc,N − CN,min        N,fill
(50)

where hN, poten is the potential rate of grain filling which is specified by potential_grain_n_filling_rate in wheat.xml and has a default value of 0.000055 g grain-1 d-1; hN, min is the minimum rate of grain filling which is specified by minimum_grain_n_filling_rate in wheat.xml and has a default value of 0.000015 g grain-1 d-1; hN,grain is a multiplier for nitrogen deficit effect on grain, which is specified by n_fact_grain in wheat.xml and has a default value of 1; CN is the nitrogen concentration of Stem or Leaf parts; CN,crit and CN,min are critical and minimum nitrogen concentration, respectively, for Stem and Leaf parts. CN,crit and CN,min are functions of growth stage and nitrogen concentration which is defined by parameters x_stage_code, y_n_conc_min_leaf, y_n_conc_crit_leaf, y_n_conc_min_stem, y_n_conc_crit_stem in wheat.xml and linearly interpolated by APSIM (Figure 36); and fc,N is a factor with a value of 1 (i.e. no impact) for Stem, and is depending on CO2 for Leaf (Figure 18).

pict

Figure 17: Response of the factor affecting the rate of grain filling in regards to daily mean temperature.

pict

Figure 18: The CO2 modifier for critical nitrogen concentration of Leaf.

Finally, Grain demand is limited by the maximum grain size (corresponding to Dgm)

        Dg = min(Dg,Dgm )
Dgm  = NgSgm − Qmeal    (Dgm  ≥ 0)
(51)

where Ng is the grain number; Qmeal is the dry weight of Meal part (i.e. the Grains); Sgm is the maximum grain size which is specified by max_grain_size in wheat.xml and is a cultivar-specific parameter with 0.04 g for default value.

6.3 Pod demand

Pod demand (Dp) is calculated by Grain demand (Dg, subsection 49) or daily biomass accumulation (ΔQ, subsection 32)

Dp =  Dghp(S)    Dg>0
      ΔQhp (S )   Dg=0
(52)

where hp(S) is a function of the growth stage (S) and of the Pod demand fraction of Dg or ΔQ. hp(S) is defined by parameters x_stage_no_partition and y_frac_pod in wheat.xml and linearly interpolated by APSIM (Figure 19).

pict

Figure 19: Pod demand over the stages (fraction of Grain demand or of daily biomass accumulation).

7 Leaf and node appearance and crop leaf area

In the current version of APSIM-Wheat, wheat plants are assumed to be uniclum (i.e. with a single stem), meaning that tillering is not simulated per se. While a node corresponds to a phytomer on the main stem, it actually represents all the phytomers that appear simultaneously on different tillers (i.e. cohort of leaves) in the real world.

7.1 Node number

7.1.1 Potential node appearance rate

At emergence (Figure 1), a number of initial leaves are specified by leaf_no_at_emerg, with a default value of 2. The initial number of nodes is the same as the initial number of leaves.

During the tiller formation phase (i.e. up to ’Harvest rips’, Figure 1), nodes appear at a thermal time interval (the equivalent of a phyllochron for leaf appearance, Pn) that depends on the node number of the main stem (nd, i.e. total number of nodes of the plant) at days after sowing (d, days).

Pn = hP(nd)
(53)

where the function hP(nd) is defined by parameters x_node_no_app and y_node_app_rate in wheat.xml and is linearly interpolated by APSIM. In the current version of APSIM-Wheat, Pn is set to 95 C d, meaning that the ’node phyllochron’ is supposed to be constant (Figure 20). No effect from water and N stress on leaf appearance is accounted for.

pict

Figure 20: Relationship function (hp(nd)) between ’node phyllochron’ (Pn) and the node number at main stem (nd).

7.1.2 Potential node number (daily increase)

The potential daily increase in the node number of this unique stem (Δnd,p) is calculated by the daily thermal time (Figure 3) and the ’node phyllochron’, and occurs during the tiller formation phase (Figure 1).

        ΔT Td
Δnd,p = -----
         Pn
(54)

where ΔTTd is the thermal time (Cd) at day d (Figure 3 and subsection 4).

7.1.3 Actual node number (daily increase)

The actual node number growth (Δnd) is the minimum between the potential daily increase of node number (Δnd,p) and the leaf number increase (Δnd,LAI, subsubsection 59).

Δnd = min(Δnd,LAI,Δnd,p)
(55)

7.2 Leaf number

7.2.1 Potential leaf number (daily increase)

In the current version of APSIM-Wheat, all leaves appeared from a main and unique stem. The potential leaf number of each node is defined by a function (hl(nd)) of node (nd) number of day d (or ’node position’; nd) (Figure 21 and subsubsection 57). hl(nd) is specified by parameters x_node_no_leaf and y_leaves_per_node in wheat.xml and linearly interpolated by APSIM.

At day d, the potential leaf number of the current node nd nodes (Nn,d,p) is determined by the potential leaf number d 1 for the past nd1 nodes (Nn,d1) and environmental stresses.

Nn,d,p = min[Nn,d−1,hl(nd−1)]+ [hl(nd− 1 + Δnd,p)− hl(nd−1)]× fS,expan
(56)

where nd1 is the node number at d 1 days after sowing, Δnd,p is the potential daily increase of node number (subsubsection 54), fS,expan is the environmental stresses for canopy expansion.

fS,expan = min{[min(fN,expan,fp,expan)]2,fw,expan}
(57)

where fN,expan, fp,expan and fw,expan are the nitrogen, phosphorus and soil water stress for canopy expansion, respectively, which is explained in subsection 3.1, section 13 and subsubsection 98, respectively.

The potential daily increase in leaf number for the whole plant is calculated based on the potential increase for the current node and the potential increase in node number (Δnd,p, subsubsection 54) as follows.

ΔNd,p = Nn,d × Δnd,p
(58)

pict

Figure 21: Number of leaves per node as a function of the number of nodes on the main stem and unique stem considered in APSIM-Wheat (nd). This relation corresponds the function hl(nd).

