# -*- coding: utf-8 -*-
# Copyright (c) 2004-2024 Wageningen Environmental Research, Wageningen-UR
# Wim de Winter(Wim.deWinter@wur.nl), April 2015
"""
LINTUL3
"""
from math import exp
from ..base import SimulationObject, ParamTemplate, RatesTemplate
from ..base import StatesWithImplicitRatesTemplate as StateVariables
from ..traitlets import Float, Instance, Bool
from ..decorators import prepare_rates, prepare_states
from ..util import limit, AfgenTrait
from ..crop.phenology import DVS_Phenology as Phenology
from ..exceptions import CarbonBalanceError, NutrientBalanceError
from .. import signals
# some lambdas to make unit conversion explicit.
cm2mm = lambda x: x*10.
joule2megajoule = lambda x: x/1e6
m2mm = lambda x: x*1000
[docs]class Lintul3(SimulationObject):
"""
LINTUL3 is a crop model that calculates biomass production based on intercepted photosynthetically
active radiation (PAR) and light use efficiency (LUE). It is an adapted version of LINTUL2 (that simulates
potential and water-limited crop growth), including nitrogen limitation. Nitrogen stress in the model is
defined through the nitrogen nutrition index (NNI): the ratio of actual nitrogen concentration and critical
nitrogen concentration in the plant. The effect of nitrogen stress on crop growth is tested in the model
either through a reduction in LUE or leaf area (LA) or a combination of these two and further evaluated
with independent datasets. However, water limitation is not considered in the present study as the
crop is paddy rice. This paper describes the model for the case of rice, test the hypotheses of N stress
on crop growth and details of model calibration and testing using independent data sets of nitrogen
treatments (with fertilizer rates of 0 - 400 kgNha-1) under varying environmental conditions in Asia.
Results of calibration and testing are compared graphically, through Root Mean Square Deviation (RMSD),
and by Average Absolute Deviation (AAD). Overall average absolute deviation values for calibration and
testing of total aboveground biomass show less than 26% mean deviation from the observations though
the values for individual experiments show a higher deviation up to 41%. In general, the model responded
well to nitrogen stress in all the treatments without fertilizer application as observed, but between
fertilized treatments the response was varying.
**Nitrogen demand, uptake and stress**
At sub-optimal nitrogen availability in the soil, nitrogen demand of the crop
cannot be satisfied, which leads to sub-optimal crop nitrogen concentration. The
crop nitrogen concentration below which a crop experiences nitrogen stress is
called the critical nitrogen concentration. Nitrogen stress results in reduced
rates of biomass production and eventually in reduced yields. Actual N content
is the accumulated N above residual (which forms part of the cell structure).
The critical N content is the one corresponding to half of the maximum. Nitrogen
contents of these three reference points include those of leaves and stems,
whereas roots are not considered since N contents of above-ground (green) parts
are more important for photosynthesis, because of their chlorophyll content.
However, calculation of N demand and N uptake also includes the belowground
part.
See:
M.E. Shibu, P.A. Leffelaar, H. van Keulena, P.K. Aggarwal (2010). LINTUL3,
a simulation model for nitrogen-limited situations: application to rice.
Eur. J. Agron. (2010) http://dx.doi.org/10.1016/j.eja.2010.01.003
*Parameters*
======== ======================================================= ==========
Name Description Unit
======== ======================================================= ==========
DVSI Initial development stage -
DVSDR Development stage above which deathOfLeaves of
leaves and roots start -
DVSNLT Development stage after which no nutrients are absorbed -
DVSNT development stage above which N translocation to
storage organs does occur -
FNTRT Nitrogen translocation from roots to storage
organs as a fraction of total amount of
nitrogen translocated from leaves and stem to
storage organs -
FRNX Critical N, as a fraction of maximum N
concentration -
K Light attenuation coefficient m²/m²
LAICR critical LAI above which mutual shading of
leaves occurs, °C/d
LRNR Maximum N concentration of root as fraction of
that of leaves g/g
LSNR Maximum N concentration of stem as fraction of
that of leaves g/g
LUE Light use efficiency g/MJ
NLAI Coefficient for the effect of N stress on LAI
reduction(during juvenile phase) -
NLUE Coefficient of reduction of LUE under nitrogen
stress, epsilon -
NMAXSO Maximum concentration of nitrogen in storage
organs g/g
NPART Coefficient for the effect of N stress on leaf
biomass reduction -
NSLA Coefficient for the effect of N stress on SLA
reduction -
RDRNS Relative death rate of leaf weight due to N
stress 1/d
RDRRT Relative death rate of roots 1/d
RDRSHM and the maximum dead rate of leaves due to
shading 1/d