7.2.2 Actual leaf number (daily increase)

The increase in actual leaf number (ΔNn,d) is calculated in relation to the fraction between the actual and stressed increase of leaf area index, as follow:

                      ΔLAI
Δnd,LAI = Δnd,p × hLAI(----d )
                     ΔLAId,s
(59)

where hLAI is a function between the fraction of leaf area index and the fraction of leaf number which is defined by parameters x_lai_ratio and y_leaf_no_frac in the wheat.xml and linearly interpolated by APSIM (Figure 22).

pict

Figure 22: Relationship between fraction of leaf area index and fraction of leaf number.

8 Leaf area expansion

8.1 Actual leaf area (daily increase)

At emergence (Figure 1), an initial leaf area is specified for each plant by initial_tpla, with a default value of 200 mm2 plant-1.

During the tiller formation phase (Figure 1), the daily increase in leaf area index (ΔLAId) is the minimum between ‘stressed’ leaf area index (ΔLAId,s) and the carbon-limited leaf area index (ΔLAId,c).

ΔLAId = min(ΔLAId,s,ΔLAId,c)
(60)

8.2 “Stressed” leaf area

During the tiller formation phase, the “stressed” daily increase in leaf area (ΔLAId,s) is calculated as the potential increase in LAI reduced by environmental factors.

ΔLAId,s = ΔLAId,p × min(fw,expan × fN,expan × fP,expan)
(61)

where fN,expan, fp,expan and fw,expan are the nitrogen, phosphorus and soil water stress factors concerning canopy expansion, respectively (subsubsection 109, section 13 and subsubsection 98).

The potential daily increase of leaf area (ΔLAId,p) is calculated by the potential daily increase in leaf number and leaf size.

ΔLAId,p = ΔNd,p ×Ln × Dp
(62)

where ΔNd,p is the potential increase in leaf number (for the whole plant), Dp is the plant population, and Ln is the potential leaf area for leaves of the “current” node (this corresponds to the new potential leaf area produced by the different tillers in the real world) and depends on the node number on the main and unique stem considered by APSIM-Wheat.

Ln = hls(nd + n0)
(63)

where n0 is the growing leaf number in the sheath (node_no_correction in wheat.xml) and equals to 2 as default value. The function hls(nd) is defined by parameters x_node_no and y_leaf_size in wheat.xml and linearly interpolated by APSIM (Figure 23).

pict

Figure 23: Leaf area per node (Ln) in regards to the main stem node number n0 + nd.

8.3 Carbon-limited leaf area

Leaf area related to carbon production is calculated by the increase in leaf dry weight (ΔQleaf subsection 32) and the maximum specific leaf area (SLAmax), which is related to leaf area index (LAI).

ΔLAId,c = ΔQ ×SLAmax
(64)

SLAmax  = hSLA(LAI)
(65)

This function is defined by parameters x_lai and y_sla_max in wheat.xml and linearly interpolated by APSIM (Figure 24).

pict

Figure 24: Relationship between maximum specific leaf area and leaf area index.

9 Root growth and distribution

9.1 Root depth growth

Between germination and start of grain filling (Figure 1), the increase in root depth (ΔDr) is a daily rate multiplied by a number of factors. Daily root depth growth (ΔDr) is calculated by root depth growth rate (Rr), temperature factor (frt), soil water factor (frw), and soil water available factor (frwa) and root exploration factor (XF(i)).

ΔDr  = Rr ×frt × min(frw,frwa )×XF (i)
(66)

where i is the soil layer number in which root tips are growing. Root depth growth rate is a function of growth stage, which is defined by parameters stage_code_list and root_depth_rate in the wheat.xml and is linearly interpolated by APSIM (Figure 25).

pict

Figure 25: Relationship between root depth growth rate (Rr) and growth stages.

The temperature factor (frt) is calculated by daily mean temperature.

         Tmax +Tmin
frt = hrt(----2-----)
(67)

where hrt is a function of factor of temperature on root length and daily mean temperature and is defined by parameters x_temp_root_advance and y_rel_root_advance in the wheat.xml which is linearly interpolated by APSIM (Figure 26).

pict

Figure 26: Relationship (hrt) between temperature factor on root length and daily mean temperature.

The soil water factor (frw) is calculated by soil water stresses of photosynthesis (fw,photo, subsubsection 96).

frw = hrw(fw,photo)
(68)

where hrw is a function of soil-water factor affecting root depth growth in response to soil water stress for photosynthesis. This function is defined by parameters x_ws_root and y_ws_root_fac, which are linearly interpolated by APSIM. The default value of frw is 1, i.e. there is no soil water stress on root depth growth in current APSIM-Wheat.

The soil water available factor (frwa) is calculated by fraction of available soil water.

frwa = hrwa(FASW )
(69)

where hrwa is a function of the fraction of available soil water (FASW) is defined in wheat.xml by parameters x_sw_ratio and y_sw_fac_root which is linearly interpolated by APSIM (Figure 27).

pict

Figure 27: Available soil water fraction (frwa) in response to the fraction of available soil water (FASW).

The fraction of available soil water (FASW) is calculated by a fraction of root length in soil layer I (Dr(I)) and depth of soil layer I (Ds(I)), and FASW at layer I + 1 and I.

        Dr (I)                  Dr (I)
FASW  = D--(I)FASW  (I + 1)+ (1− D-(I))FASW (I)
          s                      s
(70)

where FASW(I) is the fraction of available soil water in soil layer I. Dr(I) is the root depth within the deepest soil layer (I) where roots are present , Ds(I) is the thickness of this layer I, and

           SW (i)− LL(i)
FASW (i) = DUL-(i)-−-LL(i)-
(71)

where SW(i) is the soil water content at layer i (mm), LL(i) is the lower limit of plant-extractable soil water in layer i (mm), DUL(i) is drained upper limit soil water content in soil layer i (mm). XF(i), SW(i), LL(i) and DUL(i) are specified at the soil module of APSIM simulation files.