RGRL Relative growth rate of LAI at the exponential
growth phase °C/d
RNFLV Residual N concentration in leaves g/g
RNFRT Residual N concentration in roots g/g
RNFST Residual N concentration in stem g/g
ROOTDM Maximum root depth m
RRDMAX Maximum rate of increase in rooting depth m/d
SLAC Specific leaf area constant m²/g
TBASE Base temperature for crop development °C
TCNT Time coefficient for N translocation d
TRANCO Transpiration constant indicating the level of
drought tolerance of the wheat crop mm/d
TSUMAG Temperature sum for ageing of leaves °C.d
WCFC Water content at field capacity (0.03 MPa) m³/m³
WCST Water content at full saturation m³/m³
WCWET Critical Water content for oxygen stress m³/m³
WCWP Water content at wilting point (1.5 MPa) m³/m³
WMFAC water management (False = irrigated up to the
field capacity, true= irrigated up to saturation) (bool)
RNSOIL Daily amount of N available in the soil through
mineralisation of organic matter
======== ======================================================= ==========
*Tabular parameters*
======== ======================================================= =======================
Name Description Unit
======== ======================================================= =======================
FLVTB Partitioning coefficients -
FRTTB Partitioning coefficients -
FSOTB Partitioning coefficients -
FSTTB Partitioning coefficients -
NMXLV Maximum N concentration in the leaves, from kg N kg-1 dry biomass
which the values of the stem and roots are derived,
as a function of development stage
RDRT Relative death rate of leaves as a function of
Developmental stage 1/d
SLACF Leaf area correction function as a function of -
development stage, DVS. Reference: Drenth, H.,
ten Berge, H.F.M. and Riethoven, J.J.M. 1994,
p.10. (Complete reference under Observed data.)
======== ======================================================= =======================
* initial states *
======== ======================================================= ==========
Name Description Unit
======== ======================================================= ==========
ROOTDI Initial rooting depth m
NFRLVI Initial fraction of N in leaves gN/gDM
NFRRTI Initial fraction of N in roots gN/gDM
NFRSTI Initial fraction of N in stem gN/gDM
WCI Initial water content in soil m³/³
WLVGI Initial Weight of green leaves g/m²
WSTI Initial Weight of stem g/m²
WRTLI Initial Weight of roots g/m²
WSOI Initial Weight of storage organs g/m²
======== ======================================================= ==========
**State variables:**
=========== ================================================= ==== ===============
Name Description Pbl Unit
=========== ================================================= ==== ===============
ANLV Actual N content in leaves
ANRT Actual N content in root
ANSO Actual N content in storage organs
ANST Actual N content in stem
CUMPAR PAR accumulator
LAI leaf area index * m²/m²
NLOSSL total N loss by leaves
NLOSSR total N loss by roots
NUPTT Total uptake of N over time gN/m²
ROOTD Rooting depth * m
TNSOIL Amount of inorganic N available for crop uptake
WDRT dead roots (?) g/m²
WLVD Weight of dead leaves g/m²
WLVG Weight of green leaves g/m²
WRT Weight of roots g/m²
WSO Weight of storage organs g/m²
WST Weight of stem g/m²
TAGBM Total aboveground biomass g/m²
TGROWTH Total biomass growth (above and below ground) g/m²
=========== ================================================= ==== ===============
**Rate variables:**
=========== ================================================= ==== ===============
Name Description Pbl Unit
=========== ================================================= ==== ===============
PEVAP Potential soil evaporation rate Y |mmday-1|
PTRAN Potential crop transpiration rate Y |mmday-1|
TRAN Actual crop transpiration rate N |mmday-1|
TRANRF Transpiration reduction factor calculated N -
RROOTD Rate of root growth Y |mday-1|
=========== ================================================= ==== ===============
"""
# sub-model components for crop simulation
pheno = Instance(SimulationObject)
# placeholder for effective N application rate from the _on_APPLY_N event handler.
FERTNS = 0.0
# placeholder for initial leaf area index
LAII = 0.
# placeholders for initial nitrogen contents for leaves, stems, roots and storage organs
ANLVI = 0.
ANSTI = 0.
ANRTI = 0.
ANSOI = 0.
# Parameters, rates and states which are relevant at the main crop simulation level
[docs] class Parameters(ParamTemplate):
DVSI = Float(-99.) # Development stage at start of the crop
DVSDR = Float(-99) # Development stage above which deathOfLeaves of leaves and roots start.
DVSNLT = Float(-99) # development stage N-limit
DVSNT = Float(-99) # development stage N-threshold
FNTRT = Float(-99) # Nitrogen translocation from roots as a fraction of the total amount of nitrogen translocated from leaves and stem.
FRNX = Float(-99) # Optimal N concentration as the fraction of maximum N concentration.