Finally, subsection 66 is reduced to this function.

ΔDr  = Rr × frt × frwa×xf(i)
(72)

Overall, root depth is constrained by the soil profile depth. The optimum root expansion rate is 30 mm d-1 (Figure 25). This can be limited by supra- or sub-optimal mean air temperatures (Figure 26). Dry soil can slow root depth progression if the soil water content is less than 25% of the extractable soil water (drained upper limit - lower limit) in the layers they are about to reach (Figure 27). The increase of root depth through a layer can also be reduced by knowing soil constraints (soil compression) through the use of the 0-1 parameter XF, which is input for each soil layer. Root depth is used by APSIM to calculate soil available water (e.g section 11).

9.2 Root length

Daily root length growth is calculated by daily growth of Root biomass (ΔQroot, subsection 33) and specific root length (SRL, defined by specific_root_length in wheat.xml with a default value of 105000 mm g-1).

ΔLr  = ΔQroot × SRL
(73)

The daily root length growth (ΔLr) is distributed to each soil layer i according to root depth and soil water availability in soil layer i.

            frl(i)
ΔDr (i) = ∑N--------
           j=1frl(j)
(74)

where frl(i) is a factor of root length growth in soil layer i.

                          Ds(i)
frl(i) = frwa × fb(i)×XF (i)×-D--
                             r
(75)

where ΔLr(i) is the daily root length growth for soil layer i, Ds(i) is the depth of the soil layer i, Dr is total root depth from the previous day, XF(i) is root exploration factor in soil layer i, frwa is soil water available factor (subsection 69), fb(i) is branch factor at layer i.

           Lr (i)
fb(i) = hb(D-D-(i)-)
           p  s  r
(76)

where Lr(i) is the root length in soil layer i, Dp is plant population, hb is a function for branch factor that is defined by parameters x_plant_rld and y_rel_root_rate in the wheat.xml and linearly interpolated by APSIM (Figure 28).

pict

Figure 28: Root branching factor in response to root branching.

Root length has no effect on other traits in the current version of APSIM-Wheat. It is just used by the root senescence routine.

10 Senescence

10.1 Leaf number senescence

The leaf senescence phase begins 40% between floral initiation and end of juvenile, and ends at harvest ripe (Figure 1), at which stage, all green leaves are dead. During leaf senescence phase (Figure 1), leaf number senescence is calculated by daily thermal time (ΔTT, subsection 4) as follows:

                fsen,l × Nd
ΔNd,sen = ΔT T × --r-------
                   sen,l
(77)

where Nd is the total leaf number; fsen,l is the fraction of the total leaf number senescing per main stem node and specified by fr_lf_sen_rate in wheat.xml (default value 0.035); rsen,l is the rate of node senescence on main stem and specified by node_sen_rate in wheat.xml (default value 60.0 Cd node-1).

10.2 Leaf area senescence

There are five causes of leaf senescence: age (ΔLAIsen,age), water stress (ΔLAIsen,sw), light intensity (ΔLAIsen,light), frost (ΔLAIsen,frost) and heat (ΔLAIsen,heat). The maximum of these causes is the day’s total leaf area index senescence.

ΔLAIsen = max(ΔLAIsen,age,ΔLAIsen,sw,ΔLAIsen,light,ΔLAIsen,frost,ΔLAIsen,heat)
(78)

Leaf area senescence caused by age corresponds to the leaf area of the number of leaves senesced (ΔNd,sen) from the lowest leaf position.

Leaf area senescence caused by soil water (ΔLAIsen,sw) is calculated as follows.

ΔLAIsen,sw = ksen,sw × (1− fsw,photo)× LAI
(79)

where ksen,sw is the slope of the linear equation relating to soil water stress to leaf senescence rate and is specified by sen_rate_water in wheat.xml (default value 0.10); fsw,photo is soil water stress for photosynthesis (subsubsection 96); LAI is the leaf area index.

Leaf area senescence caused by light intensity (ΔLAIsen,light) is calculated as follows:

ΔLAIsen,light = ksen,light × (LAI− LAIc,light)× LAI LAI > LAIc,light
(80)

where ksen,light is sensitivity of leaf area senescence to shading and is specified by sen_light_slope in wheat.xml (default value 0.002); LAIc,light is the critical LAI when shading is starting to cause leaf area senescence and is specified by lai_sen_light in wheat.xml (default value 7).

The leaf area senescence caused by frost is a ratio of LAI.

ΔLAIsen,frost = ksen,frost×LAI
(81)

where ksen,frost is a function of daily minimum temperature and is defined by parameters x_temp_senescence and y_senescence_fac in wheat.xml, which are linearly interpolated by APSIM. The default value of ksen,frost is zero, i.e. there is no frost stress in leaf area in the current APSIM-Wheat module.

Senescence by heat calculation has been added in APSIM 7.5. The leaf area senescence by heat is a ratio of LAI (Asseng et al.2011).

ΔLAIsen,heat = ksen,heat × LAI
(82)

where ksen,heat is a function of daily maximum temperature which is defined by parameters x_maxt_senescence and y_heatsenescence_fac in wheat.xml which are linearly interpolated by APSIM.

pict

Figure 29: Fraction of senescence of leaf area index (ksen,heat) in response to maximum temperature.

The total leaf area of plant must be more than the minimum plant area (min_tpla), which has default value 5 mm2 plant-1. When some leaves are senesced, only a small amount of nitrogen is retained in the senesced leaf, the rest is made available for re-translocation included into the Stem N pool (subsection 12.3). The concentration of nitrogen in senesced material is specified in wheat.xml.

10.3 Biomass senescence

Leaf biomass senescence ΔQsl is the ratio of leaf area senescence (ΔLAIsen) with total the green LAI at the time considered (LAI).

ΔQsl = ΔQl ΔLAIsen-
             LAI
(83)

where ΔQl is the daily increase of leaf biomass.

A rate of 0.5% of Root biomass is senesced each day (x_dm_sen_frac_root and y_dm_sen_frac_root) and detaches immediately, being sent to the soil nitrogen module and distributed as fresh organic matter in the profile.

10.4 Root senescence

A rate of 0.5% of root biomass and root length is senesced each day and detaches immediately being sent to the soil nitrogen module and distributed as fresh organic matter in the profile.

ΔQsen,root = ΔQroot × fsen,root
(84)

where ΔQsen,root is the daily Root senesced biomass, and fsen,root is the fraction of senesced root biomass, which is defined in x_dm_sen_frac_root and y_dm_sen_frac_root in wheat.xml (Figure 30)

pict

Figure 30: Fraction of senescence of root biomass.

ΔLsen,root = ΔQsen,root × SRL
(85)

where ΔLsen,root is the daily root length senescence, and SRL is the specific root length.

Root senescence occurs in each of the soil layers where roots are present, as a proportion of the total root length.

                     ---Lr(i)---
Lsen,root(i) = Lsen,root × ∑ij=1Lr(j)
(86)

where Lsen,root(i) is the root length senescence in soil layer i, Lr(i) is root length in layer i, and j=1iLr(j)is the total root length for all the layers where root are present.

11 Crop Water Relations

11.1 Crop water demand

Following Sinclair (1986), transpiration demand is modeled as a function of the current day’s potential crop growth rate, estimated by the potential biomass accumulation associated with intercepted radiation (ΔQr, see subsection 13), divided by the transpiration efficiency.

     ΔQr  − R
Wd = ---TE---
(87)

where R is respiration rate and equal to zero in the current version of APSIM-Wheat, TE is transpiration efficiency. TE is related to the daylight averaged vapour pressure deficit (V PD, subsection 89) and a multiple of CO2 factor (Reyenga et al.1999).

          -fTE-
TE = fc,T EV PD
(88)

where fc,TE is the CO2 factor for transpiration efficiency, which is a function of carbon dioxide concentration and is defined by parameters x_co2_te_modifier and y_co2_te_modifier in wheat.xml and linearly interpolated by APSIM (Figure 31). fc,TE linearly increases from 1 to 1.37 when CO2 concentration increases from 350 ppm to 700 ppm (Reyenga et al.1999). fTE is the coefficient of transpiration efficiency, which values are defined in wheat.xml by parameters transp_eff_cf in wheat.xml for the different growth stages and are linearly interpolated by APSIM (Figure 32).

pict

Figure 31: Relationship between factor of carbon dioxide for transpiration efficiency (fc,TE) and CO2 concentration.

pict

Figure 32: Change in the coefficient of transpiration efficiency with growth stages.

V PD is the vapour pressure deficit, which is estimated using the method proposed by Tanner and Sinclair (1983) and only requires daily maximum and minimum temperatures.

                     17.269 × Tmax               17.269× Tmin
V PD = fv[6.1078× exp(-237.3+-Tmax-)− 6.1078× exp(237.3+-Tmin-)]
(89)

In this method, it is assumed that the air is saturated at the minimum temperature. The saturated vapour pressure is calculated at both the maximum and minimum temperatures, and the default vapour pressure deficit for the day is taken as 75% (fv, defined by svp_fract in wheat.xml) of the difference between these two vapour pressures.

Crop water demand is capped to below a given multiple of potential ET (taken as Priestly-Taylor Eo from the water balance module) as specified by eo_crop_factor_default in the wheat.xml file (default value 1.5). This limits water use to reasonable values on days with high VPD or in more arid environments.

11.2 Potential and actual extractable soil water

Potential and actual extractable soil water is the sum of root water contents available to the crop from each profile layer occupied by roots. If roots are only partially through a layer available soil water is scaled to the portion that contains roots. Potential extractable soil water (ESWp) is the difference between drained upper limit soil water content (DUL) and lower limit of plant-extractable soil water (LL) for each soil layer. The actual extractable soil water (eswa) is the difference between the soil water content (SW) and lower limit of plant-extractable soil water (LL) for each soil layer.

  ESWp (i) = DUL (i)− LL (i)
   ESW (i∑)I = SW (i) − LL (i)
ESWa  = ∑Ii=1[DUL (i)− LL(i)]
 ESWp =    i=1[SW (i)− LL(i)]
(90)

where i indicates soil layers (where roots are present), and I indicates the deepest soil water of root presented. Similar variables are calculated for the entire soil profile (i.e. roots may not occupy all the layers).

        ∑
PAWC  = ∑ Nis[DUL (i) − LL(i)]
 ESW  =   Nis[SW (i)− LL (i)]
(91)

where i indicates soil layers, Ns indicates the number of soil layers, and PAWC is the plant available water capacity.

11.3 Crop water supply, i.e. potential soil water uptake

The APSIM-Wheat module can be coupled to either the SWIM2 module (see module documentation) or the SOILWAT2 module (default). When the APSIM-Wheat module is coupled to APSIM-SOILWAT2, potential soil water uptake (or water supply, Ws) is calculated using the approach first advocated by Monteith (1986). Crop water supply is considered as the sum of potential root water uptake from each profile layer occupied by root. If roots are only partially through a layer available soil water is scaled to the portion that contains roots. The potential rate of extraction in a layer is calculated using a rate constant (KL) as actual extractable soil water. The KL defines the fraction of available water able to be extracted per day. The KL factor is empirically derived, incorporating both plant and soil factors which limit rate of water uptake. Root water extraction values (KL) must be defined for each combination of crop species and soil type.

Ws (i)  = KL (i)[SW (i)− LL (i)]       ifi ≤ I − 1
       = Dr(i)KL (i)[SW  (i)− LL(i)]        ifi = I
         Ds(i)       ∑I
               Ws =   i=1Ws (i)
(92)

where i is the soil layer, I is the deepest soil layer where roots are present, Ws(i) is the water supply available from layer i, Ws is the crop water supply, SW(i) is the soil water content in layer i, LL(i) is the lower limit of plant-extractable soil water in layer i, KL(i) is the root water extraction values in layer i, Dr(i) is the root depth within the soil layer (i) where roots are present, and Ds(i) is the thickness of this layer i.