K = Float(-99) # light extinction coefficient
LAICR = Float(-99) # (oC d)-1, critical LAI above which mutual shading of leaves occurs,
LRNR = Float(-99) #
LSNR = Float(-99) #
LUE = Float(-99) # Light use efficiency.
NLAI = Float(-99) # Coefficient for the effect of N stress on LAI reduction(during juvenile phase)
NLUE = Float(-99) # Extinction coefficient for Nitrogen distribution down the canopy
NMAXSO = Float(-99) #
NPART = Float(-99) # Coefficient for the effect of N stress on leaf biomass reduction
NSLA = Float(-99) # Coefficient for the effect of N stress on SLA reduction
RDRSHM = Float(-99) # and the maximum relative deathOfLeaves rate of leaves due to shading.
RGRL = Float(-99) # Relative totalGrowthRate rate of LAI at the exponential totalGrowthRate phase
RNFLV = Float(-99) # Residual N concentration in leaves
RNFRT = Float(-99) # Residual N concentration in roots.
RNFST = Float(-99) # Residual N concentration in stem
ROOTDM = Float(-99) # Maximum root depth for a rice crop.
RRDMAX = Float(-99) # Maximum rate of increase in rooting depth (m d-1) for a rice crop.
SLAC = Float(-99) # Specific leaf area constant.
TBASE = Float(-99) # Base temperature for spring wheat crop.
TCNT = Float(-99) # Time coefficient(days) for N translocation.
TRANCO = Float(-99) # Transpiration constant (mm/day) indicating the level of drought tolerance of the wheat crop.
TSUMAG = Float(-99) # Temperature sum for ageing of leaves
WCFC = Float(-99) # Water content at field capacity (0.03 MPa) m3/ m3
WCI = Float(-99) # Initial water content in cm3 of water/(cm3 of soil).
WCST = Float(-99) # Water content at full saturation m3/ m3
WCWET = Float(-99) # Critical Water conten for oxygen stress [m3/m3]
WCWP = Float(-99) # Water content at wilting point (1.5 MPa) m3/ m3
WMFAC = Bool(False) # water management (0 = irrigated up to the field capacity, 1= irrigated up to saturation)
RDRNS = Float(-99) # Relative deathOfLeaves rate of leaves due to N stress.
RDRRT = Float(-99) # Relative deathOfLeaves rate of roots.
RDRRT = Float(-99) # Relative deathOfLeaves rate of roots.
FLVTB = AfgenTrait() # Partitioning coefficients
FRTTB = AfgenTrait() # Partitioning coefficients
FSOTB = AfgenTrait() # Partitioning coefficients
FSTTB = AfgenTrait() # Partitioning coefficients
NMXLV = AfgenTrait() # Maximum N concentration in the leaves as a function of development stage.
RDRT = AfgenTrait() #
SLACF = AfgenTrait() # Leaf area correction function as a function of development stage, DVS.
ROOTDI = Float(-99) # initial rooting depth [m]
NFRLVI = Float(-99) # Initial fraction of N (g N g-1 DM) in leaves.
NFRRTI = Float(-99) # Initial fraction of N (g N g-1 DM) in roots.
NFRSTI = Float(-99) # Initial fraction of N (g N g-1 DM) in stem.
WLVGI = Float(-99) # Initial weight of green leaves
WSTI = Float(-99) # Initial weight of stems
WRTLI = Float(-99) # Initial weight of roots
WSOI = Float(-99) # Initial weight of storage organs
RNMIN = Float(-99) # Rate of soil mineratilation (g N/m2/day
[docs] class Lintul3States(StateVariables):
LAI = Float(-99.) # leaf area index
ANLV = Float(-99.) # Actual N content in leaves
ANST = Float(-99.) # Actual N content in stem
ANRT = Float(-99.) # Actual N content in root
ANSO = Float(-99.) # Actual N content in storage organs
NUPTT = Float(-99.) # Total uptake of N over time (g N m-2)
NLOSSL = Float(-99.) # total N loss by leaves
NLOSSR = Float(-99.) # total N loss by roots
WLVG = Float(-99.) # Weight of green leaves
WLVD = Float(-99.) # Weight of dead leaves
WST = Float(-99.) # Weight of stem
WSO = Float(-99.) # Weight of storage organs
WRT = Float(-99.) # Weight of roots
ROOTD = Float(-99.) # Actual root depth [m]
TGROWTH = Float(-99.) # Total growth
WDRT = Float(-99.) # weight of dead roots
CUMPAR = Float(-99.)
TNSOIL = Float(-99.) # Amount of inorganic N available for crop uptake.