11.4 Actual soil water uptake

The actual rate of water uptake is the lesser of the potential soil water supply (Ws, subsection 92) and the soil water demand (Wd, subsection 87), which is determining whether biomass production is limited by radiation or water uptake (subsection 32)

Wu  = min(Wd,Ws )
(93)

If the potential soil water supply (accessible by the roots) exceeds the crop water demand, then the actual soil water uptake (Wu) is removed from the occupied layers in proportion to the values of potential root water uptake in each layer. If the computed soil water supply from the profile is less than the demand then, and the actual root water uptake from a layer is equal to the computed potential uptake. If there are not soil water supply and demand, soil water update equals to zero.

                 Wd-
ΔWs (i) = − Ws (i)× Ws    ifWs  < Wd
  ΔWs (i) = − Ws(i)  ifWs > Wd
   ΔWs (i) = 0   ifWs  = Wd = 0
(94)

where ΔWs(i) is the daily change in soil water content at layer i (where roots are present), and Ws(i) is the water supply available from layer i (subsection 92) .

11.5 Soil water stresses affecting plant growth

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

Each of these factors is capped between 0 and 1, where the value of 0 corresponds to a complete stress, while 1 corresponds to no stress.

Leaf expansion is considered more sensitive to stress than photosynthesis, while soil water has no impact on crop phenology in the current APSIM-Wheat version.

11.5.1 Phenology

Soil water stress of phenology is determined by the soil water deficiency.

                  eswa--
fW,pheno = hw,pheno(eswp )
(95)

where eswa is the actual extractable soil water in root layers, eswp is the potential extractable soil water in root layers. hw,pheno is a function of soil water available ratio and soil water stress, which is defined by parameters x_sw_avail_ratio and y_swdef_pheno (default value 1) in wheat.xml and linearly interpolated by APSIM. In the current version of APSIM-Wheat module, no soil water stress for phenology is applied (Figure 33). The soil water stress of phenology for flowering (x_sw_avail_ratio_flowering and y_swdef_pheno_flowering) and grain filling (x_sw_avail_ratio_start_grain_fill and y_swdef_pheno_start_grain_fill) phases are calculated in the source code, but don’t have influence on the phenology of wheat in the current APSIM-Wheat version (default value of 1).

pict

Figure 33: Relationship between soil water stress factor affecting phenology (fW,pheno) and the ratio of available soil water (eswa-
eswp).

11.5.2 Photosynthesis

Soil water stress of biomass accumulation (fw,photo) is calculated as follows.

          Wu
fw,photo = ---
          Wd
(96)

where Wu is the total daily water update from root system (subsection 93), Wd is the soil water demand of Leaf and Head parts (subsection 87).

Finally, the biomass production (ΔQ) can limit by water uptake (fw,photo < 1, i.e. when Wu < Wd), or not (when fw,photo = 1, i.e. when Wu = Wd)

                        Wu
ΔQw  = ΔQrfw,photo = ΔQr W--
                          d
(97)

11.5.3 Leaf expansion

Soil water stress of leaf expansion is determined by the deficit of soil water.

                 W
fW,expan = hw,expan(-u)
                 Wd
(98)

where Wu is the crop water uptake (subsection 93), Wd is the crop water demand (subsection 87). hw,expan is a function of soil water content and stress, and is defined by parameters x_sw_demand_ratio and y_swdef_leaf in the wheat.xml, which is linearly interpolated by APSIM (Figure 34).

pict

Figure 34: Relationship between the soil water stress factor affecting expansion (fW,expan) and supply:demand ratio (We-
Wd).

11.6 KL factor

APSIM 7.5 introduces a modifying factor on KL (rate of maximum daily water uptake per day) where there is an excess of chloride concentration (Cl), exchangeable sodium percentage (ESP), or electrical conductivity (EC) properties in the soil (Hochman et al.2007). The KL modifier is optional and triggered by setting the ModifyKL parameter to ‘yes’.

When the KL modifier is activated, KL values are modified for each layer, by factors (concerning Cl, ESP, EC; Figure 35) applied to default KL values. The modifiers are calculated using one of the limiting factors in order of preference (Cl, ESP, EC), i.e. KL is modified only if there are no soil parameters for Cl. The parameters in the wheat.xml that control this mechanism are ClA, CLB, ESPA, ESPB, ECA, ECB (slope and intercept of linear relationship for Cl, ESP and EC).

pict

Figure 35: The KL factor in response to chloride concentration (Cl mg kg1, Exchangeable sodium percentage (ESP, %) and soil electrical conductivity (EC, dS m1.

12 Nitrogen

The nitrogen stress phase begins before 30% floral initiation to finish at the ’harvest ripe’ phase (Figure 1), which are defined by n_stress in wheat.xml.

12.1 Nitrogen supply

Ammonium (NH4+) is not taken up in wheat as wheat.xml parameter knh4 (constant for NH4 extraction) is equal to 0.

The model uses a simplified formulation for nitrate NO3 uptake somewhat similar in structure to that employed in water uptake. During the nitrogen stress phase (Figure 1), nitrogen supply for soil layer i (Ns(i), g m-2) is calculated as follows:

                        1000    ESWa (i)
Ns(i) = KNO3N (i)[N(i)BD(i)D-(i)]ESW--(i)
                           s       p
(99)

where kNO3 is a constant of extractable soil nitrogen, which is defined by kno3 with default value 0.02; N(i) is the nitrogen concentration in soil layer i (g m-2); BD(i) is the bulk density of soil layer i (g cm-3); Ds(i) is the depth of soil layer i (cm); ESW(i) is the actual extractable soil water in soil layer i (subsection 90); ESWp(i) is the potential extractable soil water in soil layer i (subsection 90).