TAGBM = Float(-99.) # Total aboveground biomass [g /m-2)
NNI = Float(-99) # Nitrogen nutrition index
# These are some rates which are not directly connected to a state (PEVAP, TRAN) of which must be published
# (RROOTD) for the water balance module. Therefore, we explicitly define them here.
[docs] class Lintul3Rates(RatesTemplate):
PEVAP = Float()
PTRAN = Float()
TRAN = Float()
TRANRF = Float()
RROOTD = Float()
[docs] def initialize(self, day, kiosk, parvalues):
"""
:param day: start date of the simulation
:param kiosk: variable kiosk of this PCSE instance
:param parvalues: `ParameterProvider` object providing parameters as
key/value pairs
"""
self.kiosk = kiosk
self.params = self.Parameters(parvalues)
self.rates = self.Lintul3Rates(self.kiosk,
publish=["PEVAP", "TRAN", "RROOTD"])
self._connect_signal(self._on_APPLY_N, signals.apply_n)
# Initialize phenology component of the crop
self.pheno = Phenology(day, kiosk, parvalues)
# Calculate initial LAI
p = self.params
SLACFI = p.SLACF(p.DVSI)
ISLA = p.SLAC * SLACFI
self.LAII = p.WLVGI * ISLA
# Initial amount of N (g/m2) in leaves, stem, roots, and storage organs.
self.ANLVI = p.NFRLVI * p.WLVGI
self.ANSTI = p.NFRSTI * p.WSTI
self.ANRTI = p.NFRRTI * p.WRTLI
self.ANSOI = 0.0
# Generate a dict with 'default' initial states (e.g. zero)
init = self.Lintul3States.initialValues()
# Initialize state variables
init["LAI"] = self.LAII
init["ANLV"] = self.ANLVI
init["ANST"] = self.ANSTI
init["ANRT"] = self.ANRTI
init["WLVG"] = p.WLVGI
init["WST"] = p.WSTI
init["WSO"] = p.WSOI
init["WRT"] = p.WRTLI
init["ROOTD"] = p.ROOTDI
# Initialize the states objects
self.states = self.Lintul3States(kiosk, publish=["LAI", "ROOTD"], **init)
# Initialize the associated rates of the states
self.states.initialize_rates()
def _on_APPLY_N(self, amount, recovery):
"""Receive signal for N application with amount the nitrogen amount in g N m-2 and
recovery the recovery fraction.
"""
self.FERTNS = amount * recovery
@prepare_rates
def calc_rates(self, day, drv):
p = self.params
s = self.states
r = self.rates
DELT = 1
DVS = self.pheno.get_variable("DVS")
TSUM = self.pheno.get_variable("TSUM")
DTR = joule2megajoule(drv.IRRAD)
PAR = DTR * 0.50
DAVTMP = 0.5 * (drv.TMIN + drv.TMAX)
DTEFF = max(0., DAVTMP - p.TBASE)
# potential rates of evaporation and transpiration:
r.PEVAP, r.PTRAN = self._calc_potential_evapotranspiration(drv)
# Water content in the rootzone
WC = self.kiosk["WC"]
# actual rate of transpiration:
r.TRAN = self._calc_actual_transpiration(r.PTRAN, WC)
"""
Crop phenology
Crop development, i.e. the order and rate of appearance of vegetative and
reproductive organs, is defined in terms of phenological developmental stage
(DVS) as a function of heat sum, which is the cumulative daily effective
temperature. Daily effective temperature is the average temperature above a
crop-specific base temperature (for rice 8C). Some crop or crop varieties are
photoperiodsensitive, i.e. flowering depends on the length of the light period
during the day in addition to the temperature during the vegetative stage.
"""
self.pheno.calc_rates(day, drv)
crop_stage = self.pheno.get_variable("STAGE")
# if before emergence there is no need to continue
# because only the phenology is running.
if crop_stage == "emerging":
return # no aboveground crop to calculate yet
# code below is executed only POST-emergence
# translocatable N in leaves, stem, roots and
# storage organs.
ATNLV, ATNST, ATNRT, ATN = self.translocatable_N()
# Relative deathOfLeaves rate of leaves due to senescence/ageing.
RDRTMP = p.RDRT(DAVTMP)
# Total living vegetative biomass.
TBGMR = s.WLVG + s.WST
# Average residual N concentration.
NRMR = (s.WLVG * p.RNFLV + s.WST * p.RNFST) / TBGMR
# Maximum N concentration in the leaves, from which the values of the
# stem and roots are derived, as a function of development stage.
NMAXLV = p.NMXLV(DVS)
NMAXST = p.LSNR * NMAXLV
NMAXRT = p.LRNR * NMAXLV
# maximum nitrogen concentration of leaves and stem.
NOPTLV = p.FRNX * NMAXLV
NOPTST = p.FRNX * NMAXST
# Maximum N content in the plant.
NOPTS = NOPTST * s.WST
NOPTL = NOPTLV * s.WLVG
NOPTMR = (NOPTL + NOPTS)/TBGMR
# Total N in green matter of the plant.
NUPGMR = s.ANLV + s.ANST
# Nitrogen Nutrition Index.
"""
Nitrogen stress
A crop is assumed to experience N stress at N concentrations below a critical
value for unrestricted growth. To quantify crop response to nitrogen shortage, a
Nitrogen Nutrition Index (NNI) is defined, ranging from 0 (maximum N shortage)
to 1 (no N shortage):
NNI = (actual crop [N] - residual [N]) / (critical [N] - residual [N])
Critical crop nitrogen concentration, the lower limit of canopy nitrogen
concentration in leaves and stems required for unrestricted growth, has been
taken as half the maximum nitrogen concentration. An experimental basis for such
an assumption can be derived from the study of Zhen and Leigh (1990), who
reported that nitrate accumulation in plant occurs in significant quantity when
the N needs to reach the maximum growth were fulfilled and the mean value of
nitrate accumulated beyond the criticalNconcentration was about 50% for
different stages.
"""
NFGMR = NUPGMR / TBGMR
NNI = limit(0.001, 1.0, ((NFGMR-NRMR)/(NOPTMR-NRMR)))
# -------- Growth rates and dry matter production of plant organs-------*
# Biomass partitioning functions under (water and nitrogen)non-stressed
# situations
"""
Biomass partitioning
Biomass formed at any time during crop growth is partitioned amongst organs
(Fig. 1), i.e. roots, stems, leaves and storage organs, with partitioning
factors defined as a function of development stage (Fig. 2) (Drenth et al.,
1994), which thus provides the rates of growth of these organs:
dW/dt[i] = Pc[i] * dW / dt
where (dW/dt) is the rate of biomass growth (gm-2 d-1); (dW/dt)[i] and Pc[i] are
the rate of growth (gm-2 d-1) of and the biomass partitioning factor to organ i
(g organ-i g-1 biomass), respectively. Leaf, stem and root weights of the
seedlings at the time of transplanting are input parameters for the model. The
time course of weights of these organs follows from integration of their net
growth rates, i.e. growth rates minus death rates, the latter being defined as a
function of physiological age, shading and stress.
"""
FRTWET = p.FRTTB(DVS)
FLVT = p.FLVTB(DVS)
FSTT = p.FSTTB(DVS)
FSOT = p.FSOTB(DVS)
"""
Leaf area development
The time course of LAI is divided into two stages: an exponential stage during
the juvenile phase, where leaf area development is a function of temperature,
and a linear stage where it depends on the increase in leaf biomass (Spitters,
1990; Spitters and Schapendonk, 1990). The death of leaves due to senescence
that may be enhanced by shading and/or stress leads to a corresponding loss in
leaf area. The specific leaf area is used for the conversion of dead leaf
biomass to corresponding loss in leaf area. The death of leaves due to
senescence occurs only after flowering and the rate depends on crop age
(function adopted from ORYZA2000, Bouman et al., 2001). The excessive growth of
leaves also result in death of leaves due to mutual shading. The death of leaves
due to shading is determined by a maximum death rate and the relative proportion
of leaf area above the critical LAI (4.0) (Spitters, 1990; Spitters and
Schapendonk, 1990). The net rate of change in leaf area (dLAI/dt) is the
difference between its growth rate and its death rate:
dLAI/dt = dGLAI / dt - dDLAI / dt
where (dGLAI/dt) is the leaf area growth rate and (dDLAI/dt) is the
leaf area death rate.
"""
# Specific Leaf area(m2/g).
SLA = p.SLAC * p.SLACF(DVS) * exp(-p.NSLA * (1.-NNI))
# Growth reduction function for water stress(actual trans/potential)
r.TRANRF = r.TRAN / r.PTRAN if (r.PTRAN != 0) else 1
# relative modification for root and shoot allocation.
FRT, FLV, FST, FSO = self.dryMatterPartitioningFractions(p.NPART, r.TRANRF, NNI, FRTWET, FLVT, FSTT, FSOT)
# total totalGrowthRate rate.
RGROWTH = self.totalGrowthRate(DTR, r.TRANRF, NNI)
# Leaf totalGrowthRate and LAI.
GLV = FLV * RGROWTH
# daily increase of leaf area index.
GLAI = self._growth_leaf_area(DTEFF, self.LAII, DELT, SLA, GLV, WC, DVS, r.TRANRF, NNI)
# relative deathOfLeaves rate of leaves.
DLV, DLAI = self.deathRateOfLeaves(TSUM, RDRTMP, NNI, SLA)
# Net rate of change of Leaf area.
RLAI = GLAI - DLAI
# Root totalGrowthRate
"""
Root growth
The root system is characterized by its vertical extension in the soil profile.
At emergence or at transplanting for transplanted rice. Effect of N stress (NNI)
on crop growth through its effect on LA and LUE. rooting depth is initialized.