During non-nitrogen stress phase (Figure 1), wheat could access to all available nitrogen.

              1000
Ns(i) = N (i)BD-(i)D-(i)
                  s
(100)

The values of Ns(i) for each layer of root presented are summed to get a total potential nitrogen uptake (or crop N supply, Ns) and then each layer Ns(i) is scaled by maximum total nitrogen uptake (Ns,max), which is defined by total_n_uptake_max with default value 0.6 g m-2.

N′s(i) = Ns(i)Ns,max
             Ns
(101)

where Ns(i) is the actual nitrogen uptake in the layer i.

12.2 Nitrogen demand

Total wheat nitrogen demand is the sum of the N demand in all parts (i.e. Leaf, Stem, and Pod). Wheat has a defined minimum (CN,min), critical (CN,crit) and maximum (CN,max) nitrogen concentration for all plant parts (Figure 36). These concentration limits change with phenological stages (Figure 36). And they are defined by parameters x_stage_code, y_n_conc_min_leaf, y_n_conc_crit_leaf, y_n_conc_max_leaf, y_n_conc_min_stem, y_n_conc_crit_stem, y_n_conc_max_stem, y_n_conc_min_pod, y_n_conc_crit_pod, y_n_conc_max_pod in wheat.xml and linearly interpolated by APSIM .

Physiologically, minimum nitrogen concentration (CN,min) corresponds to the structural N required for the plant structure, and which cannot be re-translocated. Critical nitrogen concentration (CN,crit) corresponds to the minimum concentration of N that plant parts will attempt to maintain (it drives the ‘N demand’ of the part), and maximum nitrogen concentration (CN,max) reflects to the capacity of the part to accumulate the extra available N (i.e. fulfilling more than its ‘demand’) up to a this maximum threshold N.

pict

Figure 36: Relationship between maximum, critical, minimum nitrogen concentration and growth stages for the different plant parts (Leaf, Stem and Pod). Parameters are defined by defined by parameters x_stage_code, y_n_conc_min_leaf, y_n_critonc_crit_leaf, y_n_conc_max_leaf, y_n_conc_min_stem, y_n_critonc_crit_stem, y_n_critonc_max_stem in wheat.xml.

12.2.1 Nitrogen demand of Grain

Grain nitrogen demand starts at anthesis and is calculated from grain number, thermal time and a potential grain nitrogen filling rate (g grain-1 Cd-1).

ND,grain = NgRN,poten,fN,grainhgrain(T )
(102)

where Ng is the grain number, RN,poten, is the potential nitrogen filling rate, which is defined by parameter potential_grain_n_filling_rate in wheat.xml with default value 0.000055 g grain-1 d-1. fN,grain is the nitrogen factor of grain filling (subsubsection 110). hgrain(T) is a function of daily mean temperature (T) to influence of grain filling (Figure 37).

pict

Figure 37: Relationship between nitrogen demand of Grain and daily mean temperature.

12.2.2 Nitrogen demand of other parts

Demand of nitrogen in each part (except Grain) attempts to maintain nitrogen at the critical (non-stressed) level. Nitrogen demand on any day is the sum of the demands from the pre-existing biomass of each part required to reach critical nitrogen content, plus the nitrogen required to maintain critical nitrogen concentrations in that day’s produced biomass. For each plant part (Leaf, Stem, and Pod) the nitrogen demand is given by:

         ΔQpartCN,crit
ND,crit =------------ +fn(CN,crit − CN,part)   ifCN,crit > CN,part&Qpart > 0
            fw,photo
(103)

          ΔQpartCN,max
ND,max =  ---f---------+fn(CN,max − CN,part)   ifCN,max > CN,part&Qpart > 0
             w,photo
(104)

where ΔQpart is the growth dry weight of parts, Qpart is the green (i.e. not senesced) dry weight of parts, fw,photo is soil water stress of biomass accumulation (subsubsection 96); CN,part is the nitrogen concentration of parts; fn is defined by parameter n_deficit_uptake_fraction in wheat.xml with default value 0.0001. CN,crit and CN,max are the N concentration critic and maximal of the parts, respectively (Figure 36). ND,crit and ND,max equal to 0, if Qpart = 0.

12.3 Nitrogen update, partitioning and re-translocation

12.3.1 Nitrogen concentrations in wheat parts

The N concentration in Leaf is calculated as follows:

CN,leaf = Nleaf∕Qleaf
(105)

12.3.2 Nitrogen update

Daily total nitrogen uptake (Nu) is the lesser of N demand (Nd, subsubsection 102) and N supply Ns, subsection 100).

Nu = min(Nd,Ns)
(106)

12.3.3 Nitrogen translocation

Daily total nitrogen uptake is distributed to the plant parts in proportion to their individual demands.

12.3.4 Nitrogen re-translocation

If there is insufficient nitrogen supplied from senescing material and soil nitrogen uptake, Grain nitrogen demand is met by re-translocating nitrogen from other plant parts. Nitrogen is available for re-translocation from un-senesced leaves and stems until they reach their defined minimum nitrogen concentration. No N re-translocation is attributed to other parts than Grain.

12.4 Nitrogen stresses

12.4.1 Phenology

Nitrogen stress on phenology (via fN,pheno in subsection 5) is determined by the difference between organ nitrogen concentration and organ minimum and critical nitrogen concentration.

                   ∑         CN − CN,min
fN,pheno = hN,pheno       CN,crit-×fc,N-−-CN,min
                 stem,leaf
(107)

where CN is the nitrogen concentration of Stem or Leaf parts; hN,pheno is multiple for nitrogen deficit effect on phenology which is specified by N_fact_pheno in the wheat.xml and default value is 100; CN,crit and CN,min are the N concentration critic and minimal of the parts, respectively (Figure 36); and fc,N is a factor with a value of 1 (i.e. no impact) for Stem, and is depending on CO2 for Leaf (Figure 18).