Roots elongate at a constant daily rate, until flowering, provided soil water
content is above permanent wilting point (PWP), whereas growth ceases when soil
is drier than PWP or when a certain preset maximum rooting depth is reached
(Spitters and Schapendonk, 1990; Farr� et al., 2000).
"""
r.RROOTD = min(p.RRDMAX, p.ROOTDM - s.ROOTD) if (WC > p.WCWP) else 0.0
# N loss due to deathOfLeaves of leaves and roots.
DRRT = 0. if (DVS < p.DVSDR) else s.WRT * p.RDRRT
RNLDLV = p.RNFLV * DLV
RNLDRT = p.RNFRT * DRRT
# relative totalGrowthRate rate of roots, leaves, stem
# and storage organs.
RWLVG, RWRT, RWST, RWSO = self.relativeGrowthRates(RGROWTH, FLV, FRT, FST, FSO, DLV, DRRT)
"""
Nitrogen demand
Total crop nitrogen demand equals the sum of the nitrogen demands of its
individual organs (excluding storage organs, for which nitrogen demand is met by
translocation from the other organs, i.e. roots, stems and leaves) (Fig. 3).
Nitrogen demand of the individual organs is calculated as the difference
betweenmaximum and actual organ nitrogen contents. The maximum nitrogen content
is defined as a function of canopy development stage (Drenth et al., 1994).
Total N demand (TNdem: gm-2 d-1) of the crop is:
TNdem = sum(Nmax,i - ANi / dt)
where Nmax,i is the maximum nitrogen concentration of organ i (gN/g biomass,
with i referring to leaves, stems and roots), Wi is the weight of organ i
(g biomass/m2), and ANi is the actual nitrogen content of organ i (gN/m2).
"""
# N demand of leaves, roots and stem storage organs.
NDEMLV = max(NMAXLV * s.WLVG - s.ANLV, 0.)
NDEMST = max(NMAXST * s.WST - s.ANST, 0.)
NDEMRT = max(NMAXRT * s.WRT - s.ANRT, 0.)
NDEMSO = max(p.NMAXSO * s.WSO - s.ANSO, 0.) / p.TCNT
# N supply to the storage organs.
NSUPSO = ATN / p.TCNT if (DVS > p.DVSNT) else 0.0
# Rate of N uptake in grains.
RNSO = min(NDEMSO, NSUPSO)
# Total Nitrogen demand.
NDEMTO = max(0.0, (NDEMLV + NDEMST + NDEMRT))
"""
About 75-90% of the total N uptake at harvest takes place before
anthesis and, in conditions of high soil fertility, post-anthesis N uptake
may contribute up to 25% but would exclusively end up in the grain
as protein. Therefore, this nitrogen would not play any role in the
calculation of nitrogen stress that influences the biomass formation.
Therefore, nitrogen uptake is assumed to cease at anthesis,
as nitrogen content in the vegetative parts hardly increases after
anthesis
"""
# Nitrogen uptake limiting factor at low moisture conditions in the
# rooted soil layer before anthesis. After anthesis there is no
# uptake from the soil anymore.
NLIMIT = 1.0 if (DVS < p.DVSNLT) and (WC >= p.WCWP) else 0.0
NUPTR = (max(0., min(NDEMTO, s.TNSOIL))* NLIMIT ) / DELT
# N translocated from leaves, stem, and roots.
RNTLV = RNSO* ATNLV/ ATN
RNTST = RNSO* ATNST/ ATN
RNTRT = RNSO* ATNRT/ ATN
# compute the partitioning of the total N uptake rate (NUPTR) over the leaves, stem and roots.
RNULV, RNUST, RNURT = self.N_uptakeRates(NDEMLV, NDEMST, NDEMRT, NUPTR, NDEMTO)
RNST = RNUST-RNTST
RNRT = RNURT-RNTRT-RNLDRT
# Rate of change of N in organs
RNLV = RNULV-RNTLV-RNLDLV
# ****************SOIL NITROGEN SUPPLY***********************************
"""
Soil–crop nitrogen balance
The mineral nitrogen balance of the soil is the difference between nitrogen
added through mineralization and/or fertilizer, and nitrogen removed by crop
uptake and losses. The net rate of change of N in soil (dN/dt in gm-2 d-1) is:
dN/dt[soil]= Nmin + (FERTN * NRF) - dNU/dt
where Nmin is the nitrogen supply through mineralization and biological N
fixation, FERTN is the fertilizer nitrogen application rate, NRF is the
fertilizer nitrogen recovery fraction and dNU/dt is the rate of nitrogen uptake
by the crop, which is calculated as the minimum of the N supply from the soil
and the N demand from the crop.
"""
# Change in inorganic N in soil as function of fertilizer
# input, soil N mineralization and crop uptake.
RNSOIL = self.FERTNS/DELT - NUPTR + p.RNMIN
self.FERTNS = 0.0
# # Total leaf weight.
WLV = s.WLVG + s.WLVD
# Carbon, Nitrogen balance
CBALAN = (s.TGROWTH + (p.WRTLI + p.WLVGI + p.WSTI + p.WSOI)
- (WLV + s.WST + s.WSO + s.WRT + s.WDRT))
NBALAN = (s.NUPTT + (self.ANLVI + self.ANSTI + self.ANRTI + self.ANSOI)
- (s.ANLV + s.ANST + s.ANRT + s.ANSO + s.NLOSSL + s.NLOSSR))
s.rLAI = RLAI
s.rANLV = RNLV
s.rANST = RNST
s.rANRT = RNRT
s.rANSO = RNSO
s.rNUPTT = NUPTR
s.rNLOSSL = RNLDLV
s.rNLOSSR = RNLDRT
s.rWLVG = RWLVG
s.rWLVD = DLV
s.rWST = RWST
s.rWSO = RWSO
s.rWRT = RWRT
s.rROOTD = r.RROOTD
s.rTGROWTH = RGROWTH
s.rWDRT = DRRT
s.rCUMPAR = PAR
s.rTNSOIL = RNSOIL
if abs(NBALAN) > 0.0001:
raise NutrientBalanceError("Nitrogen un-balance in crop model at day %s" % day)
if abs(CBALAN) > 0.0001:
raise CarbonBalanceError("Carbon un-balance in crop model at day %s" % day)
@prepare_states
def integrate(self, day, delt=1.0):
# if before emergence there is no need to continue
# because only the phenology is running.
# Just run a touch() to to ensure that all state variables are available
# in the kiosk
self.pheno.integrate(day, delt)
if self.pheno.get_variable("STAGE") == "emerging":
self.touch()
return
# run automatic integration on states object.
s = self.states
s.integrate(delta=1.)
# Compute some derived states
s.TAGBM = s.WLVG + s.WLVD + s.WST + s.WSO
def _calc_potential_evapotranspiration(self, drv):
"""Compute the potential evaporation and transpiration.
"""
ES0 = cm2mm(drv.ES0)
ET0 = cm2mm(drv.ET0)
pevap = exp(-0.5 * self.states.LAI) * ES0
pevap = max(0., pevap)
ptran = (1. - exp(-0.5 * self.states.LAI)) * ET0
ptran = max(0., ptran)
return pevap, ptran
def _calc_actual_transpiration(self, PTRAN, WC):
"""Compute the actual rates of evaporation and transpiration.
"""
p = self.params
# critical water content
WCCR = p.WCWP + max( 0.01, PTRAN/(PTRAN + p.TRANCO) * (p.WCFC - p.WCWP))
# If the soil is flooded for rice, : the soil is assumed to be
# permanently saturated and there is no effect of the high water
# content on crop totalGrowthRate, because rice has aerenchyma.
# Thus FR is formulated as below:
if p.WMFAC:
if (WC > WCCR):
FR = 1.
else:
FR = limit( 0., 1., (WC - p.WCWP) / (WCCR - p.WCWP))
# If soil is irrigated but not flooded, : soil water content is
# assumed to be at field capacity and the critical water content
# that affects crop totalGrowthRate (FR) is formulated as below:
else:
if (WCCR <= WC <= p.WCWET): # Between critical
FR = 1.0
elif (WC < WCCR):
FR = limit( 0., 1., (WC - p.WCWP)/(WCCR - p.WCWP))
else:
FR = limit( 0., 1., (p.WCST - WC)/(p.WCST - p.WCWET))
return PTRAN * FR
def _growth_leaf_area(self, DTEFF, LAII, DELT, SLA, GLV, WC, DVS, TRANRF, NNI):
"""This subroutine computes daily increase of leaf area index.
"""
p = self.params
LAI = self.states.LAI
#---- Growth during maturation stage:
GLAI = SLA * GLV
#---- Growth during juvenile stage:
if ((DVS < 0.2) and (LAI < 0.75)):
GLAI = (LAI * (exp(p.RGRL * DTEFF * DELT) - 1.)/ DELT )* TRANRF* exp(-p.NLAI* (1.0 - NNI))
#---- Growth at day of seedling emergence:
if ((LAI == 0.) and (WC > p.WCWP)):
GLAI = LAII / DELT
return GLAI
[docs] def dryMatterPartitioningFractions(self, NPART, TRANRF, NNI, FRTWET, FLVT, FSTT, FSOT):
""" Computes the Dry matter partitioning fractions: leaves, stem and storage organs.