The nitrogen stress on phenology is used in the calculation of the ‘adjusted’ thermal time (subsection 5). However, In the current version of APSIM-Wheat module, the default parameters are applied for no nitrogen water stress for phenology.

12.4.2 Biomass accumulation

Nitrogen stress on biomass accumulation (via fN,photo in subsubsection 18) is determined by the difference between leaf nitrogen concentration and leaf minimum and critical nitrogen concentration.

                ∑
fN,photo = hN,photo    -----CN-−-CN,min----
                leafCN,crit × fc,N − CN,min
(108)

where CN is the nitrogen concentration of Leaf parts; hN,expan is multiplier for nitrogen deficit effect on phenology which is specified by N_fact_photo in the wheat.xml and default value is 1.5; CN,crit and CN,min are the N concentration critic and minimal of the parts, respectively (Figure 36); and fc,N is a factor with a value of 1 (i.e. no impact) for Stem, and is depending on CO2 for Leaf (Figure 18).

The nitrogen stress on biomass accumulation affects the radiation-limited biomass accumulation (ΔQr, subsection 32).

12.4.3 Leaf appearance and expansion (i.e. leaf number and LAI)

Nitrogen stress on leaf appearance and expansion (via fN,expan in subsubsection 57) is determined by the difference between leaf nitrogen concentration and leaf minimum and critical nitrogen concentration.

                 ∑       CN − CN,min
fN,expan = hN,expan    CN,crit ×-fc,N-− CN,min
                 leaf
(109)

where CN is the nitrogen concentration of Leaf parts; hN,expan is multiplier for nitrogen deficit effect on phenology which is specified by N_fact_expansion in the wheat.xml (default value 1); CN,crit and CN,min are the N concentration critic and minimal of the parts, respectively (Figure 36); and fc,N is a factor with a value of 1 (i.e. no impact) for Stem, and is depending on CO2 for Leaf (Figure 18).

The nitrogen stress on leaf appearance and expansion affects the potential leaf number (Nd,pot; subsubsection 56) and the stressed leaf area index (ΔLAId,s, subsection 61).

12.4.4 Grain filling (biomass and nitrogen demand of grain)

Nitrogen stress on grain filling affects the biomass demand of Grain (via fN,grain in subsection 49) and the N demand of Grain (subsubsection 102).

The nitrogen factor fN,grain (that impacts N demand of grain) is determined by the difference between organ nitrogen concentration and organ minimum and critical nitrogen concentration as follows:.

                          ∑
fN,grain = hN,-potenhN,grain      -----CN-−-CN,min----    (0 ≤ fN,fill ≤ 1)
          hN, min       stem,leafCN,crit × fc,N − CN,min
(110)

where hN, poten is the potential rate of grain filling which is specified by potential_grain_n_filling_rate in wheat.xml and has a default value of 0.000055 g grain-1 d-1; hN, min is the minimum rate of grain filling which is specified by minimum_grain_n_filling_rate in wheat.xml and has a default value of 0.000015 g grain-1 d-1; hN,grain is a multiplier for nitrogen deficit effect on grain, which is specified by n_fact_grain in wheat.xml and has a default value of 1; CN is the nitrogen concentration of Stem or Leaf parts; CN,crit and CN,min are critical and minimum nitrogen concentration, respectively, for Stem and Leaf parts. CN,crit and CN,min are functions of growth stage and nitrogen concentration which is defined by parameters x_stage_code, y_n_conc_min_leaf, y_n_conc_crit_leaf, y_n_conc_min_stem, y_n_conc_crit_stem in wheat.xml and linearly interpolated by APSIM (Figure 36); and fc,N is a factor with a value of 1 (i.e. no impact) for Stem, and is depending on CO2 for Leaf (Figure 18).

13 Phosphorus

In the current version of APSIM-Wheat module, no phosphorus stress fP,pheno = 1 is applied in the soil system through parameter labile_p in the source codes.

14 Temperature

As mentioned in previous sections, the temperature affects:

15 Light

Light photoperiod is calculated as detailed in subsection 3.4. Photoperiod affects wheat phenology.

Light intensity and photoperiod also have an effect on diffuse light fraction (paragraph 4.1.3), so that it could impact the diffuse factor (fd; subsection 13; subsection 4.1) and reduce the radiation-limited biomass accumulation (ΔQr; subsection 4.1). However, in the current APSIM-Wheat, the diffuse factor equals to 1 (i.e. no impact of diffuse light on biomass production).

Light intensity affects

16 CO2

As mentioned in previous sections, CO2 concentration affects:

17 Vapour pressure deficit (VPD)

The vapour pressure deficit (VPD) is calculated as presented in subsection 89. VPD affects the transpiration efficiency (subsection 88) and thus the crop water demand (subsection 87).

References

   Asseng, S., Fillery, I. R. P., Anderson, G. C., Dolling, P. J., Dunin, F. X., Keating, B. A., Jan. 1998a. Use of the APSIM wheat model to predict yield, drainage, and NO3- leaching for a deep sand. Australian Journal of Experimental Agriculture 49 (3), 363–378.

   Asseng, S., Foster, I., Turner, N. C., 2011. The impact of temperature variability on wheat yields. Global Change Biology 17 (2), 997–1012.

   Asseng, S., Keating, B. A., Fillery, I. R. P., Gregory, P. J., Bowden, J. W., Turner, N. C., Palta, J. A., Abrecht, D. G., May 1998b. Performance of the APSIM-wheat model in western australia. Field Crops Research 57 (2), 163–179.

   Hochman, Z., Dang, Y. P., Schwenke, G. D., Dalgliesh, N. P., Routley, R., McDonald, M., Daniells, I. G., Manning, W., Poulton, P. L., 2007. Simulating the effects of saline and sodic subsoils on wheat crops growing on vertosols. Australian Journal of Agricultural Research 58 (8), 802–810.