"""
p = self.params
NRF = exp(-p.NLUE * (1.0 - NNI))
if(TRANRF < NRF):
# Water stress is more severe as compared to nitrogen stress and
# partitioning will follow the original assumptions of LINTUL2*
FRTMOD = max(1., 1./(TRANRF+0.5))
FRT = FRTWET * FRTMOD
FSHMOD = (1.-FRT) / (1.-FRT/FRTMOD)
FLV = FLVT * FSHMOD
FST = FSTT * FSHMOD
FSO = FSOT * FSHMOD
else:
# Nitrogen stress is more severe as compared to water stress and the
# less partitioning to leaves will go to the roots*
FLVMOD = exp(-NPART* (1.0-NNI))
FLV = FLVT * FLVMOD
MODIF = (1.-FLV)/(1.-(FLV/FLVMOD))
FST = FSTT * MODIF
FRT = FRTWET* MODIF
FSO = FSOT * MODIF
return FRT, FLV, FST, FSO # FLVMOD removed from signature - WdW
[docs] def totalGrowthRate(self, DTR, TRANRF, NNI):
"""Compute the total total Growth Rate.
Monteith, (1977), Gallagher and Biscoe, (1978) and Monteith (1990) have
shown that biomass formed per unit intercepted light, LUE (Light
Use Efficiency, g dry matter MJ-1), is relatively stable. Hence,
maximum daily growth rate can be defined as the product of
intercepted PAR (photosynthetically active radiation, |MJm-2d-1|)
and LUE.
Intercepted PAR depends on incident solar radiation,
the fraction that is photosynthetically active (0.5) (Monteith and
Unsworth, 1990; Spitters, 1990), and LAI (|m2| leaf |m-2| soil) according
to Lambert Beer's law:
:math:`Q = 0.5 Q0 (1 - e^{-k LAI})`
where *Q* is intercepted PAR |MJm-2d-1|, *Q0* is daily global radiation
|MJm-2d-1|, and *k* is the attenuation coefficient for PAR in the
canopy.
"""
p = self.params
PARINT = 0.5 * DTR * (1.- exp(-p.K * self.states.LAI))
RGROWTH = p.LUE * PARINT
NRF = exp(-p.NLUE * (1.0 - NNI))
GRF = 1.0
if(TRANRF <= NRF):
# Water stress is more severe as compared to nitrogen stress and
# partitioning will follow the original assumptions of LINTUL2*
GRF = TRANRF
else:
# Nitrogen stress is more severe as compared to water stress and the
# less partitioning to leaves will go to the roots*
GRF = NRF
RGROWTH *= GRF
return RGROWTH
[docs] def relativeGrowthRates(self, RGROWTH, FLV, FRT, FST, FSO, DLV, DRRT):
"""Compute the relative total Growth Rate rate of roots, leaves, stem
and storage organs.
"""
RWLVG = RGROWTH * FLV - DLV
RWRT = RGROWTH * FRT - DRRT
RWST = RGROWTH * FST
RWSO = RGROWTH * FSO
return RWLVG, RWRT, RWST, RWSO
[docs] def N_uptakeRates(self, NDEML, NDEMS, NDEMR, NUPTR, NDEMTO):
"""Compute the partitioning of the total N uptake rate (NUPTR)
over the leaves, stem, and roots.
"""
if (NDEMTO > 0):
RNULV = (NDEML / NDEMTO)* NUPTR
RNUST = (NDEMS / NDEMTO)* NUPTR
RNURT = (NDEMR / NDEMTO)* NUPTR
return RNULV, RNUST, RNURT
else:
return 0.0, 0.0, 0.0
[docs] def translocatable_N(self):
"""Compute the translocatable N in the organs.
"""
s = self.states
p = self.params
ATNLV = max (0., s.ANLV - s.WLVG * p.RNFLV)
ATNST = max (0., s.ANST - s.WST * p.RNFST)
ATNRT = min((ATNLV + ATNST) * p.FNTRT, s.ANRT - s.WRT * p.RNFRT)
ATN = ATNLV + ATNST + ATNRT
return ATNLV, ATNST, ATNRT, ATN
[docs] def deathRateOfLeaves(self, TSUM, RDRTMP, NNI, SLA):
"""Compute the relative death rate of leaves due to age, shading amd due to nitrogen stress.
"""
p = self.params
s = self.states
RDRDV = 0. if (TSUM < p.TSUMAG) else RDRTMP
RDRSH = max(0., p.RDRSHM * (s.LAI - p.LAICR) / p.LAICR)
RDR = max(RDRDV, RDRSH)
if (NNI < 1.):
DLVNS = s.WLVG * p.RDRNS * (1. - NNI)
DLAINS = DLVNS * SLA
else:
DLVNS = 0.
DLAINS = 0.
DLVS = s.WLVG * RDR
DLAIS = s.LAI * RDR
DLV = DLVS + DLVNS
DLAI = DLAIS + DLAINS
return DLV, DLAI