   Meinke, H., Hammer, G. L., van Keulen, H., Rabbinge, R., Keating, B. A., 1997. Improving wheat simulation capabilities in australia from a cropping systems perspective: water and nitrogen effects on spring wheat in a semi-arid environment. European Journal of Agronomy 7 (1-3), 75–88.

   Meinke, H., Rabbinge, R., Hammer, G. L., van Vankeulen, H., Jamieson, P., 1998. Improving wheat simulation capabilities in australia from a cropping systems perspective II. testing simulation capabilities of wheat growth. European Journal of Agronomy 8 (1-2), 83–99.

   Monsi, M., Saeki, T., 2005. On the factor light in plant communities and its importance for matter production. Annals of Botany 95 (3), 549–567.

   Reyenga, P. J., Howden, S. M., Meinke, H., McKeon, G. M., 1999. Modelling global change impacts on wheat cropping in south-east queensland, australia. Environmental Modelling & Software 14 (4), 297–306.

   Roderick, M. L., 1999. Estimating the diffuse component from daily and monthly measurements of global radiation. Agricultural and Forest Meteorology 95 (3), 169–185.

   Sinclair, T. R., Nov. 1986. Water and nitrogen limitations in soybean grain production i. model development. Field Crops Research 15 (2), 125–141.

   Tanner, C. B., Sinclair, T. R., 1983. Efficient water use in crop production: research or re-search. In: Taylor, H. M., Jordan, W. R., Sinclair, T. R. (Eds.), Limitations to efficient water use in crop production. American Society of Agronomy, Madison, WI, pp. 1–27.

   Wang, E., van Oosterom, E. J., Meinke, H., Asseng, S., Robertson, M. J., Huth, N. I., Keating, B. A., Probert, M., 2003. The new APSIM-Wheat model: Performance and future improvements. In: Unkovich, M., O’Leary, G. (Eds.), Proceedings of the 11th Australian Agronomy Conference. Australian Society of Agronomy, Geelong Victoria.

A Parameter list of wheat module

Phenology

Variables

Units

Default Value

Description

tt_<phase_name>, (tt_emergence, tt_end_of_juvenile,tt_floral_initiation, tt_flowering, tt_start_grain_fill, tt_end_grain_fill, tt_maturity, tt_end_crop, tt_harvest_ripe)

C

Figure 1

The thermal time target for all phases

x_temp, y_tt

C, Cd

Figure 3

The function between cardinal temperature and effective thermal time.

pesw_germ

mm mm-1

0

Plant extractable soil water in seedling layer inadequate for germination

x_node_no_leaf, y_leaves_per_node

node rank in main stem

Figure 21

The function to define the potential new tiller number

shoot_lag

Cd

40

Time lag before linear coleoptile growth starts

shoot_rate

Cd mm-1

1.5

Growing deg day increase with depth for coleoptile

fasw_emerg

[]

0.0 1.0

Fraction of available soil water

rel_emerg_rate

[]

1.0 1.0

Stress factor for thermal time calculation between germination and emergence

tt_emergence

Cd

1

The thermal time for seed emergence

tt_end_of_juvenile

Cd

400

The potential period from end of juvenile stage to terminal spikelet stage

twilight

-6.0

Twilight is defined as the interval between sunrise or sunset and the time when the true

photop_sens

[]

3

Sensitivities to photoperiod

vern_sens

[]

1.5

Sensitivities to vernalisation

N_fact_pheno

[]

100

Multiplier for N deficit effect on phenology

Biomass production

x_stage_rue

[]

1 2 3 4 5 6 7 8 9 10 11

Numeric code for phenological stages

y_rue

g MJ-1

0 0 1.24 1.24 1.24 1.24 1.24 1.24 0.00 0.00 0

The radiation use efficiency for each phenological stage

sen_rate_water

[]

0.10

slope in linear equation relating soil water stress during photosynthesis to leaf senescence rate

sen_light_slope

[]

0.002

sensitivity of leaf area senescence to shading

lai_sen_light

m2 m-2

7.0

induced senescence occurs by shading

x_sw_avail_ratio, y_swdef_pheno

[], []

Figure 33

The function between available soil water ratio and soil water stress of phenology.

x_sw_avail_ratio_flowering, y_swdef_pheno_flowering

[], []

Figure 33

The function between available soil water ratio and soil water stress of phenology for flowering phase.

x_sw_avail_ratio_start_grain_fill, y_swdef_pheno_start_grain_fill

[], []

Figure 33

The function between available soil water ratio and soil water stress of phenology for grain filling phase.

x_stage_code, y_n_conc_min_leaf, y_n_conc_crit_leaf

y_n_conc_min_stem, y_n_conc_crit_stem

The function between growth stage and minimum can critical nitrogen concentration.

x_row_spacing

mm

200 350 1000

y_extinct_coef

[]

0.50 0.50 0.50

Leaf growth

leaf_no_at_emerg

[]

2

Leaf number at emergence

initial_tpla

mm2 plant-1

200

Initial leaf area per plant

node_no_correction

[]

2

The node number correction

min_tpla

mm2 plant-1

5.0

Lower limit of total leaf area per plant

x_lai, y_sla_max

mm2 mm2, mm2 g-1

Figure 24

The function between leaf area index and specific leaf area.

x_lai_ratio, y_leaf_no_frac

[], []

Figure 22

The function between fraction of leaf area index and fraction of node number.

fr_lf_sen_rate

[]

0.035

Fraction of total leaf number senescing per main stem node

node_sen_rate

Cd node-1

60.0

Rate of node senescence on main stem

x_node_no, y_leaf_size

node rank in main stem, mm2

The leaf size as a function of leaf number

leaf_no_pot_option

[]

2

The option to calculate the potential leaf number. The option 2 is for wheat.

x_sw_demand_ratio, y_swdef_leaf

[], []

The function between supply of soil water and water stress for leaf expansion.

N_fact_expansion

[],

1

Multiplier for N deficit effect on leaf expansion